J.T. Conklin's latest version of the Sun math library.

-- Begin comments from J.T. Conklin:
The most significant improvement is the addition of "float" versions
of the math functions that take float arguments, return floats, and do
all operations in floating point.  This doesn't help (performance)
much on the i386, but they are still nice to have.

The float versions were orginally done by Cygnus' Ian Taylor when
fdlibm was integrated into the libm we support for embedded systems.
I gave Ian a copy of my libm as a starting point since I had already
fixed a lot of bugs & problems in Sun's original code.  After he was
done, I cleaned it up a bit and integrated the changes back into my
libm.
-- End comments

Reviewed by:	jkh
Submitted by:	jtc

lib/msun/Makefile

@@ -0,0 +1,113 @@
+#  @(#)Makefile 5.1beta 93/09/24 
+#  $Id: Makefile,v 1.22 1994/08/10 20:30:00 jtc Exp $
+# 
+#  ====================================================
+#  Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+# 
+#  Developed at SunPro, a Sun Microsystems, Inc. business.
+#  Permission to use, copy, modify, and distribute this
+#  software is freely granted, provided that this notice 
+#  is preserved.
+#  ====================================================
+# 
+# 
+
+#
+# There are two options in making libm at fdlibm compile time:
+# 	_IEEE_LIBM 	--- IEEE libm; smaller, and somewhat faster
+#	_MULTI_LIBM	--- Support multi-standard at runtime by 
+#			    imposing wrapper functions defined in 
+#			    fdlibm.h:
+#				_IEEE_MODE 	-- IEEE
+#				_XOPEN_MODE 	-- X/OPEN
+#				_POSIX_MODE 	-- POSIX/ANSI
+#				_SVID3_MODE 	-- SVID
+#
+# Here is how to set up CFLAGS to create the desired libm at 
+# compile time:
+#
+# 	CFLAGS = -D_IEEE_LIBM		... IEEE libm (recommended)
+#	CFLAGS = -D_SVID3_MODE	... Multi-standard supported
+#					    libm with SVID as the 
+#					    default standard
+#	CFLAGS = -D_XOPEN_MODE	... Multi-standard supported
+#					    libm with XOPEN as the 
+#					    default standard
+#	CFLAGS = -D_POSIX_MODE	... Multi-standard supported
+#					    libm with POSIX as the 
+#					    default standard
+#	CFLAGS = 			... Multi-standard supported
+#					    libm with IEEE as the 
+#					    default standard
+# 
+
+# Enable if you have a i387 (or i486 or Pentium)
+.if defined(HAVE_FPU)
+.PATH:	${.CURDIR}/arch/i387
+ARCH_SRCS = e_acos.S e_asin.S e_atan2.S e_exp.S e_fmod.S e_log.S e_log10.S \
+	    e_remainder.S e_scalb.S e_sqrt.S s_atan.S s_ceil.S s_copysign.S \
+	    s_cos.S s_finite.S s_floor.S s_ilogb.S s_log1p.S s_logb.S \
+	    s_rint.S s_scalbn.S s_significand.S s_sin.S s_tan.S
+.endif
+
+.PATH:	${.CURDIR}/man
+.PATH:	${.CURDIR}/src
+
+CFLAGS+= -D_MULTI_LIBM -D_POSIX_MODE -D_IEEE_LIBM 
+
+LIB=	m
+COMMON_SRCS =	e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \
+	e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \
+	e_expf.c e_fmod.c e_fmodf.c e_gamma.c e_gamma_r.c e_gammaf.c \
+	e_gammaf_r.c e_hypot.c e_hypotf.c e_j0.c e_j0f.c e_j1.c e_j1f.c \
+	e_jn.c e_jnf.c e_lgamma.c e_lgamma_r.c e_lgammaf.c e_lgammaf_r.c \
+	e_log.c e_log10.c e_log10f.c e_logf.c e_pow.c e_powf.c e_rem_pio2.c \
+	e_rem_pio2f.c e_remainder.c e_remainderf.c e_scalb.c e_scalbf.c \
+	e_sinh.c e_sinhf.c e_sqrt.c e_sqrtf.c \
+	k_cos.c k_cosf.c k_rem_pio2.c k_rem_pio2f.c k_sin.c k_sinf.c \
+	k_standard.c k_tan.c k_tanf.c \
+	s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_cbrt.c s_cbrtf.c s_ceil.c \
+	s_ceilf.c s_copysign.c s_copysignf.c s_cos.c s_cosf.c s_erf.c s_erff.c \
+	s_expm1.c s_expm1f.c s_fabsf.c s_finite.c s_finitef.c \
+	s_floor.c s_floorf.c s_frexpf.c s_ilogb.c s_ilogbf.c \
+	s_isnanf.c s_ldexpf.c s_lib_version.c s_log1p.c \
+	s_log1pf.c s_logb.c s_logbf.c s_matherr.c s_modff.c \
+	s_nextafter.c s_nextafterf.c s_rint.c s_rintf.c s_scalbn.c s_scalbnf.c \
+	s_signgam.c s_significand.c s_significandf.c s_sin.c s_sinf.c s_tan.c \
+	s_tanf.c s_tanh.c s_tanhf.c \
+	w_acos.c w_acosf.c w_acosh.c w_acoshf.c w_asin.c w_asinf.c w_atan2.c \
+	w_atan2f.c w_atanh.c w_atanhf.c w_cabs.c w_cabsf.c w_cosh.c w_coshf.c \
+	w_drem.c w_dremf.c w_exp.c w_expf.c w_fmod.c w_fmodf.c w_gamma.c \
+	w_gamma_r.c w_gammaf.c w_gammaf_r.c w_hypot.c w_hypotf.c w_j0.c \
+	w_j0f.c w_j1.c w_j1f.c w_jn.c w_jnf.c w_lgamma.c w_lgamma_r.c \
+	w_lgammaf.c w_lgammaf_r.c w_log.c w_log10.c w_log10f.c w_logf.c \
+	w_pow.c w_powf.c w_remainder.c w_remainderf.c w_scalb.c w_scalbf.c \
+	w_sinh.c w_sinhf.c w_sqrt.c w_sqrtf.c
+
+# FreeBSD's C library supplies these functions:
+#COMMON_SRCS+=	s_fabs.c s_frexp.c s_isnan.c s_ldexp.c s_modf.c
+
+
+SRCS=${COMMON_SRCS} ${ARCH_SRCS}
+
+# Substitute common sources with any arch specific sources
+MANSRC= ${.CURDIR}/man
+
+MAN3+=	acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 \
+	cos.3 cosh.3 erf.3 exp.3 fabs.3 floor.3 fmod.3 hypot.3 ieee.3 \
+	ieee_test.3 j0.3 lgamma.3 math.3 rint.3 sin.3 sinh.3 sqrt.3 \
+	tan.3 tanh.3
+
+MLINKS+=erf.3 erfc.3
+MLINKS+=exp.3 expm1.3 exp.3 log.3 exp.3 log10.3 exp.3 log1p.3 exp.3 pow.3
+MLINKS+=hypot.3 cabs.3
+MLINKS+=ieee.3 copysign.3 ieee.3 finite.3 ieee.3 ilogb.3 \
+	ieee.3 nextafter.3 ieee.3 remainder.3 ieee.3 scalbn.3
+MLINKS+=ieee_test.3 logb.3
+MLINKS+=ieee_test.3 scalb.3
+MLINKS+=ieee_test.3 significand.3
+MLINKS+=j0.3 j1.3 j0.3 jn.3 j0.3 y0.3 j0.3 y1.3 j0.3 yn.3
+MLINKS+=lgamma.3 gamma.3
+MLINKS+=sqrt.3 cbrt.3
+
+.include <bsd.lib.mk>

lib/msun/i387/e_acos.S

@@ -0,0 +1,50 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_acos.S,v 1.2 1994/03/12 01:30:22 jtc Exp $")
+
+/* acos = atan (sqrt(1 - x^2) / x) */
+ENTRY(__ieee754_acos)
+	fldl	4(%esp)			/* x */
+	fst	%st(1)
+	fmul	%st(0)			/* x^2 */
+	fld1				
+	fsubp				/* 1 - x^2 */
+	fsqrt				/* sqrt (1 - x^2) */
+	fxch	%st(1)
+	fpatan
+	ret

lib/msun/i387/e_asin.S

@@ -0,0 +1,49 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_asin.S,v 1.2 1994/03/12 01:30:25 jtc Exp $")
+
+/* asin = atan (x / sqrt(1 - x^2)) */
+ENTRY(__ieee754_asin)
+	fldl	4(%esp)			/* x */
+	fst	%st(1)
+	fmul	%st(0)			/* x^2 */
+	fld1
+	fsubp				/* 1 - x^2 */
+	fsqrt				/* sqrt (1 - x^2) */
+	fpatan
+	ret

lib/msun/i387/e_atan2.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1994 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_atan2.S,v 1.2 1994/03/12 01:30:26 jtc Exp $")
+
+ENTRY(__ieee754_atan2)
+	fldl	 4(%esp)
+	fldl	12(%esp)
+	fpatan
+	ret

lib/msun/i387/e_exp.S

@@ -0,0 +1,53 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_exp.S,v 1.2 1994/03/12 01:30:27 jtc Exp $")
+
+/* e^x = 2^(x * log2(e)) */
+ENTRY(__ieee754_exp)
+	fldl	4(%esp)
+	fldl2e
+	fmulp				/* x * log2(e) */
+	fstl	%st(1)
+	frndint				/* int(x * log2(e)) */
+	fstl	%st(2)
+	fsubrp				/* fract(x * log2(e)) */
+	f2xm1				/* 2^(fract(x * log2(e))) - 1 */ 
+	fld1
+	faddp				/* 2^(fract(x * log2(e))) */
+	fscale				/* e^x */
+	ret

lib/msun/i387/e_fmod.S

@@ -0,0 +1,48 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_fmod.S,v 1.2 1994/03/12 01:30:28 jtc Exp $")
+
+ENTRY(__ieee754_fmod)
+	fldl	12(%esp)
+	fldl	4(%esp)
+1:	fprem
+	fstsw	%ax
+	sahf
+	jp	1b
+	fstpl	%st(1)
+	ret

lib/msun/i387/e_log.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_log.S,v 1.2 1994/03/12 01:30:29 jtc Exp $")
+
+ENTRY(__ieee754_log)
+	fldln2
+	fldl	4(%esp)
+	fyl2x
+	ret

lib/msun/i387/e_log10.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_log10.S,v 1.2 1994/03/12 01:30:30 jtc Exp $")
+
+ENTRY(__ieee754_log10)
+	fldlg2
+	fldl	4(%esp)
+	fyl2x
+	ret

lib/msun/i387/e_remainder.S

@@ -0,0 +1,48 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_remainder.S,v 1.2 1994/03/12 01:30:31 jtc Exp $")
+
+ENTRY(__ieee754_remainder)
+	fldl	12(%esp)
+	fldl	4(%esp)
+1:	fprem1
+	fstsw	%ax
+	sahf
+	jp	1b
+	fstpl	%st(1)
+	ret

lib/msun/i387/e_scalb.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1994 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_scalb.S,v 1.2 1994/03/12 01:30:32 jtc Exp $")
+
+ENTRY(__ieee754_scalb)
+	fldl	12(%esp)
+	fldl	4(%esp)
+	fscale
+	ret

lib/msun/i387/e_sqrt.S

@@ -0,0 +1,43 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: e_sqrt.S,v 1.2 1994/03/12 01:30:33 jtc Exp $")
+
+ENTRY(__ieee754_sqrt)
+	fldl	4(%esp)
+	fsqrt
+	ret

lib/msun/i387/s_atan.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_atan.S,v 1.2 1994/03/12 01:30:34 jtc Exp $")
+
+ENTRY(atan)
+	fldl	4(%esp)
+	fld1
+	fpatan
+	ret

lib/msun/i387/s_ceil.S

@@ -0,0 +1,58 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_ceil.S,v 1.2 1994/03/12 01:30:35 jtc Exp $")
+
+ENTRY(ceil)
+	pushl	%ebp
+	movl	%esp,%ebp
+	subl	$8,%esp
+
+	fstcw	-12(%ebp)		/* store fpu control word */
+	movw	-12(%ebp),%dx
+	orw	$0x0800,%dx		/* round towards +oo */
+	andw	$0xfbff,%dx
+	movw	%dx,-16(%ebp)
+	fldcw	-16(%ebp)		/* load modfied control word */
+
+	fldl	8(%ebp);		/* round */
+	frndint
+
+	fldcw	-12(%ebp)		/* restore original control word */
+
+	leave
+	ret

lib/msun/i387/s_copysign.S

@@ -0,0 +1,48 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_copysign.S,v 1.2 1994/03/12 01:30:36 jtc Exp $")
+
+ENTRY(copysign)
+	movl	16(%esp),%edx
+	andl	$0x80000000,%edx
+	movl	8(%esp),%eax
+	andl	$0x7fffffff,%eax
+	orl	%edx,%eax
+	movl	%eax,8(%esp)
+	fldl	4(%esp)
+	ret

lib/msun/i387/s_cos.S

@@ -0,0 +1,56 @@
+/*
+ * Copyright (c) 1994 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_cos.S,v 1.3 1994/03/12 01:30:37 jtc Exp $")
+
+ENTRY(cos)
+	fldl	4(%esp)
+	fcos
+	fnstsw	%ax
+	andw	$0x400,%ax
+	jnz	1f
+	ret	
+1:	fldpi
+	fadd	%st(0)
+	fxch	%st(1)
+2:	fprem1
+	fnstsw	%ax
+	andw	$0x400,%ax
+	jnz	2b
+	fstp	%st(1)
+	fcos
+	ret

lib/msun/i387/s_finite.S

@@ -0,0 +1,46 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_finite.S,v 1.2 1994/03/12 01:30:38 jtc Exp $")
+
+ENTRY(finite)
+	movl	8(%esp),%eax
+	andl	$0x7ff00000, %eax
+	cmpl	$0x7ff00000, %eax
+	setnel	%al
+	andl	$0x000000ff, %eax
+	ret

lib/msun/i387/s_floor.S

@@ -0,0 +1,58 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_floor.S,v 1.2 1994/03/12 01:30:40 jtc Exp $")
+
+ENTRY(floor)
+	pushl	%ebp
+	movl	%esp,%ebp
+	subl	$8,%esp
+
+	fstcw	-12(%ebp)		/* store fpu control word */
+	movw	-12(%ebp),%dx
+	orw	$0x0400,%dx		/* round towards -oo */
+	andw	$0xf7ff,%dx
+	movw	%dx,-16(%ebp)
+	fldcw	-16(%ebp)		/* load modfied control word */
+
+	fldl	8(%ebp);		/* round */
+	frndint
+
+	fldcw	-12(%ebp)		/* restore original control word */
+
+	leave
+	ret

lib/msun/i387/s_ilogb.S

@@ -0,0 +1,53 @@
+/*
+ * Copyright (c) 1994 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_ilogb.S,v 1.2 1994/03/12 01:30:41 jtc Exp $")
+
+ENTRY(ilogb)
+	pushl	%esp
+	movl	%esp,%ebp
+	subl	$4,%esp
+
+	fldl	8(%ebp)
+	fxtract
+	fstpl	%st
+
+	fistpl	-4(%ebp)
+	movl	-4(%ebp),%eax
+
+	leave
+	ret

lib/msun/i387/s_log1p.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_log1p.S,v 1.3 1994/08/18 20:42:35 jtc Exp $")
+
+ENTRY(log1p)
+	fldln2
+	fldl 4(%esp)
+	fyl2xp1
+	ret

lib/msun/i387/s_logb.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_logb.S,v 1.2 1994/03/12 01:30:43 jtc Exp $")
+
+ENTRY(logb)
+	fldl	4(%esp)
+	fxtract
+	fstpl	%st
+	ret

lib/msun/i387/s_rint.S

@@ -0,0 +1,43 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_rint.S,v 1.2 1994/03/12 01:30:45 jtc Exp $")
+
+ENTRY(rint)
+	fldl	4(%esp)
+	frndint
+	ret

lib/msun/i387/s_scalbn.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1994 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_scalbn.S,v 1.2 1994/03/12 01:30:46 jtc Exp $")
+
+ENTRY(scalbn)
+	fildl	12(%esp)
+	fldl	4(%esp)
+	fscale
+	ret

lib/msun/i387/s_significand.S

@@ -0,0 +1,44 @@
+/*
+ * Copyright (c) 1993,94 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_significand.S,v 1.2 1994/03/12 01:30:48 jtc Exp $")
+
+ENTRY(significand)
+	fldl	4(%esp)
+	fxtract
+	fstpl	%st(1)
+	ret

lib/msun/i387/s_sin.S

@@ -0,0 +1,56 @@
+/*
+ * Copyright (c) 1994 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_sin.S,v 1.3 1994/03/12 01:30:50 jtc Exp $")
+
+ENTRY(sin)
+	fldl	4(%esp)
+	fsin
+	fnstsw	%ax
+	andw	$0x400,%ax
+	jnz	1f
+	ret
+1:	fldpi
+	fadd	%st(0)
+	fxch	%st(1)
+2:	fprem1
+	fnstsw	%ax
+	andw	$0x400,%ax
+	jnz	2b
+	fstp	%st(1)
+	fsin
+	ret

lib/msun/i387/s_tan.S

@@ -0,0 +1,58 @@
+/*
+ * Copyright (c) 1994 Winning Strategies, Inc.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ * 3. All advertising materials mentioning features or use of this software
+ *    must display the following acknowledgement:
+ *      This product includes software developed by Winning Strategies, Inc.
+ * 4. The name of the author may not be used to endorse or promote products
+ *    derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*
+ * Written by:
+ *	J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc.
+ */
+
+#include <machine/asm.h>
+
+RCSID("$Id: s_tan.S,v 1.3 1994/03/12 01:30:52 jtc Exp $")
+
+ENTRY(tan)
+	fldl	4(%esp)
+	fptan
+	fnstsw	%ax
+	andw	$0x400,%ax
+	jnz	1f
+	fstp	%st(0)
+	ret
+1:	fldpi
+	fadd	%st(0)
+	fxch	%st(1)
+2:	fprem1
+	fstsw	%ax
+	andw	$0x400,%ax
+	jnz	2b
+	fstp	%st(1)
+	fptan
+	fstp	%st(0)
+	ret

lib/msun/man/acos.3

@@ -0,0 +1,89 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)acos.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: acos.3,v 1.4 1993/10/29 22:57:17 jtc Exp $
+.\"
+.Dd May 2, 1991
+.Dt ACOS 3
+.Os
+.Sh NAME
+.Nm acos
+.Nd arc cosine function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn acos "double x"
+.Sh DESCRIPTION
+The
+.Fn acos
+function computes the principal value of the arc cosine of
+.Fa x .
+A domain error occurs for arguments not in the range [-1, +1].
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The 
+.Fn acos
+function returns the arc cosine in the range
+.Bq 0 , \*(Pi
+radians.
+On the
+.Tn VAX
+and
+.Tn Tahoe ,
+if:
+.Bd -unfilled -offset indent
+.Pf \&| Ns Ar x Ns \&| > 1 ,
+.Ed
+.Pp
+.Fn acos x
+sets the global variable
+.Va errno
+to
+.Dv EDOM
+and a reserved operand fault is generated.
+.Sh SEE ALSO
+.Xr sin 3 ,
+.Xr cos 3 ,
+.Xr tan 3 ,
+.Xr asin 3 ,
+.Xr atan 3 ,
+.Xr atan2 3 ,
+.Xr sinh 3 ,
+.Xr cosh 3 ,
+.Xr tanh 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn acos
+function conforms to
+.St -ansiC .

lib/msun/man/acosh.3

@@ -0,0 +1,82 @@
+.\" Copyright (c) 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)acosh.3	5.2 (Berkeley) 5/6/91
+.\"	$Id: acosh.3,v 1.4 1993/10/29 22:57:20 jtc Exp $
+.\"
+.Dd May 6, 1991
+.Dt ACOSH 3
+.Os BSD 4.3
+.Sh NAME
+.Nm acosh
+.Nd inverse hyperbolic cosine function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn acosh "double x"
+.Sh DESCRIPTION
+The
+.Fn acosh
+function computes the inverse hyperbolic cosine
+of the real
+argument
+.Ar x .
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The
+.Fn acosh
+function
+returns the inverse hyperbolic cosine of
+.Ar x .
+On the
+.Tn VAX
+and
+.Tn Tahoe ,
+if the argument is less than one
+.Fn acosh
+sets the global variable
+.Va errno
+to
+.Er EDOM
+and
+causes a reserved operand fault.
+.Sh SEE ALSO
+.Xr asinh 3 ,
+.Xr atanh 3 ,
+.Xr exp 3 ,
+.Xr infnan 3 ,
+.Xr math 3
+.Sh HISTORY
+The
+.Fn acosh
+function appeared in 
+.Bx 4.3 .

lib/msun/man/asin.3

@@ -0,0 +1,91 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)asin.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: asin.3,v 1.4 1993/10/29 22:57:22 jtc Exp $
+.\"
+.Dd May 2, 1991
+.Dt ASIN 3
+.Os
+.Sh NAME
+.Nm asin
+.Nd arc sine function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn asin "double  x"
+.Sh DESCRIPTION
+The
+.Fn asin
+function computes the principal value of the arc sine of
+.Fa x .
+A domain error occurs for arguments not in the range [-1, +1].
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The
+.Fn asin
+function returns the arc sine in the range
+.Bk -words
+.Bq -\*(Pi/2, +\*(Pi/2
+.Ek
+radians.
+On the
+.Tn VAX ,
+and Tahoe ,
+if:
+.Bd -unfilled -offset indent
+.Pf \&| Ns Ar x Ns \&| > 1
+.Ed
+.Pp
+the
+global variable
+.Va errno
+is set to
+.Er EDOM
+and
+a reserved operand fault generated.
+.Sh SEE ALSO
+.Xr acos 3 ,
+.Xr atan 3 ,
+.Xr atan2 3 ,
+.Xr cos 3 ,
+.Xr cosh 3 ,
+.Xr sin 3 ,
+.Xr sinh 3 ,
+.Xr tan 3 ,
+.Xr tanh 3 ,
+.Xr math 3 
+.Sh STANDARDS
+The
+.Fn asin
+function conforms to
+.St -ansiC .

lib/msun/man/asinh.3

@@ -0,0 +1,70 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)asinh.3	6.4 (Berkeley) 5/6/91
+.\"	$Id: asinh.3,v 1.4 1993/10/29 22:57:23 jtc Exp $
+.\"
+.Dd May 6, 1991
+.Dt ASINH 3
+.Os BSD 4.3
+.Sh NAME
+.Nm asinh
+.Nd inverse hyperbolic sine function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn asinh "double x"
+.Sh DESCRIPTION
+The
+.Fn asinh
+function computes the inverse hyperbolic sine
+of the real
+argument
+.Ar x .
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The
+.Fn asinh
+function
+returns the inverse hyperbolic sine of
+.Ar x .
+.Sh SEE ALSO
+.Xr acosh 3 ,
+.Xr atanh 3 ,
+.Xr exp 3 ,
+.Xr infnan 3 ,
+.Xr math 3
+.Sh HISTORY
+The
+.Fn asinh
+function appeared in 
+.Bx 4.3 .

lib/msun/man/atan.3

@@ -0,0 +1,75 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)atan.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: atan.3,v 1.4 1993/10/04 18:07:15 jtc Exp $
+.\"
+.Dd May 2, 1991
+.Dt ATAN 3
+.Os
+.Sh NAME
+.Nm atan
+.Nd arc tangent function of one variable
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn atan "double x"
+.Sh DESCRIPTION
+The
+.Fn atan
+function computes the principal value of the arc tangent of
+.Fa x .
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The
+.Fn atan
+function returns the arc tangent in the range
+.Bk -words
+.Bq -\*(Pi/2 , +\*(Pi/2
+.Ek
+radians.
+.Sh SEE ALSO
+.Xr acos 3 ,
+.Xr asin 3 ,
+.Xr atan2 3 ,
+.Xr cos 3 ,
+.Xr cosh 3 ,
+.Xr sin 3 ,
+.Xr sinh 3 ,
+.Xr tan 3 ,
+.Xr tanh 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn atan
+function conforms to
+.St -ansiC .

lib/msun/man/atan2.3

@@ -0,0 +1,189 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)atan2.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: atan2.3,v 1.3 1993/08/14 13:42:32 mycroft Exp $
+.\"
+.Dd May 2, 1991
+.Dt ATAN2 3
+.Os
+.Sh NAME
+.Nm atan2
+.Nd arc tangent function of two variables
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn atan2 "double y" "double x"
+.Sh DESCRIPTION
+The
+.Xr atan2
+function computes the principal value of the arc tangent of
+.Ar y/ Ns Ar x ,
+using the signs of both arguments to determine the quadrant of
+the return value.
+.Sh RETURN VALUES
+The
+.Xr atan2
+function, if successful,
+returns the arc tangent of 
+.Ar y/ Ns Ar x
+in the range
+.Bk -words
+.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi
+.Ek
+radians.
+If both
+.Ar x
+and
+.Ar y
+are zero, the global variable
+.Va errno
+is set to
+.Er EDOM .
+On the
+.Tn VAX :
+.Bl -column atan_(y,x)_:=____  sign(y)_(Pi_atan2(Xy_xX))___
+.It Fn atan2 y x No := Ta
+.Fn atan y/x Ta
+if
+.Ar x
+> 0,
+.It Ta sign( Ns Ar y Ns )*(\*(Pi -
+.Fn atan "\\*(Bay/x\\*(Ba" ) Ta
+if
+.Ar x
+< 0,
+.It Ta
+.No 0 Ta
+if x = y = 0, or
+.It Ta
+.Pf sign( Ar y Ns )*\\*(Pi/2 Ta
+if
+.Ar x
+= 0 \*(!=
+.Ar y .
+.El
+.Sh NOTES
+The function
+.Fn atan2
+defines "if x > 0,"
+.Fn atan2 0 0
+= 0 on a
+.Tn VAX
+despite that previously
+.Fn atan2 0 0
+may have generated an error message.
+The reasons for assigning a value to
+.Fn atan2 0 0
+are these:
+.Bl -enum -offset indent
+.It
+Programs that test arguments to avoid computing
+.Fn atan2 0 0
+must be indifferent to its value.
+Programs that require it to be invalid are vulnerable
+to diverse reactions to that invalidity on diverse computer systems.
+.It
+The
+.Fn atan2
+function is used mostly to convert from rectangular (x,y)
+to polar
+.if n\
+(r,theta)
+.if t\
+(r,\(*h)
+coordinates that must satisfy x =
+.if n\
+r\(**cos theta
+.if t\
+r\(**cos\(*h
+and y =
+.if n\
+r\(**sin theta.
+.if t\
+r\(**sin\(*h.
+These equations are satisfied when (x=0,y=0)
+is mapped to
+.if n \
+(r=0,theta=0)
+.if t \
+(r=0,\(*h=0)
+on a VAX.  In general, conversions to polar coordinates
+should be computed thus:
+.Bd -unfilled -offset indent
+.if n \{\
+r	:= hypot(x,y);  ... := sqrt(x\(**x+y\(**y)
+theta	:= atan2(y,x).
+.\}
+.if t \{\
+r	:= hypot(x,y);  ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d)
+\(*h	:= atan2(y,x).
+.\}
+.Ed
+.It
+The foregoing formulas need not be altered to cope in a
+reasonable way with signed zeros and infinities
+on a machine that conforms to
+.Tn IEEE 754 ;
+the versions of
+.Xr hypot 3
+and
+.Fn atan2
+provided for
+such a machine are designed to handle all cases.
+That is why
+.Fn atan2 \(+-0 \-0
+= \(+-\*(Pi
+for instance.
+In general the formulas above are equivalent to these:
+.Bd -unfilled -offset indent
+.if n \
+r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x);
+.if t \
+r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x);
+.Ed
+.El
+.Sh SEE ALSO
+.Xr acos 3 ,
+.Xr asin 3 ,
+.Xr atan 3 ,
+.Xr cos 3 ,
+.Xr cosh 3 ,
+.Xr sin 3 ,
+.Xr sinh 3 ,
+.Xr tan 3 ,
+.Xr tanh 3 ,
+.Xr math 3 ,
+.Sh STANDARDS
+The
+.Fn atan2
+function conforms to
+.St -ansiC .

lib/msun/man/atanh.3

@@ -0,0 +1,84 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)atanh.3	5.2 (Berkeley) 5/6/91
+.\"	$Id: atanh.3,v 1.4 1993/10/29 22:57:24 jtc Exp $
+.\"
+.Dd May 6, 1991
+.Dt ATANH 3
+.Os BSD 4.3
+.Sh NAME
+.Nm atanh
+.Nd inverse hyperbolic tangent function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn atanh "double x"
+.Sh DESCRIPTION
+The
+.Fn  atanh
+function computes the inverse hyperbolic tangent
+of the real
+argument
+.Ar x .
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The
+.Fn atanh
+function
+returns the inverse hyperbolic tangent of
+.Ar x
+if successful.
+On the
+.Tn VAX
+and
+.Tn Tahoe ,
+if the argument has absolute value
+bigger than or equal to 1,
+.Fn atanh
+sets the global variable
+.Va errno
+to
+.Er EDOM
+and
+a reserved operand fault is generated.
+.Sh SEE ALSO
+.Xr acosh 3 ,
+.Xr asinh 3 ,
+.Xr exp 3 ,
+.Xr infnan 3 ,
+.Xr math 3
+.Sh HISTORY
+The
+.Fn atanh
+function appeared in
+.Bx 4.3 .

lib/msun/man/ceil.3

@@ -0,0 +1,63 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)ceil.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: ceil.3,v 1.6 1994/03/11 01:32:08 jtc Exp $
+.\"
+.Dd March 10, 1994
+.Dt CEIL 3
+.Os
+.Sh NAME
+.Nm ceil
+.Nd round to smallest integral value not greater than x
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn ceil "double x"
+.Sh DESCRIPTION
+The
+.Fn ceil
+function returns the smallest integral value
+(represented as a double precision number)
+greater than or equal to
+.Fa x .
+.Sh SEE ALSO
+.Xr abs 3 ,
+.Xr fabs 3 ,
+.Xr floor 3 ,
+.Xr ieee 3 ,
+.Xr rint 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn ceil
+function conforms to
+.St -ansiC .

lib/msun/man/cos.3

@@ -0,0 +1,74 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)cos.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: cos.3,v 1.5 1993/10/29 22:57:25 jtc Exp $
+.\"
+.Dd May 2, 1991
+.Dt COS 3
+.Os
+.Sh NAME
+.Nm cos
+.Nd cosine function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn cos "double x"
+.Sh DESCRIPTION
+The
+.Fn cos
+function computes the cosine of
+.Fa x
+(measured in radians).
+A large magnitude argument may yield a result with little or no 
+significance.
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The
+.Fn cos
+function returns the cosine value.
+.Sh SEE ALSO
+.Xr sin 3 ,
+.Xr tan 3 ,
+.Xr asin 3 ,
+.Xr acos 3 ,
+.Xr atan 3 ,
+.Xr atan2 3 ,
+.Xr sinh 3 ,
+.Xr cosh 3 ,
+.Xr tanh 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn cos
+function conforms to
+.St -ansiC .

lib/msun/man/cosh.3

@@ -0,0 +1,75 @@
+.\" Copyright (c) 1989, 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)cosh.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: cosh.3,v 1.4 1993/10/29 22:57:26 jtc Exp $
+.\"
+.Dd May 2, 1991
+.Dt COSH 3
+.Os
+.Sh NAME
+.Nm cosh
+.Nd hyperbolic cosine function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn cosh "double x"
+.Sh DESCRIPTION
+The
+.Fn cosh
+function computes the hyperbolic cosine of
+.Fa x .
+.Sh RETURN VALUES
+The
+.Fn cosh
+function returns the hyperbolic cosine unless the magnitude
+of
+.Fa x
+is too large; in this event, the global variable
+.Va errno
+is set to
+.Er ERANGE . 
+.Sh SEE ALSO
+.Xr acos 3 ,
+.Xr asin 3 ,
+.Xr atan 3 ,
+.Xr atan2 3 ,
+.Xr cos 3 ,
+.Xr sin 3 ,
+.Xr sinh 3 ,
+.Xr tan 3 ,
+.Xr tanh 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn cosh
+function conforms to
+.St -ansiC .

lib/msun/man/erf.3

@@ -0,0 +1,83 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)erf.3	6.4 (Berkeley) 4/20/91
+.\"	$Id: erf.3,v 1.3 1993/08/14 13:42:38 mycroft Exp $
+.\"
+.Dd April 20, 1991
+.Dt ERF 3
+.Os BSD 4.3
+.Sh NAME
+.Nm erf ,
+.Nm erfc
+.Nd error function operators
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn erf "double x"
+.Ft double
+.Fn erfc "double x"
+.Sh DESCRIPTION
+These functions calculate the error function of
+.Fa x .
+.Pp
+The
+.Fn erf
+calculates the error function of x; where
+.Bd -filled -offset indent
+.if n \{\
+erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \}
+.if t \{\
+erf\|(x) := 
+(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \}
+.Ed
+.Pp
+The
+.Fn erfc
+function calculates the complementary error function of
+.Fa x ;
+that is
+.Fn erfc
+subtracts the result of the error function
+.Fn erf x
+from 1.0.
+This is useful, since for large
+.Fa x
+places disappear.
+.Sh SEE ALSO
+.Xr math 3
+.Sh HISTORY
+The
+.Fn erf
+and
+.Fn erfc
+functions appeared in
+.Bx 4.3 .

lib/msun/man/exp.3

@@ -0,0 +1,287 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)exp.3	6.12 (Berkeley) 7/31/91
+.\"	$Id: exp.3,v 1.7 1994/02/11 18:34:05 jtc Exp $
+.\"
+.Dd July 31, 1991
+.Dt EXP 3
+.Os BSD 4
+.Sh NAME
+.Nm exp ,
+.Nm exp2 ,
+.Nm exp10 ,
+.Nm expm1 ,
+.Nm log ,
+.Nm log2 ,
+.Nm log10 ,
+.Nm log1p ,
+.Nm pow
+.Nd exponential, logarithm, power functions
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn exp "double x"
+.Ft double
+.Fn expm1 "double x"
+.Ft double
+.Fn log "double x"
+.Ft double
+.Fn log10 "double x"
+.Ft double
+.Fn log1p "double x"
+.Ft double
+.Fn pow "double x" "double y"
+.Sh DESCRIPTION
+The
+.Fn exp
+function computes the exponential value of the given argument
+.Fa x .
+.Pp
+The
+.Fn expm1
+function computes the value exp(x)\-1 accurately even for tiny argument
+.Fa x .
+.Pp
+The
+.Fn log
+function computes the value of the natural logarithm of argument 
+.Fa x.
+.Pp
+The
+.Fn log10
+function computes the value of the logarithm of argument
+.Fa x
+to base 10.
+.Pp
+The
+.Fn log1p
+function computes
+the value of log(1+x) accurately even for tiny argument
+.Fa x .
+.Pp
+The
+.Fn pow
+computes the value
+of
+.Ar x
+to the exponent
+.Ar y .
+.Sh ERROR (due to Roundoff etc.)
+exp(x), log(x), expm1(x) and log1p(x) are accurate to within 
+an
+.Em ulp ,
+and log10(x) to within about 2
+.Em ulps ;
+an
+.Em ulp
+is one
+.Em Unit
+in the
+.Em Last
+.Em Place .
+The error in
+.Fn pow x y
+is below about 2
+.Em ulps
+when its
+magnitude is moderate, but increases as
+.Fn pow x y
+approaches
+the over/underflow thresholds until almost as many bits could be
+lost as are occupied by the floating\-point format's exponent
+field; that is 8 bits for
+.Tn "VAX D"
+and 11 bits for IEEE 754 Double.
+No such drastic loss has been exposed by testing; the worst
+errors observed have been below 20
+.Em ulps
+for
+.Tn "VAX D" ,
+300
+.Em ulps
+for
+.Tn IEEE
+754 Double.
+Moderate values of
+.Fn pow
+are accurate enough that
+.Fn pow integer integer
+is exact until it is bigger than 2**56 on a
+.Tn VAX ,
+2**53 for
+.Tn IEEE
+754.
+.Sh RETURN VALUES
+These functions will return the appropriate computation unless an error
+occurs or an argument is out of range.
+The functions
+.Fn exp ,
+.Fn expm1
+and
+.Fn pow
+detect if the computed value will overflow,
+set the global variable
+.Va errno to
+.Er ERANGE
+and cause a reserved operand fault on a
+.Tn VAX
+or
+.Tn Tahoe .
+The function
+.Fn pow x y
+checks to see if
+.Fa x
+< 0 and
+.Fa y
+is not an integer, in the event this is true,
+the global variable
+.Va errno
+is set to
+.Er EDOM
+and on the
+.Tn VAX
+and
+.Tn Tahoe
+generate a reserved operand fault.
+On a
+.Tn VAX
+and
+.Tn Tahoe ,
+.Va errno
+is set to
+.Er EDOM
+and the reserved operand is returned
+by log unless
+.Fa x
+> 0, by
+.Fn log1p
+unless
+.Fa x
+> \-1.
+.Sh NOTES
+The functions exp(x)\-1 and log(1+x) are called
+expm1 and logp1 in
+.Tn BASIC
+on the Hewlett\-Packard
+.Tn HP Ns \-71B
+and
+.Tn APPLE
+Macintosh,
+.Tn EXP1
+and
+.Tn LN1
+in Pascal, exp1 and log1 in C
+on
+.Tn APPLE
+Macintoshes, where they have been provided to make
+sure financial calculations of ((1+x)**n\-1)/x, namely
+expm1(n\(**log1p(x))/x, will be accurate when x is tiny.
+They also provide accurate inverse hyperbolic functions.
+.Pp
+The function
+.Fn pow x 0
+returns x**0 = 1 for all x including x = 0,
+.if n \
+Infinity
+.if t \
+\(if
+(not found on a
+.Tn VAX ) ,
+and
+.Em NaN
+(the reserved
+operand on a
+.Tn VAX ) .  Previous implementations of pow may
+have defined x**0 to be undefined in some or all of these
+cases.  Here are reasons for returning x**0 = 1 always:
+.Bl -enum -width indent
+.It
+Any program that already tests whether x is zero (or
+infinite or \*(Na) before computing x**0 cannot care
+whether 0**0 = 1 or not. Any program that depends
+upon 0**0 to be invalid is dubious anyway since that
+expression's meaning and, if invalid, its consequences 
+vary from one computer system to another.
+.It
+Some Algebra texts (e.g. Sigler's) define x**0 = 1 for 
+all x, including x = 0.
+This is compatible with the convention that accepts a[0]
+as the value of polynomial
+.Bd -literal -offset indent
+p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n
+.Ed
+.Pp
+at x = 0 rather than reject a[0]\(**0**0 as invalid.
+.It
+Analysts will accept 0**0 = 1 despite that x**y can
+approach anything or nothing as x and y approach 0
+independently.
+The reason for setting 0**0 = 1 anyway is this:
+.Bd -filled -offset indent
+If x(z) and y(z) are
+.Em any
+functions analytic (expandable
+in power series) in z around z = 0, and if there 
+x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
+.Ed
+.It
+If 0**0 = 1, then
+.if n \
+infinity**0 = 1/0**0 = 1 too; and
+.if t \
+\(if**0 = 1/0**0 = 1 too; and
+then \*(Na**0 = 1 too because x**0 = 1 for all finite
+and infinite x, i.e., independently of x.
+.El
+.Sh SEE ALSO
+.Xr math 3 ,
+.Xr infnan 3
+.Sh HISTORY
+A
+.Fn exp ,
+.Fn log
+and
+.Fn pow
+functions
+appeared in
+.At v6 .
+A
+.Fn log10
+function
+appeared in
+.At v7 .
+The
+.Fn log1p
+and
+.Fn expm1
+functions appeared in
+.Bx 4.3 .

lib/msun/man/fabs.3

@@ -0,0 +1,67 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\"	@(#)fabs.3	5.1 (Berkeley) 5/2/91
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)fabs.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: fabs.3,v 1.4 1993/10/04 18:04:34 jtc Exp $
+.\"
+.Dd May 2, 1991
+.Dt FABS 3
+.Os
+.Sh NAME
+.Nm fabs
+.Nd floating-point absolute value function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn fabs "double x"
+.Sh DESCRIPTION
+The
+.Fn fabs
+function computes the absolute value of a floating-point number
+.Fa x .
+.Sh RETURN VALUES
+The
+.Fn fabs
+function returns the absolute value of
+.Fa x .
+.Sh SEE ALSO
+.Xr abs 3 ,
+.Xr ceil 3 ,
+.Xr floor 3 ,
+.Xr rint 3 ,
+.Xr ieee 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn fabs
+function conforms to
+.St -ansiC .

lib/msun/man/floor.3

@@ -0,0 +1,63 @@
+.\" Copyright (c) 1985, 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)floor.3	6.5 (Berkeley) 4/19/91
+.\"	$Id: floor.3,v 1.5 1994/03/11 01:32:10 jtc Exp $
+.\"
+.Dd March 10, 1994
+.Dt FLOOR 3
+.Os
+.Sh NAME
+.Nm floor
+.Nd round to largest integral value not greater than x
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn floor "double x"
+.Sh DESCRIPTION
+The
+.Fn floor
+function returns the largest integral value 
+(represented as a double precision number)
+less than or equal to
+.Fa x .
+.Sh SEE ALSO
+.Xr abs 3 ,
+.Xr ceil 3 ,
+.Xr fabs 3 ,
+.Xr ieee 3 ,
+.Xr rint 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn floor
+function conforms to
+.St -ansiC .

lib/msun/man/fmod.3

@@ -0,0 +1,76 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)fmod.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: fmod.3,v 1.3 1993/08/14 13:42:46 mycroft Exp $
+.\"
+.Dd May 2, 1991
+.Dt FMOD 3
+.Os
+.Sh NAME
+.Nm fmod
+.Nd floating-point remainder function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn fmod "double x" "double y"
+.Sh DESCRIPTION
+The
+.Fn fmod
+function computes the floating-point remainder of
+.Fa x Ns / Fa y .
+.Sh RETURN VALUES
+The
+.Fn fmod
+function returns the value
+.Sm off
+.Fa x - Em i * Fa y ,
+.Sm on
+for some integer
+.Em i
+such that, if
+.Fa y
+is non-zero, the result has the same sign as
+.Fa x
+and magnitude less than the magnitude of
+.Fa y .
+If
+.Fa y
+is zero, whether a domain error occurs or the
+.Fn fmod
+function returns zero is implementation-defined.
+.Sh SEE ALSO
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn fmod
+function conforms to
+.St -ansiC .

lib/msun/man/hypot.3

@@ -0,0 +1,125 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)hypot.3	6.7 (Berkeley) 5/6/91
+.\"	$Id: hypot.3,v 1.3 1993/08/14 13:42:48 mycroft Exp $
+.\"
+.Dd May 6, 1991
+.Dt HYPOT 3
+.Os BSD 4
+.Sh NAME
+.Nm hypot ,
+.Nm cabs
+.Nd euclidean distance and complex absolute value functions
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn hypot "double x" "double y"
+.Fd struct {double x, y;} z;
+.Ft double
+.Fn cabs z
+.Sh DESCRIPTION
+The
+.Fn hypot
+and
+.Fn cabs
+functions
+computes the
+sqrt(x*x+y*y)
+in such a way that underflow will not happen, and overflow
+occurs only if the final result deserves it.
+.Pp
+.Fn hypot "\*(If" "v"
+=
+.Fn hypot "v" "\*(If"
+= +\*(If for all
+.Ar v ,
+including \*(Na.
+.Sh ERROR (due to Roundoff, etc.)
+Below 0.97
+.Em ulps .
+Consequently
+.Fn hypot "5.0" "12.0"
+= 13.0
+exactly;
+in general, hypot and cabs return an integer whenever an
+integer might be expected.
+.Pp
+The same cannot be said for the shorter and faster version of hypot
+and cabs that is provided in the comments in cabs.c; its error can
+exceed 1.2
+.Em ulps .
+.Sh NOTES
+As might be expected,
+.Fn hypot "v" "\*(Na"
+and
+.Fn hypot "\*(Na" "v"
+are \*(Na for all
+.Em finite
+.Ar v ;
+with "reserved operand" in place of "\*(Na", the
+same is true on a
+.Tn VAX .
+But programmers on machines other than a
+.Tn VAX
+(if has no \*(If)
+might be surprised at first to discover that
+.Fn hypot "\(+-\*(If" "\*(Na"
+= +\*(If.
+This is intentional; it happens because
+.Fn hypot "\*(If" "v"
+= +\*(If
+for
+.Em all
+.Ar v ,
+finite or infinite.
+Hence
+.Fn hypot "\*(If" "v"
+is independent of
+.Ar v .
+Unlike the reserved operand fault on a
+.Tn VAX ,
+the
+.Tn IEEE
+\*(Na is designed to
+disappear when it turns out to be irrelevant, as it does in
+.Fn hypot "\*(If" "\*(Na" .
+.Sh SEE ALSO
+.Xr math 3 ,
+.Xr sqrt 3
+.Sh HISTORY
+Both a
+.Fn hypot
+function and a
+.Fn cabs
+function
+appeared in
+.At v7 .

lib/msun/man/ieee.3

@@ -0,0 +1,152 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)ieee.3	6.4 (Berkeley) 5/6/91
+.\"	$Id: ieee.3,v 1.7 1994/03/10 18:15:07 jtc Exp $
+.\"
+.Dd Feb 25, 1994
+.Dt IEEE 3
+.Os
+.Sh NAME
+.Nm copysign ,
+.Nm finite ,
+.Nm ilogb ,
+.Nm nextafter ,
+.Nm remainder ,
+.Nm scalbn
+.Nd Functions for IEEE arithmetic
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double 
+.Fn copysign "double x" "double y"
+.Ft int 
+.Fn finite "double x"
+.Ft int
+.Fn ilogb "double x"
+.Ft double 
+.Fn nextafter "double x" "double y"
+.Ft double
+.Fn remainder "double x" "double y"
+.Ft double 
+.Fn scalbn "double x" "int n"
+.Sh DESCRIPTION
+These functions are required or recommended by 
+.St -ieee754 .
+.Pp
+.Fn copysign
+returns
+.Fa x
+with its sign changed to
+.Fa y Ns 's.
+.Pp
+.Fn finite
+returns the value 1 just when
+\-\*(If \*(Lt
+.Fa x
+\*(Lt +\*(If;
+otherwise a
+zero is returned
+(when
+.Pf \\*(Ba Ns Fa x Ns \\*(Ba
+= \*(If or
+.Fa x
+is \*(Na
+.Pp
+.Fn ilogb
+returns
+.Fa x Ns 's exponent
+.Fa n ,
+in integer format.
+.Fn ilogb \*(Pm\*(If 
+returns 
+.Dv INT_MAX
+and
+.Fn ilogb 0
+returns 
+.Dv INT_MIN .
+.Pp
+.Fn nextafter 
+returns the next machine representable number from 
+.Fa x
+in direction
+.Fa y .
+.Pp
+.Fn remainder
+returns the remainder
+.Fa r
+:=
+.Fa x
+\-
+.Fa n\(**y
+where
+.Fa n
+is the integer nearest the exact value of
+.Bk -words
+.Fa x Ns / Ns Fa y ;
+.Ek
+moreover if
+.Pf \\*(Ba Fa n
+\-
+.Sm off
+.Fa x No / Fa y No \\*(Ba
+.Sm on
+=
+1/2
+then
+.Fa n
+is even.  Consequently
+the remainder is computed exactly and
+.Sm off
+.Pf \\*(Ba Fa r No \\*(Ba
+.Sm on
+\*(Le
+.Sm off
+.Pf \\*(Ba Fa y No \\*(Ba/2.
+.Sm on
+But
+.Fn remainder x 0
+and
+.Fn remainder \*(If 0
+are invalid operations that produce a \*(Na.
+.Pp
+.Fn scalbn
+returns
+.Fa x Ns \(**(2** Ns Fa n )
+computed by exponent manipulation.
+.Sh SEE ALSO
+.Xr math 3
+.Sh HISTORY
+The
+.Nm ieee
+functions appeared in 
+.Bx 4.3 .
+.Sh STANDARDS
+.St -ieee754

lib/msun/man/ieee_test.3

@@ -0,0 +1,90 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)ieee.3	6.4 (Berkeley) 5/6/91
+.\"	$Id: ieee_test.3,v 1.1 1994/03/11 17:19:01 jtc Exp $
+.\"
+.Dd March 10, 1994
+.Dt IEEE_TEST 3
+.Os 
+.Sh NAME
+.Nm logb ,
+.Nm scalb ,
+.Nm significand
+.Nd IEEE test functions
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double 
+.Fn logb "double x"
+.Ft double 
+.Fn scalb "double x" "double n"
+.Ft double
+.Fn significand "double x"
+.Sh DESCRIPTION
+These functions allow users to test conformance to 
+.St -ieee754 .
+Their use is not otherwise recommended.
+.Pp
+.Fn logb x
+returns
+.Fa x Ns 's exponent
+.Fa n ,
+a signed integer converted to double\-precision floating\-point.
+.Fn logb \*(Pm\*(If
+= +\*(If;
+.Fn logb 0
+= -\*(If with a division by zero exception.
+.Pp
+.Fn scalbn x n
+returns
+.Fa x Ns \(**(2** Ns Fa n )
+computed by exponent manipulation.
+.Pp
+.Fn significand x 
+returns 
+.Fa sig ,
+where 
+.Fa x 
+:= 
+.Fa sig No \(** 2** Ns Fa n
+with 1 \(<= 
+.Fa sig
+< 2.
+.Fn significand x
+is not defined when 
+.Fa x
+is 0, \*(Pm\*(If, or \*(Na.
+.Sh SEE ALSO
+.Xr ieee 3 ,
+.Xr math 3
+
+.Sh STANDARDS
+.St -ieee754

lib/msun/man/j0.3

@@ -0,0 +1,128 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)j0.3	6.7 (Berkeley) 4/19/91
+.\"	$Id: j0.3,v 1.5 1994/01/11 00:46:54 jtc Exp $
+.\"
+.Dd April 19, 1991
+.Dt J0 3
+.Os BSD 4
+.Sh NAME
+.Nm j0 ,
+.Nm j1 ,
+.Nm jn ,
+.Nm y0 ,
+.Nm y1 ,
+.Nm yn
+.Nd bessel functions of first and second kind
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn j0 "double x"
+.Ft double
+.Fn j1 "double x"
+.Ft double
+.Fn jn "int n" "double x"
+.Ft double
+.Fn y0 "double x"
+.Ft double
+.Fn y1 "double x"
+.Ft double
+.Fn yn "int n" "double x"
+.Sh DESCRIPTION
+The functions
+.Fn j0
+and
+.Fn j1
+compute the
+.Em Bessel function of the first kind of the order
+0 and the
+.Em order
+1, respectively,
+for the
+real value
+.Fa x ;
+the function
+.Fn jn
+computes the
+.Em Bessel function of the first kind of the integer order
+.Fa n
+for the real value
+.Fa x .
+.Pp
+The functions
+.Fn y0
+and
+.Fn y1
+compute the linearly independent
+.Em Bessel function of the second kind of the order
+0 and the
+.Em order
+1, respectively,
+for the
+positive
+.Em integer
+value
+.Fa x
+(expressed as a double);
+the function
+.Fn yn
+computes the
+.Em Bessel function of the second kind for the integer order
+.Fa n
+for the positive 
+.Em integer
+value
+.Fa x
+(expressed as a double).
+.Sh RETURN VALUES
+If these functions are successful,
+the computed value is returned. On the
+.Tn VAX
+and
+.Tn Tahoe
+architectures,
+a negative
+.Fa x
+value
+results in an error; the global
+variable
+.Va errno
+is set to
+.Er EDOM
+and a reserve operand fault is generated.
+.Sh SEE ALSO
+.Xr math 3 ,
+.Xr infnan 3
+.Sh HISTORY
+This set of functions
+appeared in
+.At v7 .

lib/msun/man/lgamma.3

@@ -0,0 +1,124 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)lgamma.3	6.6 (Berkeley) 12/3/92
+.\"	$Id: lgamma.3,v 1.6 1994/01/11 00:46:56 jtc Exp $
+.\"
+.Dd December 3, 1992
+.Dt LGAMMA 3
+.Os BSD 4.3
+.Sh NAME
+.Nm lgamma ,
+.Nm gamma
+.Nd log gamma function, gamma function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft extern int
+.Fa signgam ;
+.sp
+.Ft double
+.Fn lgamma "double x"
+.Ft double
+.Fn gamma "double x"
+.Sh DESCRIPTION
+.Fn Lgamma x
+.if t \{\
+returns ln\||\(*G(x)| where
+.Bd -unfilled -offset indent
+\(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt	for x > 0 and
+.br
+\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px))	for x < 1.
+.Ed
+.\}
+.if n \
+returns ln\||\(*G(x)|.
+.Pp
+The external integer
+.Fa signgam
+returns the sign of \(*G(x).
+.Pp
+.Fn Gamma x
+returns \(*G(x), with no effect on
+.Fa signgam .
+.Sh IDIOSYNCRASIES
+Do not use the expression
+.Dq Li signgam\(**exp(lgamma(x))
+to compute g := \(*G(x).
+Instead use a program like this (in C):
+.Bd -literal -offset indent
+lg = lgamma(x); g = signgam\(**exp(lg);
+.Ed
+.Pp
+Only after
+.Fn lgamma
+has returned can signgam be correct.
+.Pp
+For arguments in its range,
+.Fn gamma
+is preferred, as for positive arguments
+it is accurate to within one unit in the last place.
+Exponentiation of
+.Fn lgamma
+will lose up to 10 significant bits.
+.Sh RETURN VALUES
+.Fn Gamma
+and
+.Fn lgamma
+return appropriate values unless an argument is out of range.
+Overflow will occur for sufficiently large positive values, and
+non-positive integers.
+On the
+.Tn VAX,
+the reserved operator is returned,
+and
+.Va errno
+is set to
+.Er ERANGE
+For large non-integer negative values,
+.Fn gamma
+will underflow.
+.Sh SEE ALSO
+.Xr math 3 ,
+.Xr infnan 3
+.Sh HISTORY
+The
+.Nm lgamma
+function appeared in 
+.Bx 4.3 .
+The
+.Nm gamma
+function appeared in
+.Bx 4.4 .
+The name
+.Fn gamma
+was originally dedicated to the
+.Fn lgamma
+function, so some old code may no longer be compatible.

lib/msun/man/math.3

@@ -0,0 +1,633 @@
+.\" Copyright (c) 1985 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"	from: @(#)math.3	6.10 (Berkeley) 5/6/91
+.\"	$Id: math.3,v 1.4 1994/02/25 19:43:56 jtc Exp $
+.\"
+.TH MATH 3M "May 6, 1991"
+.UC 4
+.ds up \fIulp\fR
+.ds nn \fINaN\fR
+.de If
+.if n \\
+\\$1Infinity\\$2
+.if t \\
+\\$1\\(if\\$2
+..
+.SH NAME
+math \- introduction to mathematical library functions
+.SH DESCRIPTION
+These functions constitute the C math library,
+.I libm.
+The link editor searches this library under the \*(lq\-lm\*(rq option.
+Declarations for these functions may be obtained from the include file
+.RI < math.h >.
+The Fortran math library is described in ``man 3f intro''.
+.SH "LIST OF FUNCTIONS"
+.sp 2
+.nf
+.ta \w'copysign'u+2n +\w'infnan.3m'u+10n +\w'inverse trigonometric func'u
+\fIName\fP	\fIAppears on Page\fP	\fIDescription\fP	\fIError Bound (ULPs)\fP
+.ta \w'copysign'u+4n +\w'infnan.3m'u+4n +\w'inverse trigonometric function'u+6nC
+.sp 5p
+acos	sin.3m	inverse trigonometric function	3
+acosh	asinh.3m	inverse hyperbolic function	3
+asin	sin.3m	inverse trigonometric function	3
+asinh	asinh.3m	inverse hyperbolic function	3
+atan	sin.3m	inverse trigonometric function	1
+atanh	asinh.3m	inverse hyperbolic function	3
+atan2	sin.3m	inverse trigonometric function	2
+cabs	hypot.3m	complex absolute value	1
+cbrt	sqrt.3m	cube root	1
+ceil	floor.3m	integer no less than	0
+copysign	ieee.3m	copy sign bit	0
+cos	sin.3m	trigonometric function	1
+cosh	sinh.3m	hyperbolic function	3
+erf	erf.3m	error function	???
+erfc	erf.3m	complementary error function	???
+exp	exp.3m	exponential	1
+expm1	exp.3m	exp(x)\-1	1
+fabs	floor.3m	absolute value	0
+floor	floor.3m	integer no greater than	0
+hypot	hypot.3m	Euclidean distance	1
+ilogb	ieee.3m	exponent extraction	0
+infnan	infnan.3m	signals exceptions
+j0	j0.3m	bessel function	???
+j1	j0.3m	bessel function	???
+jn	j0.3m	bessel function	???
+lgamma	lgamma.3m	log gamma function; (formerly gamma.3m)
+log	exp.3m	natural logarithm	1
+log10	exp.3m	logarithm to base 10	3
+log1p	exp.3m	log(1+x)	1
+pow	exp.3m	exponential x**y	60\-500
+remainder	ieee.3m	remainder	0
+rint	floor.3m	round to nearest integer	0
+scalbn	ieee.3m	exponent adjustment	0
+sin	sin.3m	trigonometric function	1
+sinh	sinh.3m	hyperbolic function	3
+sqrt	sqrt.3m	square root	1
+tan	sin.3m	trigonometric function	3
+tanh	sinh.3m	hyperbolic function	3
+y0	j0.3m	bessel function	???
+y1	j0.3m	bessel function	???
+yn	j0.3m	bessel function	???
+.ta
+.fi
+.SH NOTES
+In 4.3 BSD, distributed from the University of California
+in late 1985, most of the foregoing functions come in two
+versions, one for the double\-precision "D" format in the
+DEC VAX\-11 family of computers, another for double\-precision
+arithmetic conforming to the IEEE Standard 754 for Binary
+Floating\-Point Arithmetic.  The two versions behave very
+similarly, as should be expected from programs more accurate
+and robust than was the norm when UNIX was born.  For
+instance, the programs are accurate to within the numbers
+of \*(ups tabulated above; an \*(up is one \fIU\fRnit in the \fIL\fRast
+\fIP\fRlace.  And the programs have been cured of anomalies that
+afflicted the older math library \fIlibm\fR in which incidents like
+the following had been reported:
+.RS
+sqrt(\-1.0) = 0.0 and log(\-1.0) = \-1.7e38.
+.br
+cos(1.0e\-11) > cos(0.0) > 1.0.
+.br
+pow(x,1.0)
+.if n \
+!=
+.if t \
+\(!=
+x when x = 2.0, 3.0, 4.0, ..., 9.0.
+.br
+pow(\-1.0,1.0e10) trapped on Integer Overflow.
+.br
+sqrt(1.0e30) and sqrt(1.0e\-30) were very slow.
+.RE
+However the two versions do differ in ways that have to be
+explained, to which end the following notes are provided.
+.PP
+\fBDEC VAX\-11 D_floating\-point:\fR
+.PP
+This is the format for which the original math library \fIlibm\fR
+was developed, and to which this manual is still principally
+dedicated.  It is \fIthe\fR double\-precision format for the PDP\-11
+and the earlier VAX\-11 machines; VAX\-11s after 1983 were
+provided with an optional "G" format closer to the IEEE
+double\-precision format.  The earlier DEC MicroVAXs have no
+D format, only G double\-precision. (Why?  Why not?)
+.PP
+Properties of D_floating\-point:
+.RS
+Wordsize: 64 bits, 8 bytes.  Radix: Binary.
+.br
+Precision: 56
+.if n \
+sig.
+.if t \
+significant
+bits, roughly like 17
+.if n \
+sig.
+.if t \
+significant
+decimals.
+.RS
+If x and x' are consecutive positive D_floating\-point
+numbers (they differ by 1 \*(up), then
+.br
+1.3e\-17 < 0.5**56 < (x'\-x)/x \(<= 0.5**55 < 2.8e\-17.
+.RE
+.nf
+.ta \w'Range:'u+1n +\w'Underflow threshold'u+1n +\w'= 2.0**127'u+1n
+Range:	Overflow threshold	= 2.0**127	= 1.7e38.
+	Underflow threshold	= 0.5**128	= 2.9e\-39.
+	NOTE:  THIS RANGE IS COMPARATIVELY NARROW.
+.ta
+.fi
+.RS
+Overflow customarily stops computation.
+.br
+Underflow is customarily flushed quietly to zero.
+.br
+CAUTION:
+.RS
+It is possible to have x
+.if n \
+!=
+.if t \
+\(!=
+y and yet
+x\-y = 0 because of underflow.  Similarly
+x > y > 0 cannot prevent either x\(**y = 0
+or  y/x = 0 from happening without warning.
+.RE
+.RE
+Zero is represented ambiguously.
+.RS
+Although 2**55 different representations of zero are accepted by
+the hardware, only the obvious representation is ever produced.
+There is no \-0 on a VAX.
+.RE
+.If
+is not part of the VAX architecture.
+.br
+Reserved operands:
+.RS
+of the 2**55 that the hardware
+recognizes, only one of them is ever produced.
+Any floating\-point operation upon a reserved
+operand, even a MOVF or MOVD, customarily stops
+computation, so they are not much used.
+.RE
+Exceptions:
+.RS
+Divisions by zero and operations that
+overflow are invalid operations that customarily
+stop computation or, in earlier machines, produce
+reserved operands that will stop computation.
+.RE
+Rounding:
+.RS
+Every rational operation  (+, \-, \(**, /) on a
+VAX (but not necessarily on a PDP\-11), if not an
+over/underflow nor division by zero, is rounded to
+within half an \*(up, and when the rounding error is
+exactly half an \*(up then rounding is away from 0.
+.RE
+.RE
+.PP
+Except for its narrow range, D_floating\-point is one of the
+better computer arithmetics designed in the 1960's.
+Its properties are reflected fairly faithfully in the elementary
+functions for a VAX distributed in 4.3 BSD.
+They over/underflow only if their results have to lie out of range
+or very nearly so, and then they behave much as any rational
+arithmetic operation that over/underflowed would behave.
+Similarly, expressions like log(0) and atanh(1) behave
+like 1/0; and sqrt(\-3) and acos(3) behave like 0/0;
+they all produce reserved operands and/or stop computation!
+The situation is described in more detail in manual pages.
+.RS
+.ll -0.5i
+\fIThis response seems excessively punitive, so it is destined
+to be replaced at some time in the foreseeable future by a
+more flexible but still uniform scheme being developed to
+handle all floating\-point arithmetic exceptions neatly.
+See infnan(3M) for the present state of affairs.\fR
+.ll +0.5i
+.RE
+.PP
+How do the functions in 4.3 BSD's new \fIlibm\fR for UNIX
+compare with their counterparts in DEC's VAX/VMS library?
+Some of the VMS functions are a little faster, some are
+a little more accurate, some are more puritanical about
+exceptions (like pow(0.0,0.0) and atan2(0.0,0.0)),
+and most occupy much more memory than their counterparts in
+\fIlibm\fR.
+The VMS codes interpolate in large table to achieve
+speed and accuracy; the \fIlibm\fR codes use tricky formulas
+compact enough that all of them may some day fit into a ROM.
+.PP
+More important, DEC regards the VMS codes as proprietary
+and guards them zealously against unauthorized use.  But the
+\fIlibm\fR codes in 4.3 BSD are intended for the public domain;
+they may be copied freely provided their provenance is always
+acknowledged, and provided users assist the authors in their
+researches by reporting experience with the codes.
+Therefore no user of UNIX on a machine whose arithmetic resembles
+VAX D_floating\-point need use anything worse than the new \fIlibm\fR.
+.PP
+\fBIEEE STANDARD 754 Floating\-Point Arithmetic:\fR
+.PP
+This standard is on its way to becoming more widely adopted
+than any other design for computer arithmetic.
+VLSI chips that conform to some version of that standard have been
+produced by a host of manufacturers, among them ...
+.nf
+.ta 0.5i +\w'Intel i8070, i80287'u+6n
+	Intel i8087, i80287	National Semiconductor  32081
+	Motorola 68881	Weitek WTL-1032, ... , -1165
+	Zilog Z8070	Western Electric (AT&T) WE32106.
+.ta
+.fi
+Other implementations range from software, done thoroughly
+in the Apple Macintosh, through VLSI in the Hewlett\-Packard
+9000 series, to the ELXSI 6400 running ECL at 3 Megaflops.
+Several other companies have adopted the formats
+of IEEE 754 without, alas, adhering to the standard's way
+of handling rounding and exceptions like over/underflow.
+The DEC VAX G_floating\-point format is very similar to the IEEE
+754 Double format, so similar that the C programs for the
+IEEE versions of most of the elementary functions listed
+above could easily be converted to run on a MicroVAX, though
+nobody has volunteered to do that yet.
+.PP
+The codes in 4.3 BSD's \fIlibm\fR for machines that conform to
+IEEE 754 are intended primarily for the National Semi. 32081
+and WTL 1164/65.  To use these codes with the Intel or Zilog
+chips, or with the Apple Macintosh or ELXSI 6400, is to
+forego the use of better codes provided (perhaps freely) by
+those companies and designed by some of the authors of the
+codes above.
+Except for \fIatan\fR, \fIcabs\fR, \fIcbrt\fR, \fIerf\fR,
+\fIerfc\fR, \fIhypot\fR, \fIj0\-jn\fR, \fIlgamma\fR, \fIpow\fR
+and \fIy0\-yn\fR,
+the Motorola 68881 has all the functions in \fIlibm\fR on chip,
+and faster and more accurate;
+it, Apple, the i8087, Z8070 and WE32106 all use 64
+.if n \
+sig.
+.if t \
+significant
+bits.
+The main virtue of 4.3 BSD's
+\fIlibm\fR codes is that they are intended for the public domain;
+they may be copied freely provided their provenance is always
+acknowledged, and provided users assist the authors in their
+researches by reporting experience with the codes.
+Therefore no user of UNIX on a machine that conforms to
+IEEE 754 need use anything worse than the new \fIlibm\fR.
+.PP
+Properties of IEEE 754 Double\-Precision:
+.RS
+Wordsize: 64 bits, 8 bytes.  Radix: Binary.
+.br
+Precision: 53
+.if n \
+sig.
+.if t \
+significant
+bits, roughly like 16
+.if n \
+sig.
+.if t \
+significant
+decimals.
+.RS
+If x and x' are consecutive positive Double\-Precision
+numbers (they differ by 1 \*(up), then
+.br
+1.1e\-16 < 0.5**53 < (x'\-x)/x \(<= 0.5**52 < 2.3e\-16.
+.RE
+.nf
+.ta \w'Range:'u+1n +\w'Underflow threshold'u+1n +\w'= 2.0**1024'u+1n
+Range:	Overflow threshold	= 2.0**1024	= 1.8e308
+	Underflow threshold	= 0.5**1022	= 2.2e\-308
+.ta
+.fi
+.RS
+Overflow goes by default to a signed
+.If "" .
+.br
+Underflow is \fIGradual,\fR rounding to the nearest
+integer multiple of 0.5**1074 = 4.9e\-324.
+.RE
+Zero is represented ambiguously as +0 or \-0.
+.RS
+Its sign transforms correctly through multiplication or
+division, and is preserved by addition of zeros
+with like signs; but x\-x yields +0 for every
+finite x.  The only operations that reveal zero's
+sign are division by zero and copysign(x,\(+-0).
+In particular, comparison (x > y, x \(>= y, etc.)
+cannot be affected by the sign of zero; but if
+finite x = y then
+.If
+\&= 1/(x\-y)
+.if n \
+!=
+.if t \
+\(!=
+\-1/(y\-x) =
+.If \- .
+.RE
+.If
+is signed.
+.RS
+it persists when added to itself
+or to any finite number.  Its sign transforms
+correctly through multiplication and division, and
+.If (finite)/\(+- \0=\0\(+-0
+(nonzero)/0 =
+.If \(+- .
+But 
+.if n \
+Infinity\-Infinity, Infinity\(**0 and Infinity/Infinity
+.if t \
+\(if\-\(if, \(if\(**0 and \(if/\(if
+are, like 0/0 and sqrt(\-3),
+invalid operations that produce \*(nn. ...
+.RE
+Reserved operands:
+.RS
+there are 2**53\-2 of them, all
+called \*(nn (\fIN\fRot \fIa N\fRumber).
+Some, called Signaling \*(nns, trap any floating\-point operation
+performed upon them; they are used to mark missing
+or uninitialized values, or nonexistent elements
+of arrays.  The rest are Quiet \*(nns; they are
+the default results of Invalid Operations, and
+propagate through subsequent arithmetic operations.
+If x
+.if n \
+!=
+.if t \
+\(!=
+x then x is \*(nn; every other predicate
+(x > y, x = y, x < y, ...) is FALSE if \*(nn is involved.
+.br
+NOTE: Trichotomy is violated by \*(nn.
+.RS
+Besides being FALSE, predicates that entail ordered
+comparison, rather than mere (in)equality,
+signal Invalid Operation when \*(nn is involved.
+.RE
+.RE
+Rounding:
+.RS
+Every algebraic operation (+, \-, \(**, /,
+.if n \
+sqrt)
+.if t \
+\(sr)
+is rounded by default to within half an \*(up, and
+when the rounding error is exactly half an \*(up then
+the rounded value's least significant bit is zero.
+This kind of rounding is usually the best kind,
+sometimes provably so; for instance, for every
+x = 1.0, 2.0, 3.0, 4.0, ..., 2.0**52, we find
+(x/3.0)\(**3.0 == x and (x/10.0)\(**10.0 == x and ...
+despite that both the quotients and the products
+have been rounded.  Only rounding like IEEE 754
+can do that.  But no single kind of rounding can be
+proved best for every circumstance, so IEEE 754
+provides rounding towards zero or towards
+.If +
+or towards
+.If \-
+at the programmer's option.  And the
+same kinds of rounding are specified for
+Binary\-Decimal Conversions, at least for magnitudes
+between roughly 1.0e\-10 and 1.0e37.
+.RE
+Exceptions:
+.RS
+IEEE 754 recognizes five kinds of floating\-point exceptions,
+listed below in declining order of probable importance.
+.RS
+.nf
+.ta \w'Invalid Operation'u+6n +\w'Gradual Underflow'u+2n
+Exception	Default Result
+.tc \(ru
+		
+.tc
+Invalid Operation	\*(nn, or FALSE
+.if n \{\
+Overflow	\(+-Infinity
+Divide by Zero	\(+-Infinity \}
+.if t \{\
+Overflow	\(+-\(if
+Divide by Zero	\(+-\(if \}
+Underflow	Gradual Underflow
+Inexact	Rounded value
+.ta
+.fi
+.RE
+NOTE:  An Exception is not an Error unless handled
+badly.  What makes a class of exceptions exceptional
+is that no single default response can be satisfactory
+in every instance.  On the other hand, if a default
+response will serve most instances satisfactorily,
+the unsatisfactory instances cannot justify aborting
+computation every time the exception occurs.
+.RE
+.PP
+For each kind of floating\-point exception, IEEE 754
+provides a Flag that is raised each time its exception
+is signaled, and stays raised until the program resets
+it.  Programs may also test, save and restore a flag.
+Thus, IEEE 754 provides three ways by which programs
+may cope with exceptions for which the default result
+might be unsatisfactory:
+.IP 1) \w'\0\0\0\0'u
+Test for a condition that might cause an exception
+later, and branch to avoid the exception.
+.IP 2) \w'\0\0\0\0'u
+Test a flag to see whether an exception has occurred
+since the program last reset its flag.
+.IP 3) \w'\0\0\0\0'u
+Test a result to see whether it is a value that only
+an exception could have produced.
+.RS
+CAUTION: The only reliable ways to discover
+whether Underflow has occurred are to test whether
+products or quotients lie closer to zero than the
+underflow threshold, or to test the Underflow
+flag.  (Sums and differences cannot underflow in
+IEEE 754; if x
+.if n \
+!=
+.if t \
+\(!=
+y then x\-y is correct to
+full precision and certainly nonzero regardless of
+how tiny it may be.)  Products and quotients that
+underflow gradually can lose accuracy gradually
+without vanishing, so comparing them with zero
+(as one might on a VAX) will not reveal the loss.
+Fortunately, if a gradually underflowed value is
+destined to be added to something bigger than the
+underflow threshold, as is almost always the case,
+digits lost to gradual underflow will not be missed
+because they would have been rounded off anyway.
+So gradual underflows are usually \fIprovably\fR ignorable.
+The same cannot be said of underflows flushed to 0.
+.RE
+.PP
+At the option of an implementor conforming to IEEE 754,
+other ways to cope with exceptions may be provided:
+.IP 4) \w'\0\0\0\0'u
+ABORT.  This mechanism classifies an exception in
+advance as an incident to be handled by means
+traditionally associated with error\-handling
+statements like "ON ERROR GO TO ...".  Different
+languages offer different forms of this statement,
+but most share the following characteristics:
+.IP \(em \w'\0\0\0\0'u
+No means is provided to substitute a value for
+the offending operation's result and resume
+computation from what may be the middle of an
+expression.  An exceptional result is abandoned.
+.IP \(em \w'\0\0\0\0'u
+In a subprogram that lacks an error\-handling
+statement, an exception causes the subprogram to
+abort within whatever program called it, and so
+on back up the chain of calling subprograms until
+an error\-handling statement is encountered or the
+whole task is aborted and memory is dumped.
+.IP 5) \w'\0\0\0\0'u
+STOP.  This mechanism, requiring an interactive
+debugging environment, is more for the programmer
+than the program.  It classifies an exception in
+advance as a symptom of a programmer's error; the
+exception suspends execution as near as it can to
+the offending operation so that the programmer can
+look around to see how it happened.  Quite often
+the first several exceptions turn out to be quite
+unexceptionable, so the programmer ought ideally
+to be able to resume execution after each one as if
+execution had not been stopped.
+.IP 6) \w'\0\0\0\0'u
+\&... Other ways lie beyond the scope of this document.
+.RE
+.PP
+The crucial problem for exception handling is the problem of
+Scope, and the problem's solution is understood, but not
+enough manpower was available to implement it fully in time
+to be distributed in 4.3 BSD's \fIlibm\fR.  Ideally, each
+elementary function should act as if it were indivisible, or
+atomic, in the sense that ...
+.IP i) \w'iii)'u+2n
+No exception should be signaled that is not deserved by
+the data supplied to that function.
+.IP ii) \w'iii)'u+2n
+Any exception signaled should be identified with that
+function rather than with one of its subroutines.
+.IP iii) \w'iii)'u+2n
+The internal behavior of an atomic function should not
+be disrupted when a calling program changes from
+one to another of the five or so ways of handling
+exceptions listed above, although the definition
+of the function may be correlated intentionally
+with exception handling.
+.PP
+Ideally, every programmer should be able \fIconveniently\fR to
+turn a debugged subprogram into one that appears atomic to
+its users.  But simulating all three characteristics of an
+atomic function is still a tedious affair, entailing hosts
+of tests and saves\-restores; work is under way to ameliorate
+the inconvenience.
+.PP
+Meanwhile, the functions in \fIlibm\fR are only approximately
+atomic.  They signal no inappropriate exception except
+possibly ...
+.RS
+Over/Underflow
+.RS
+when a result, if properly computed, might have lain barely within range, and
+.RE
+Inexact in \fIcabs\fR, \fIcbrt\fR, \fIhypot\fR, \fIlog10\fR and \fIpow\fR
+.RS
+when it happens to be exact, thanks to fortuitous cancellation of errors.
+.RE
+.RE
+Otherwise, ...
+.RS
+Invalid Operation is signaled only when
+.RS
+any result but \*(nn would probably be misleading.
+.RE
+Overflow is signaled only when
+.RS
+the exact result would be finite but beyond the overflow threshold.
+.RE
+Divide\-by\-Zero is signaled only when
+.RS
+a function takes exactly infinite values at finite operands.
+.RE
+Underflow is signaled only when
+.RS
+the exact result would be nonzero but tinier than the underflow threshold.
+.RE
+Inexact is signaled only when
+.RS
+greater range or precision would be needed to represent the exact result.
+.RE
+.RE
+.SH BUGS
+When signals are appropriate, they are emitted by certain
+operations within the codes, so a subroutine\-trace may be
+needed to identify the function with its signal in case
+method 5) above is in use.  And the codes all take the
+IEEE 754 defaults for granted; this means that a decision to
+trap all divisions by zero could disrupt a code that would
+otherwise get correct results despite division by zero.
+.SH SEE ALSO
+An explanation of IEEE 754 and its proposed extension p854
+was published in the IEEE magazine MICRO in August 1984 under
+the title "A Proposed Radix\- and Word\-length\-independent
+Standard for Floating\-point Arithmetic" by W. J. Cody et al.
+The manuals for Pascal, C and BASIC on the Apple Macintosh
+document the features of IEEE 754 pretty well.
+Articles in the IEEE magazine COMPUTER vol. 14 no. 3 (Mar.
+1981), and in the ACM SIGNUM Newsletter Special Issue of
+Oct. 1979, may be helpful although they pertain to
+superseded drafts of the standard.

lib/msun/man/rint.3

@@ -0,0 +1,63 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)rint.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: rint.3,v 1.4 1994/03/11 01:32:11 jtc Exp $
+.\"
+.Dd March 10, 1994
+.Dt RINT 3
+.Os
+.Sh NAME
+.Nm rint
+.Nd round to integral value in floating-point format
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn rint "double x"
+.Sh DESCRIPTION
+The
+.Fn rint
+function returns the integral value (represented as a double precision number)
+nearest to
+.Fa x
+according to the prevailing rounding mode.
+.Sh SEE ALSO
+.Xr abs 3 ,
+.Xr fabs 3 ,
+.Xr ceil 3 ,
+.Xr floor 3 ,
+.Xr ieee 3 ,
+.Xr math 3
+.Sh HISTORY
+A
+.Fn rint
+function appeared in
+.At v6 .

lib/msun/man/sin.3

@@ -0,0 +1,73 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\"	@(#)sin.3	6.7 (Berkeley) 4/19/91
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)sin.3	6.7 (Berkeley) 4/19/91
+.\"	$Id: sin.3,v 1.4 1993/10/29 22:57:28 jtc Exp $
+.\"
+.Dd April 19, 1991
+.Dt SIN 3
+.Os
+.Sh NAME
+.Nm sin
+.Nd sine function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn sin "double x"
+.Sh DESCRIPTION
+The
+.Fn sin
+function computes the sine of
+.Fa x
+(measured in radians).
+A large magnitude argument may yield a result with little
+or no significance.
+.Sh RETURN VALUES
+The
+.Fn sin
+function returns the sine value.
+.Sh SEE ALSO
+.Xr acos 3 ,
+.Xr asin 3 ,
+.Xr atan 3 ,
+.Xr atan2 3 ,
+.Xr cos 3 ,
+.Xr cosh 3 ,
+.Xr sinh 3 ,
+.Xr tan 3 ,
+.Xr tanh 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn sin
+function conforms to
+.St -ansiC .

lib/msun/man/sinh.3

@@ -0,0 +1,75 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"	from: @(#)sinh.3	6.6 (Berkeley) 4/19/91
+.\"	$Id: sinh.3,v 1.4 1993/10/29 22:57:30 jtc Exp $
+.Dd April 19, 1991
+.Dt SINH 3
+.Os
+.Sh NAME
+.Nm sinh
+.Nd hyperbolic sine function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn sinh "double  x"
+.Sh DESCRIPTION
+The
+.Fn sinh
+function computes the hyperbolic sine of
+.Fa x .
+.Sh RETURN VALUES
+The
+.Fn sinh
+function returns the hyperbolic sine value unless
+the  magnitude 
+of
+.Fa x
+is too large; in this event, the global variable
+.Va errno
+is set to
+.Er ERANGE .
+.Sh SEE ALSO
+.Xr acos 3 ,
+.Xr asin 3 ,
+.Xr atan 3 ,
+.Xr atan2 3 ,
+.Xr cos 3 ,
+.Xr cosh 3 ,
+.Xr sin 3 ,
+.Xr tan 3 ,
+.Xr tanh 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn sinh
+function conforms to
+.St -ansiC .

lib/msun/man/sqrt.3

@@ -0,0 +1,121 @@
+.\" Copyright (c) 1985, 1991 Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)sqrt.3	6.4 (Berkeley) 5/6/91
+.\"	$Id: sqrt.3,v 1.3 1993/08/14 13:43:05 mycroft Exp $
+.\"
+.Dd May 6, 1991
+.Dt SQRT 3
+.Os
+.Sh NAME
+.Nm cbrt ,
+.Nm sqrt
+.Nd cube root and square root functions
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn cbrt "double x"
+.Ft double
+.Fn sqrt "double x"
+.Sh DESCRIPTION
+The
+.Fn cbrt
+function computes
+the cube root of
+.Ar x .
+.Pp
+The
+.Fn sqrt
+computes the
+non-negative square root of x.
+.Sh RETURN VALUES
+The
+.Fn cbrt
+function returns the requested cube root.
+The
+.Fn sqrt
+function returns the requested square root
+unless an error occurs.
+On the
+.Tn VAX
+or
+.Tn Tahoe
+processor an attempt to take the
+.Fn sqrt
+of negative
+.Fa x
+causes an error; in this event,
+the global variable
+.Va errno
+is set to
+.Dv EDOM
+and a reserved operand fault is generated.
+.Sh ERROR (due to Roundoff etc.)
+The
+.Fn cbrt
+function
+is accurate to within 0.7
+.Em ulps .
+.Pp
+The
+.Fn sqrt
+function on a
+.Tn VAX
+is accurate to within 0.501
+.Em ulps .
+Sqrt on a machine that conforms to
+.Tn IEEE
+754 is correctly rounded
+in accordance with the rounding mode in force; the error is less than
+half an
+.Em ulp
+in the default mode (round\-to\-nearest).
+An
+.Em ulp
+is one
+.Em U Ns nit
+in the
+.Em L Ns ast
+.Em P Ns lace
+carried.
+.Sh SEE ALSO
+.Xr math 3 ,
+.Xr infnan 3
+.Sh STANDARDS
+The
+.Nm sqrt
+function conforms to
+.St -ansiC .
+.Sh HISTORY
+The
+.Nm cbrt
+function appeared in
+.Bx 4.3 .

lib/msun/man/tan.3

@@ -0,0 +1,74 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)tan.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: tan.3,v 1.4 1993/10/05 16:33:47 jtc Exp $
+.\"
+.Dd May 2, 1991
+.Dt TAN 3
+.Os
+.Sh NAME
+.Nm tan
+.Nd tangent function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn tan "double x"
+.Sh DESCRIPTION
+The
+.Fn tan
+function computes the tangent of
+.Fa x
+(measured in radians).
+A large magnitude argument may yield a result
+with little or no significance.
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The
+.Fn tan
+function returns the tangent value.
+.Sh SEE ALSO
+.Xr acos 3 ,
+.Xr asin 3 ,
+.Xr atan 3 ,
+.Xr atan2 3 ,
+.Xr cos 3 ,
+.Xr cosh 3 ,
+.Xr sin 3 ,
+.Xr sinh 3 ,
+.Xr tanh 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn tan
+function conforms to
+.St -ansiC .

lib/msun/man/tanh.3

@@ -0,0 +1,71 @@
+.\" Copyright (c) 1991 The Regents of the University of California.
+.\" All rights reserved.
+.\"
+.\" Redistribution and use in source and binary forms, with or without
+.\" modification, are permitted provided that the following conditions
+.\" are met:
+.\" 1. Redistributions of source code must retain the above copyright
+.\"    notice, this list of conditions and the following disclaimer.
+.\" 2. Redistributions in binary form must reproduce the above copyright
+.\"    notice, this list of conditions and the following disclaimer in the
+.\"    documentation and/or other materials provided with the distribution.
+.\" 3. All advertising materials mentioning features or use of this software
+.\"    must display the following acknowledgement:
+.\"	This product includes software developed by the University of
+.\"	California, Berkeley and its contributors.
+.\" 4. Neither the name of the University nor the names of its contributors
+.\"    may be used to endorse or promote products derived from this software
+.\"    without specific prior written permission.
+.\"
+.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
+.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
+.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+.\" SUCH DAMAGE.
+.\"
+.\"     from: @(#)tanh.3	5.1 (Berkeley) 5/2/91
+.\"	$Id: tanh.3,v 1.4 1993/10/05 16:33:49 jtc Exp $
+.\"
+.Dd May 2, 1991
+.Dt TANH 3
+.Os
+.Sh NAME
+.Nm tanh
+.Nd hyperbolic tangent function
+.Sh SYNOPSIS
+.Fd #include <math.h>
+.Ft double
+.Fn tanh "double x"
+.Sh DESCRIPTION
+The
+.Fn tanh
+function computes the hyperbolic tangent of
+.Fa x .
+For a discussion of error due to roundoff, see
+.Xr math 3 .
+.Sh RETURN VALUES
+The
+.Fn tanh
+function returns the hyperbolic tangent value.
+.Sh SEE ALSO
+.Xr acos 3 ,
+.Xr asin 3 ,
+.Xr atan 3 ,
+.Xr atan2 3 ,
+.Xr cos 3 ,
+.Xr cosh 3 ,
+.Xr sin 3 ,
+.Xr sinh 3 ,
+.Xr tan 3 ,
+.Xr math 3
+.Sh STANDARDS
+The
+.Fn tanh
+function conforms to
+.St -ansiC .

lib/msun/src/e_acos.c

@@ -0,0 +1,111 @@
+/* @(#)e_acos.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_acos.c,v 1.6 1994/08/18 23:04:51 jtc Exp $";
+#endif
+
+/* __ieee754_acos(x)
+ * Method :                  
+ *	acos(x)  = pi/2 - asin(x)
+ *	acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ *	acos(x) = pi/2 - (x + x*x^2*R(x^2))	(see asin.c)
+ * For x>0.5
+ * 	acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ *		= 2asin(sqrt((1-x)/2))  
+ *		= 2s + 2s*z*R(z) 	...z=(1-x)/2, s=sqrt(z)
+ *		= 2f + (2c + 2s*z*R(z))
+ *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ *     for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ *	acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ *		= pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ *	if x is NaN, return x itself;
+ *	if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: sqrt
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+one=  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pi =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+#ifdef __STDC__
+	double __ieee754_acos(double x)
+#else
+	double __ieee754_acos(x)
+	double x;
+#endif
+{
+	double z,p,q,r,w,s,c,df;
+	int32_t hx,ix;
+	GET_HIGH_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x3ff00000) {	/* |x| >= 1 */
+	    u_int32_t lx;
+	    GET_LOW_WORD(lx,x);
+	    if(((ix-0x3ff00000)|lx)==0) {	/* |x|==1 */
+		if(hx>0) return 0.0;		/* acos(1) = 0  */
+		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
+	    }
+	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
+	}
+	if(ix<0x3fe00000) {	/* |x| < 0.5 */
+	    if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
+	    z = x*x;
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    r = p/q;
+	    return pio2_hi - (x - (pio2_lo-x*r));
+	} else  if (hx<0) {		/* x < -0.5 */
+	    z = (one+x)*0.5;
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    s = sqrt(z);
+	    r = p/q;
+	    w = r*s-pio2_lo;
+	    return pi - 2.0*(s+w);
+	} else {			/* x > 0.5 */
+	    z = (one-x)*0.5;
+	    s = sqrt(z);
+	    df = s;
+	    SET_LOW_WORD(df,0);
+	    c  = (z-df*df)/(s+df);
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    r = p/q;
+	    w = r*s+c;
+	    return 2.0*(df+w);
+	}
+}

lib/msun/src/e_acosf.c

@@ -0,0 +1,89 @@
+/* e_acosf.c -- float version of e_acos.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_acosf.c,v 1.2 1994/08/18 23:04:53 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float 
+#else
+static float 
+#endif
+one =  1.0000000000e+00, /* 0x3F800000 */
+pi =  3.1415925026e+00, /* 0x40490fda */
+pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
+pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
+pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
+pS1 = -3.2556581497e-01, /* 0xbea6b090 */
+pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
+pS3 = -4.0055535734e-02, /* 0xbd241146 */
+pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
+pS5 =  3.4793309169e-05, /* 0x3811ef08 */
+qS1 = -2.4033949375e+00, /* 0xc019d139 */
+qS2 =  2.0209457874e+00, /* 0x4001572d */
+qS3 = -6.8828397989e-01, /* 0xbf303361 */
+qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
+
+#ifdef __STDC__
+	float __ieee754_acosf(float x)
+#else
+	float __ieee754_acosf(x)
+	float x;
+#endif
+{
+	float z,p,q,r,w,s,c,df;
+	int32_t hx,ix;
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix==0x3f800000) {		/* |x|==1 */
+	    if(hx>0) return 0.0;	/* acos(1) = 0  */
+	    else return pi+(float)2.0*pio2_lo;	/* acos(-1)= pi */
+	} else if(ix>0x3f800000) {	/* |x| >= 1 */
+	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
+	}
+	if(ix<0x3f000000) {	/* |x| < 0.5 */
+	    if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
+	    z = x*x;
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    r = p/q;
+	    return pio2_hi - (x - (pio2_lo-x*r));
+	} else  if (hx<0) {		/* x < -0.5 */
+	    z = (one+x)*(float)0.5;
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    s = sqrtf(z);
+	    r = p/q;
+	    w = r*s-pio2_lo;
+	    return pi - (float)2.0*(s+w);
+	} else {			/* x > 0.5 */
+	    int32_t idf;
+	    z = (one-x)*(float)0.5;
+	    s = sqrtf(z);
+	    df = s;
+	    GET_FLOAT_WORD(idf,df);
+	    SET_FLOAT_WORD(df,idf&0xfffff000);
+	    c  = (z-df*df)/(s+df);
+	    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+	    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+	    r = p/q;
+	    w = r*s+c;
+	    return (float)2.0*(df+w);
+	}
+}

lib/msun/src/e_acosh.c

@@ -0,0 +1,69 @@
+/* @(#)e_acosh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_acosh.c,v 1.6 1994/08/18 23:04:54 jtc Exp $";
+#endif
+
+/* __ieee754_acosh(x)
+ * Method :
+ *	Based on 
+ *		acosh(x) = log [ x + sqrt(x*x-1) ]
+ *	we have
+ *		acosh(x) := log(x)+ln2,	if x is large; else
+ *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
+ *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
+ *
+ * Special cases:
+ *	acosh(x) is NaN with signal if x<1.
+ *	acosh(NaN) is NaN without signal.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+one	= 1.0,
+ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
+
+#ifdef __STDC__
+	double __ieee754_acosh(double x)
+#else
+	double __ieee754_acosh(x)
+	double x;
+#endif
+{	
+	double t;
+	int32_t hx;
+	u_int32_t lx;
+	EXTRACT_WORDS(hx,lx,x);
+	if(hx<0x3ff00000) {		/* x < 1 */
+	    return (x-x)/(x-x);
+	} else if(hx >=0x41b00000) {	/* x > 2**28 */
+	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
+	        return x+x;
+	    } else 
+		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
+	} else if(((hx-0x3ff00000)|lx)==0) {
+	    return 0.0;			/* acosh(1) = 0 */
+	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
+	    t=x*x;
+	    return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
+	} else {			/* 1<x<2 */
+	    t = x-one;
+	    return log1p(t+sqrt(2.0*t+t*t));
+	}
+}

lib/msun/src/e_acoshf.c

@@ -0,0 +1,57 @@
+/* e_acoshf.c -- float version of e_acosh.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_acoshf.c,v 1.2 1994/08/18 23:04:57 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float 
+#else
+static float 
+#endif
+one	= 1.0,
+ln2	= 6.9314718246e-01;  /* 0x3f317218 */
+
+#ifdef __STDC__
+	float __ieee754_acoshf(float x)
+#else
+	float __ieee754_acoshf(x)
+	float x;
+#endif
+{	
+	float t;
+	int32_t hx;
+	GET_FLOAT_WORD(hx,x);
+	if(hx<0x3f800000) {		/* x < 1 */
+	    return (x-x)/(x-x);
+	} else if(hx >=0x4d800000) {	/* x > 2**28 */
+	    if(hx >=0x7f800000) {	/* x is inf of NaN */
+	        return x+x;
+	    } else 
+		return __ieee754_logf(x)+ln2;	/* acosh(huge)=log(2x) */
+	} else if (hx==0x3f800000) {
+	    return 0.0;			/* acosh(1) = 0 */
+	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
+	    t=x*x;
+	    return __ieee754_logf((float)2.0*x-one/(x+sqrtf(t-one)));
+	} else {			/* 1<x<2 */
+	    t = x-one;
+	    return log1pf(t+sqrtf((float)2.0*t+t*t));
+	}
+}

lib/msun/src/e_asin.c

@@ -0,0 +1,120 @@
+/* @(#)e_asin.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_asin.c,v 1.6 1994/08/18 23:05:01 jtc Exp $";
+#endif
+
+/* __ieee754_asin(x)
+ * Method :                  
+ *	Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ *	we approximate asin(x) on [0,0.5] by
+ *		asin(x) = x + x*x^2*R(x^2)
+ *	where
+ *		R(x^2) is a rational approximation of (asin(x)-x)/x^3 
+ *	and its remez error is bounded by
+ *		|(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ *	For x in [0.5,1]
+ *		asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ *	Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ *	then for x>0.98
+ *		asin(x) = pi/2 - 2*(s+s*z*R(z))
+ *			= pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ *	For x<=0.98, let pio4_hi = pio2_hi/2, then
+ *		f = hi part of s;
+ *		c = sqrt(z) - f = (z-f*f)/(s+f) 	...f+c=sqrt(z)
+ *	and
+ *		asin(x) = pi/2 - 2*(s+s*z*R(z))
+ *			= pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ *			= pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ *	if x is NaN, return x itself;
+ *	if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+huge =  1.000e+300,
+pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
+	/* coefficient for R(x^2) */
+pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+#ifdef __STDC__
+	double __ieee754_asin(double x)
+#else
+	double __ieee754_asin(x)
+	double x;
+#endif
+{
+	double t,w,p,q,c,r,s;
+	int32_t hx,ix;
+	GET_HIGH_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>= 0x3ff00000) {		/* |x|>= 1 */
+	    u_int32_t lx;
+	    GET_LOW_WORD(lx,x);
+	    if(((ix-0x3ff00000)|lx)==0)
+		    /* asin(1)=+-pi/2 with inexact */
+		return x*pio2_hi+x*pio2_lo;	
+	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */   
+	} else if (ix<0x3fe00000) {	/* |x|<0.5 */
+	    if(ix<0x3e400000) {		/* if |x| < 2**-27 */
+		if(huge+x>one) return x;/* return x with inexact if x!=0*/
+	    } else 
+		t = x*x;
+		p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+		q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+		w = p/q;
+		return x+x*w;
+	}
+	/* 1> |x|>= 0.5 */
+	w = one-fabs(x);
+	t = w*0.5;
+	p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+	q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+	s = sqrt(t);
+	if(ix>=0x3FEF3333) { 	/* if |x| > 0.975 */
+	    w = p/q;
+	    t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
+	} else {
+	    w  = s;
+	    SET_LOW_WORD(w,0);
+	    c  = (t-w*w)/(s+w);
+	    r  = p/q;
+	    p  = 2.0*s*r-(pio2_lo-2.0*c);
+	    q  = pio4_hi-2.0*w;
+	    t  = pio4_hi-(p-q);
+	}    
+	if(hx>0) return t; else return -t;    
+}

lib/msun/src/e_asinf.c

@@ -0,0 +1,92 @@
+/* e_asinf.c -- float version of e_asin.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_asinf.c,v 1.2 1994/08/18 23:05:05 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float 
+#else
+static float 
+#endif
+one =  1.0000000000e+00, /* 0x3F800000 */
+huge =  1.000e+30,
+pio2_hi =  1.5707962513e+00, /* 0x3fc90fda */
+pio2_lo =  7.5497894159e-08, /* 0x33a22168 */
+pio4_hi =  7.8539818525e-01, /* 0x3f490fdb */
+	/* coefficient for R(x^2) */
+pS0 =  1.6666667163e-01, /* 0x3e2aaaab */
+pS1 = -3.2556581497e-01, /* 0xbea6b090 */
+pS2 =  2.0121252537e-01, /* 0x3e4e0aa8 */
+pS3 = -4.0055535734e-02, /* 0xbd241146 */
+pS4 =  7.9153501429e-04, /* 0x3a4f7f04 */
+pS5 =  3.4793309169e-05, /* 0x3811ef08 */
+qS1 = -2.4033949375e+00, /* 0xc019d139 */
+qS2 =  2.0209457874e+00, /* 0x4001572d */
+qS3 = -6.8828397989e-01, /* 0xbf303361 */
+qS4 =  7.7038154006e-02; /* 0x3d9dc62e */
+
+#ifdef __STDC__
+	float __ieee754_asinf(float x)
+#else
+	float __ieee754_asinf(x)
+	float x;
+#endif
+{
+	float t,w,p,q,c,r,s;
+	int32_t hx,ix;
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix==0x3f800000) {
+		/* asin(1)=+-pi/2 with inexact */
+	    return x*pio2_hi+x*pio2_lo;	
+	} else if(ix> 0x3f800000) {	/* |x|>= 1 */
+	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */   
+	} else if (ix<0x3f000000) {	/* |x|<0.5 */
+	    if(ix<0x32000000) {		/* if |x| < 2**-27 */
+		if(huge+x>one) return x;/* return x with inexact if x!=0*/
+	    } else 
+		t = x*x;
+		p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+		q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+		w = p/q;
+		return x+x*w;
+	}
+	/* 1> |x|>= 0.5 */
+	w = one-fabsf(x);
+	t = w*(float)0.5;
+	p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+	q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+	s = sqrtf(t);
+	if(ix>=0x3F79999A) { 	/* if |x| > 0.975 */
+	    w = p/q;
+	    t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
+	} else {
+	    int32_t iw;
+	    w  = s;
+	    GET_FLOAT_WORD(iw,w);
+	    SET_FLOAT_WORD(w,iw&0xfffff000);
+	    c  = (t-w*w)/(s+w);
+	    r  = p/q;
+	    p  = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
+	    q  = pio4_hi-(float)2.0*w;
+	    t  = pio4_hi-(p-q);
+	}    
+	if(hx>0) return t; else return -t;    
+}

lib/msun/src/e_atan2.c

@@ -0,0 +1,130 @@
+/* @(#)e_atan2.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_atan2.c,v 1.6 1994/08/18 23:05:08 jtc Exp $";
+#endif
+
+/* __ieee754_atan2(y,x)
+ * Method :
+ *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
+ *	2. Reduce x to positive by (if x and y are unexceptional): 
+ *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
+ *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
+ *
+ * Special cases:
+ *
+ *	ATAN2((anything), NaN ) is NaN;
+ *	ATAN2(NAN , (anything) ) is NaN;
+ *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
+ *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
+ *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
+ *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
+ *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
+ *	ATAN2(+-INF,+INF ) is +-pi/4 ;
+ *	ATAN2(+-INF,-INF ) is +-3pi/4;
+ *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following 
+ * constants. The decimal values may be used, provided that the 
+ * compiler will convert from decimal to binary accurately enough 
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+tiny  = 1.0e-300,
+zero  = 0.0,
+pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
+pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
+pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
+pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
+
+#ifdef __STDC__
+	double __ieee754_atan2(double y, double x)
+#else
+	double __ieee754_atan2(y,x)
+	double  y,x;
+#endif
+{  
+	double z;
+	int32_t k,m,hx,hy,ix,iy;
+	u_int32_t lx,ly;
+
+	EXTRACT_WORDS(hx,lx,x);
+	ix = hx&0x7fffffff;
+	EXTRACT_WORDS(hy,ly,y);
+	iy = hy&0x7fffffff;
+	if(((ix|((lx|-lx)>>31))>0x7ff00000)||
+	   ((iy|((ly|-ly)>>31))>0x7ff00000))	/* x or y is NaN */
+	   return x+y;
+	if((hx-0x3ff00000|lx)==0) return atan(y);   /* x=1.0 */
+	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
+
+    /* when y = 0 */
+	if((iy|ly)==0) {
+	    switch(m) {
+		case 0: 
+		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
+		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
+		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
+	    }
+	}
+    /* when x = 0 */
+	if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
+	    
+    /* when x is INF */
+	if(ix==0x7ff00000) {
+	    if(iy==0x7ff00000) {
+		switch(m) {
+		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
+		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
+		    case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
+		    case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
+		}
+	    } else {
+		switch(m) {
+		    case 0: return  zero  ;	/* atan(+...,+INF) */
+		    case 1: return -zero  ;	/* atan(-...,+INF) */
+		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
+		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
+		}
+	    }
+	}
+    /* when y is INF */
+	if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+    /* compute y/x */
+	k = (iy-ix)>>20;
+	if(k > 60) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**60 */
+	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
+	else z=atan(fabs(y/x));		/* safe to do y/x */
+	switch (m) {
+	    case 0: return       z  ;	/* atan(+,+) */
+	    case 1: {
+	    	      u_int32_t zh;
+		      GET_HIGH_WORD(zh,z);
+		      SET_HIGH_WORD(z,zh ^ 0x80000000);
+		    }
+		    return       z  ;	/* atan(-,+) */
+	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
+	    default: /* case 3 */
+	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
+	}
+}

lib/msun/src/e_atan2f.c

@@ -0,0 +1,105 @@
+/* e_atan2f.c -- float version of e_atan2.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_atan2f.c,v 1.2 1994/08/18 23:05:11 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float 
+#else
+static float 
+#endif
+tiny  = 1.0e-30,
+zero  = 0.0,
+pi_o_4  = 7.8539818525e-01, /* 0x3f490fdb */
+pi_o_2  = 1.5707963705e+00, /* 0x3fc90fdb */
+pi      = 3.1415925026e+00, /* 0x40490fda */
+pi_lo   = 1.5099578832e-07; /* 0x34222168 */
+
+#ifdef __STDC__
+	float __ieee754_atan2f(float y, float x)
+#else
+	float __ieee754_atan2f(y,x)
+	float  y,x;
+#endif
+{  
+	float z;
+	int32_t k,m,hx,hy,ix,iy;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	GET_FLOAT_WORD(hy,y);
+	iy = hy&0x7fffffff;
+	if((ix>0x7f800000)||
+	   (iy>0x7f800000))	/* x or y is NaN */
+	   return x+y;
+	if(hx==0x3f800000) return atanf(y);   /* x=1.0 */
+	m = ((hy>>31)&1)|((hx>>30)&2);	/* 2*sign(x)+sign(y) */
+
+    /* when y = 0 */
+	if(iy==0) {
+	    switch(m) {
+		case 0: 
+		case 1: return y; 	/* atan(+-0,+anything)=+-0 */
+		case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
+		case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
+	    }
+	}
+    /* when x = 0 */
+	if(ix==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
+	    
+    /* when x is INF */
+	if(ix==0x7f800000) {
+	    if(iy==0x7f800000) {
+		switch(m) {
+		    case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
+		    case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
+		    case 2: return  (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
+		    case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
+		}
+	    } else {
+		switch(m) {
+		    case 0: return  zero  ;	/* atan(+...,+INF) */
+		    case 1: return -zero  ;	/* atan(-...,+INF) */
+		    case 2: return  pi+tiny  ;	/* atan(+...,-INF) */
+		    case 3: return -pi-tiny  ;	/* atan(-...,-INF) */
+		}
+	    }
+	}
+    /* when y is INF */
+	if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+    /* compute y/x */
+	k = (iy-ix)>>23;
+	if(k > 60) z=pi_o_2+(float)0.5*pi_lo; 	/* |y/x| >  2**60 */
+	else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
+	else z=atanf(fabsf(y/x));	/* safe to do y/x */
+	switch (m) {
+	    case 0: return       z  ;	/* atan(+,+) */
+	    case 1: {
+	    	      u_int32_t zh;
+		      GET_FLOAT_WORD(zh,z);
+		      SET_FLOAT_WORD(z,zh ^ 0x80000000);
+		    }
+		    return       z  ;	/* atan(-,+) */
+	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */
+	    default: /* case 3 */
+	    	    return  (z-pi_lo)-pi;/* atan(-,-) */
+	}
+}

lib/msun/src/e_atanh.c

@@ -0,0 +1,74 @@
+/* @(#)e_atanh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_atanh.c,v 1.6 1994/08/18 23:05:12 jtc Exp $";
+#endif
+
+/* __ieee754_atanh(x)
+ * Method :
+ *    1.Reduced x to positive by atanh(-x) = -atanh(x)
+ *    2.For x>=0.5
+ *                  1              2x                          x
+ *	atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
+ *                  2             1 - x                      1 - x
+ *	
+ * 	For x<0.5
+ *	atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
+ *
+ * Special cases:
+ *	atanh(x) is NaN if |x| > 1 with signal;
+ *	atanh(NaN) is that NaN with no signal;
+ *	atanh(+-1) is +-INF with signal.
+ *
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, huge = 1e300;
+#else
+static double one = 1.0, huge = 1e300;
+#endif
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_atanh(double x)
+#else
+	double __ieee754_atanh(x)
+	double x;
+#endif
+{
+	double t;
+	int32_t hx,ix;
+	u_int32_t lx;
+	EXTRACT_WORDS(hx,lx,x);
+	ix = hx&0x7fffffff;
+	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
+	    return (x-x)/(x-x);
+	if(ix==0x3ff00000) 
+	    return x/zero;
+	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
+	SET_HIGH_WORD(x,ix);
+	if(ix<0x3fe00000) {		/* x < 0.5 */
+	    t = x+x;
+	    t = 0.5*log1p(t+t*x/(one-x));
+	} else 
+	    t = 0.5*log1p((x+x)/(one-x));
+	if(hx>=0) return t; else return -t;
+}

lib/msun/src/e_atanhf.c

@@ -0,0 +1,58 @@
+/* e_atanhf.c -- float version of e_atanh.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_atanhf.c,v 1.2 1994/08/18 23:05:14 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float one = 1.0, huge = 1e30;
+#else
+static float one = 1.0, huge = 1e30;
+#endif
+
+#ifdef __STDC__
+static const float zero = 0.0;
+#else
+static float zero = 0.0;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_atanhf(float x)
+#else
+	float __ieee754_atanhf(x)
+	float x;
+#endif
+{
+	float t;
+	int32_t hx,ix;
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if (ix>0x3f800000) 		/* |x|>1 */
+	    return (x-x)/(x-x);
+	if(ix==0x3f800000) 
+	    return x/zero;
+	if(ix<0x31800000&&(huge+x)>zero) return x;	/* x<2**-28 */
+	SET_FLOAT_WORD(x,ix);
+	if(ix<0x3f000000) {		/* x < 0.5 */
+	    t = x+x;
+	    t = (float)0.5*log1pf(t+t*x/(one-x));
+	} else 
+	    t = (float)0.5*log1pf((x+x)/(one-x));
+	if(hx>=0) return t; else return -t;
+}

lib/msun/src/e_cosh.c

@@ -0,0 +1,93 @@
+/* @(#)e_cosh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_cosh.c,v 1.5 1994/08/18 23:05:15 jtc Exp $";
+#endif
+
+/* __ieee754_cosh(x)
+ * Method : 
+ * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
+ *	1. Replace x by |x| (cosh(x) = cosh(-x)). 
+ *	2. 
+ *		                                        [ exp(x) - 1 ]^2 
+ *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
+ *			       			           2*exp(x)
+ *
+ *		                                  exp(x) +  1/exp(x)
+ *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
+ *			       			          2
+ *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2 
+ *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
+ *	    ln2ovft  <  x	    :  cosh(x) := huge*huge (overflow)
+ *
+ * Special cases:
+ *	cosh(x) is |x| if x is +INF, -INF, or NaN.
+ *	only cosh(0)=1 is exact for finite x.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, half=0.5, huge = 1.0e300;
+#else
+static double one = 1.0, half=0.5, huge = 1.0e300;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_cosh(double x)
+#else
+	double __ieee754_cosh(x)
+	double x;
+#endif
+{	
+	double t,w;
+	int32_t ix;
+	u_int32_t lx;
+
+    /* High word of |x|. */
+	GET_HIGH_WORD(ix,x);
+	ix &= 0x7fffffff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7ff00000) return x*x;	
+
+    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
+	if(ix<0x3fd62e43) {
+	    t = expm1(fabs(x));
+	    w = one+t;
+	    if (ix<0x3c800000) return w;	/* cosh(tiny) = 1 */
+	    return one+(t*t)/(w+w);
+	}
+
+    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
+	if (ix < 0x40360000) {
+		t = __ieee754_exp(fabs(x));
+		return half*t+half/t;
+	}
+
+    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
+	if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));
+
+    /* |x| in [log(maxdouble), overflowthresold] */
+	GET_LOW_WORD(lx,x);
+	if (ix<0x408633CE || 
+	      (ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) {
+	    w = __ieee754_exp(half*fabs(x));
+	    t = half*w;
+	    return t*w;
+	}
+
+    /* |x| > overflowthresold, cosh(x) overflow */
+	return huge*huge;
+}

lib/msun/src/e_coshf.c

@@ -0,0 +1,71 @@
+/* e_coshf.c -- float version of e_cosh.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_coshf.c,v 1.2 1994/08/18 23:05:17 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float one = 1.0, half=0.5, huge = 1.0e30;
+#else
+static float one = 1.0, half=0.5, huge = 1.0e30;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_coshf(float x)
+#else
+	float __ieee754_coshf(x)
+	float x;
+#endif
+{	
+	float t,w;
+	int32_t ix;
+
+	GET_FLOAT_WORD(ix,x);
+	ix &= 0x7fffffff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7f800000) return x*x;	
+
+    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
+	if(ix<0x3eb17218) {
+	    t = expm1f(fabsf(x));
+	    w = one+t;
+	    if (ix<0x24000000) return w;	/* cosh(tiny) = 1 */
+	    return one+(t*t)/(w+w);
+	}
+
+    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
+	if (ix < 0x41b00000) {
+		t = __ieee754_expf(fabsf(x));
+		return half*t+half/t;
+	}
+
+    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
+	if (ix < 0x42b17180)  return half*__ieee754_expf(fabsf(x));
+
+    /* |x| in [log(maxdouble), overflowthresold] */
+	if (ix<=0x42b2d4fc) {
+	    w = __ieee754_expf(half*fabsf(x));
+	    t = half*w;
+	    return t*w;
+	}
+
+    /* |x| > overflowthresold, cosh(x) overflow */
+	return huge*huge;
+}

lib/msun/src/e_exp.c

@@ -0,0 +1,167 @@
+/* @(#)e_exp.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_exp.c,v 1.6 1994/08/18 23:05:18 jtc Exp $";
+#endif
+
+/* __ieee754_exp(x)
+ * Returns the exponential of x.
+ *
+ * Method
+ *   1. Argument reduction:
+ *      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
+ *	Given x, find r and integer k such that
+ *
+ *               x = k*ln2 + r,  |r| <= 0.5*ln2.  
+ *
+ *      Here r will be represented as r = hi-lo for better 
+ *	accuracy.
+ *
+ *   2. Approximation of exp(r) by a special rational function on
+ *	the interval [0,0.34658]:
+ *	Write
+ *	    R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
+ *      We use a special Reme algorithm on [0,0.34658] to generate 
+ * 	a polynomial of degree 5 to approximate R. The maximum error 
+ *	of this polynomial approximation is bounded by 2**-59. In
+ *	other words,
+ *	    R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
+ *  	(where z=r*r, and the values of P1 to P5 are listed below)
+ *	and
+ *	    |                  5          |     -59
+ *	    | 2.0+P1*z+...+P5*z   -  R(z) | <= 2 
+ *	    |                             |
+ *	The computation of exp(r) thus becomes
+ *                             2*r
+ *		exp(r) = 1 + -------
+ *		              R - r
+ *                                 r*R1(r)	
+ *		       = 1 + r + ----------- (for better accuracy)
+ *		                  2 - R1(r)
+ *	where
+ *			         2       4             10
+ *		R1(r) = r - (P1*r  + P2*r  + ... + P5*r   ).
+ *	
+ *   3. Scale back to obtain exp(x):
+ *	From step 1, we have
+ *	   exp(x) = 2^k * exp(r)
+ *
+ * Special cases:
+ *	exp(INF) is INF, exp(NaN) is NaN;
+ *	exp(-INF) is 0, and
+ *	for finite argument, only exp(0)=1 is exact.
+ *
+ * Accuracy:
+ *	according to an error analysis, the error is always less than
+ *	1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ *	For IEEE double 
+ *	    if x >  7.09782712893383973096e+02 then exp(x) overflow
+ *	    if x < -7.45133219101941108420e+02 then exp(x) underflow
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following 
+ * constants. The decimal values may be used, provided that the 
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one	= 1.0,
+halF[2]	= {0.5,-0.5,},
+huge	= 1.0e+300,
+twom1000= 9.33263618503218878990e-302,     /* 2**-1000=0x01700000,0*/
+o_threshold=  7.09782712893383973096e+02,  /* 0x40862E42, 0xFEFA39EF */
+u_threshold= -7.45133219101941108420e+02,  /* 0xc0874910, 0xD52D3051 */
+ln2HI[2]   ={ 6.93147180369123816490e-01,  /* 0x3fe62e42, 0xfee00000 */
+	     -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
+ln2LO[2]   ={ 1.90821492927058770002e-10,  /* 0x3dea39ef, 0x35793c76 */
+	     -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
+invln2 =  1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
+P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+P5   =  4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
+
+
+#ifdef __STDC__
+	double __ieee754_exp(double x)	/* default IEEE double exp */
+#else
+	double __ieee754_exp(x)	/* default IEEE double exp */
+	double x;
+#endif
+{
+	double y,hi,lo,c,t;
+	int32_t k,xsb;
+	u_int32_t hx;
+
+	GET_HIGH_WORD(hx,x);
+	xsb = (hx>>31)&1;		/* sign bit of x */
+	hx &= 0x7fffffff;		/* high word of |x| */
+
+    /* filter out non-finite argument */
+	if(hx >= 0x40862E42) {			/* if |x|>=709.78... */
+            if(hx>=0x7ff00000) {
+	        u_int32_t lx;
+		GET_LOW_WORD(lx,x);
+		if(((hx&0xfffff)|lx)!=0) 
+		     return x+x; 		/* NaN */
+		else return (xsb==0)? x:0.0;	/* exp(+-inf)={inf,0} */
+	    }
+	    if(x > o_threshold) return huge*huge; /* overflow */
+	    if(x < u_threshold) return twom1000*twom1000; /* underflow */
+	}
+
+    /* argument reduction */
+	if(hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */ 
+	    if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */
+		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
+	    } else {
+		k  = invln2*x+halF[xsb];
+		t  = k;
+		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
+		lo = t*ln2LO[0];
+	    }
+	    x  = hi - lo;
+	} 
+	else if(hx < 0x3e300000)  {	/* when |x|<2**-28 */
+	    if(huge+x>one) return one+x;/* trigger inexact */
+	}
+	else k = 0;
+
+    /* x is now in primary range */
+	t  = x*x;
+	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+	if(k==0) 	return one-((x*c)/(c-2.0)-x); 
+	else 		y = one-((lo-(x*c)/(2.0-c))-hi);
+	if(k >= -1021) {
+	    u_int32_t hy;
+	    GET_HIGH_WORD(hy,y);
+	    SET_HIGH_WORD(y,hy+(k<<20));	/* add k to y's exponent */
+	    return y;
+	} else {
+	    u_int32_t hy;
+	    GET_HIGH_WORD(hy,y);
+	    SET_HIGH_WORD(y,hy+((k+1000)<<20));	/* add k to y's exponent */
+	    return y*twom1000;
+	}
+}

lib/msun/src/e_expf.c

@@ -0,0 +1,103 @@
+/* e_expf.c -- float version of e_exp.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_expf.c,v 1.2 1994/08/18 23:05:20 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float
+#else
+static float
+#endif
+one	= 1.0,
+halF[2]	= {0.5,-0.5,},
+huge	= 1.0e+30,
+twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
+o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
+u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
+ln2HI[2]   ={ 6.9313812256e-01,		/* 0x3f317180 */
+	     -6.9313812256e-01,},	/* 0xbf317180 */
+ln2LO[2]   ={ 9.0580006145e-06,  	/* 0x3717f7d1 */
+	     -9.0580006145e-06,},	/* 0xb717f7d1 */
+invln2 =  1.4426950216e+00, 		/* 0x3fb8aa3b */
+P1   =  1.6666667163e-01, /* 0x3e2aaaab */
+P2   = -2.7777778450e-03, /* 0xbb360b61 */
+P3   =  6.6137559770e-05, /* 0x388ab355 */
+P4   = -1.6533901999e-06, /* 0xb5ddea0e */
+P5   =  4.1381369442e-08; /* 0x3331bb4c */
+
+#ifdef __STDC__
+	float __ieee754_expf(float x)	/* default IEEE double exp */
+#else
+	float __ieee754_expf(x)	/* default IEEE double exp */
+	float x;
+#endif
+{
+	float y,hi,lo,c,t;
+	int32_t k,xsb;
+	u_int32_t hx;
+
+	GET_FLOAT_WORD(hx,x);
+	xsb = (hx>>31)&1;		/* sign bit of x */
+	hx &= 0x7fffffff;		/* high word of |x| */
+
+    /* filter out non-finite argument */
+	if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
+	    if(hx>0x7f800000)
+		 return x+x;	 		/* NaN */
+            if(hx==0x7f800000)
+		return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
+	    if(x > o_threshold) return huge*huge; /* overflow */
+	    if(x < u_threshold) return twom100*twom100; /* underflow */
+	}
+
+    /* argument reduction */
+	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */ 
+	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
+		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
+	    } else {
+		k  = invln2*x+halF[xsb];
+		t  = k;
+		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
+		lo = t*ln2LO[0];
+	    }
+	    x  = hi - lo;
+	} 
+	else if(hx < 0x31800000)  {	/* when |x|<2**-28 */
+	    if(huge+x>one) return one+x;/* trigger inexact */
+	}
+	else k = 0;
+
+    /* x is now in primary range */
+	t  = x*x;
+	c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x); 
+	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);
+	if(k >= -125) {
+	    u_int32_t hy;
+	    GET_FLOAT_WORD(hy,y);
+	    SET_FLOAT_WORD(y,hy+(k<<23));	/* add k to y's exponent */
+	    return y;
+	} else {
+	    u_int32_t hy;
+	    GET_FLOAT_WORD(hy,y);
+	    SET_FLOAT_WORD(y,hy+((k+100)<<23));	/* add k to y's exponent */
+	    return y*twom100;
+	}
+}

lib/msun/src/e_fmod.c

@@ -0,0 +1,140 @@
+/* @(#)e_fmod.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_fmod.c,v 1.6 1994/08/18 23:05:21 jtc Exp $";
+#endif
+
+/* 
+ * __ieee754_fmod(x,y)
+ * Return x mod y in exact arithmetic
+ * Method: shift and subtract
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, Zero[] = {0.0, -0.0,};
+#else
+static double one = 1.0, Zero[] = {0.0, -0.0,};
+#endif
+
+#ifdef __STDC__
+	double __ieee754_fmod(double x, double y)
+#else
+	double __ieee754_fmod(x,y)
+	double x,y ;
+#endif
+{
+	int32_t n,hx,hy,hz,ix,iy,sx,i;
+	u_int32_t lx,ly,lz;
+
+	EXTRACT_WORDS(hx,lx,x);
+	EXTRACT_WORDS(hy,ly,y);
+	sx = hx&0x80000000;		/* sign of x */
+	hx ^=sx;		/* |x| */
+	hy &= 0x7fffffff;	/* |y| */
+
+    /* purge off exception values */
+	if((hy|ly)==0||(hx>=0x7ff00000)||	/* y=0,or x not finite */
+	  ((hy|((ly|-ly)>>31))>0x7ff00000))	/* or y is NaN */
+	    return (x*y)/(x*y);
+	if(hx<=hy) {
+	    if((hx<hy)||(lx<ly)) return x;	/* |x|<|y| return x */
+	    if(lx==ly) 
+		return Zero[(u_int32_t)sx>>31];	/* |x|=|y| return x*0*/
+	}
+
+    /* determine ix = ilogb(x) */
+	if(hx<0x00100000) {	/* subnormal x */
+	    if(hx==0) {
+		for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
+	    } else {
+		for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
+	    }
+	} else ix = (hx>>20)-1023;
+
+    /* determine iy = ilogb(y) */
+	if(hy<0x00100000) {	/* subnormal y */
+	    if(hy==0) {
+		for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
+	    } else {
+		for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
+	    }
+	} else iy = (hy>>20)-1023;
+
+    /* set up {hx,lx}, {hy,ly} and align y to x */
+	if(ix >= -1022) 
+	    hx = 0x00100000|(0x000fffff&hx);
+	else {		/* subnormal x, shift x to normal */
+	    n = -1022-ix;
+	    if(n<=31) {
+	        hx = (hx<<n)|(lx>>(32-n));
+	        lx <<= n;
+	    } else {
+		hx = lx<<(n-32);
+		lx = 0;
+	    }
+	}
+	if(iy >= -1022) 
+	    hy = 0x00100000|(0x000fffff&hy);
+	else {		/* subnormal y, shift y to normal */
+	    n = -1022-iy;
+	    if(n<=31) {
+	        hy = (hy<<n)|(ly>>(32-n));
+	        ly <<= n;
+	    } else {
+		hy = ly<<(n-32);
+		ly = 0;
+	    }
+	}
+
+    /* fix point fmod */
+	n = ix - iy;
+	while(n--) {
+	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
+	    if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
+	    else {
+	    	if((hz|lz)==0) 		/* return sign(x)*0 */
+		    return Zero[(u_int32_t)sx>>31];
+	    	hx = hz+hz+(lz>>31); lx = lz+lz;
+	    }
+	}
+	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
+	if(hz>=0) {hx=hz;lx=lz;}
+
+    /* convert back to floating value and restore the sign */
+	if((hx|lx)==0) 			/* return sign(x)*0 */
+	    return Zero[(u_int32_t)sx>>31];	
+	while(hx<0x00100000) {		/* normalize x */
+	    hx = hx+hx+(lx>>31); lx = lx+lx;
+	    iy -= 1;
+	}
+	if(iy>= -1022) {	/* normalize output */
+	    hx = ((hx-0x00100000)|((iy+1023)<<20));
+	    INSERT_WORDS(x,hx|sx,lx);
+	} else {		/* subnormal output */
+	    n = -1022 - iy;
+	    if(n<=20) {
+		lx = (lx>>n)|((u_int32_t)hx<<(32-n));
+		hx >>= n;
+	    } else if (n<=31) {
+		lx = (hx<<(32-n))|(lx>>n); hx = sx;
+	    } else {
+		lx = hx>>(n-32); hx = sx;
+	    }
+	    INSERT_WORDS(x,hx|sx,lx);
+	    x *= one;		/* create necessary signal */
+	}
+	return x;		/* exact output */
+}

lib/msun/src/e_fmodf.c

@@ -0,0 +1,113 @@
+/* e_fmodf.c -- float version of e_fmod.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_fmodf.c,v 1.2 1994/08/18 23:05:23 jtc Exp $";
+#endif
+
+/* 
+ * __ieee754_fmodf(x,y)
+ * Return x mod y in exact arithmetic
+ * Method: shift and subtract
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float one = 1.0, Zero[] = {0.0, -0.0,};
+#else
+static float one = 1.0, Zero[] = {0.0, -0.0,};
+#endif
+
+#ifdef __STDC__
+	float __ieee754_fmodf(float x, float y)
+#else
+	float __ieee754_fmodf(x,y)
+	float x,y ;
+#endif
+{
+	int32_t n,hx,hy,hz,ix,iy,sx,i;
+
+	GET_FLOAT_WORD(hx,x);
+	GET_FLOAT_WORD(hy,y);
+	sx = hx&0x80000000;		/* sign of x */
+	hx ^=sx;		/* |x| */
+	hy &= 0x7fffffff;	/* |y| */
+
+    /* purge off exception values */
+	if(hy==0||(hx>=0x7f800000)||		/* y=0,or x not finite */
+	   (hy>0x7f800000))			/* or y is NaN */
+	    return (x*y)/(x*y);
+	if(hx<hy) return x;			/* |x|<|y| return x */
+	if(hx==hy)
+	    return Zero[(u_int32_t)sx>>31];	/* |x|=|y| return x*0*/
+
+    /* determine ix = ilogb(x) */
+	if(hx<0x00800000) {	/* subnormal x */
+	    for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
+	} else ix = (hx>>23)-127;
+
+    /* determine iy = ilogb(y) */
+	if(hy<0x00800000) {	/* subnormal y */
+	    for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
+	} else iy = (hy>>23)-127;
+
+    /* set up {hx,lx}, {hy,ly} and align y to x */
+	if(ix >= -126) 
+	    hx = 0x00800000|(0x007fffff&hx);
+	else {		/* subnormal x, shift x to normal */
+	    n = -126-ix;
+	    hx = hx<<n;
+	}
+	if(iy >= -126) 
+	    hy = 0x00800000|(0x007fffff&hy);
+	else {		/* subnormal y, shift y to normal */
+	    n = -126-iy;
+	    hy = hy<<n;
+	}
+
+    /* fix point fmod */
+	n = ix - iy;
+	while(n--) {
+	    hz=hx-hy;
+	    if(hz<0){hx = hx+hx;}
+	    else {
+	    	if(hz==0) 		/* return sign(x)*0 */
+		    return Zero[(u_int32_t)sx>>31];
+	    	hx = hz+hz;
+	    }
+	}
+	hz=hx-hy;
+	if(hz>=0) {hx=hz;}
+
+    /* convert back to floating value and restore the sign */
+	if(hx==0) 			/* return sign(x)*0 */
+	    return Zero[(u_int32_t)sx>>31];	
+	while(hx<0x00800000) {		/* normalize x */
+	    hx = hx+hx;
+	    iy -= 1;
+	}
+	if(iy>= -126) {		/* normalize output */
+	    hx = ((hx-0x00800000)|((iy+127)<<23));
+	    SET_FLOAT_WORD(x,hx|sx);
+	} else {		/* subnormal output */
+	    n = -126 - iy;
+	    hx >>= n;
+	    SET_FLOAT_WORD(x,hx|sx);
+	    x *= one;		/* create necessary signal */
+	}
+	return x;		/* exact output */
+}

lib/msun/src/e_gamma.c

@@ -0,0 +1,37 @@
+/* @(#)e_gamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ *
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_gamma.c,v 1.4 1994/08/10 20:30:51 jtc Exp $";
+#endif
+
+/* __ieee754_gamma(x)
+ * Return the logarithm of the Gamma function of x.
+ *
+ * Method: call __ieee754_gamma_r
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+extern int signgam;
+
+#ifdef __STDC__
+	double __ieee754_gamma(double x)
+#else
+	double __ieee754_gamma(x)
+	double x;
+#endif
+{
+	return __ieee754_gamma_r(x,&signgam);
+}

lib/msun/src/e_gamma_r.c

@@ -0,0 +1,35 @@
+/* @(#)er_gamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_gamma_r.c,v 1.4 1994/08/10 20:30:52 jtc Exp $";
+#endif
+
+/* __ieee754_gamma_r(x, signgamp)
+ * Reentrant version of the logarithm of the Gamma function 
+ * with user provide pointer for the sign of Gamma(x). 
+ *
+ * Method: See __ieee754_lgamma_r
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+	double __ieee754_gamma_r(double x, int *signgamp)
+#else
+	double __ieee754_gamma_r(x,signgamp)
+	double x; int *signgamp;
+#endif
+{
+	return __ieee754_lgamma_r(x,signgamp);
+}

lib/msun/src/e_gammaf.c

@@ -0,0 +1,39 @@
+/* e_gammaf.c -- float version of e_gamma.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_gammaf.c,v 1.1 1994/08/10 20:30:53 jtc Exp $";
+#endif
+
+/* __ieee754_gammaf(x)
+ * Return the logarithm of the Gamma function of x.
+ *
+ * Method: call __ieee754_gammaf_r
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+extern int signgam;
+
+#ifdef __STDC__
+	float __ieee754_gammaf(float x)
+#else
+	float __ieee754_gammaf(x)
+	float x;
+#endif
+{
+	return __ieee754_gammaf_r(x,&signgam);
+}

lib/msun/src/e_gammaf_r.c

@@ -0,0 +1,38 @@
+/* e_gammaf_r.c -- float version of e_gamma_r.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_gammaf_r.c,v 1.1 1994/08/10 20:30:54 jtc Exp $";
+#endif
+
+/* __ieee754_gammaf_r(x, signgamp)
+ * Reentrant version of the logarithm of the Gamma function 
+ * with user provide pointer for the sign of Gamma(x). 
+ *
+ * Method: See __ieee754_lgammaf_r
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+	float __ieee754_gammaf_r(float x, int *signgamp)
+#else
+	float __ieee754_gammaf_r(x,signgamp)
+	float x; int *signgamp;
+#endif
+{
+	return __ieee754_lgammaf_r(x,signgamp);
+}

lib/msun/src/e_hypot.c

@@ -0,0 +1,128 @@
+/* @(#)e_hypot.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_hypot.c,v 1.6 1994/08/18 23:05:24 jtc Exp $";
+#endif
+
+/* __ieee754_hypot(x,y)
+ *
+ * Method :                  
+ *	If (assume round-to-nearest) z=x*x+y*y 
+ *	has error less than sqrt(2)/2 ulp, than 
+ *	sqrt(z) has error less than 1 ulp (exercise).
+ *
+ *	So, compute sqrt(x*x+y*y) with some care as 
+ *	follows to get the error below 1 ulp:
+ *
+ *	Assume x>y>0;
+ *	(if possible, set rounding to round-to-nearest)
+ *	1. if x > 2y  use
+ *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
+ *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
+ *	2. if x <= 2y use
+ *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
+ *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 
+ *	y1= y with lower 32 bits chopped, y2 = y-y1.
+ *		
+ *	NOTE: scaling may be necessary if some argument is too 
+ *	      large or too tiny
+ *
+ * Special cases:
+ *	hypot(x,y) is INF if x or y is +INF or -INF; else
+ *	hypot(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ * 	hypot(x,y) returns sqrt(x^2+y^2) with error less 
+ * 	than 1 ulps (units in the last place) 
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+	double __ieee754_hypot(double x, double y)
+#else
+	double __ieee754_hypot(x,y)
+	double x, y;
+#endif
+{
+	double a=x,b=y,t1,t2,y1,y2,w;
+	int32_t j,k,ha,hb;
+
+	GET_HIGH_WORD(ha,x);
+	ha &= 0x7fffffff;
+	GET_HIGH_WORD(hb,y);
+	hb &= 0x7fffffff;
+	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
+	SET_HIGH_WORD(a,ha);	/* a <- |a| */
+	SET_HIGH_WORD(b,hb);	/* b <- |b| */
+	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
+	k=0;
+	if(ha > 0x5f300000) {	/* a>2**500 */
+	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
+	       u_int32_t low;
+	       w = a+b;			/* for sNaN */
+	       GET_LOW_WORD(low,a);
+	       if(((ha&0xfffff)|low)==0) w = a;
+	       GET_LOW_WORD(low,b);
+	       if(((hb^0x7ff00000)|low)==0) w = b;
+	       return w;
+	   }
+	   /* scale a and b by 2**-600 */
+	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
+	   SET_HIGH_WORD(a,ha);
+	   SET_HIGH_WORD(b,hb);
+	}
+	if(hb < 0x20b00000) {	/* b < 2**-500 */
+	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */	
+	        u_int32_t low;
+		GET_LOW_WORD(low,b);
+		if((hb|low)==0) return a;
+		t1=0;
+		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
+		b *= t1;
+		a *= t1;
+		k -= 1022;
+	    } else {		/* scale a and b by 2^600 */
+	        ha += 0x25800000; 	/* a *= 2^600 */
+		hb += 0x25800000;	/* b *= 2^600 */
+		k -= 600;
+		SET_HIGH_WORD(a,ha);
+		SET_HIGH_WORD(b,hb);
+	    }
+	}
+    /* medium size a and b */
+	w = a-b;
+	if (w>b) {
+	    t1 = 0;
+	    SET_HIGH_WORD(t1,ha);
+	    t2 = a-t1;
+	    w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
+	} else {
+	    a  = a+a;
+	    y1 = 0;
+	    SET_HIGH_WORD(y1,hb);
+	    y2 = b - y1;
+	    t1 = 0;
+	    SET_HIGH_WORD(t1,ha+0x00100000);
+	    t2 = a - t1;
+	    w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+	}
+	if(k!=0) {
+	    u_int32_t high;
+	    t1 = 1.0;
+	    GET_HIGH_WORD(high,t1);
+	    SET_HIGH_WORD(t1,high+(k<<20));
+	    return t1*w;
+	} else return w;
+}

lib/msun/src/e_hypotf.c

@@ -0,0 +1,87 @@
+/* e_hypotf.c -- float version of e_hypot.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_hypotf.c,v 1.2 1994/08/18 23:05:26 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+	float __ieee754_hypotf(float x, float y)
+#else
+	float __ieee754_hypot(x,y)
+	float x, y;
+#endif
+{
+	float a=x,b=y,t1,t2,y1,y2,w;
+	int32_t j,k,ha,hb;
+
+	GET_FLOAT_WORD(ha,x);
+	ha &= 0x7fffffff;
+	GET_FLOAT_WORD(hb,y);
+	hb &= 0x7fffffff;
+	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
+	SET_FLOAT_WORD(a,ha);	/* a <- |a| */
+	SET_FLOAT_WORD(b,hb);	/* b <- |b| */
+	if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */
+	k=0;
+	if(ha > 0x58800000) {	/* a>2**50 */
+	   if(ha >= 0x7f800000) {	/* Inf or NaN */
+	       w = a+b;			/* for sNaN */
+	       if(ha == 0x7f800000) w = a;
+	       if(hb == 0x7f800000) w = b;
+	       return w;
+	   }
+	   /* scale a and b by 2**-60 */
+	   ha -= 0x5d800000; hb -= 0x5d800000;	k += 60;
+	   SET_FLOAT_WORD(a,ha);
+	   SET_FLOAT_WORD(b,hb);
+	}
+	if(hb < 0x26800000) {	/* b < 2**-50 */
+	    if(hb <= 0x007fffff) {	/* subnormal b or 0 */	
+	        if(hb==0) return a;
+		SET_FLOAT_WORD(t1,0x3f000000);	/* t1=2^126 */
+		b *= t1;
+		a *= t1;
+		k -= 126;
+	    } else {		/* scale a and b by 2^60 */
+	        ha += 0x5d800000; 	/* a *= 2^60 */
+		hb += 0x5d800000;	/* b *= 2^60 */
+		k -= 60;
+		SET_FLOAT_WORD(a,ha);
+		SET_FLOAT_WORD(b,hb);
+	    }
+	}
+    /* medium size a and b */
+	w = a-b;
+	if (w>b) {
+	    SET_FLOAT_WORD(t1,ha&0xfffff000);
+	    t2 = a-t1;
+	    w  = sqrtf(t1*t1-(b*(-b)-t2*(a+t1)));
+	} else {
+	    a  = a+a;
+	    SET_FLOAT_WORD(y1,hb&0xfffff000);
+	    y2 = b - y1;
+	    SET_FLOAT_WORD(t1,ha+0x00800000);
+	    t2 = a - t1;
+	    w  = sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+	}
+	if(k!=0) {
+	    SET_FLOAT_WORD(t1,0x3f800000+(k<<23));
+	    return t1*w;
+	} else return w;
+}

lib/msun/src/e_j0.c

@@ -0,0 +1,487 @@
+/* @(#)e_j0.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_j0.c,v 1.6 1994/08/18 23:05:29 jtc Exp $";
+#endif
+
+/* __ieee754_j0(x), __ieee754_y0(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j0(x):
+ *	1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
+ *	2. Reduce x to |x| since j0(x)=j0(-x),  and
+ *	   for x in (0,2)
+ *		j0(x) = 1-z/4+ z^2*R0/S0,  where z = x*x;
+ *	   (precision:  |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
+ *	   for x in (2,inf)
+ * 		j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
+ * 	   where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ *	   as follow:
+ *		cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+ *			= 1/sqrt(2) * (cos(x) + sin(x))
+ *		sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
+ *			= 1/sqrt(2) * (sin(x) - cos(x))
+ * 	   (To avoid cancellation, use
+ *		sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ * 	    to compute the worse one.)
+ *	   
+ *	3 Special cases
+ *		j0(nan)= nan
+ *		j0(0) = 1
+ *		j0(inf) = 0
+ *		
+ * Method -- y0(x):
+ *	1. For x<2.
+ *	   Since 
+ *		y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
+ *	   therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
+ *	   We use the following function to approximate y0,
+ *		y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
+ *	   where 
+ *		U(z) = u00 + u01*z + ... + u06*z^6
+ *		V(z) = 1  + v01*z + ... + v04*z^4
+ *	   with absolute approximation error bounded by 2**-72.
+ *	   Note: For tiny x, U/V = u0 and j0(x)~1, hence
+ *		y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
+ *	2. For x>=2.
+ * 		y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
+ * 	   where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
+ *	   by the method mentioned above.
+ *	3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static double pzero(double), qzero(double);
+#else
+static double pzero(), qzero();
+#endif
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+huge 	= 1e300,
+one	= 1.0,
+invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
+tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+ 		/* R0/S0 on [0, 2.00] */
+R02  =  1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
+R03  = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
+R04  =  1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
+R05  = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
+S01  =  1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
+S02  =  1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
+S03  =  5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
+S04  =  1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_j0(double x) 
+#else
+	double __ieee754_j0(x) 
+	double x;
+#endif
+{
+	double z, s,c,ss,cc,r,u,v;
+	int32_t hx,ix;
+
+	GET_HIGH_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x7ff00000) return one/(x*x);
+	x = fabs(x);
+	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
+		s = sin(x);
+		c = cos(x);
+		ss = s-c;
+		cc = s+c;
+		if(ix<0x7fe00000) {  /* make sure x+x not overflow */
+		    z = -cos(x+x);
+		    if ((s*c)<zero) cc = z/ss;
+		    else 	    ss = z/cc;
+		}
+	/*
+	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+	 */
+		if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x);
+		else {
+		    u = pzero(x); v = qzero(x);
+		    z = invsqrtpi*(u*cc-v*ss)/sqrt(x);
+		}
+		return z;
+	}
+	if(ix<0x3f200000) {	/* |x| < 2**-13 */
+	    if(huge+x>one) {	/* raise inexact if x != 0 */
+	        if(ix<0x3e400000) return one;	/* |x|<2**-27 */
+	        else 	      return one - 0.25*x*x;
+	    }
+	}
+	z = x*x;
+	r =  z*(R02+z*(R03+z*(R04+z*R05)));
+	s =  one+z*(S01+z*(S02+z*(S03+z*S04)));
+	if(ix < 0x3FF00000) {	/* |x| < 1.00 */
+	    return one + z*(-0.25+(r/s));
+	} else {
+	    u = 0.5*x;
+	    return((one+u)*(one-u)+z*(r/s));
+	}
+}
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+u00  = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
+u01  =  1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
+u02  = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
+u03  =  3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
+u04  = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
+u05  =  1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
+u06  = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
+v01  =  1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
+v02  =  7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
+v03  =  2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
+v04  =  4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
+
+#ifdef __STDC__
+	double __ieee754_y0(double x) 
+#else
+	double __ieee754_y0(x) 
+	double x;
+#endif
+{
+	double z, s,c,ss,cc,u,v;
+	int32_t hx,ix,lx;
+
+	EXTRACT_WORDS(hx,lx,x);
+        ix = 0x7fffffff&hx;
+    /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
+	if(ix>=0x7ff00000) return  one/(x+x*x); 
+        if((ix|lx)==0) return -one/zero;
+        if(hx<0) return zero/zero;
+        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
+        /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
+         * where x0 = x-pi/4
+         *      Better formula:
+         *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+         *                      =  1/sqrt(2) * (sin(x) + cos(x))
+         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+         *                      =  1/sqrt(2) * (sin(x) - cos(x))
+         * To avoid cancellation, use
+         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+         * to compute the worse one.
+         */
+                s = sin(x);
+                c = cos(x);
+                ss = s-c;
+                cc = s+c;
+	/*
+	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+	 */
+                if(ix<0x7fe00000) {  /* make sure x+x not overflow */
+                    z = -cos(x+x);
+                    if ((s*c)<zero) cc = z/ss;
+                    else            ss = z/cc;
+                }
+                if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
+                else {
+                    u = pzero(x); v = qzero(x);
+                    z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
+                }
+                return z;
+	}
+	if(ix<=0x3e400000) {	/* x < 2**-27 */
+	    return(u00 + tpi*__ieee754_log(x));
+	}
+	z = x*x;
+	u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
+	v = one+z*(v01+z*(v02+z*(v03+z*v04)));
+	return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
+}
+
+/* The asymptotic expansions of pzero is
+ *	1 - 9/128 s^2 + 11025/98304 s^4 - ...,	where s = 1/x.
+ * For x >= 2, We approximate pzero by
+ * 	pzero(x) = 1 + (R/S)
+ * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
+ * 	  S = 1 + pS0*s^2 + ... + pS4*s^10
+ * and
+ *	| pzero(x)-1-R/S | <= 2  ** ( -60.26)
+ */
+#ifdef __STDC__
+static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
+ -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
+ -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
+ -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
+ -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
+};
+#ifdef __STDC__
+static const double pS8[5] = {
+#else
+static double pS8[5] = {
+#endif
+  1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
+  3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
+  4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
+  1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
+  4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
+};
+
+#ifdef __STDC__
+static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+ -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
+ -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
+ -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
+ -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
+ -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
+ -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
+};
+#ifdef __STDC__
+static const double pS5[5] = {
+#else
+static double pS5[5] = {
+#endif
+  6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
+  1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
+  5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
+  9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
+  2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
+};
+
+#ifdef __STDC__
+static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#else
+static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+ -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
+ -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
+ -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
+ -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
+ -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
+ -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
+};
+#ifdef __STDC__
+static const double pS3[5] = {
+#else
+static double pS3[5] = {
+#endif
+  3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
+  3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
+  1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
+  1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
+  1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
+};
+
+#ifdef __STDC__
+static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+ -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
+ -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
+ -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
+ -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
+ -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
+ -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
+};
+#ifdef __STDC__
+static const double pS2[5] = {
+#else
+static double pS2[5] = {
+#endif
+  2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
+  1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
+  2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
+  1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
+  1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
+};
+
+#ifdef __STDC__
+	static double pzero(double x)
+#else
+	static double pzero(x)
+	double x;
+#endif
+{
+#ifdef __STDC__
+	const double *p,*q;
+#else
+	double *p,*q;
+#endif
+	double z,r,s;
+	int32_t ix;
+	GET_HIGH_WORD(ix,x);
+	ix &= 0x7fffffff;
+	if(ix>=0x40200000)     {p = pR8; q= pS8;}
+	else if(ix>=0x40122E8B){p = pR5; q= pS5;}
+	else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
+	else if(ix>=0x40000000){p = pR2; q= pS2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
+	return one+ r/s;
+}
+		
+
+/* For x >= 8, the asymptotic expansions of qzero is
+ *	-1/8 s + 75/1024 s^3 - ..., where s = 1/x.
+ * We approximate pzero by
+ * 	qzero(x) = s*(-1.25 + (R/S))
+ * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
+ * 	  S = 1 + qS0*s^2 + ... + qS5*s^12
+ * and
+ *	| qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
+ */
+#ifdef __STDC__
+static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+  7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
+  1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
+  5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
+  8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
+  3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
+};
+#ifdef __STDC__
+static const double qS8[6] = {
+#else
+static double qS8[6] = {
+#endif
+  1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
+  8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
+  1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
+  8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
+  8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
+ -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
+};
+
+#ifdef __STDC__
+static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+  1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
+  7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
+  5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
+  1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
+  1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
+  1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
+};
+#ifdef __STDC__
+static const double qS5[6] = {
+#else
+static double qS5[6] = {
+#endif
+  8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
+  2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
+  1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
+  5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
+  3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
+ -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
+};
+
+#ifdef __STDC__
+static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#else
+static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+  4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
+  7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
+  3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
+  4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
+  1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
+  1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
+};
+#ifdef __STDC__
+static const double qS3[6] = {
+#else
+static double qS3[6] = {
+#endif
+  4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
+  7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
+  3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
+  6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
+  2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
+ -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
+};
+
+#ifdef __STDC__
+static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+  1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
+  7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
+  1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
+  1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
+  3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
+  1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
+};
+#ifdef __STDC__
+static const double qS2[6] = {
+#else
+static double qS2[6] = {
+#endif
+  3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
+  2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
+  8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
+  8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
+  2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
+ -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
+};
+
+#ifdef __STDC__
+	static double qzero(double x)
+#else
+	static double qzero(x)
+	double x;
+#endif
+{
+#ifdef __STDC__
+	const double *p,*q;
+#else
+	double *p,*q;
+#endif
+	double s,r,z;
+	int32_t ix;
+	GET_HIGH_WORD(ix,x);
+	ix &= 0x7fffffff;
+	if(ix>=0x40200000)     {p = qR8; q= qS8;}
+	else if(ix>=0x40122E8B){p = qR5; q= qS5;}
+	else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
+	else if(ix>=0x40000000){p = qR2; q= qS2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
+	return (-.125 + r/s)/x;
+}

lib/msun/src/e_j0f.c

@@ -0,0 +1,444 @@
+/* e_j0f.c -- float version of e_j0.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_j0f.c,v 1.2 1994/08/18 23:05:32 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static float pzerof(float), qzerof(float);
+#else
+static float pzerof(), qzerof();
+#endif
+
+#ifdef __STDC__
+static const float 
+#else
+static float 
+#endif
+huge 	= 1e30,
+one	= 1.0,
+invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
+tpi      =  6.3661974669e-01, /* 0x3f22f983 */
+ 		/* R0/S0 on [0, 2.00] */
+R02  =  1.5625000000e-02, /* 0x3c800000 */
+R03  = -1.8997929874e-04, /* 0xb947352e */
+R04  =  1.8295404516e-06, /* 0x35f58e88 */
+R05  = -4.6183270541e-09, /* 0xb19eaf3c */
+S01  =  1.5619102865e-02, /* 0x3c7fe744 */
+S02  =  1.1692678527e-04, /* 0x38f53697 */
+S03  =  5.1354652442e-07, /* 0x3509daa6 */
+S04  =  1.1661400734e-09; /* 0x30a045e8 */
+
+#ifdef __STDC__
+static const float zero = 0.0;
+#else
+static float zero = 0.0;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_j0f(float x) 
+#else
+	float __ieee754_j0f(x) 
+	float x;
+#endif
+{
+	float z, s,c,ss,cc,r,u,v;
+	int32_t hx,ix;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x7f800000) return one/(x*x);
+	x = fabsf(x);
+	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
+		s = sinf(x);
+		c = cosf(x);
+		ss = s-c;
+		cc = s+c;
+		if(ix<0x7f000000) {  /* make sure x+x not overflow */
+		    z = -cosf(x+x);
+		    if ((s*c)<zero) cc = z/ss;
+		    else 	    ss = z/cc;
+		}
+	/*
+	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+	 */
+		if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x);
+		else {
+		    u = pzerof(x); v = qzerof(x);
+		    z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
+		}
+		return z;
+	}
+	if(ix<0x39000000) {	/* |x| < 2**-13 */
+	    if(huge+x>one) {	/* raise inexact if x != 0 */
+	        if(ix<0x32000000) return one;	/* |x|<2**-27 */
+	        else 	      return one - (float)0.25*x*x;
+	    }
+	}
+	z = x*x;
+	r =  z*(R02+z*(R03+z*(R04+z*R05)));
+	s =  one+z*(S01+z*(S02+z*(S03+z*S04)));
+	if(ix < 0x3F800000) {	/* |x| < 1.00 */
+	    return one + z*((float)-0.25+(r/s));
+	} else {
+	    u = (float)0.5*x;
+	    return((one+u)*(one-u)+z*(r/s));
+	}
+}
+
+#ifdef __STDC__
+static const float
+#else
+static float
+#endif
+u00  = -7.3804296553e-02, /* 0xbd9726b5 */
+u01  =  1.7666645348e-01, /* 0x3e34e80d */
+u02  = -1.3818567619e-02, /* 0xbc626746 */
+u03  =  3.4745343146e-04, /* 0x39b62a69 */
+u04  = -3.8140706238e-06, /* 0xb67ff53c */
+u05  =  1.9559013964e-08, /* 0x32a802ba */
+u06  = -3.9820518410e-11, /* 0xae2f21eb */
+v01  =  1.2730483897e-02, /* 0x3c509385 */
+v02  =  7.6006865129e-05, /* 0x389f65e0 */
+v03  =  2.5915085189e-07, /* 0x348b216c */
+v04  =  4.4111031494e-10; /* 0x2ff280c2 */
+
+#ifdef __STDC__
+	float __ieee754_y0f(float x) 
+#else
+	float __ieee754_y0f(x) 
+	float x;
+#endif
+{
+	float z, s,c,ss,cc,u,v;
+	int32_t hx,ix;
+
+	GET_FLOAT_WORD(hx,x);
+        ix = 0x7fffffff&hx;
+    /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
+	if(ix>=0x7f800000) return  one/(x+x*x); 
+        if(ix==0) return -one/zero;
+        if(hx<0) return zero/zero;
+        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
+        /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
+         * where x0 = x-pi/4
+         *      Better formula:
+         *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
+         *                      =  1/sqrt(2) * (sin(x) + cos(x))
+         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+         *                      =  1/sqrt(2) * (sin(x) - cos(x))
+         * To avoid cancellation, use
+         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+         * to compute the worse one.
+         */
+                s = sinf(x);
+                c = cosf(x);
+                ss = s-c;
+                cc = s+c;
+	/*
+	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
+	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
+	 */
+                if(ix<0x7f000000) {  /* make sure x+x not overflow */
+                    z = -cosf(x+x);
+                    if ((s*c)<zero) cc = z/ss;
+                    else            ss = z/cc;
+                }
+                if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x);
+                else {
+                    u = pzerof(x); v = qzerof(x);
+                    z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
+                }
+                return z;
+	}
+	if(ix<=0x32000000) {	/* x < 2**-27 */
+	    return(u00 + tpi*__ieee754_logf(x));
+	}
+	z = x*x;
+	u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
+	v = one+z*(v01+z*(v02+z*(v03+z*v04)));
+	return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));
+}
+
+/* The asymptotic expansions of pzero is
+ *	1 - 9/128 s^2 + 11025/98304 s^4 - ...,	where s = 1/x.
+ * For x >= 2, We approximate pzero by
+ * 	pzero(x) = 1 + (R/S)
+ * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
+ * 	  S = 1 + pS0*s^2 + ... + pS4*s^10
+ * and
+ *	| pzero(x)-1-R/S | <= 2  ** ( -60.26)
+ */
+#ifdef __STDC__
+static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+  0.0000000000e+00, /* 0x00000000 */
+ -7.0312500000e-02, /* 0xbd900000 */
+ -8.0816707611e+00, /* 0xc1014e86 */
+ -2.5706311035e+02, /* 0xc3808814 */
+ -2.4852163086e+03, /* 0xc51b5376 */
+ -5.2530439453e+03, /* 0xc5a4285a */
+};
+#ifdef __STDC__
+static const float pS8[5] = {
+#else
+static float pS8[5] = {
+#endif
+  1.1653436279e+02, /* 0x42e91198 */
+  3.8337448730e+03, /* 0x456f9beb */
+  4.0597855469e+04, /* 0x471e95db */
+  1.1675296875e+05, /* 0x47e4087c */
+  4.7627726562e+04, /* 0x473a0bba */
+};
+#ifdef __STDC__
+static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+ -1.1412546255e-11, /* 0xad48c58a */
+ -7.0312492549e-02, /* 0xbd8fffff */
+ -4.1596107483e+00, /* 0xc0851b88 */
+ -6.7674766541e+01, /* 0xc287597b */
+ -3.3123129272e+02, /* 0xc3a59d9b */
+ -3.4643338013e+02, /* 0xc3ad3779 */
+};
+#ifdef __STDC__
+static const float pS5[5] = {
+#else
+static float pS5[5] = {
+#endif
+  6.0753936768e+01, /* 0x42730408 */
+  1.0512523193e+03, /* 0x44836813 */
+  5.9789707031e+03, /* 0x45bad7c4 */
+  9.6254453125e+03, /* 0x461665c8 */
+  2.4060581055e+03, /* 0x451660ee */
+};
+
+#ifdef __STDC__
+static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#else
+static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+ -2.5470459075e-09, /* 0xb12f081b */
+ -7.0311963558e-02, /* 0xbd8fffb8 */
+ -2.4090321064e+00, /* 0xc01a2d95 */
+ -2.1965976715e+01, /* 0xc1afba52 */
+ -5.8079170227e+01, /* 0xc2685112 */
+ -3.1447946548e+01, /* 0xc1fb9565 */
+};
+#ifdef __STDC__
+static const float pS3[5] = {
+#else
+static float pS3[5] = {
+#endif
+  3.5856033325e+01, /* 0x420f6c94 */
+  3.6151397705e+02, /* 0x43b4c1ca */
+  1.1936077881e+03, /* 0x44953373 */
+  1.1279968262e+03, /* 0x448cffe6 */
+  1.7358093262e+02, /* 0x432d94b8 */
+};
+
+#ifdef __STDC__
+static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+ -8.8753431271e-08, /* 0xb3be98b7 */
+ -7.0303097367e-02, /* 0xbd8ffb12 */
+ -1.4507384300e+00, /* 0xbfb9b1cc */
+ -7.6356959343e+00, /* 0xc0f4579f */
+ -1.1193166733e+01, /* 0xc1331736 */
+ -3.2336456776e+00, /* 0xc04ef40d */
+};
+#ifdef __STDC__
+static const float pS2[5] = {
+#else
+static float pS2[5] = {
+#endif
+  2.2220300674e+01, /* 0x41b1c32d */
+  1.3620678711e+02, /* 0x430834f0 */
+  2.7047027588e+02, /* 0x43873c32 */
+  1.5387539673e+02, /* 0x4319e01a */
+  1.4657617569e+01, /* 0x416a859a */
+};
+
+#ifdef __STDC__
+	static float pzerof(float x)
+#else
+	static float pzerof(x)
+	float x;
+#endif
+{
+#ifdef __STDC__
+	const float *p,*q;
+#else
+	float *p,*q;
+#endif
+	float z,r,s;
+	int32_t ix;
+	GET_FLOAT_WORD(ix,x);
+	ix &= 0x7fffffff;
+	if(ix>=0x41000000)     {p = pR8; q= pS8;}
+	else if(ix>=0x40f71c58){p = pR5; q= pS5;}
+	else if(ix>=0x4036db68){p = pR3; q= pS3;}
+	else if(ix>=0x40000000){p = pR2; q= pS2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
+	return one+ r/s;
+}
+		
+
+/* For x >= 8, the asymptotic expansions of qzero is
+ *	-1/8 s + 75/1024 s^3 - ..., where s = 1/x.
+ * We approximate pzero by
+ * 	qzero(x) = s*(-1.25 + (R/S))
+ * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
+ * 	  S = 1 + qS0*s^2 + ... + qS5*s^12
+ * and
+ *	| qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
+ */
+#ifdef __STDC__
+static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+  0.0000000000e+00, /* 0x00000000 */
+  7.3242187500e-02, /* 0x3d960000 */
+  1.1768206596e+01, /* 0x413c4a93 */
+  5.5767340088e+02, /* 0x440b6b19 */
+  8.8591972656e+03, /* 0x460a6cca */
+  3.7014625000e+04, /* 0x471096a0 */
+};
+#ifdef __STDC__
+static const float qS8[6] = {
+#else
+static float qS8[6] = {
+#endif
+  1.6377603149e+02, /* 0x4323c6aa */
+  8.0983447266e+03, /* 0x45fd12c2 */
+  1.4253829688e+05, /* 0x480b3293 */
+  8.0330925000e+05, /* 0x49441ed4 */
+  8.4050156250e+05, /* 0x494d3359 */
+ -3.4389928125e+05, /* 0xc8a7eb69 */
+};
+
+#ifdef __STDC__
+static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+  1.8408595828e-11, /* 0x2da1ec79 */
+  7.3242180049e-02, /* 0x3d95ffff */
+  5.8356351852e+00, /* 0x40babd86 */
+  1.3511157227e+02, /* 0x43071c90 */
+  1.0272437744e+03, /* 0x448067cd */
+  1.9899779053e+03, /* 0x44f8bf4b */
+};
+#ifdef __STDC__
+static const float qS5[6] = {
+#else
+static float qS5[6] = {
+#endif
+  8.2776611328e+01, /* 0x42a58da0 */
+  2.0778142090e+03, /* 0x4501dd07 */
+  1.8847289062e+04, /* 0x46933e94 */
+  5.6751113281e+04, /* 0x475daf1d */
+  3.5976753906e+04, /* 0x470c88c1 */
+ -5.3543427734e+03, /* 0xc5a752be */
+};
+
+#ifdef __STDC__
+static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#else
+static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+  4.3774099900e-09, /* 0x3196681b */
+  7.3241114616e-02, /* 0x3d95ff70 */
+  3.3442313671e+00, /* 0x405607e3 */
+  4.2621845245e+01, /* 0x422a7cc5 */
+  1.7080809021e+02, /* 0x432acedf */
+  1.6673394775e+02, /* 0x4326bbe4 */
+};
+#ifdef __STDC__
+static const float qS3[6] = {
+#else
+static float qS3[6] = {
+#endif
+  4.8758872986e+01, /* 0x42430916 */
+  7.0968920898e+02, /* 0x44316c1c */
+  3.7041481934e+03, /* 0x4567825f */
+  6.4604252930e+03, /* 0x45c9e367 */
+  2.5163337402e+03, /* 0x451d4557 */
+ -1.4924745178e+02, /* 0xc3153f59 */
+};
+
+#ifdef __STDC__
+static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+  1.5044444979e-07, /* 0x342189db */
+  7.3223426938e-02, /* 0x3d95f62a */
+  1.9981917143e+00, /* 0x3fffc4bf */
+  1.4495602608e+01, /* 0x4167edfd */
+  3.1666231155e+01, /* 0x41fd5471 */
+  1.6252708435e+01, /* 0x4182058c */
+};
+#ifdef __STDC__
+static const float qS2[6] = {
+#else
+static float qS2[6] = {
+#endif
+  3.0365585327e+01, /* 0x41f2ecb8 */
+  2.6934811401e+02, /* 0x4386ac8f */
+  8.4478375244e+02, /* 0x44533229 */
+  8.8293585205e+02, /* 0x445cbbe5 */
+  2.1266638184e+02, /* 0x4354aa98 */
+ -5.3109550476e+00, /* 0xc0a9f358 */
+};
+
+#ifdef __STDC__
+	static float qzerof(float x)
+#else
+	static float qzerof(x)
+	float x;
+#endif
+{
+#ifdef __STDC__
+	const float *p,*q;
+#else
+	float *p,*q;
+#endif
+	float s,r,z;
+	int32_t ix;
+	GET_FLOAT_WORD(ix,x);
+	ix &= 0x7fffffff;
+	if(ix>=0x41000000)     {p = qR8; q= qS8;}
+	else if(ix>=0x40f71c58){p = qR5; q= qS5;}
+	else if(ix>=0x4036db68){p = qR3; q= qS3;}
+	else if(ix>=0x40000000){p = qR2; q= qS2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
+	return (-(float).125 + r/s)/x;
+}

lib/msun/src/e_j1.c

@@ -0,0 +1,486 @@
+/* @(#)e_j1.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_j1.c,v 1.6 1994/08/18 23:05:33 jtc Exp $";
+#endif
+
+/* __ieee754_j1(x), __ieee754_y1(x)
+ * Bessel function of the first and second kinds of order zero.
+ * Method -- j1(x):
+ *	1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
+ *	2. Reduce x to |x| since j1(x)=-j1(-x),  and
+ *	   for x in (0,2)
+ *		j1(x) = x/2 + x*z*R0/S0,  where z = x*x;
+ *	   (precision:  |j1/x - 1/2 - R0/S0 |<2**-61.51 )
+ *	   for x in (2,inf)
+ * 		j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
+ * 		y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
+ * 	   where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
+ *	   as follow:
+ *		cos(x1) =  cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+ *			=  1/sqrt(2) * (sin(x) - cos(x))
+ *		sin(x1) =  sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+ *			= -1/sqrt(2) * (sin(x) + cos(x))
+ * 	   (To avoid cancellation, use
+ *		sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+ * 	    to compute the worse one.)
+ *	   
+ *	3 Special cases
+ *		j1(nan)= nan
+ *		j1(0) = 0
+ *		j1(inf) = 0
+ *		
+ * Method -- y1(x):
+ *	1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN 
+ *	2. For x<2.
+ *	   Since 
+ *		y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
+ *	   therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
+ *	   We use the following function to approximate y1,
+ *		y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
+ *	   where for x in [0,2] (abs err less than 2**-65.89)
+ *		U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
+ *		V(z) = 1  + v0[0]*z + ... + v0[4]*z^5
+ *	   Note: For tiny x, 1/x dominate y1 and hence
+ *		y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
+ *	3. For x>=2.
+ * 		y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
+ * 	   where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
+ *	   by method mentioned above.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static double pone(double), qone(double);
+#else
+static double pone(), qone();
+#endif
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+huge    = 1e300,
+one	= 1.0,
+invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
+tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+	/* R0/S0 on [0,2] */
+r00  = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
+r01  =  1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
+r02  = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
+r03  =  4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
+s01  =  1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
+s02  =  1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
+s03  =  1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
+s04  =  5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
+s05  =  1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
+
+#ifdef __STDC__
+static const double zero    = 0.0;
+#else
+static double zero    = 0.0;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_j1(double x) 
+#else
+	double __ieee754_j1(x) 
+	double x;
+#endif
+{
+	double z, s,c,ss,cc,r,u,v,y;
+	int32_t hx,ix;
+
+	GET_HIGH_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x7ff00000) return one/x;
+	y = fabs(x);
+	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
+		s = sin(y);
+		c = cos(y);
+		ss = -s-c;
+		cc = s-c;
+		if(ix<0x7fe00000) {  /* make sure y+y not overflow */
+		    z = cos(y+y);
+		    if ((s*c)>zero) cc = z/ss;
+		    else 	    ss = z/cc;
+		}
+	/*
+	 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
+	 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
+	 */
+		if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
+		else {
+		    u = pone(y); v = qone(y);
+		    z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
+		}
+		if(hx<0) return -z;
+		else  	 return  z;
+	}
+	if(ix<0x3e400000) {	/* |x|<2**-27 */
+	    if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
+	}
+	z = x*x;
+	r =  z*(r00+z*(r01+z*(r02+z*r03)));
+	s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
+	r *= x;
+	return(x*0.5+r/s);
+}
+
+#ifdef __STDC__
+static const double U0[5] = {
+#else
+static double U0[5] = {
+#endif
+ -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
+  5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
+ -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
+  2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
+ -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
+};
+#ifdef __STDC__
+static const double V0[5] = {
+#else
+static double V0[5] = {
+#endif
+  1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
+  2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
+  1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
+  6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
+  1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
+};
+
+#ifdef __STDC__
+	double __ieee754_y1(double x) 
+#else
+	double __ieee754_y1(x) 
+	double x;
+#endif
+{
+	double z, s,c,ss,cc,u,v;
+	int32_t hx,ix,lx;
+
+	EXTRACT_WORDS(hx,lx,x);
+        ix = 0x7fffffff&hx;
+    /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
+	if(ix>=0x7ff00000) return  one/(x+x*x); 
+        if((ix|lx)==0) return -one/zero;
+        if(hx<0) return zero/zero;
+        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
+                s = sin(x);
+                c = cos(x);
+                ss = -s-c;
+                cc = s-c;
+                if(ix<0x7fe00000) {  /* make sure x+x not overflow */
+                    z = cos(x+x);
+                    if ((s*c)>zero) cc = z/ss;
+                    else            ss = z/cc;
+                }
+        /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
+         * where x0 = x-3pi/4
+         *      Better formula:
+         *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+         *                      =  1/sqrt(2) * (sin(x) - cos(x))
+         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+         *                      = -1/sqrt(2) * (cos(x) + sin(x))
+         * To avoid cancellation, use
+         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+         * to compute the worse one.
+         */
+                if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
+                else {
+                    u = pone(x); v = qone(x);
+                    z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
+                }
+                return z;
+        } 
+        if(ix<=0x3c900000) {    /* x < 2**-54 */
+            return(-tpi/x);
+        } 
+        z = x*x;
+        u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
+        v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
+        return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
+}
+
+/* For x >= 8, the asymptotic expansions of pone is
+ *	1 + 15/128 s^2 - 4725/2^15 s^4 - ...,	where s = 1/x.
+ * We approximate pone by
+ * 	pone(x) = 1 + (R/S)
+ * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
+ * 	  S = 1 + ps0*s^2 + ... + ps4*s^10
+ * and
+ *	| pone(x)-1-R/S | <= 2  ** ( -60.06)
+ */
+
+#ifdef __STDC__
+static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+  1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
+  1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
+  4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
+  3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
+  7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
+};
+#ifdef __STDC__
+static const double ps8[5] = {
+#else
+static double ps8[5] = {
+#endif
+  1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
+  3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
+  3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
+  9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
+  3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
+};
+
+#ifdef __STDC__
+static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+  1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
+  1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
+  6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
+  1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
+  5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
+  5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
+};
+#ifdef __STDC__
+static const double ps5[5] = {
+#else
+static double ps5[5] = {
+#endif
+  5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
+  9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
+  5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
+  7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
+  1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
+};
+
+#ifdef __STDC__
+static const double pr3[6] = {
+#else
+static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+  3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
+  1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
+  3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
+  3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
+  9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
+  4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
+};
+#ifdef __STDC__
+static const double ps3[5] = {
+#else
+static double ps3[5] = {
+#endif
+  3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
+  3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
+  1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
+  8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
+  1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
+};
+
+#ifdef __STDC__
+static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+  1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
+  1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
+  2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
+  1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
+  1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
+  5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
+};
+#ifdef __STDC__
+static const double ps2[5] = {
+#else
+static double ps2[5] = {
+#endif
+  2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
+  1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
+  2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
+  1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
+  8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
+};
+
+#ifdef __STDC__
+	static double pone(double x)
+#else
+	static double pone(x)
+	double x;
+#endif
+{
+#ifdef __STDC__
+	const double *p,*q;
+#else
+	double *p,*q;
+#endif
+	double z,r,s;
+        int32_t ix;
+	GET_HIGH_WORD(ix,x);
+	ix &= 0x7fffffff;
+        if(ix>=0x40200000)     {p = pr8; q= ps8;}
+        else if(ix>=0x40122E8B){p = pr5; q= ps5;}
+        else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
+        else if(ix>=0x40000000){p = pr2; q= ps2;}
+        z = one/(x*x);
+        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
+        return one+ r/s;
+}
+		
+
+/* For x >= 8, the asymptotic expansions of qone is
+ *	3/8 s - 105/1024 s^3 - ..., where s = 1/x.
+ * We approximate pone by
+ * 	qone(x) = s*(0.375 + (R/S))
+ * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
+ * 	  S = 1 + qs1*s^2 + ... + qs6*s^12
+ * and
+ *	| qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
+ */
+
+#ifdef __STDC__
+static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+ -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
+ -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
+ -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
+ -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
+ -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
+};
+#ifdef __STDC__
+static const double qs8[6] = {
+#else
+static double qs8[6] = {
+#endif
+  1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
+  7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
+  1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
+  7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
+  6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
+ -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
+};
+
+#ifdef __STDC__
+static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+ -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
+ -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
+ -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
+ -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
+ -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
+ -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
+};
+#ifdef __STDC__
+static const double qs5[6] = {
+#else
+static double qs5[6] = {
+#endif
+  8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
+  1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
+  1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
+  4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
+  2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
+ -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
+};
+
+#ifdef __STDC__
+static const double qr3[6] = {
+#else
+static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+ -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
+ -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
+ -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
+ -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
+ -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
+ -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
+};
+#ifdef __STDC__
+static const double qs3[6] = {
+#else
+static double qs3[6] = {
+#endif
+  4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
+  6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
+  3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
+  5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
+  1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
+ -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
+};
+
+#ifdef __STDC__
+static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+ -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
+ -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
+ -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
+ -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
+ -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
+ -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
+};
+#ifdef __STDC__
+static const double qs2[6] = {
+#else
+static double qs2[6] = {
+#endif
+  2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
+  2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
+  7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
+  7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
+  1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
+ -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
+};
+
+#ifdef __STDC__
+	static double qone(double x)
+#else
+	static double qone(x)
+	double x;
+#endif
+{
+#ifdef __STDC__
+	const double *p,*q;
+#else
+	double *p,*q;
+#endif
+	double  s,r,z;
+	int32_t ix;
+	GET_HIGH_WORD(ix,x);
+	ix &= 0x7fffffff;
+	if(ix>=0x40200000)     {p = qr8; q= qs8;}
+	else if(ix>=0x40122E8B){p = qr5; q= qs5;}
+	else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
+	else if(ix>=0x40000000){p = qr2; q= qs2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
+	return (.375 + r/s)/x;
+}

lib/msun/src/e_j1f.c

@@ -0,0 +1,444 @@
+/* e_j1f.c -- float version of e_j1.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_j1f.c,v 1.2 1994/08/18 23:05:35 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static float ponef(float), qonef(float);
+#else
+static float ponef(), qonef();
+#endif
+
+#ifdef __STDC__
+static const float 
+#else
+static float 
+#endif
+huge    = 1e30,
+one	= 1.0,
+invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
+tpi      =  6.3661974669e-01, /* 0x3f22f983 */
+	/* R0/S0 on [0,2] */
+r00  = -6.2500000000e-02, /* 0xbd800000 */
+r01  =  1.4070566976e-03, /* 0x3ab86cfd */
+r02  = -1.5995563444e-05, /* 0xb7862e36 */
+r03  =  4.9672799207e-08, /* 0x335557d2 */
+s01  =  1.9153760746e-02, /* 0x3c9ce859 */
+s02  =  1.8594678841e-04, /* 0x3942fab6 */
+s03  =  1.1771846857e-06, /* 0x359dffc2 */
+s04  =  5.0463624390e-09, /* 0x31ad6446 */
+s05  =  1.2354227016e-11; /* 0x2d59567e */
+
+#ifdef __STDC__
+static const float zero    = 0.0;
+#else
+static float zero    = 0.0;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_j1f(float x) 
+#else
+	float __ieee754_j1f(x) 
+	float x;
+#endif
+{
+	float z, s,c,ss,cc,r,u,v,y;
+	int32_t hx,ix;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix>=0x7f800000) return one/x;
+	y = fabsf(x);
+	if(ix >= 0x40000000) {	/* |x| >= 2.0 */
+		s = sinf(y);
+		c = cosf(y);
+		ss = -s-c;
+		cc = s-c;
+		if(ix<0x7f000000) {  /* make sure y+y not overflow */
+		    z = cosf(y+y);
+		    if ((s*c)>zero) cc = z/ss;
+		    else 	    ss = z/cc;
+		}
+	/*
+	 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
+	 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
+	 */
+		if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(y);
+		else {
+		    u = ponef(y); v = qonef(y);
+		    z = invsqrtpi*(u*cc-v*ss)/sqrtf(y);
+		}
+		if(hx<0) return -z;
+		else  	 return  z;
+	}
+	if(ix<0x32000000) {	/* |x|<2**-27 */
+	    if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */
+	}
+	z = x*x;
+	r =  z*(r00+z*(r01+z*(r02+z*r03)));
+	s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
+	r *= x;
+	return(x*(float)0.5+r/s);
+}
+
+#ifdef __STDC__
+static const float U0[5] = {
+#else
+static float U0[5] = {
+#endif
+ -1.9605709612e-01, /* 0xbe48c331 */
+  5.0443872809e-02, /* 0x3d4e9e3c */
+ -1.9125689287e-03, /* 0xbafaaf2a */
+  2.3525259166e-05, /* 0x37c5581c */
+ -9.1909917899e-08, /* 0xb3c56003 */
+};
+#ifdef __STDC__
+static const float V0[5] = {
+#else
+static float V0[5] = {
+#endif
+  1.9916731864e-02, /* 0x3ca3286a */
+  2.0255257550e-04, /* 0x3954644b */
+  1.3560879779e-06, /* 0x35b602d4 */
+  6.2274145840e-09, /* 0x31d5f8eb */
+  1.6655924903e-11, /* 0x2d9281cf */
+};
+
+#ifdef __STDC__
+	float __ieee754_y1f(float x) 
+#else
+	float __ieee754_y1f(x) 
+	float x;
+#endif
+{
+	float z, s,c,ss,cc,u,v;
+	int32_t hx,ix;
+
+	GET_FLOAT_WORD(hx,x);
+        ix = 0x7fffffff&hx;
+    /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
+	if(ix>=0x7f800000) return  one/(x+x*x); 
+        if(ix==0) return -one/zero;
+        if(hx<0) return zero/zero;
+        if(ix >= 0x40000000) {  /* |x| >= 2.0 */
+                s = sinf(x);
+                c = cosf(x);
+                ss = -s-c;
+                cc = s-c;
+                if(ix<0x7f000000) {  /* make sure x+x not overflow */
+                    z = cosf(x+x);
+                    if ((s*c)>zero) cc = z/ss;
+                    else            ss = z/cc;
+                }
+        /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
+         * where x0 = x-3pi/4
+         *      Better formula:
+         *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
+         *                      =  1/sqrt(2) * (sin(x) - cos(x))
+         *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
+         *                      = -1/sqrt(2) * (cos(x) + sin(x))
+         * To avoid cancellation, use
+         *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
+         * to compute the worse one.
+         */
+                if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x);
+                else {
+                    u = ponef(x); v = qonef(x);
+                    z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
+                }
+                return z;
+        } 
+        if(ix<=0x24800000) {    /* x < 2**-54 */
+            return(-tpi/x);
+        } 
+        z = x*x;
+        u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
+        v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
+        return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x));
+}
+
+/* For x >= 8, the asymptotic expansions of pone is
+ *	1 + 15/128 s^2 - 4725/2^15 s^4 - ...,	where s = 1/x.
+ * We approximate pone by
+ * 	pone(x) = 1 + (R/S)
+ * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
+ * 	  S = 1 + ps0*s^2 + ... + ps4*s^10
+ * and
+ *	| pone(x)-1-R/S | <= 2  ** ( -60.06)
+ */
+
+#ifdef __STDC__
+static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+  0.0000000000e+00, /* 0x00000000 */
+  1.1718750000e-01, /* 0x3df00000 */
+  1.3239480972e+01, /* 0x4153d4ea */
+  4.1205184937e+02, /* 0x43ce06a3 */
+  3.8747453613e+03, /* 0x45722bed */
+  7.9144794922e+03, /* 0x45f753d6 */
+};
+#ifdef __STDC__
+static const float ps8[5] = {
+#else
+static float ps8[5] = {
+#endif
+  1.1420736694e+02, /* 0x42e46a2c */
+  3.6509309082e+03, /* 0x45642ee5 */
+  3.6956207031e+04, /* 0x47105c35 */
+  9.7602796875e+04, /* 0x47bea166 */
+  3.0804271484e+04, /* 0x46f0a88b */
+};
+
+#ifdef __STDC__
+static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+  1.3199052094e-11, /* 0x2d68333f */
+  1.1718749255e-01, /* 0x3defffff */
+  6.8027510643e+00, /* 0x40d9b023 */
+  1.0830818176e+02, /* 0x42d89dca */
+  5.1763616943e+02, /* 0x440168b7 */
+  5.2871520996e+02, /* 0x44042dc6 */
+};
+#ifdef __STDC__
+static const float ps5[5] = {
+#else
+static float ps5[5] = {
+#endif
+  5.9280597687e+01, /* 0x426d1f55 */
+  9.9140142822e+02, /* 0x4477d9b1 */
+  5.3532670898e+03, /* 0x45a74a23 */
+  7.8446904297e+03, /* 0x45f52586 */
+  1.5040468750e+03, /* 0x44bc0180 */
+};
+
+#ifdef __STDC__
+static const float pr3[6] = {
+#else
+static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+  3.0250391081e-09, /* 0x314fe10d */
+  1.1718686670e-01, /* 0x3defffab */
+  3.9329774380e+00, /* 0x407bb5e7 */
+  3.5119403839e+01, /* 0x420c7a45 */
+  9.1055007935e+01, /* 0x42b61c2a */
+  4.8559066772e+01, /* 0x42423c7c */
+};
+#ifdef __STDC__
+static const float ps3[5] = {
+#else
+static float ps3[5] = {
+#endif
+  3.4791309357e+01, /* 0x420b2a4d */
+  3.3676245117e+02, /* 0x43a86198 */
+  1.0468714600e+03, /* 0x4482dbe3 */
+  8.9081134033e+02, /* 0x445eb3ed */
+  1.0378793335e+02, /* 0x42cf936c */
+};
+
+#ifdef __STDC__
+static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+  1.0771083225e-07, /* 0x33e74ea8 */
+  1.1717621982e-01, /* 0x3deffa16 */
+  2.3685150146e+00, /* 0x401795c0 */
+  1.2242610931e+01, /* 0x4143e1bc */
+  1.7693971634e+01, /* 0x418d8d41 */
+  5.0735230446e+00, /* 0x40a25a4d */
+};
+#ifdef __STDC__
+static const float ps2[5] = {
+#else
+static float ps2[5] = {
+#endif
+  2.1436485291e+01, /* 0x41ab7dec */
+  1.2529022980e+02, /* 0x42fa9499 */
+  2.3227647400e+02, /* 0x436846c7 */
+  1.1767937469e+02, /* 0x42eb5bd7 */
+  8.3646392822e+00, /* 0x4105d590 */
+};
+
+#ifdef __STDC__
+	static float ponef(float x)
+#else
+	static float ponef(x)
+	float x;
+#endif
+{
+#ifdef __STDC__
+	const float *p,*q;
+#else
+	float *p,*q;
+#endif
+	float z,r,s;
+        int32_t ix;
+	GET_FLOAT_WORD(ix,x);
+	ix &= 0x7fffffff;
+        if(ix>=0x41000000)     {p = pr8; q= ps8;}
+        else if(ix>=0x40f71c58){p = pr5; q= ps5;}
+        else if(ix>=0x4036db68){p = pr3; q= ps3;}
+        else if(ix>=0x40000000){p = pr2; q= ps2;}
+        z = one/(x*x);
+        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
+        return one+ r/s;
+}
+		
+
+/* For x >= 8, the asymptotic expansions of qone is
+ *	3/8 s - 105/1024 s^3 - ..., where s = 1/x.
+ * We approximate pone by
+ * 	qone(x) = s*(0.375 + (R/S))
+ * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
+ * 	  S = 1 + qs1*s^2 + ... + qs6*s^12
+ * and
+ *	| qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
+ */
+
+#ifdef __STDC__
+static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#else
+static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
+#endif
+  0.0000000000e+00, /* 0x00000000 */
+ -1.0253906250e-01, /* 0xbdd20000 */
+ -1.6271753311e+01, /* 0xc1822c8d */
+ -7.5960174561e+02, /* 0xc43de683 */
+ -1.1849806641e+04, /* 0xc639273a */
+ -4.8438511719e+04, /* 0xc73d3683 */
+};
+#ifdef __STDC__
+static const float qs8[6] = {
+#else
+static float qs8[6] = {
+#endif
+  1.6139537048e+02, /* 0x43216537 */
+  7.8253862305e+03, /* 0x45f48b17 */
+  1.3387534375e+05, /* 0x4802bcd6 */
+  7.1965775000e+05, /* 0x492fb29c */
+  6.6660125000e+05, /* 0x4922be94 */
+ -2.9449025000e+05, /* 0xc88fcb48 */
+};
+
+#ifdef __STDC__
+static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#else
+static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
+#endif
+ -2.0897993405e-11, /* 0xadb7d219 */
+ -1.0253904760e-01, /* 0xbdd1fffe */
+ -8.0564479828e+00, /* 0xc100e736 */
+ -1.8366960144e+02, /* 0xc337ab6b */
+ -1.3731937256e+03, /* 0xc4aba633 */
+ -2.6124443359e+03, /* 0xc523471c */
+};
+#ifdef __STDC__
+static const float qs5[6] = {
+#else
+static float qs5[6] = {
+#endif
+  8.1276550293e+01, /* 0x42a28d98 */
+  1.9917987061e+03, /* 0x44f8f98f */
+  1.7468484375e+04, /* 0x468878f8 */
+  4.9851425781e+04, /* 0x4742bb6d */
+  2.7948074219e+04, /* 0x46da5826 */
+ -4.7191835938e+03, /* 0xc5937978 */
+};
+
+#ifdef __STDC__
+static const float qr3[6] = {
+#else
+static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
+#endif
+ -5.0783124372e-09, /* 0xb1ae7d4f */
+ -1.0253783315e-01, /* 0xbdd1ff5b */
+ -4.6101160049e+00, /* 0xc0938612 */
+ -5.7847221375e+01, /* 0xc267638e */
+ -2.2824453735e+02, /* 0xc3643e9a */
+ -2.1921012878e+02, /* 0xc35b35cb */
+};
+#ifdef __STDC__
+static const float qs3[6] = {
+#else
+static float qs3[6] = {
+#endif
+  4.7665153503e+01, /* 0x423ea91e */
+  6.7386511230e+02, /* 0x4428775e */
+  3.3801528320e+03, /* 0x45534272 */
+  5.5477290039e+03, /* 0x45ad5dd5 */
+  1.9031191406e+03, /* 0x44ede3d0 */
+ -1.3520118713e+02, /* 0xc3073381 */
+};
+
+#ifdef __STDC__
+static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#else
+static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
+#endif
+ -1.7838172539e-07, /* 0xb43f8932 */
+ -1.0251704603e-01, /* 0xbdd1f475 */
+ -2.7522056103e+00, /* 0xc0302423 */
+ -1.9663616180e+01, /* 0xc19d4f16 */
+ -4.2325313568e+01, /* 0xc2294d1f */
+ -2.1371921539e+01, /* 0xc1aaf9b2 */
+};
+#ifdef __STDC__
+static const float qs2[6] = {
+#else
+static float qs2[6] = {
+#endif
+  2.9533363342e+01, /* 0x41ec4454 */
+  2.5298155212e+02, /* 0x437cfb47 */
+  7.5750280762e+02, /* 0x443d602e */
+  7.3939318848e+02, /* 0x4438d92a */
+  1.5594900513e+02, /* 0x431bf2f2 */
+ -4.9594988823e+00, /* 0xc09eb437 */
+};
+
+#ifdef __STDC__
+	static float qonef(float x)
+#else
+	static float qonef(x)
+	float x;
+#endif
+{
+#ifdef __STDC__
+	const float *p,*q;
+#else
+	float *p,*q;
+#endif
+	float  s,r,z;
+	int32_t ix;
+	GET_FLOAT_WORD(ix,x);
+	ix &= 0x7fffffff;
+	if(ix>=0x40200000)     {p = qr8; q= qs8;}
+	else if(ix>=0x40f71c58){p = qr5; q= qs5;}
+	else if(ix>=0x4036db68){p = qr3; q= qs3;}
+	else if(ix>=0x40000000){p = qr2; q= qs2;}
+	z = one/(x*x);
+	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
+	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
+	return ((float).375 + r/s)/x;
+}

lib/msun/src/e_jn.c

@@ -0,0 +1,281 @@
+/* @(#)e_jn.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_jn.c,v 1.6 1994/08/18 23:05:37 jtc Exp $";
+#endif
+
+/*
+ * __ieee754_jn(n, x), __ieee754_yn(n, x)
+ * floating point Bessel's function of the 1st and 2nd kind
+ * of order n
+ *          
+ * Special cases:
+ *	y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal;
+ *	y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal.
+ * Note 2. About jn(n,x), yn(n,x)
+ *	For n=0, j0(x) is called,
+ *	for n=1, j1(x) is called,
+ *	for n<x, forward recursion us used starting
+ *	from values of j0(x) and j1(x).
+ *	for n>x, a continued fraction approximation to
+ *	j(n,x)/j(n-1,x) is evaluated and then backward
+ *	recursion is used starting from a supposed value
+ *	for j(n,x). The resulting value of j(0,x) is
+ *	compared with the actual value to correct the
+ *	supposed value of j(n,x).
+ *
+ *	yn(n,x) is similar in all respects, except
+ *	that forward recursion is used for all
+ *	values of n>1.
+ *	
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
+two   =  2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
+one   =  1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
+
+#ifdef __STDC__
+static const double zero  =  0.00000000000000000000e+00;
+#else
+static double zero  =  0.00000000000000000000e+00;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_jn(int n, double x)
+#else
+	double __ieee754_jn(n,x)
+	int n; double x;
+#endif
+{
+	int32_t i,hx,ix,lx, sgn;
+	double a, b, temp, di;
+	double z, w;
+
+    /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
+     * Thus, J(-n,x) = J(n,-x)
+     */
+	EXTRACT_WORDS(hx,lx,x);
+	ix = 0x7fffffff&hx;
+    /* if J(n,NaN) is NaN */
+	if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
+	if(n<0){		
+		n = -n;
+		x = -x;
+		hx ^= 0x80000000;
+	}
+	if(n==0) return(__ieee754_j0(x));
+	if(n==1) return(__ieee754_j1(x));
+	sgn = (n&1)&(hx>>31);	/* even n -- 0, odd n -- sign(x) */
+	x = fabs(x);
+	if((ix|lx)==0||ix>=0x7ff00000) 	/* if x is 0 or inf */
+	    b = zero;
+	else if((double)n<=x) {   
+		/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+	    if(ix>=0x52D00000) { /* x > 2**302 */
+    /* (x >> n**2) 
+     *	    Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+     *	    Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+     *	    Let s=sin(x), c=cos(x), 
+     *		xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+     *
+     *		   n	sin(xn)*sqt2	cos(xn)*sqt2
+     *		----------------------------------
+     *		   0	 s-c		 c+s
+     *		   1	-s-c 		-c+s
+     *		   2	-s+c		-c-s
+     *		   3	 s+c		 c-s
+     */
+		switch(n&3) {
+		    case 0: temp =  cos(x)+sin(x); break;
+		    case 1: temp = -cos(x)+sin(x); break;
+		    case 2: temp = -cos(x)-sin(x); break;
+		    case 3: temp =  cos(x)-sin(x); break;
+		}
+		b = invsqrtpi*temp/sqrt(x);
+	    } else {	
+	        a = __ieee754_j0(x);
+	        b = __ieee754_j1(x);
+	        for(i=1;i<n;i++){
+		    temp = b;
+		    b = b*((double)(i+i)/x) - a; /* avoid underflow */
+		    a = temp;
+	        }
+	    }
+	} else {
+	    if(ix<0x3e100000) {	/* x < 2**-29 */
+    /* x is tiny, return the first Taylor expansion of J(n,x) 
+     * J(n,x) = 1/n!*(x/2)^n  - ...
+     */
+		if(n>33)	/* underflow */
+		    b = zero;
+		else {
+		    temp = x*0.5; b = temp;
+		    for (a=one,i=2;i<=n;i++) {
+			a *= (double)i;		/* a = n! */
+			b *= temp;		/* b = (x/2)^n */
+		    }
+		    b = b/a;
+		}
+	    } else {
+		/* use backward recurrence */
+		/* 			x      x^2      x^2       
+		 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
+		 *			2n  - 2(n+1) - 2(n+2)
+		 *
+		 * 			1      1        1       
+		 *  (for large x)   =  ----  ------   ------   .....
+		 *			2n   2(n+1)   2(n+2)
+		 *			-- - ------ - ------ - 
+		 *			 x     x         x
+		 *
+		 * Let w = 2n/x and h=2/x, then the above quotient
+		 * is equal to the continued fraction:
+		 *		    1
+		 *	= -----------------------
+		 *		       1
+		 *	   w - -----------------
+		 *			  1
+		 * 	        w+h - ---------
+		 *		       w+2h - ...
+		 *
+		 * To determine how many terms needed, let
+		 * Q(0) = w, Q(1) = w(w+h) - 1,
+		 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+		 * When Q(k) > 1e4	good for single 
+		 * When Q(k) > 1e9	good for double 
+		 * When Q(k) > 1e17	good for quadruple 
+		 */
+	    /* determine k */
+		double t,v;
+		double q0,q1,h,tmp; int32_t k,m;
+		w  = (n+n)/(double)x; h = 2.0/(double)x;
+		q0 = w;  z = w+h; q1 = w*z - 1.0; k=1;
+		while(q1<1.0e9) {
+			k += 1; z += h;
+			tmp = z*q1 - q0;
+			q0 = q1;
+			q1 = tmp;
+		}
+		m = n+n;
+		for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
+		a = t;
+		b = one;
+		/*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+		 *  Hence, if n*(log(2n/x)) > ...
+		 *  single 8.8722839355e+01
+		 *  double 7.09782712893383973096e+02
+		 *  long double 1.1356523406294143949491931077970765006170e+04
+		 *  then recurrent value may overflow and the result is 
+		 *  likely underflow to zero
+		 */
+		tmp = n;
+		v = two/x;
+		tmp = tmp*__ieee754_log(fabs(v*tmp));
+		if(tmp<7.09782712893383973096e+02) {
+	    	    for(i=n-1,di=(double)(i+i);i>0;i--){
+		        temp = b;
+			b *= di;
+			b  = b/x - a;
+		        a = temp;
+			di -= two;
+	     	    }
+		} else {
+	    	    for(i=n-1,di=(double)(i+i);i>0;i--){
+		        temp = b;
+			b *= di;
+			b  = b/x - a;
+		        a = temp;
+			di -= two;
+		    /* scale b to avoid spurious overflow */
+			if(b>1e100) {
+			    a /= b;
+			    t /= b;
+			    b  = one;
+			}
+	     	    }
+		}
+	    	b = (t*__ieee754_j0(x)/b);
+	    }
+	}
+	if(sgn==1) return -b; else return b;
+}
+
+#ifdef __STDC__
+	double __ieee754_yn(int n, double x) 
+#else
+	double __ieee754_yn(n,x) 
+	int n; double x;
+#endif
+{
+	int32_t i,hx,ix,lx;
+	int32_t sign;
+	double a, b, temp;
+
+	EXTRACT_WORDS(hx,lx,x);
+	ix = 0x7fffffff&hx;
+    /* if Y(n,NaN) is NaN */
+	if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x;
+	if((ix|lx)==0) return -one/zero;
+	if(hx<0) return zero/zero;
+	sign = 1;
+	if(n<0){
+		n = -n;
+		sign = 1 - ((n&1)<<2);
+	}
+	if(n==0) return(__ieee754_y0(x));
+	if(n==1) return(sign*__ieee754_y1(x));
+	if(ix==0x7ff00000) return zero;
+	if(ix>=0x52D00000) { /* x > 2**302 */
+    /* (x >> n**2) 
+     *	    Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+     *	    Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi)
+     *	    Let s=sin(x), c=cos(x), 
+     *		xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then
+     *
+     *		   n	sin(xn)*sqt2	cos(xn)*sqt2
+     *		----------------------------------
+     *		   0	 s-c		 c+s
+     *		   1	-s-c 		-c+s
+     *		   2	-s+c		-c-s
+     *		   3	 s+c		 c-s
+     */
+		switch(n&3) {
+		    case 0: temp =  sin(x)-cos(x); break;
+		    case 1: temp = -sin(x)-cos(x); break;
+		    case 2: temp = -sin(x)+cos(x); break;
+		    case 3: temp =  sin(x)+cos(x); break;
+		}
+		b = invsqrtpi*temp/sqrt(x);
+	} else {
+	    u_int32_t high;
+	    a = __ieee754_y0(x);
+	    b = __ieee754_y1(x);
+	/* quit if b is -inf */
+	    GET_HIGH_WORD(high,b);
+	    for(i=1;i<n&&high!=0xfff00000;i++){ 
+		temp = b;
+		b = ((double)(i+i)/x)*b - a;
+		GET_HIGH_WORD(high,b);
+		a = temp;
+	    }
+	}
+	if(sign>0) return b; else return -b;
+}

lib/msun/src/e_jnf.c

@@ -0,0 +1,212 @@
+/* e_jnf.c -- float version of e_jn.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_jnf.c,v 1.2 1994/08/18 23:05:39 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float
+#else
+static float
+#endif
+invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
+two   =  2.0000000000e+00, /* 0x40000000 */
+one   =  1.0000000000e+00; /* 0x3F800000 */
+
+#ifdef __STDC__
+static const float zero  =  0.0000000000e+00;
+#else
+static float zero  =  0.0000000000e+00;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_jnf(int n, float x)
+#else
+	float __ieee754_jnf(n,x)
+	int n; float x;
+#endif
+{
+	int32_t i,hx,ix, sgn;
+	float a, b, temp, di;
+	float z, w;
+
+    /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
+     * Thus, J(-n,x) = J(n,-x)
+     */
+	GET_FLOAT_WORD(hx,x);
+	ix = 0x7fffffff&hx;
+    /* if J(n,NaN) is NaN */
+	if(ix>0x7f800000) return x+x;
+	if(n<0){		
+		n = -n;
+		x = -x;
+		hx ^= 0x80000000;
+	}
+	if(n==0) return(__ieee754_j0f(x));
+	if(n==1) return(__ieee754_j1f(x));
+	sgn = (n&1)&(hx>>31);	/* even n -- 0, odd n -- sign(x) */
+	x = fabsf(x);
+	if(ix==0||ix>=0x7f800000) 	/* if x is 0 or inf */
+	    b = zero;
+	else if((float)n<=x) {   
+		/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
+	    a = __ieee754_j0f(x);
+	    b = __ieee754_j1f(x);
+	    for(i=1;i<n;i++){
+		temp = b;
+		b = b*((float)(i+i)/x) - a; /* avoid underflow */
+		a = temp;
+	    }
+	} else {
+	    if(ix<0x30800000) {	/* x < 2**-29 */
+    /* x is tiny, return the first Taylor expansion of J(n,x) 
+     * J(n,x) = 1/n!*(x/2)^n  - ...
+     */
+		if(n>33)	/* underflow */
+		    b = zero;
+		else {
+		    temp = x*(float)0.5; b = temp;
+		    for (a=one,i=2;i<=n;i++) {
+			a *= (float)i;		/* a = n! */
+			b *= temp;		/* b = (x/2)^n */
+		    }
+		    b = b/a;
+		}
+	    } else {
+		/* use backward recurrence */
+		/* 			x      x^2      x^2       
+		 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
+		 *			2n  - 2(n+1) - 2(n+2)
+		 *
+		 * 			1      1        1       
+		 *  (for large x)   =  ----  ------   ------   .....
+		 *			2n   2(n+1)   2(n+2)
+		 *			-- - ------ - ------ - 
+		 *			 x     x         x
+		 *
+		 * Let w = 2n/x and h=2/x, then the above quotient
+		 * is equal to the continued fraction:
+		 *		    1
+		 *	= -----------------------
+		 *		       1
+		 *	   w - -----------------
+		 *			  1
+		 * 	        w+h - ---------
+		 *		       w+2h - ...
+		 *
+		 * To determine how many terms needed, let
+		 * Q(0) = w, Q(1) = w(w+h) - 1,
+		 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
+		 * When Q(k) > 1e4	good for single 
+		 * When Q(k) > 1e9	good for double 
+		 * When Q(k) > 1e17	good for quadruple 
+		 */
+	    /* determine k */
+		float t,v;
+		float q0,q1,h,tmp; int32_t k,m;
+		w  = (n+n)/(float)x; h = (float)2.0/(float)x;
+		q0 = w;  z = w+h; q1 = w*z - (float)1.0; k=1;
+		while(q1<(float)1.0e9) {
+			k += 1; z += h;
+			tmp = z*q1 - q0;
+			q0 = q1;
+			q1 = tmp;
+		}
+		m = n+n;
+		for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
+		a = t;
+		b = one;
+		/*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
+		 *  Hence, if n*(log(2n/x)) > ...
+		 *  single 8.8722839355e+01
+		 *  double 7.09782712893383973096e+02
+		 *  long double 1.1356523406294143949491931077970765006170e+04
+		 *  then recurrent value may overflow and the result is 
+		 *  likely underflow to zero
+		 */
+		tmp = n;
+		v = two/x;
+		tmp = tmp*__ieee754_logf(fabsf(v*tmp));
+		if(tmp<(float)8.8721679688e+01) {
+	    	    for(i=n-1,di=(float)(i+i);i>0;i--){
+		        temp = b;
+			b *= di;
+			b  = b/x - a;
+		        a = temp;
+			di -= two;
+	     	    }
+		} else {
+	    	    for(i=n-1,di=(float)(i+i);i>0;i--){
+		        temp = b;
+			b *= di;
+			b  = b/x - a;
+		        a = temp;
+			di -= two;
+		    /* scale b to avoid spurious overflow */
+			if(b>(float)1e10) {
+			    a /= b;
+			    t /= b;
+			    b  = one;
+			}
+	     	    }
+		}
+	    	b = (t*__ieee754_j0f(x)/b);
+	    }
+	}
+	if(sgn==1) return -b; else return b;
+}
+
+#ifdef __STDC__
+	float __ieee754_ynf(int n, float x) 
+#else
+	float __ieee754_ynf(n,x) 
+	int n; float x;
+#endif
+{
+	int32_t i,hx,ix,ib;
+	int32_t sign;
+	float a, b, temp;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = 0x7fffffff&hx;
+    /* if Y(n,NaN) is NaN */
+	if(ix>0x7f800000) return x+x;
+	if(ix==0) return -one/zero;
+	if(hx<0) return zero/zero;
+	sign = 1;
+	if(n<0){
+		n = -n;
+		sign = 1 - ((n&1)<<2);
+	}
+	if(n==0) return(__ieee754_y0f(x));
+	if(n==1) return(sign*__ieee754_y1f(x));
+	if(ix==0x7f800000) return zero;
+
+	a = __ieee754_y0f(x);
+	b = __ieee754_y1f(x);
+	/* quit if b is -inf */
+	GET_FLOAT_WORD(ib,b);
+	for(i=1;i<n&&ib!=0xff800000;i++){ 
+	    temp = b;
+	    b = ((float)(i+i)/x)*b - a;
+	    GET_FLOAT_WORD(ib,b);
+	    a = temp;
+	}
+	if(sign>0) return b; else return -b;
+}

lib/msun/src/e_lgamma.c

@@ -0,0 +1,36 @@
+/* @(#)e_lgamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_lgamma.c,v 1.4 1994/08/10 20:31:05 jtc Exp $";
+#endif
+
+/* __ieee754_lgamma(x)
+ * Return the logarithm of the Gamma function of x.
+ *
+ * Method: call __ieee754_lgamma_r
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+extern int signgam;
+
+#ifdef __STDC__
+	double __ieee754_lgamma(double x)
+#else
+	double __ieee754_lgamma(x)
+	double x;
+#endif
+{
+	return __ieee754_lgamma_r(x,&signgam);
+}

lib/msun/src/e_lgamma_r.c

@@ -0,0 +1,312 @@
+/* @(#)er_lgamma.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_lgamma_r.c,v 1.5 1994/08/10 20:31:07 jtc Exp $";
+#endif
+
+/* __ieee754_lgamma_r(x, signgamp)
+ * Reentrant version of the logarithm of the Gamma function 
+ * with user provide pointer for the sign of Gamma(x). 
+ *
+ * Method:
+ *   1. Argument Reduction for 0 < x <= 8
+ * 	Since gamma(1+s)=s*gamma(s), for x in [0,8], we may 
+ * 	reduce x to a number in [1.5,2.5] by
+ * 		lgamma(1+s) = log(s) + lgamma(s)
+ *	for example,
+ *		lgamma(7.3) = log(6.3) + lgamma(6.3)
+ *			    = log(6.3*5.3) + lgamma(5.3)
+ *			    = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
+ *   2. Polynomial approximation of lgamma around its
+ *	minimun ymin=1.461632144968362245 to maintain monotonicity.
+ *	On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
+ *		Let z = x-ymin;
+ *		lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
+ *	where
+ *		poly(z) is a 14 degree polynomial.
+ *   2. Rational approximation in the primary interval [2,3]
+ *	We use the following approximation:
+ *		s = x-2.0;
+ *		lgamma(x) = 0.5*s + s*P(s)/Q(s)
+ *	with accuracy
+ *		|P/Q - (lgamma(x)-0.5s)| < 2**-61.71
+ *	Our algorithms are based on the following observation
+ *
+ *                             zeta(2)-1    2    zeta(3)-1    3
+ * lgamma(2+s) = s*(1-Euler) + --------- * s  -  --------- * s  + ...
+ *                                 2                 3
+ *
+ *	where Euler = 0.5771... is the Euler constant, which is very
+ *	close to 0.5.
+ *
+ *   3. For x>=8, we have
+ *	lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
+ *	(better formula:
+ *	   lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
+ *	Let z = 1/x, then we approximation
+ *		f(z) = lgamma(x) - (x-0.5)(log(x)-1)
+ *	by
+ *	  			    3       5             11
+ *		w = w0 + w1*z + w2*z  + w3*z  + ... + w6*z
+ *	where 
+ *		|w - f(z)| < 2**-58.74
+ *		
+ *   4. For negative x, since (G is gamma function)
+ *		-x*G(-x)*G(x) = pi/sin(pi*x),
+ * 	we have
+ * 		G(x) = pi/(sin(pi*x)*(-x)*G(-x))
+ *	since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
+ *	Hence, for x<0, signgam = sign(sin(pi*x)) and 
+ *		lgamma(x) = log(|Gamma(x)|)
+ *			  = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
+ *	Note: one should avoid compute pi*(-x) directly in the 
+ *	      computation of sin(pi*(-x)).
+ *		
+ *   5. Special Cases
+ *		lgamma(2+s) ~ s*(1-Euler) for tiny s
+ *		lgamma(1)=lgamma(2)=0
+ *		lgamma(x) ~ -log(x) for tiny x
+ *		lgamma(0) = lgamma(inf) = inf
+ *	 	lgamma(-integer) = +-inf
+ *	
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+two52=  4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
+half=  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pi  =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+a0  =  7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */
+a1  =  3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */
+a2  =  6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */
+a3  =  2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */
+a4  =  7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */
+a5  =  2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */
+a6  =  1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */
+a7  =  5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */
+a8  =  2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */
+a9  =  1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */
+a10 =  2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */
+a11 =  4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */
+tc  =  1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */
+tf  = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */
+/* tt = -(tail of tf) */
+tt  = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */
+t0  =  4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */
+t1  = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */
+t2  =  6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */
+t3  = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */
+t4  =  1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */
+t5  = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */
+t6  =  6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */
+t7  = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */
+t8  =  2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */
+t9  = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */
+t10 =  8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */
+t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */
+t12 =  3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */
+t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */
+t14 =  3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */
+u0  = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
+u1  =  6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */
+u2  =  1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */
+u3  =  9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */
+u4  =  2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */
+u5  =  1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */
+v1  =  2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */
+v2  =  2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */
+v3  =  7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */
+v4  =  1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */
+v5  =  3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */
+s0  = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */
+s1  =  2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */
+s2  =  3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */
+s3  =  1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */
+s4  =  2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */
+s5  =  1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */
+s6  =  3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */
+r1  =  1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */
+r2  =  7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */
+r3  =  1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */
+r4  =  1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */
+r5  =  7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */
+r6  =  7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */
+w0  =  4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */
+w1  =  8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */
+w2  = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */
+w3  =  7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */
+w4  = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
+w5  =  8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
+w6  = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
+
+#ifdef __STDC__
+static const double zero=  0.00000000000000000000e+00;
+#else
+static double zero=  0.00000000000000000000e+00;
+#endif
+
+#ifdef __STDC__
+	static double sin_pi(double x)
+#else
+	static double sin_pi(x)
+	double x;
+#endif
+{
+	double y,z;
+	int n,ix;
+
+	GET_HIGH_WORD(ix,x);
+	ix &= 0x7fffffff;
+
+	if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
+	y = -x;		/* x is assume negative */
+
+    /*
+     * argument reduction, make sure inexact flag not raised if input
+     * is an integer
+     */
+	z = floor(y);
+	if(z!=y) {				/* inexact anyway */
+	    y  *= 0.5;
+	    y   = 2.0*(y - floor(y));		/* y = |x| mod 2.0 */
+	    n   = (int) (y*4.0);
+	} else {
+            if(ix>=0x43400000) {
+                y = zero; n = 0;                 /* y must be even */
+            } else {
+                if(ix<0x43300000) z = y+two52;	/* exact */
+		GET_LOW_WORD(n,z);
+		n &= 1;
+                y  = n;
+                n<<= 2;
+            }
+        }
+	switch (n) {
+	    case 0:   y =  __kernel_sin(pi*y,zero,0); break;
+	    case 1:   
+	    case 2:   y =  __kernel_cos(pi*(0.5-y),zero); break;
+	    case 3:  
+	    case 4:   y =  __kernel_sin(pi*(one-y),zero,0); break;
+	    case 5:
+	    case 6:   y = -__kernel_cos(pi*(y-1.5),zero); break;
+	    default:  y =  __kernel_sin(pi*(y-2.0),zero,0); break;
+	    }
+	return -y;
+}
+
+
+#ifdef __STDC__
+	double __ieee754_lgamma_r(double x, int *signgamp)
+#else
+	double __ieee754_lgamma_r(x,signgamp)
+	double x; int *signgamp;
+#endif
+{
+	double t,y,z,nadj,p,p1,p2,p3,q,r,w;
+	int i,hx,lx,ix;
+
+	EXTRACT_WORDS(hx,lx,x);
+
+    /* purge off +-inf, NaN, +-0, and negative arguments */
+	*signgamp = 1;
+	ix = hx&0x7fffffff;
+	if(ix>=0x7ff00000) return x*x;
+	if((ix|lx)==0) return one/zero;
+	if(ix<0x3b900000) {	/* |x|<2**-70, return -log(|x|) */
+	    if(hx<0) {
+	        *signgamp = -1;
+	        return -__ieee754_log(-x);
+	    } else return -__ieee754_log(x);
+	}
+	if(hx<0) {
+	    if(ix>=0x43300000) 	/* |x|>=2**52, must be -integer */
+		return one/zero;
+	    t = sin_pi(x);
+	    if(t==zero) return one/zero; /* -integer */
+	    nadj = __ieee754_log(pi/fabs(t*x));
+	    if(t<zero) *signgamp = -1;
+	    x = -x;
+	}
+
+    /* purge off 1 and 2 */
+	if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
+    /* for x < 2.0 */
+	else if(ix<0x40000000) {
+	    if(ix<=0x3feccccc) { 	/* lgamma(x) = lgamma(x+1)-log(x) */
+		r = -__ieee754_log(x);
+		if(ix>=0x3FE76944) {y = one-x; i= 0;}
+		else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
+	  	else {y = x; i=2;}
+	    } else {
+	  	r = zero;
+	        if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
+	        else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
+		else {y=x-one;i=2;}
+	    }
+	    switch(i) {
+	      case 0:
+		z = y*y;
+		p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
+		p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
+		p  = y*p1+p2;
+		r  += (p-0.5*y); break;
+	      case 1:
+		z = y*y;
+		w = z*y;
+		p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));	/* parallel comp */
+		p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
+		p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
+		p  = z*p1-(tt-w*(p2+y*p3));
+		r += (tf + p); break;
+	      case 2:	
+		p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
+		p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
+		r += (-0.5*y + p1/p2);
+	    }
+	}
+	else if(ix<0x40200000) { 			/* x < 8.0 */
+	    i = (int)x;
+	    t = zero;
+	    y = x-(double)i;
+	    p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
+	    q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
+	    r = half*y+p/q;
+	    z = one;	/* lgamma(1+s) = log(s) + lgamma(s) */
+	    switch(i) {
+	    case 7: z *= (y+6.0);	/* FALLTHRU */
+	    case 6: z *= (y+5.0);	/* FALLTHRU */
+	    case 5: z *= (y+4.0);	/* FALLTHRU */
+	    case 4: z *= (y+3.0);	/* FALLTHRU */
+	    case 3: z *= (y+2.0);	/* FALLTHRU */
+		    r += __ieee754_log(z); break;
+	    }
+    /* 8.0 <= x < 2**58 */
+	} else if (ix < 0x43900000) {
+	    t = __ieee754_log(x);
+	    z = one/x;
+	    y = z*z;
+	    w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
+	    r = (x-half)*(t-one)+w;
+	} else 
+    /* 2**58 <= x <= inf */
+	    r =  x*(__ieee754_log(x)-one);
+	if(hx<0) r = nadj - r;
+	return r;
+}

lib/msun/src/e_lgammaf.c

@@ -0,0 +1,39 @@
+/* e_lgammaf.c -- float version of e_lgamma.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_lgammaf.c,v 1.1 1994/08/10 20:31:08 jtc Exp $";
+#endif
+
+/* __ieee754_lgammaf(x)
+ * Return the logarithm of the Gamma function of x.
+ *
+ * Method: call __ieee754_lgammaf_r
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+extern int signgam;
+
+#ifdef __STDC__
+	float __ieee754_lgammaf(float x)
+#else
+	float __ieee754_lgammaf(x)
+	float x;
+#endif
+{
+	return __ieee754_lgammaf_r(x,&signgam);
+}

lib/msun/src/e_lgammaf_r.c

@@ -0,0 +1,248 @@
+/* e_lgammaf_r.c -- float version of e_lgamma_r.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_lgammaf_r.c,v 1.1 1994/08/10 20:31:09 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float 
+#else
+static float 
+#endif
+two23=  8.3886080000e+06, /* 0x4b000000 */
+half=  5.0000000000e-01, /* 0x3f000000 */
+one =  1.0000000000e+00, /* 0x3f800000 */
+pi  =  3.1415927410e+00, /* 0x40490fdb */
+a0  =  7.7215664089e-02, /* 0x3d9e233f */
+a1  =  3.2246702909e-01, /* 0x3ea51a66 */
+a2  =  6.7352302372e-02, /* 0x3d89f001 */
+a3  =  2.0580807701e-02, /* 0x3ca89915 */
+a4  =  7.3855509982e-03, /* 0x3bf2027e */
+a5  =  2.8905137442e-03, /* 0x3b3d6ec6 */
+a6  =  1.1927076848e-03, /* 0x3a9c54a1 */
+a7  =  5.1006977446e-04, /* 0x3a05b634 */
+a8  =  2.2086278477e-04, /* 0x39679767 */
+a9  =  1.0801156895e-04, /* 0x38e28445 */
+a10 =  2.5214456400e-05, /* 0x37d383a2 */
+a11 =  4.4864096708e-05, /* 0x383c2c75 */
+tc  =  1.4616321325e+00, /* 0x3fbb16c3 */
+tf  = -1.2148628384e-01, /* 0xbdf8cdcd */
+/* tt = -(tail of tf) */
+tt  =  6.6971006518e-09, /* 0x31e61c52 */
+t0  =  4.8383611441e-01, /* 0x3ef7b95e */
+t1  = -1.4758771658e-01, /* 0xbe17213c */
+t2  =  6.4624942839e-02, /* 0x3d845a15 */
+t3  = -3.2788541168e-02, /* 0xbd064d47 */
+t4  =  1.7970675603e-02, /* 0x3c93373d */
+t5  = -1.0314224288e-02, /* 0xbc28fcfe */
+t6  =  6.1005386524e-03, /* 0x3bc7e707 */
+t7  = -3.6845202558e-03, /* 0xbb7177fe */
+t8  =  2.2596477065e-03, /* 0x3b141699 */
+t9  = -1.4034647029e-03, /* 0xbab7f476 */
+t10 =  8.8108185446e-04, /* 0x3a66f867 */
+t11 = -5.3859531181e-04, /* 0xba0d3085 */
+t12 =  3.1563205994e-04, /* 0x39a57b6b */
+t13 = -3.1275415677e-04, /* 0xb9a3f927 */
+t14 =  3.3552918467e-04, /* 0x39afe9f7 */
+u0  = -7.7215664089e-02, /* 0xbd9e233f */
+u1  =  6.3282704353e-01, /* 0x3f2200f4 */
+u2  =  1.4549225569e+00, /* 0x3fba3ae7 */
+u3  =  9.7771751881e-01, /* 0x3f7a4bb2 */
+u4  =  2.2896373272e-01, /* 0x3e6a7578 */
+u5  =  1.3381091878e-02, /* 0x3c5b3c5e */
+v1  =  2.4559779167e+00, /* 0x401d2ebe */
+v2  =  2.1284897327e+00, /* 0x4008392d */
+v3  =  7.6928514242e-01, /* 0x3f44efdf */
+v4  =  1.0422264785e-01, /* 0x3dd572af */
+v5  =  3.2170924824e-03, /* 0x3b52d5db */
+s0  = -7.7215664089e-02, /* 0xbd9e233f */
+s1  =  2.1498242021e-01, /* 0x3e5c245a */
+s2  =  3.2577878237e-01, /* 0x3ea6cc7a */
+s3  =  1.4635047317e-01, /* 0x3e15dce6 */
+s4  =  2.6642270386e-02, /* 0x3cda40e4 */
+s5  =  1.8402845599e-03, /* 0x3af135b4 */
+s6  =  3.1947532989e-05, /* 0x3805ff67 */
+r1  =  1.3920053244e+00, /* 0x3fb22d3b */
+r2  =  7.2193557024e-01, /* 0x3f38d0c5 */
+r3  =  1.7193385959e-01, /* 0x3e300f6e */
+r4  =  1.8645919859e-02, /* 0x3c98bf54 */
+r5  =  7.7794247773e-04, /* 0x3a4beed6 */
+r6  =  7.3266842264e-06, /* 0x36f5d7bd */
+w0  =  4.1893854737e-01, /* 0x3ed67f1d */
+w1  =  8.3333335817e-02, /* 0x3daaaaab */
+w2  = -2.7777778450e-03, /* 0xbb360b61 */
+w3  =  7.9365057172e-04, /* 0x3a500cfd */
+w4  = -5.9518753551e-04, /* 0xba1c065c */
+w5  =  8.3633989561e-04, /* 0x3a5b3dd2 */
+w6  = -1.6309292987e-03; /* 0xbad5c4e8 */
+
+#ifdef __STDC__
+static const float zero=  0.0000000000e+00;
+#else
+static float zero=  0.0000000000e+00;
+#endif
+
+#ifdef __STDC__
+	static float sin_pif(float x)
+#else
+	static float sin_pif(x)
+	float x;
+#endif
+{
+	float y,z;
+	int n,ix;
+
+	GET_FLOAT_WORD(ix,x);
+	ix &= 0x7fffffff;
+
+	if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0);
+	y = -x;		/* x is assume negative */
+
+    /*
+     * argument reduction, make sure inexact flag not raised if input
+     * is an integer
+     */
+	z = floorf(y);
+	if(z!=y) {				/* inexact anyway */
+	    y  *= (float)0.5;
+	    y   = (float)2.0*(y - floorf(y));	/* y = |x| mod 2.0 */
+	    n   = (int) (y*(float)4.0);
+	} else {
+            if(ix>=0x4b800000) {
+                y = zero; n = 0;                 /* y must be even */
+            } else {
+                if(ix<0x4b000000) z = y+two23;	/* exact */
+		GET_FLOAT_WORD(n,z);
+		n &= 1;
+                y  = n;
+                n<<= 2;
+            }
+        }
+	switch (n) {
+	    case 0:   y =  __kernel_sinf(pi*y,zero,0); break;
+	    case 1:   
+	    case 2:   y =  __kernel_cosf(pi*((float)0.5-y),zero); break;
+	    case 3:  
+	    case 4:   y =  __kernel_sinf(pi*(one-y),zero,0); break;
+	    case 5:
+	    case 6:   y = -__kernel_cosf(pi*(y-(float)1.5),zero); break;
+	    default:  y =  __kernel_sinf(pi*(y-(float)2.0),zero,0); break;
+	    }
+	return -y;
+}
+
+
+#ifdef __STDC__
+	float __ieee754_lgammaf_r(float x, int *signgamp)
+#else
+	float __ieee754_lgammaf_r(x,signgamp)
+	float x; int *signgamp;
+#endif
+{
+	float t,y,z,nadj,p,p1,p2,p3,q,r,w;
+	int i,hx,ix;
+
+	GET_FLOAT_WORD(hx,x);
+
+    /* purge off +-inf, NaN, +-0, and negative arguments */
+	*signgamp = 1;
+	ix = hx&0x7fffffff;
+	if(ix>=0x7f800000) return x*x;
+	if(ix==0) return one/zero;
+	if(ix<0x1c800000) {	/* |x|<2**-70, return -log(|x|) */
+	    if(hx<0) {
+	        *signgamp = -1;
+	        return -__ieee754_logf(-x);
+	    } else return -__ieee754_logf(x);
+	}
+	if(hx<0) {
+	    if(ix>=0x4b000000) 	/* |x|>=2**23, must be -integer */
+		return one/zero;
+	    t = sin_pif(x);
+	    if(t==zero) return one/zero; /* -integer */
+	    nadj = __ieee754_logf(pi/fabsf(t*x));
+	    if(t<zero) *signgamp = -1;
+	    x = -x;
+	}
+
+    /* purge off 1 and 2 */
+	if (ix==0x3f800000||ix==0x40000000) r = 0;
+    /* for x < 2.0 */
+	else if(ix<0x40000000) {
+	    if(ix<=0x3f666666) { 	/* lgamma(x) = lgamma(x+1)-log(x) */
+		r = -__ieee754_logf(x);
+		if(ix>=0x3f3b4a20) {y = one-x; i= 0;}
+		else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}
+	  	else {y = x; i=2;}
+	    } else {
+	  	r = zero;
+	        if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
+	        else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
+		else {y=x-one;i=2;}
+	    }
+	    switch(i) {
+	      case 0:
+		z = y*y;
+		p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
+		p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
+		p  = y*p1+p2;
+		r  += (p-(float)0.5*y); break;
+	      case 1:
+		z = y*y;
+		w = z*y;
+		p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12)));	/* parallel comp */
+		p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
+		p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
+		p  = z*p1-(tt-w*(p2+y*p3));
+		r += (tf + p); break;
+	      case 2:	
+		p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
+		p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
+		r += (-(float)0.5*y + p1/p2);
+	    }
+	}
+	else if(ix<0x41000000) { 			/* x < 8.0 */
+	    i = (int)x;
+	    t = zero;
+	    y = x-(float)i;
+	    p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
+	    q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
+	    r = half*y+p/q;
+	    z = one;	/* lgamma(1+s) = log(s) + lgamma(s) */
+	    switch(i) {
+	    case 7: z *= (y+(float)6.0);	/* FALLTHRU */
+	    case 6: z *= (y+(float)5.0);	/* FALLTHRU */
+	    case 5: z *= (y+(float)4.0);	/* FALLTHRU */
+	    case 4: z *= (y+(float)3.0);	/* FALLTHRU */
+	    case 3: z *= (y+(float)2.0);	/* FALLTHRU */
+		    r += __ieee754_logf(z); break;
+	    }
+    /* 8.0 <= x < 2**58 */
+	} else if (ix < 0x5c800000) {
+	    t = __ieee754_logf(x);
+	    z = one/x;
+	    y = z*z;
+	    w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
+	    r = (x-half)*(t-one)+w;
+	} else 
+    /* 2**58 <= x <= inf */
+	    r =  x*(__ieee754_logf(x)-one);
+	if(hx<0) r = nadj - r;
+	return r;
+}

lib/msun/src/e_log.c

@@ -0,0 +1,146 @@
+/* @(#)e_log.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_log.c,v 1.6 1994/08/18 23:05:41 jtc Exp $";
+#endif
+
+/* __ieee754_log(x)
+ * Return the logrithm of x
+ *
+ * Method :                  
+ *   1. Argument Reduction: find k and f such that 
+ *			x = 2^k * (1+f), 
+ *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ *   2. Approximation of log(1+f).
+ *	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ *	     	 = 2s + s*R
+ *      We use a special Reme algorithm on [0,0.1716] to generate 
+ * 	a polynomial of degree 14 to approximate R The maximum error 
+ *	of this polynomial approximation is bounded by 2**-58.45. In
+ *	other words,
+ *		        2      4      6      8      10      12      14
+ *	    R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
+ *  	(the values of Lg1 to Lg7 are listed in the program)
+ *	and
+ *	    |      2          14          |     -58.45
+ *	    | Lg1*s +...+Lg7*s    -  R(z) | <= 2 
+ *	    |                             |
+ *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ *	In order to guarantee error in log below 1ulp, we compute log
+ *	by
+ *		log(1+f) = f - s*(f - R)	(if f is not too large)
+ *		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
+ *	
+ *	3. Finally,  log(x) = k*ln2 + log(1+f).  
+ *			    = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+ *	   Here ln2 is split into two floating point number: 
+ *			ln2_hi + ln2_lo,
+ *	   where n*ln2_hi is always exact for |n| < 2000.
+ *
+ * Special cases:
+ *	log(x) is NaN with signal if x < 0 (including -INF) ; 
+ *	log(+INF) is +INF; log(0) is -INF with signal;
+ *	log(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ *	according to an error analysis, the error is always less than
+ *	1 ulp (unit in the last place).
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following 
+ * constants. The decimal values may be used, provided that the 
+ * compiler will convert from decimal to binary accurately enough 
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
+ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
+two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
+Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
+
+#ifdef __STDC__
+static const double zero   =  0.0;
+#else
+static double zero   =  0.0;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_log(double x)
+#else
+	double __ieee754_log(x)
+	double x;
+#endif
+{
+	double hfsq,f,s,z,R,w,t1,t2,dk;
+	int32_t k,hx,i,j;
+	u_int32_t lx;
+
+	EXTRACT_WORDS(hx,lx,x);
+
+	k=0;
+	if (hx < 0x00100000) {			/* x < 2**-1022  */
+	    if (((hx&0x7fffffff)|lx)==0) 
+		return -two54/zero;		/* log(+-0)=-inf */
+	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
+	    k -= 54; x *= two54; /* subnormal number, scale up x */
+	    GET_HIGH_WORD(hx,x);
+	} 
+	if (hx >= 0x7ff00000) return x+x;
+	k += (hx>>20)-1023;
+	hx &= 0x000fffff;
+	i = (hx+0x95f64)&0x100000;
+	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
+	k += (i>>20);
+	f = x-1.0;
+	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
+	    if(f==zero) if(k==0) return zero;  else {dk=(double)k;
+				 return dk*ln2_hi+dk*ln2_lo;}
+	    R = f*f*(0.5-0.33333333333333333*f);
+	    if(k==0) return f-R; else {dk=(double)k;
+	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
+	}
+ 	s = f/(2.0+f); 
+	dk = (double)k;
+	z = s*s;
+	i = hx-0x6147a;
+	w = z*z;
+	j = 0x6b851-hx;
+	t1= w*(Lg2+w*(Lg4+w*Lg6)); 
+	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
+	i |= j;
+	R = t2+t1;
+	if(i>0) {
+	    hfsq=0.5*f*f;
+	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
+		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
+	} else {
+	    if(k==0) return f-s*(f-R); else
+		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
+	}
+}

lib/msun/src/e_log10.c

@@ -0,0 +1,99 @@
+/* @(#)e_log10.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_log10.c,v 1.6 1994/08/18 23:05:44 jtc Exp $";
+#endif
+
+/* __ieee754_log10(x)
+ * Return the base 10 logarithm of x
+ * 
+ * Method :
+ *	Let log10_2hi = leading 40 bits of log10(2) and
+ *	    log10_2lo = log10(2) - log10_2hi,
+ *	    ivln10   = 1/log(10) rounded.
+ *	Then
+ *		n = ilogb(x), 
+ *		if(n<0)  n = n+1;
+ *		x = scalbn(x,-n);
+ *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
+ *
+ * Note 1:
+ *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding 
+ *	mode must set to Round-to-Nearest.
+ * Note 2:
+ *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
+ *	log10 is monotonic at all binary break points.
+ *
+ * Special cases:
+ *	log10(x) is NaN with signal if x < 0; 
+ *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
+ *	log10(NaN) is that NaN with no signal;
+ *	log10(10**N) = N  for N=0,1,...,22.
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following constants.
+ * The decimal values may be used, provided that the compiler will convert
+ * from decimal to binary accurately enough to produce the hexadecimal values
+ * shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+one	  = 1.0,
+two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
+log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
+log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
+
+#ifdef __STDC__
+static const double zero   =  0.0;
+#else
+static double zero   =  0.0;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_log10(double x)
+#else
+	double __ieee754_log10(x)
+	double x;
+#endif
+{
+	double y,z;
+	int32_t i,k,hx;
+	u_int32_t lx;
+
+	EXTRACT_WORDS(hx,lx,x);
+
+        k=0;
+        if (hx < 0x00100000) {                  /* x < 2**-1022  */
+            if (((hx&0x7fffffff)|lx)==0)
+                return -two54/zero;             /* log(+-0)=-inf */
+            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
+            k -= 54; x *= two54; /* subnormal number, scale up x */
+	    GET_HIGH_WORD(hx,x);
+        }
+	if (hx >= 0x7ff00000) return x+x;
+	k += (hx>>20)-1023;
+	i  = ((u_int32_t)k&0x80000000)>>31;
+        hx = (hx&0x000fffff)|((0x3ff-i)<<20);
+        y  = (double)(k+i);
+	SET_HIGH_WORD(x,hx);
+	z  = y*log10_2lo + ivln10*__ieee754_log(x);
+	return  z+y*log10_2hi;
+}

lib/msun/src/e_log10f.c

@@ -0,0 +1,68 @@
+/* e_log10f.c -- float version of e_log10.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_log10f.c,v 1.2 1994/08/18 23:05:46 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float
+#else
+static float
+#endif
+one	  = 1.0,
+two25      =  3.3554432000e+07, /* 0x4c000000 */
+ivln10     =  4.3429449201e-01, /* 0x3ede5bd9 */
+log10_2hi  =  3.0102920532e-01, /* 0x3e9a2080 */
+log10_2lo  =  7.9034151668e-07; /* 0x355427db */
+
+#ifdef __STDC__
+static const float zero   =  0.0;
+#else
+static float zero   =  0.0;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_log10f(float x)
+#else
+	float __ieee754_log10f(x)
+	float x;
+#endif
+{
+	float y,z;
+	int32_t i,k,hx;
+
+	GET_FLOAT_WORD(hx,x);
+
+        k=0;
+        if (hx < 0x00800000) {                  /* x < 2**-126  */
+            if ((hx&0x7fffffff)==0)
+                return -two25/zero;             /* log(+-0)=-inf */
+            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
+            k -= 25; x *= two25; /* subnormal number, scale up x */
+	    GET_FLOAT_WORD(hx,x);
+        }
+	if (hx >= 0x7f800000) return x+x;
+	k += (hx>>23)-127;
+	i  = ((u_int32_t)k&0x80000000)>>31;
+        hx = (hx&0x007fffff)|((0x7f-i)<<23);
+        y  = (float)(k+i);
+	SET_FLOAT_WORD(x,hx);
+	z  = y*log10_2lo + ivln10*__ieee754_logf(x);
+	return  z+y*log10_2hi;
+}

lib/msun/src/e_logf.c

@@ -0,0 +1,97 @@
+/* e_logf.c -- float version of e_log.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_logf.c,v 1.2 1994/08/18 23:05:48 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float
+#else
+static float
+#endif
+ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
+ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
+two25 =    3.355443200e+07,	/* 0x4c000000 */
+Lg1 = 6.6666668653e-01,	/* 3F2AAAAB */
+Lg2 = 4.0000000596e-01,	/* 3ECCCCCD */
+Lg3 = 2.8571429849e-01, /* 3E924925 */
+Lg4 = 2.2222198546e-01, /* 3E638E29 */
+Lg5 = 1.8183572590e-01, /* 3E3A3325 */
+Lg6 = 1.5313838422e-01, /* 3E1CD04F */
+Lg7 = 1.4798198640e-01; /* 3E178897 */
+
+#ifdef __STDC__
+static const float zero   =  0.0;
+#else
+static float zero   =  0.0;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_logf(float x)
+#else
+	float __ieee754_logf(x)
+	float x;
+#endif
+{
+	float hfsq,f,s,z,R,w,t1,t2,dk;
+	int32_t k,ix,i,j;
+
+	GET_FLOAT_WORD(ix,x);
+
+	k=0;
+	if (ix < 0x00800000) {			/* x < 2**-126  */
+	    if ((ix&0x7fffffff)==0) 
+		return -two25/zero;		/* log(+-0)=-inf */
+	    if (ix<0) return (x-x)/zero;	/* log(-#) = NaN */
+	    k -= 25; x *= two25; /* subnormal number, scale up x */
+	    GET_FLOAT_WORD(ix,x);
+	} 
+	if (ix >= 0x7f800000) return x+x;
+	k += (ix>>23)-127;
+	ix &= 0x007fffff;
+	i = (ix+(0x95f64<<3))&0x800000;
+	SET_FLOAT_WORD(x,ix|(i^0x3f800000));	/* normalize x or x/2 */
+	k += (i>>23);
+	f = x-(float)1.0;
+	if((0x007fffff&(15+ix))<16) {	/* |f| < 2**-20 */
+	    if(f==zero) if(k==0) return zero;  else {dk=(float)k;
+				 return dk*ln2_hi+dk*ln2_lo;}
+	    R = f*f*((float)0.5-(float)0.33333333333333333*f);
+	    if(k==0) return f-R; else {dk=(float)k;
+	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
+	}
+ 	s = f/((float)2.0+f); 
+	dk = (float)k;
+	z = s*s;
+	i = ix-(0x6147a<<3);
+	w = z*z;
+	j = (0x6b851<<3)-ix;
+	t1= w*(Lg2+w*(Lg4+w*Lg6)); 
+	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); 
+	i |= j;
+	R = t2+t1;
+	if(i>0) {
+	    hfsq=(float)0.5*f*f;
+	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
+		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
+	} else {
+	    if(k==0) return f-s*(f-R); else
+		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
+	}
+}

lib/msun/src/e_pow.c

@@ -0,0 +1,312 @@
+/* @(#)e_pow.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_pow.c,v 1.5 1994/08/18 23:05:51 jtc Exp $";
+#endif
+
+/* __ieee754_pow(x,y) return x**y
+ *
+ *		      n
+ * Method:  Let x =  2   * (1+f)
+ *	1. Compute and return log2(x) in two pieces:
+ *		log2(x) = w1 + w2,
+ *	   where w1 has 53-24 = 29 bit trailing zeros.
+ *	2. Perform y*log2(x) = n+y' by simulating muti-precision 
+ *	   arithmetic, where |y'|<=0.5.
+ *	3. Return x**y = 2**n*exp(y'*log2)
+ *
+ * Special cases:
+ *	1.  (anything) ** 0  is 1
+ *	2.  (anything) ** 1  is itself
+ *	3.  (anything) ** NAN is NAN
+ *	4.  NAN ** (anything except 0) is NAN
+ *	5.  +-(|x| > 1) **  +INF is +INF
+ *	6.  +-(|x| > 1) **  -INF is +0
+ *	7.  +-(|x| < 1) **  +INF is +0
+ *	8.  +-(|x| < 1) **  -INF is +INF
+ *	9.  +-1         ** +-INF is NAN
+ *	10. +0 ** (+anything except 0, NAN)               is +0
+ *	11. -0 ** (+anything except 0, NAN, odd integer)  is +0
+ *	12. +0 ** (-anything except 0, NAN)               is +INF
+ *	13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
+ *	14. -0 ** (odd integer) = -( +0 ** (odd integer) )
+ *	15. +INF ** (+anything except 0,NAN) is +INF
+ *	16. +INF ** (-anything except 0,NAN) is +0
+ *	17. -INF ** (anything)  = -0 ** (-anything)
+ *	18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+ *	19. (-anything except 0 and inf) ** (non-integer) is NAN
+ *
+ * Accuracy:
+ *	pow(x,y) returns x**y nearly rounded. In particular
+ *			pow(integer,integer)
+ *	always returns the correct integer provided it is 
+ *	representable.
+ *
+ * Constants :
+ * The hexadecimal values are the intended ones for the following 
+ * constants. The decimal values may be used, provided that the 
+ * compiler will convert from decimal to binary accurately enough 
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+bp[] = {1.0, 1.5,},
+dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
+dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
+zero    =  0.0,
+one	=  1.0,
+two	=  2.0,
+two53	=  9007199254740992.0,	/* 0x43400000, 0x00000000 */
+huge	=  1.0e300,
+tiny    =  1.0e-300,
+	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
+L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
+L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
+L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
+L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
+L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
+P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
+P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
+P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
+P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
+P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
+lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
+lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
+lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
+ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
+cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
+cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
+cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
+ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
+ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
+ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
+
+#ifdef __STDC__
+	double __ieee754_pow(double x, double y)
+#else
+	double __ieee754_pow(x,y)
+	double x, y;
+#endif
+{
+	double z,ax,z_h,z_l,p_h,p_l;
+	double y1,t1,t2,r,s,t,u,v,w;
+	int32_t i,j,k,yisint,n;
+	int32_t hx,hy,ix,iy;
+	u_int32_t lx,ly;
+
+	EXTRACT_WORDS(hx,lx,x);
+	EXTRACT_WORDS(hy,ly,y);
+	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
+
+    /* y==zero: x**0 = 1 */
+	if((iy|ly)==0) return one; 	
+
+    /* +-NaN return x+y */
+	if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
+	   iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 
+		return x+y;	
+
+    /* determine if y is an odd int when x < 0
+     * yisint = 0	... y is not an integer
+     * yisint = 1	... y is an odd int
+     * yisint = 2	... y is an even int
+     */
+	yisint  = 0;
+	if(hx<0) {	
+	    if(iy>=0x43400000) yisint = 2; /* even integer y */
+	    else if(iy>=0x3ff00000) {
+		k = (iy>>20)-0x3ff;	   /* exponent */
+		if(k>20) {
+		    j = ly>>(52-k);
+		    if((j<<(52-k))==ly) yisint = 2-(j&1);
+		} else if(ly==0) {
+		    j = iy>>(20-k);
+		    if((j<<(20-k))==iy) yisint = 2-(j&1);
+		}
+	    }		
+	} 
+
+    /* special value of y */
+	if(ly==0) { 	
+	    if (iy==0x7ff00000) {	/* y is +-inf */
+	        if(((ix-0x3ff00000)|lx)==0)
+		    return  y - y;	/* inf**+-1 is NaN */
+	        else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
+		    return (hy>=0)? y: zero;
+	        else			/* (|x|<1)**-,+inf = inf,0 */
+		    return (hy<0)?-y: zero;
+	    } 
+	    if(iy==0x3ff00000) {	/* y is  +-1 */
+		if(hy<0) return one/x; else return x;
+	    }
+	    if(hy==0x40000000) return x*x; /* y is  2 */
+	    if(hy==0x3fe00000) {	/* y is  0.5 */
+		if(hx>=0)	/* x >= +0 */
+		return sqrt(x);	
+	    }
+	}
+
+	ax   = fabs(x);
+    /* special value of x */
+	if(lx==0) {
+	    if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
+		z = ax;			/*x is +-0,+-inf,+-1*/
+		if(hy<0) z = one/z;	/* z = (1/|x|) */
+		if(hx<0) {
+		    if(((ix-0x3ff00000)|yisint)==0) {
+			z = (z-z)/(z-z); /* (-1)**non-int is NaN */
+		    } else if(yisint==1) 
+			z = -z;		/* (x<0)**odd = -(|x|**odd) */
+		}
+		return z;
+	    }
+	}
+    
+    /* (x<0)**(non-int) is NaN */
+    /* CYGNUS LOCAL: This used to be
+	if((((hx>>31)+1)|yisint)==0) return (x-x)/(x-x);
+       but ANSI C says a right shift of a signed negative quantity is
+       implementation defined.  */
+	if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
+
+    /* |y| is huge */
+	if(iy>0x41e00000) { /* if |y| > 2**31 */
+	    if(iy>0x43f00000){	/* if |y| > 2**64, must o/uflow */
+		if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
+		if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
+	    }
+	/* over/underflow if x is not close to one */
+	    if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
+	    if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
+	/* now |1-x| is tiny <= 2**-20, suffice to compute 
+	   log(x) by x-x^2/2+x^3/3-x^4/4 */
+	    t = x-1;		/* t has 20 trailing zeros */
+	    w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
+	    u = ivln2_h*t;	/* ivln2_h has 21 sig. bits */
+	    v = t*ivln2_l-w*ivln2;
+	    t1 = u+v;
+	    SET_LOW_WORD(t1,0);
+	    t2 = v-(t1-u);
+	} else {
+	    double s2,s_h,s_l,t_h,t_l;
+	    n = 0;
+	/* take care subnormal number */
+	    if(ix<0x00100000)
+		{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
+	    n  += ((ix)>>20)-0x3ff;
+	    j  = ix&0x000fffff;
+	/* determine interval */
+	    ix = j|0x3ff00000;		/* normalize ix */
+	    if(j<=0x3988E) k=0;		/* |x|<sqrt(3/2) */
+	    else if(j<0xBB67A) k=1;	/* |x|<sqrt(3)   */
+	    else {k=0;n+=1;ix -= 0x00100000;}
+	    SET_HIGH_WORD(ax,ix);
+
+	/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+	    u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
+	    v = one/(ax+bp[k]);
+	    s = u*v;
+	    s_h = s;
+	    SET_LOW_WORD(s_h,0);
+	/* t_h=ax+bp[k] High */
+	    t_h = zero;
+	    SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
+	    t_l = ax - (t_h-bp[k]);
+	    s_l = v*((u-s_h*t_h)-s_h*t_l);
+	/* compute log(ax) */
+	    s2 = s*s;
+	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
+	    r += s_l*(s_h+s);
+	    s2  = s_h*s_h;
+	    t_h = 3.0+s2+r;
+	    SET_LOW_WORD(t_h,0);
+	    t_l = r-((t_h-3.0)-s2);
+	/* u+v = s*(1+...) */
+	    u = s_h*t_h;
+	    v = s_l*t_h+t_l*s;
+	/* 2/(3log2)*(s+...) */
+	    p_h = u+v;
+	    SET_LOW_WORD(p_h,0);
+	    p_l = v-(p_h-u);
+	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
+	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
+	/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+	    t = (double)n;
+	    t1 = (((z_h+z_l)+dp_h[k])+t);
+	    SET_LOW_WORD(t1,0);
+	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+	}
+
+	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+	if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
+	    s = -one;/* (-ve)**(odd int) */
+
+    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+	y1  = y;
+	SET_LOW_WORD(y1,0);
+	p_l = (y-y1)*t1+y*t2;
+	p_h = y1*t1;
+	z = p_l+p_h;
+	EXTRACT_WORDS(j,i,z);
+	if (j>=0x40900000) {				/* z >= 1024 */
+	    if(((j-0x40900000)|i)!=0)			/* if z > 1024 */
+		return s*huge*huge;			/* overflow */
+	    else {
+		if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
+	    }
+	} else if((j&0x7fffffff)>=0x4090cc00 ) {	/* z <= -1075 */
+	    if(((j-0xc090cc00)|i)!=0) 		/* z < -1075 */
+		return s*tiny*tiny;		/* underflow */
+	    else {
+		if(p_l<=z-p_h) return s*tiny*tiny;	/* underflow */
+	    }
+	}
+    /*
+     * compute 2**(p_h+p_l)
+     */
+	i = j&0x7fffffff;
+	k = (i>>20)-0x3ff;
+	n = 0;
+	if(i>0x3fe00000) {		/* if |z| > 0.5, set n = [z+0.5] */
+	    n = j+(0x00100000>>(k+1));
+	    k = ((n&0x7fffffff)>>20)-0x3ff;	/* new k for n */
+	    t = zero;
+	    SET_HIGH_WORD(t,n&~(0x000fffff>>k));
+	    n = ((n&0x000fffff)|0x00100000)>>(20-k);
+	    if(j<0) n = -n;
+	    p_h -= t;
+	} 
+	t = p_l+p_h;
+	SET_LOW_WORD(t,0);
+	u = t*lg2_h;
+	v = (p_l-(t-p_h))*lg2+t*lg2_l;
+	z = u+v;
+	w = v-(z-u);
+	t  = z*z;
+	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+	r  = (z*t1)/(t1-two)-(w+z*w);
+	z  = one-(r-z);
+	GET_HIGH_WORD(j,z);
+	j += (n<<20);
+	if((j>>20)<=0) z = scalbn(z,n);	/* subnormal output */
+	else SET_HIGH_WORD(z,j);
+	return s*z;
+}

lib/msun/src/e_powf.c

@@ -0,0 +1,253 @@
+/* e_powf.c -- float version of e_pow.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_powf.c,v 1.2 1994/08/18 23:05:54 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float
+#else
+static float
+#endif
+bp[] = {1.0, 1.5,},
+dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
+dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
+zero    =  0.0,
+one	=  1.0,
+two	=  2.0,
+two24	=  16777216.0,	/* 0x4b800000 */
+huge	=  1.0e30,
+tiny    =  1.0e-30,
+	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
+L1  =  6.0000002384e-01, /* 0x3f19999a */
+L2  =  4.2857143283e-01, /* 0x3edb6db7 */
+L3  =  3.3333334327e-01, /* 0x3eaaaaab */
+L4  =  2.7272811532e-01, /* 0x3e8ba305 */
+L5  =  2.3066075146e-01, /* 0x3e6c3255 */
+L6  =  2.0697501302e-01, /* 0x3e53f142 */
+P1   =  1.6666667163e-01, /* 0x3e2aaaab */
+P2   = -2.7777778450e-03, /* 0xbb360b61 */
+P3   =  6.6137559770e-05, /* 0x388ab355 */
+P4   = -1.6533901999e-06, /* 0xb5ddea0e */
+P5   =  4.1381369442e-08, /* 0x3331bb4c */
+lg2  =  6.9314718246e-01, /* 0x3f317218 */
+lg2_h  =  6.93145752e-01, /* 0x3f317200 */
+lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
+ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
+cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
+cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
+cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
+ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
+ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
+ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
+
+#ifdef __STDC__
+	float __ieee754_powf(float x, float y)
+#else
+	float __ieee754_powf(x,y)
+	float x, y;
+#endif
+{
+	float z,ax,z_h,z_l,p_h,p_l;
+	float y1,t1,t2,r,s,t,u,v,w;
+	int32_t i,j,k,yisint,n;
+	int32_t hx,hy,ix,iy,is;
+
+	GET_FLOAT_WORD(hx,x);
+	GET_FLOAT_WORD(hy,y);
+	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
+
+    /* y==zero: x**0 = 1 */
+	if(iy==0) return one; 	
+
+    /* +-NaN return x+y */
+	if(ix > 0x7f800000 ||
+	   iy > 0x7f800000)
+		return x+y;	
+
+    /* determine if y is an odd int when x < 0
+     * yisint = 0	... y is not an integer
+     * yisint = 1	... y is an odd int
+     * yisint = 2	... y is an even int
+     */
+	yisint  = 0;
+	if(hx<0) {	
+	    if(iy>=0x4b800000) yisint = 2; /* even integer y */
+	    else if(iy>=0x3f800000) {
+		k = (iy>>23)-0x7f;	   /* exponent */
+		j = iy>>(23-k);
+		if((j<<(23-k))==iy) yisint = 2-(j&1);
+	    }		
+	} 
+
+    /* special value of y */
+	if (iy==0x7f800000) {	/* y is +-inf */
+	    if (ix==0x3f800000)
+	        return  y - y;	/* inf**+-1 is NaN */
+	    else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
+	        return (hy>=0)? y: zero;
+	    else			/* (|x|<1)**-,+inf = inf,0 */
+	        return (hy<0)?-y: zero;
+	} 
+	if(iy==0x3f800000) {	/* y is  +-1 */
+	    if(hy<0) return one/x; else return x;
+	}
+	if(hy==0x40000000) return x*x; /* y is  2 */
+	if(hy==0x3f000000) {	/* y is  0.5 */
+	    if(hx>=0)	/* x >= +0 */
+	    return sqrtf(x);	
+	}
+
+	ax   = fabsf(x);
+    /* special value of x */
+	if(ix==0x7f800000||ix==0||ix==0x3f800000){
+	    z = ax;			/*x is +-0,+-inf,+-1*/
+	    if(hy<0) z = one/z;	/* z = (1/|x|) */
+	    if(hx<0) {
+		if(((ix-0x3f800000)|yisint)==0) {
+		    z = (z-z)/(z-z); /* (-1)**non-int is NaN */
+		} else if(yisint==1) 
+		    z = -z;		/* (x<0)**odd = -(|x|**odd) */
+	    }
+	    return z;
+	}
+    
+    /* (x<0)**(non-int) is NaN */
+	if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
+
+    /* |y| is huge */
+	if(iy>0x4d000000) { /* if |y| > 2**27 */
+	/* over/underflow if x is not close to one */
+	    if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
+	    if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
+	/* now |1-x| is tiny <= 2**-20, suffice to compute 
+	   log(x) by x-x^2/2+x^3/3-x^4/4 */
+	    t = x-1;		/* t has 20 trailing zeros */
+	    w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
+	    u = ivln2_h*t;	/* ivln2_h has 16 sig. bits */
+	    v = t*ivln2_l-w*ivln2;
+	    t1 = u+v;
+	    GET_FLOAT_WORD(is,t1);
+	    SET_FLOAT_WORD(t1,is&0xfffff000);
+	    t2 = v-(t1-u);
+	} else {
+	    float s2,s_h,s_l,t_h,t_l;
+	    n = 0;
+	/* take care subnormal number */
+	    if(ix<0x00800000)
+		{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
+	    n  += ((ix)>>23)-0x7f;
+	    j  = ix&0x007fffff;
+	/* determine interval */
+	    ix = j|0x3f800000;		/* normalize ix */
+	    if(j<=0x1cc471) k=0;	/* |x|<sqrt(3/2) */
+	    else if(j<0x5db3d7) k=1;	/* |x|<sqrt(3)   */
+	    else {k=0;n+=1;ix -= 0x00800000;}
+	    SET_FLOAT_WORD(ax,ix);
+
+	/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+	    u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
+	    v = one/(ax+bp[k]);
+	    s = u*v;
+	    s_h = s;
+	    GET_FLOAT_WORD(is,s_h);
+	    SET_FLOAT_WORD(s_h,is&0xfffff000);
+	/* t_h=ax+bp[k] High */
+	    SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
+	    t_l = ax - (t_h-bp[k]);
+	    s_l = v*((u-s_h*t_h)-s_h*t_l);
+	/* compute log(ax) */
+	    s2 = s*s;
+	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
+	    r += s_l*(s_h+s);
+	    s2  = s_h*s_h;
+	    t_h = (float)3.0+s2+r;
+	    GET_FLOAT_WORD(is,t_h);
+	    SET_FLOAT_WORD(t_h,is&0xfffff000);
+	    t_l = r-((t_h-(float)3.0)-s2);
+	/* u+v = s*(1+...) */
+	    u = s_h*t_h;
+	    v = s_l*t_h+t_l*s;
+	/* 2/(3log2)*(s+...) */
+	    p_h = u+v;
+	    GET_FLOAT_WORD(is,p_h);
+	    SET_FLOAT_WORD(p_h,is&0xfffff000);
+	    p_l = v-(p_h-u);
+	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
+	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
+	/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
+	    t = (float)n;
+	    t1 = (((z_h+z_l)+dp_h[k])+t);
+	    GET_FLOAT_WORD(is,t1);
+	    SET_FLOAT_WORD(t1,is&0xfffff000);
+	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+	}
+
+	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+	if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
+	    s = -one;	/* (-ve)**(odd int) */
+
+    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+	GET_FLOAT_WORD(is,y);
+	SET_FLOAT_WORD(y1,is&0xfffff000);
+	p_l = (y-y1)*t1+y*t2;
+	p_h = y1*t1;
+	z = p_l+p_h;
+	GET_FLOAT_WORD(j,z);
+	if (j>0x43000000)				/* if z > 128 */
+	    return s*huge*huge;				/* overflow */
+	else if (j==0x43000000) {			/* if z == 128 */
+	    if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
+	}
+	else if ((j&0x7fffffff)>0x43160000)		/* z <= -150 */
+	    return s*tiny*tiny;				/* underflow */
+	else if (j==0xc3160000){			/* z == -150 */
+	    if(p_l<=z-p_h) return s*tiny*tiny;		/* underflow */
+	}
+    /*
+     * compute 2**(p_h+p_l)
+     */
+	i = j&0x7fffffff;
+	k = (i>>23)-0x7f;
+	n = 0;
+	if(i>0x3f000000) {		/* if |z| > 0.5, set n = [z+0.5] */
+	    n = j+(0x00800000>>(k+1));
+	    k = ((n&0x7fffffff)>>23)-0x7f;	/* new k for n */
+	    SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
+	    n = ((n&0x007fffff)|0x00800000)>>(23-k);
+	    if(j<0) n = -n;
+	    p_h -= t;
+	} 
+	t = p_l+p_h;
+	GET_FLOAT_WORD(is,t);
+	SET_FLOAT_WORD(t,is&0xfffff000);
+	u = t*lg2_h;
+	v = (p_l-(t-p_h))*lg2+t*lg2_l;
+	z = u+v;
+	w = v-(z-u);
+	t  = z*z;
+	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+	r  = (z*t1)/(t1-two)-(w+z*w);
+	z  = one-(r-z);
+	GET_FLOAT_WORD(j,z);
+	j += (n<<23);
+	if((j>>23)<=0) z = scalbnf(z,n);	/* subnormal output */
+	else SET_FLOAT_WORD(z,j);
+	return s*z;
+}

lib/msun/src/e_rem_pio2.c

@@ -0,0 +1,158 @@
+/* @(#)e_rem_pio2.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_rem_pio2.c,v 1.5 1994/08/18 23:05:56 jtc Exp $";
+#endif
+
+/* __ieee754_rem_pio2(x,y)
+ * 
+ * return the remainder of x rem pi/2 in y[0]+y[1] 
+ * use __kernel_rem_pio2()
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+/*
+ * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 
+ */
+#ifdef __STDC__
+static const int32_t two_over_pi[] = {
+#else
+static int32_t two_over_pi[] = {
+#endif
+0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 
+0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 
+0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 
+0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 
+0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 
+0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 
+0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 
+0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 
+0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 
+0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 
+0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 
+};
+
+#ifdef __STDC__
+static const int32_t npio2_hw[] = {
+#else
+static int32_t npio2_hw[] = {
+#endif
+0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
+0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
+0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
+0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
+0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
+0x404858EB, 0x404921FB,
+};
+
+/*
+ * invpio2:  53 bits of 2/pi
+ * pio2_1:   first  33 bit of pi/2
+ * pio2_1t:  pi/2 - pio2_1
+ * pio2_2:   second 33 bit of pi/2
+ * pio2_2t:  pi/2 - (pio2_1+pio2_2)
+ * pio2_3:   third  33 bit of pi/2
+ * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
+ */
+
+#ifdef __STDC__
+static const double 
+#else
+static double 
+#endif
+zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
+invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
+pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
+pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
+pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
+pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
+pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
+
+#ifdef __STDC__
+	int32_t __ieee754_rem_pio2(double x, double *y)
+#else
+	int32_t __ieee754_rem_pio2(x,y)
+	double x,y[];
+#endif
+{
+	double z,w,t,r,fn;
+	double tx[3];
+	int32_t e0,i,j,nx,n,ix,hx;
+	u_int32_t low;
+
+	GET_HIGH_WORD(hx,x);		/* high word of x */
+	ix = hx&0x7fffffff;
+	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
+	    {y[0] = x; y[1] = 0; return 0;}
+	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
+	    t  = fabs(x);
+	    n  = (int32_t) (t*invpio2+half);
+	    fn = (double)n;
+	    r  = t-fn*pio2_1;
+	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
+	    if(n<32&&ix!=npio2_hw[n-1]) {	
+		y[0] = r-w;	/* quick check no cancellation */
+	    } else {
+	        u_int32_t high;
+	        j  = ix>>20;
+	        y[0] = r-w; 
+		GET_HIGH_WORD(high,y[0]);
+	        i = j-((high>>20)&0x7ff);
+	        if(i>16) {  /* 2nd iteration needed, good to 118 */
+		    t  = r;
+		    w  = fn*pio2_2;	
+		    r  = t-w;
+		    w  = fn*pio2_2t-((t-r)-w);	
+		    y[0] = r-w;
+		    GET_HIGH_WORD(high,y[0]);
+		    i = j-((high>>20)&0x7ff);
+		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
+		    	t  = r;	/* will cover all possible cases */
+		    	w  = fn*pio2_3;	
+		    	r  = t-w;
+		    	w  = fn*pio2_3t-((t-r)-w);	
+		    	y[0] = r-w;
+		    }
+		}
+	    }
+	    y[1] = (r-y[0])-w;
+	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
+	    else	 return n;
+	}
+    /* 
+     * all other (large) arguments
+     */
+	if(ix>=0x7ff00000) {		/* x is inf or NaN */
+	    y[0]=y[1]=x-x; return 0;
+	}
+    /* set z = scalbn(|x|,ilogb(x)-23) */
+	GET_LOW_WORD(low,x);
+	SET_LOW_WORD(z,low);
+	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
+	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
+	for(i=0;i<2;i++) {
+		tx[i] = (double)((int32_t)(z));
+		z     = (z-tx[i])*two24;
+	}
+	tx[2] = z;
+	nx = 3;
+	while(tx[nx-1]==zero) nx--;	/* skip zero term */
+	n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
+	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
+	return n;
+}

lib/msun/src/e_rem_pio2f.c

@@ -0,0 +1,171 @@
+/* e_rem_pio2f.c -- float version of e_rem_pio2.c
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_rem_pio2f.c,v 1.2 1994/08/18 23:05:58 jtc Exp $";
+#endif
+
+/* __ieee754_rem_pio2f(x,y)
+ * 
+ * return the remainder of x rem pi/2 in y[0]+y[1] 
+ * use __kernel_rem_pio2f()
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+/*
+ * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 
+ */
+#ifdef __STDC__
+static const int32_t two_over_pi[] = {
+#else
+static int32_t two_over_pi[] = {
+#endif
+0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
+0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, 
+0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
+0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, 
+0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
+0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, 
+0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
+0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, 
+0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
+0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, 
+0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
+0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, 
+0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
+0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, 
+0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
+0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, 
+0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
+0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, 
+0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
+0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, 
+0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
+0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, 
+};
+
+/* This array is like the one in e_rem_pio2.c, but the numbers are
+   single precision and the last 8 bits are forced to 0.  */
+#ifdef __STDC__
+static const int32_t npio2_hw[] = {
+#else
+static int32_t npio2_hw[] = {
+#endif
+0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
+0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
+0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
+0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
+0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
+0x4242c700, 0x42490f00
+};
+
+/*
+ * invpio2:  24 bits of 2/pi
+ * pio2_1:   first  17 bit of pi/2
+ * pio2_1t:  pi/2 - pio2_1
+ * pio2_2:   second 17 bit of pi/2
+ * pio2_2t:  pi/2 - (pio2_1+pio2_2)
+ * pio2_3:   third  17 bit of pi/2
+ * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
+ */
+
+#ifdef __STDC__
+static const float 
+#else
+static float 
+#endif
+zero =  0.0000000000e+00, /* 0x00000000 */
+half =  5.0000000000e-01, /* 0x3f000000 */
+two8 =  2.5600000000e+02, /* 0x43800000 */
+invpio2 =  6.3661980629e-01, /* 0x3f22f984 */
+pio2_1  =  1.5707855225e+00, /* 0x3fc90f80 */
+pio2_1t =  1.0804334124e-05, /* 0x37354443 */
+pio2_2  =  1.0804273188e-05, /* 0x37354400 */
+pio2_2t =  6.0770999344e-11, /* 0x2e85a308 */
+pio2_3  =  6.0770943833e-11, /* 0x2e85a300 */
+pio2_3t =  6.1232342629e-17; /* 0x248d3132 */
+
+#ifdef __STDC__
+	int32_t __ieee754_rem_pio2f(float x, float *y)
+#else
+	int32_t __ieee754_rem_pio2f(x,y)
+	float x,y[];
+#endif
+{
+	float z,w,t,r,fn;
+	float tx[3];
+	int32_t e0,i,j,nx,n,ix,hx;
+
+	GET_FLOAT_WORD(hx,x);
+	ix = hx&0x7fffffff;
+	if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
+	    {y[0] = x; y[1] = 0; return 0;}
+	if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
+	    t  = fabsf(x);
+	    n  = (int32_t) (t*invpio2+half);
+	    fn = (float)n;
+	    r  = t-fn*pio2_1;
+	    w  = fn*pio2_1t;	/* 1st round good to 40 bit */
+	    if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {	
+		y[0] = r-w;	/* quick check no cancellation */
+	    } else {
+	        u_int32_t high;
+	        j  = ix>>23;
+	        y[0] = r-w; 
+		GET_FLOAT_WORD(high,y[0]);
+	        i = j-((high>>23)&0xff);
+	        if(i>8) {  /* 2nd iteration needed, good to 57 */
+		    t  = r;
+		    w  = fn*pio2_2;	
+		    r  = t-w;
+		    w  = fn*pio2_2t-((t-r)-w);	
+		    y[0] = r-w;
+		    GET_FLOAT_WORD(high,y[0]);
+		    i = j-((high>>23)&0xff);
+		    if(i>25)  {	/* 3rd iteration need, 74 bits acc */
+		    	t  = r;	/* will cover all possible cases */
+		    	w  = fn*pio2_3;	
+		    	r  = t-w;
+		    	w  = fn*pio2_3t-((t-r)-w);	
+		    	y[0] = r-w;
+		    }
+		}
+	    }
+	    y[1] = (r-y[0])-w;
+	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
+	    else	 return n;
+	}
+    /* 
+     * all other (large) arguments
+     */
+	if(ix>=0x7f800000) {		/* x is inf or NaN */
+	    y[0]=y[1]=x-x; return 0;
+	}
+    /* set z = scalbn(|x|,ilogb(x)-7) */
+	e0 	= (ix>>23)-134;		/* e0 = ilogb(z)-7; */
+	SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
+	for(i=0;i<2;i++) {
+		tx[i] = (float)((int32_t)(z));
+		z     = (z-tx[i])*two8;
+	}
+	tx[2] = z;
+	nx = 3;
+	while(tx[nx-1]==zero) nx--;	/* skip zero term */
+	n  =  __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
+	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
+	return n;
+}

lib/msun/src/e_remainder.c

@@ -0,0 +1,80 @@
+/* @(#)e_remainder.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_remainder.c,v 1.6 1994/08/18 23:06:00 jtc Exp $";
+#endif
+
+/* __ieee754_remainder(x,p)
+ * Return :                  
+ * 	returns  x REM p  =  x - [x/p]*p as if in infinite 
+ * 	precise arithmetic, where [x/p] is the (infinite bit) 
+ *	integer nearest x/p (in half way case choose the even one).
+ * Method : 
+ *	Based on fmod() return x-[x/p]chopped*p exactlp.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double zero = 0.0;
+#else
+static double zero = 0.0;
+#endif
+
+
+#ifdef __STDC__
+	double __ieee754_remainder(double x, double p)
+#else
+	double __ieee754_remainder(x,p)
+	double x,p;
+#endif
+{
+	int32_t hx,hp;
+	u_int32_t sx,lx,lp;
+	double p_half;
+
+	EXTRACT_WORDS(hx,lx,x);
+	EXTRACT_WORDS(hp,lp,p);
+	sx = hx&0x80000000;
+	hp &= 0x7fffffff;
+	hx &= 0x7fffffff;
+
+    /* purge off exception values */
+	if((hp|lp)==0) return (x*p)/(x*p); 	/* p = 0 */
+	if((hx>=0x7ff00000)||			/* x not finite */
+	  ((hp>=0x7ff00000)&&			/* p is NaN */
+	  (((hp-0x7ff00000)|lp)!=0)))
+	    return (x*p)/(x*p);
+
+
+	if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p);	/* now x < 2p */
+	if (((hx-hp)|(lx-lp))==0) return zero*x;
+	x  = fabs(x);
+	p  = fabs(p);
+	if (hp<0x00200000) {
+	    if(x+x>p) {
+		x-=p;
+		if(x+x>=p) x -= p;
+	    }
+	} else {
+	    p_half = 0.5*p;
+	    if(x>p_half) {
+		x-=p;
+		if(x>=p_half) x -= p;
+	    }
+	}
+	GET_HIGH_WORD(hx,x);
+	SET_HIGH_WORD(x,hx^sx);
+	return x;
+}

lib/msun/src/e_remainderf.c

@@ -0,0 +1,73 @@
+/* e_remainderf.c -- float version of e_remainder.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_remainderf.c,v 1.2 1994/08/18 23:06:02 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float zero = 0.0;
+#else
+static float zero = 0.0;
+#endif
+
+
+#ifdef __STDC__
+	float __ieee754_remainderf(float x, float p)
+#else
+	float __ieee754_remainderf(x,p)
+	float x,p;
+#endif
+{
+	int32_t hx,hp;
+	u_int32_t sx;
+	float p_half;
+
+	GET_FLOAT_WORD(hx,x);
+	GET_FLOAT_WORD(hp,p);
+	sx = hx&0x80000000;
+	hp &= 0x7fffffff;
+	hx &= 0x7fffffff;
+
+    /* purge off exception values */
+	if(hp==0) return (x*p)/(x*p);	 	/* p = 0 */
+	if((hx>=0x7f800000)||			/* x not finite */
+	  ((hp>0x7f800000)))			/* p is NaN */
+	    return (x*p)/(x*p);
+
+
+	if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p);	/* now x < 2p */
+	if ((hx-hp)==0) return zero*x;
+	x  = fabsf(x);
+	p  = fabsf(p);
+	if (hp<0x01000000) {
+	    if(x+x>p) {
+		x-=p;
+		if(x+x>=p) x -= p;
+	    }
+	} else {
+	    p_half = (float)0.5*p;
+	    if(x>p_half) {
+		x-=p;
+		if(x>=p_half) x -= p;
+	    }
+	}
+	GET_FLOAT_WORD(hx,x);
+	SET_FLOAT_WORD(x,hx^sx);
+	return x;
+}

lib/msun/src/e_scalb.c

@@ -0,0 +1,55 @@
+/* @(#)e_scalb.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_scalb.c,v 1.4 1994/08/10 20:31:26 jtc Exp $";
+#endif
+
+/*
+ * __ieee754_scalb(x, fn) is provide for
+ * passing various standard test suite. One 
+ * should use scalbn() instead.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef _SCALB_INT
+#ifdef __STDC__
+	double __ieee754_scalb(double x, int fn)
+#else
+	double __ieee754_scalb(x,fn)
+	double x; int fn;
+#endif
+#else
+#ifdef __STDC__
+	double __ieee754_scalb(double x, double fn)
+#else
+	double __ieee754_scalb(x,fn)
+	double x, fn;
+#endif
+#endif
+{
+#ifdef _SCALB_INT
+	return scalbn(x,fn);
+#else
+	if (isnan(x)||isnan(fn)) return x*fn;
+	if (!finite(fn)) {
+	    if(fn>0.0) return x*fn;
+	    else       return x/(-fn);
+	}
+	if (rint(fn)!=fn) return (fn-fn)/(fn-fn);
+	if ( fn > 65000.0) return scalbn(x, 65000);
+	if (-fn > 65000.0) return scalbn(x,-65000);
+	return scalbn(x,(int)fn);
+#endif
+}

lib/msun/src/e_scalbf.c

@@ -0,0 +1,52 @@
+/* e_scalbf.c -- float version of e_scalb.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_scalbf.c,v 1.1 1994/08/10 20:31:27 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef _SCALB_INT
+#ifdef __STDC__
+	float __ieee754_scalbf(float x, int fn)
+#else
+	float __ieee754_scalbf(x,fn)
+	float x; int fn;
+#endif
+#else
+#ifdef __STDC__
+	float __ieee754_scalbf(float x, float fn)
+#else
+	float __ieee754_scalbf(x,fn)
+	float x, fn;
+#endif
+#endif
+{
+#ifdef _SCALB_INT
+	return scalbnf(x,fn);
+#else
+	if (isnanf(x)||isnanf(fn)) return x*fn;
+	if (!finitef(fn)) {
+	    if(fn>(float)0.0) return x*fn;
+	    else       return x/(-fn);
+	}
+	if (rintf(fn)!=fn) return (fn-fn)/(fn-fn);
+	if ( fn > (float)65000.0) return scalbnf(x, 65000);
+	if (-fn > (float)65000.0) return scalbnf(x,-65000);
+	return scalbnf(x,(int)fn);
+#endif
+}

lib/msun/src/e_sinh.c

@@ -0,0 +1,86 @@
+/* @(#)e_sinh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_sinh.c,v 1.5 1994/08/18 23:06:03 jtc Exp $";
+#endif
+
+/* __ieee754_sinh(x)
+ * Method : 
+ * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
+ *	1. Replace x by |x| (sinh(-x) = -sinh(x)). 
+ *	2. 
+ *		                                    E + E/(E+1)
+ *	    0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
+ *			       			        2
+ *
+ *	    22       <= x <= lnovft :  sinh(x) := exp(x)/2 
+ *	    lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
+ *	    ln2ovft  <  x	    :  sinh(x) := x*shuge (overflow)
+ *
+ * Special cases:
+ *	sinh(x) is |x| if x is +INF, -INF, or NaN.
+ *	only sinh(0)=0 is exact for finite x.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double one = 1.0, shuge = 1.0e307;
+#else
+static double one = 1.0, shuge = 1.0e307;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_sinh(double x)
+#else
+	double __ieee754_sinh(x)
+	double x;
+#endif
+{	
+	double t,w,h;
+	int32_t ix,jx;
+	u_int32_t lx;
+
+    /* High word of |x|. */
+	GET_HIGH_WORD(jx,x);
+	ix = jx&0x7fffffff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7ff00000) return x+x;	
+
+	h = 0.5;
+	if (jx<0) h = -h;
+    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
+	if (ix < 0x40360000) {		/* |x|<22 */
+	    if (ix<0x3e300000) 		/* |x|<2**-28 */
+		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
+	    t = expm1(fabs(x));
+	    if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
+	    return h*(t+t/(t+one));
+	}
+
+    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
+	if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));
+
+    /* |x| in [log(maxdouble), overflowthresold] */
+	GET_LOW_WORD(lx,x);
+	if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d)) {
+	    w = __ieee754_exp(0.5*fabs(x));
+	    t = h*w;
+	    return t*w;
+	}
+
+    /* |x| > overflowthresold, sinh(x) overflow */
+	return x*shuge;
+}

lib/msun/src/e_sinhf.c

@@ -0,0 +1,68 @@
+/* e_sinhf.c -- float version of e_sinh.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_sinhf.c,v 1.2 1994/08/18 23:06:04 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const float one = 1.0, shuge = 1.0e37;
+#else
+static float one = 1.0, shuge = 1.0e37;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_sinhf(float x)
+#else
+	float __ieee754_sinhf(x)
+	float x;
+#endif
+{	
+	float t,w,h;
+	int32_t ix,jx;
+
+	GET_FLOAT_WORD(jx,x);
+	ix = jx&0x7fffffff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7f800000) return x+x;	
+
+	h = 0.5;
+	if (jx<0) h = -h;
+    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
+	if (ix < 0x41b00000) {		/* |x|<22 */
+	    if (ix<0x31800000) 		/* |x|<2**-28 */
+		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
+	    t = expm1f(fabsf(x));
+	    if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one));
+	    return h*(t+t/(t+one));
+	}
+
+    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
+	if (ix < 0x42b17180)  return h*__ieee754_expf(fabsf(x));
+
+    /* |x| in [log(maxdouble), overflowthresold] */
+	if (ix<=0x42b2d4fc) {
+	    w = __ieee754_expf((float)0.5*fabsf(x));
+	    t = h*w;
+	    return t*w;
+	}
+
+    /* |x| > overflowthresold, sinh(x) overflow */
+	return x*shuge;
+}

lib/msun/src/e_sqrt.c

@@ -0,0 +1,453 @@
+/* @(#)e_sqrt.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_sqrt.c,v 1.6 1994/08/18 23:06:06 jtc Exp $";
+#endif
+
+/* __ieee754_sqrt(x)
+ * Return correctly rounded sqrt.
+ *           ------------------------------------------
+ *	     |  Use the hardware sqrt if you have one |
+ *           ------------------------------------------
+ * Method: 
+ *   Bit by bit method using integer arithmetic. (Slow, but portable) 
+ *   1. Normalization
+ *	Scale x to y in [1,4) with even powers of 2: 
+ *	find an integer k such that  1 <= (y=x*2^(2k)) < 4, then
+ *		sqrt(x) = 2^k * sqrt(y)
+ *   2. Bit by bit computation
+ *	Let q  = sqrt(y) truncated to i bit after binary point (q = 1),
+ *	     i							 0
+ *                                     i+1         2
+ *	    s  = 2*q , and	y  =  2   * ( y - q  ).		(1)
+ *	     i      i            i                 i
+ *                                                        
+ *	To compute q    from q , one checks whether 
+ *		    i+1       i                       
+ *
+ *			      -(i+1) 2
+ *			(q + 2      ) <= y.			(2)
+ *     			  i
+ *							      -(i+1)
+ *	If (2) is false, then q   = q ; otherwise q   = q  + 2      .
+ *		 	       i+1   i             i+1   i
+ *
+ *	With some algebric manipulation, it is not difficult to see
+ *	that (2) is equivalent to 
+ *                             -(i+1)
+ *			s  +  2       <= y			(3)
+ *			 i                i
+ *
+ *	The advantage of (3) is that s  and y  can be computed by 
+ *				      i      i
+ *	the following recurrence formula:
+ *	    if (3) is false
+ *
+ *	    s     =  s  ,	y    = y   ;			(4)
+ *	     i+1      i		 i+1    i
+ *
+ *	    otherwise,
+ *                         -i                     -(i+1)
+ *	    s	  =  s  + 2  ,  y    = y  -  s  - 2  		(5)
+ *           i+1      i          i+1    i     i
+ *				
+ *	One may easily use induction to prove (4) and (5). 
+ *	Note. Since the left hand side of (3) contain only i+2 bits,
+ *	      it does not necessary to do a full (53-bit) comparison 
+ *	      in (3).
+ *   3. Final rounding
+ *	After generating the 53 bits result, we compute one more bit.
+ *	Together with the remainder, we can decide whether the
+ *	result is exact, bigger than 1/2ulp, or less than 1/2ulp
+ *	(it will never equal to 1/2ulp).
+ *	The rounding mode can be detected by checking whether
+ *	huge + tiny is equal to huge, and whether huge - tiny is
+ *	equal to huge for some floating point number "huge" and "tiny".
+ *		
+ * Special cases:
+ *	sqrt(+-0) = +-0 	... exact
+ *	sqrt(inf) = inf
+ *	sqrt(-ve) = NaN		... with invalid signal
+ *	sqrt(NaN) = NaN		... with invalid signal for signaling NaN
+ *
+ * Other methods : see the appended file at the end of the program below.
+ *---------------
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static	const double	one	= 1.0, tiny=1.0e-300;
+#else
+static	double	one	= 1.0, tiny=1.0e-300;
+#endif
+
+#ifdef __STDC__
+	double __ieee754_sqrt(double x)
+#else
+	double __ieee754_sqrt(x)
+	double x;
+#endif
+{
+	double z;
+	int32_t sign = (int)0x80000000; 
+	int32_t ix0,s0,q,m,t,i;
+	u_int32_t r,t1,s1,ix1,q1;
+
+	EXTRACT_WORDS(ix0,ix1,x);
+
+    /* take care of Inf and NaN */
+	if((ix0&0x7ff00000)==0x7ff00000) {			
+	    return x*x+x;		/* sqrt(NaN)=NaN, sqrt(+inf)=+inf
+					   sqrt(-inf)=sNaN */
+	} 
+    /* take care of zero */
+	if(ix0<=0) {
+	    if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
+	    else if(ix0<0)
+		return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */
+	}
+    /* normalize x */
+	m = (ix0>>20);
+	if(m==0) {				/* subnormal x */
+	    while(ix0==0) {
+		m -= 21;
+		ix0 |= (ix1>>11); ix1 <<= 21;
+	    }
+	    for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
+	    m -= i-1;
+	    ix0 |= (ix1>>(32-i));
+	    ix1 <<= i;
+	}
+	m -= 1023;	/* unbias exponent */
+	ix0 = (ix0&0x000fffff)|0x00100000;
+	if(m&1){	/* odd m, double x to make it even */
+	    ix0 += ix0 + ((ix1&sign)>>31);
+	    ix1 += ix1;
+	}
+	m >>= 1;	/* m = [m/2] */
+
+    /* generate sqrt(x) bit by bit */
+	ix0 += ix0 + ((ix1&sign)>>31);
+	ix1 += ix1;
+	q = q1 = s0 = s1 = 0;	/* [q,q1] = sqrt(x) */
+	r = 0x00200000;		/* r = moving bit from right to left */
+
+	while(r!=0) {
+	    t = s0+r; 
+	    if(t<=ix0) { 
+		s0   = t+r; 
+		ix0 -= t; 
+		q   += r; 
+	    } 
+	    ix0 += ix0 + ((ix1&sign)>>31);
+	    ix1 += ix1;
+	    r>>=1;
+	}
+
+	r = sign;
+	while(r!=0) {
+	    t1 = s1+r; 
+	    t  = s0;
+	    if((t<ix0)||((t==ix0)&&(t1<=ix1))) { 
+		s1  = t1+r;
+		if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
+		ix0 -= t;
+		if (ix1 < t1) ix0 -= 1;
+		ix1 -= t1;
+		q1  += r;
+	    }
+	    ix0 += ix0 + ((ix1&sign)>>31);
+	    ix1 += ix1;
+	    r>>=1;
+	}
+
+    /* use floating add to find out rounding direction */
+	if((ix0|ix1)!=0) {
+	    z = one-tiny; /* trigger inexact flag */
+	    if (z>=one) {
+	        z = one+tiny;
+	        if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;}
+		else if (z>one) {
+		    if (q1==(u_int32_t)0xfffffffe) q+=1;
+		    q1+=2; 
+		} else
+	            q1 += (q1&1);
+	    }
+	}
+	ix0 = (q>>1)+0x3fe00000;
+	ix1 =  q1>>1;
+	if ((q&1)==1) ix1 |= sign;
+	ix0 += (m <<20);
+	INSERT_WORDS(z,ix0,ix1);
+	return z;
+}
+
+/*
+Other methods  (use floating-point arithmetic)
+-------------
+(This is a copy of a drafted paper by Prof W. Kahan 
+and K.C. Ng, written in May, 1986)
+
+	Two algorithms are given here to implement sqrt(x) 
+	(IEEE double precision arithmetic) in software.
+	Both supply sqrt(x) correctly rounded. The first algorithm (in
+	Section A) uses newton iterations and involves four divisions.
+	The second one uses reciproot iterations to avoid division, but
+	requires more multiplications. Both algorithms need the ability
+	to chop results of arithmetic operations instead of round them, 
+	and the INEXACT flag to indicate when an arithmetic operation
+	is executed exactly with no roundoff error, all part of the 
+	standard (IEEE 754-1985). The ability to perform shift, add,
+	subtract and logical AND operations upon 32-bit words is needed
+	too, though not part of the standard.
+
+A.  sqrt(x) by Newton Iteration
+
+   (1)	Initial approximation
+
+	Let x0 and x1 be the leading and the trailing 32-bit words of
+	a floating point number x (in IEEE double format) respectively 
+
+	    1    11		     52				  ...widths
+	   ------------------------------------------------------
+	x: |s|	  e     |	      f				|
+	   ------------------------------------------------------
+	      msb    lsb  msb				      lsb ...order
+
+ 
+	     ------------------------  	     ------------------------
+	x0:  |s|   e    |    f1     |	 x1: |          f2           |
+	     ------------------------  	     ------------------------
+
+	By performing shifts and subtracts on x0 and x1 (both regarded
+	as integers), we obtain an 8-bit approximation of sqrt(x) as
+	follows.
+
+		k  := (x0>>1) + 0x1ff80000;
+		y0 := k - T1[31&(k>>15)].	... y ~ sqrt(x) to 8 bits
+	Here k is a 32-bit integer and T1[] is an integer array containing
+	correction terms. Now magically the floating value of y (y's
+	leading 32-bit word is y0, the value of its trailing word is 0)
+	approximates sqrt(x) to almost 8-bit.
+
+	Value of T1:
+	static int T1[32]= {
+	0,	1024,	3062,	5746,	9193,	13348,	18162,	23592,
+	29598,	36145,	43202,	50740,	58733,	67158,	75992,	85215,
+	83599,	71378,	60428,	50647,	41945,	34246,	27478,	21581,
+	16499,	12183,	8588,	5674,	3403,	1742,	661,	130,};
+
+    (2)	Iterative refinement
+
+	Apply Heron's rule three times to y, we have y approximates 
+	sqrt(x) to within 1 ulp (Unit in the Last Place):
+
+		y := (y+x/y)/2		... almost 17 sig. bits
+		y := (y+x/y)/2		... almost 35 sig. bits
+		y := y-(y-x/y)/2	... within 1 ulp
+
+
+	Remark 1.
+	    Another way to improve y to within 1 ulp is:
+
+		y := (y+x/y)		... almost 17 sig. bits to 2*sqrt(x)
+		y := y - 0x00100006	... almost 18 sig. bits to sqrt(x)
+
+				2
+			    (x-y )*y
+		y := y + 2* ----------	...within 1 ulp
+			       2
+			     3y  + x
+
+
+	This formula has one division fewer than the one above; however,
+	it requires more multiplications and additions. Also x must be
+	scaled in advance to avoid spurious overflow in evaluating the
+	expression 3y*y+x. Hence it is not recommended uless division
+	is slow. If division is very slow, then one should use the 
+	reciproot algorithm given in section B.
+
+    (3) Final adjustment
+
+	By twiddling y's last bit it is possible to force y to be 
+	correctly rounded according to the prevailing rounding mode
+	as follows. Let r and i be copies of the rounding mode and
+	inexact flag before entering the square root program. Also we
+	use the expression y+-ulp for the next representable floating
+	numbers (up and down) of y. Note that y+-ulp = either fixed
+	point y+-1, or multiply y by nextafter(1,+-inf) in chopped
+	mode.
+
+		I := FALSE;	... reset INEXACT flag I
+		R := RZ;	... set rounding mode to round-toward-zero
+		z := x/y;	... chopped quotient, possibly inexact
+		If(not I) then {	... if the quotient is exact
+		    if(z=y) {
+		        I := i;	 ... restore inexact flag
+		        R := r;  ... restore rounded mode
+		        return sqrt(x):=y.
+		    } else {
+			z := z - ulp;	... special rounding
+		    }
+		}
+		i := TRUE;		... sqrt(x) is inexact
+		If (r=RN) then z=z+ulp	... rounded-to-nearest
+		If (r=RP) then {	... round-toward-+inf
+		    y = y+ulp; z=z+ulp;
+		}
+		y := y+z;		... chopped sum
+		y0:=y0-0x00100000;	... y := y/2 is correctly rounded.
+	        I := i;	 		... restore inexact flag
+	        R := r;  		... restore rounded mode
+	        return sqrt(x):=y.
+		    
+    (4)	Special cases
+
+	Square root of +inf, +-0, or NaN is itself;
+	Square root of a negative number is NaN with invalid signal.
+
+
+B.  sqrt(x) by Reciproot Iteration
+
+   (1)	Initial approximation
+
+	Let x0 and x1 be the leading and the trailing 32-bit words of
+	a floating point number x (in IEEE double format) respectively
+	(see section A). By performing shifs and subtracts on x0 and y0,
+	we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
+
+	    k := 0x5fe80000 - (x0>>1);
+	    y0:= k - T2[63&(k>>14)].	... y ~ 1/sqrt(x) to 7.8 bits
+
+	Here k is a 32-bit integer and T2[] is an integer array 
+	containing correction terms. Now magically the floating
+	value of y (y's leading 32-bit word is y0, the value of
+	its trailing word y1 is set to zero) approximates 1/sqrt(x)
+	to almost 7.8-bit.
+
+	Value of T2:
+	static int T2[64]= {
+	0x1500,	0x2ef8,	0x4d67,	0x6b02,	0x87be,	0xa395,	0xbe7a,	0xd866,
+	0xf14a,	0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
+	0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
+	0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
+	0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
+	0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
+	0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
+	0x1527f,0x1334a,0x11051,0xe951,	0xbe01,	0x8e0d,	0x5924,	0x1edd,};
+
+    (2)	Iterative refinement
+
+	Apply Reciproot iteration three times to y and multiply the
+	result by x to get an approximation z that matches sqrt(x)
+	to about 1 ulp. To be exact, we will have 
+		-1ulp < sqrt(x)-z<1.0625ulp.
+	
+	... set rounding mode to Round-to-nearest
+	   y := y*(1.5-0.5*x*y*y)	... almost 15 sig. bits to 1/sqrt(x)
+	   y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
+	... special arrangement for better accuracy
+	   z := x*y			... 29 bits to sqrt(x), with z*y<1
+	   z := z + 0.5*z*(1-z*y)	... about 1 ulp to sqrt(x)
+
+	Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
+	(a) the term z*y in the final iteration is always less than 1; 
+	(b) the error in the final result is biased upward so that
+		-1 ulp < sqrt(x) - z < 1.0625 ulp
+	    instead of |sqrt(x)-z|<1.03125ulp.
+
+    (3)	Final adjustment
+
+	By twiddling y's last bit it is possible to force y to be 
+	correctly rounded according to the prevailing rounding mode
+	as follows. Let r and i be copies of the rounding mode and
+	inexact flag before entering the square root program. Also we
+	use the expression y+-ulp for the next representable floating
+	numbers (up and down) of y. Note that y+-ulp = either fixed
+	point y+-1, or multiply y by nextafter(1,+-inf) in chopped
+	mode.
+
+	R := RZ;		... set rounding mode to round-toward-zero
+	switch(r) {
+	    case RN:		... round-to-nearest
+	       if(x<= z*(z-ulp)...chopped) z = z - ulp; else
+	       if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
+	       break;
+	    case RZ:case RM:	... round-to-zero or round-to--inf
+	       R:=RP;		... reset rounding mod to round-to-+inf
+	       if(x<z*z ... rounded up) z = z - ulp; else
+	       if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
+	       break;
+	    case RP:		... round-to-+inf
+	       if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
+	       if(x>z*z ...chopped) z = z+ulp;
+	       break;
+	}
+
+	Remark 3. The above comparisons can be done in fixed point. For
+	example, to compare x and w=z*z chopped, it suffices to compare
+	x1 and w1 (the trailing parts of x and w), regarding them as
+	two's complement integers.
+
+	...Is z an exact square root?
+	To determine whether z is an exact square root of x, let z1 be the
+	trailing part of z, and also let x0 and x1 be the leading and
+	trailing parts of x.
+
+	If ((z1&0x03ffffff)!=0)	... not exact if trailing 26 bits of z!=0
+	    I := 1;		... Raise Inexact flag: z is not exact
+	else {
+	    j := 1 - [(x0>>20)&1]	... j = logb(x) mod 2
+	    k := z1 >> 26;		... get z's 25-th and 26-th 
+					    fraction bits
+	    I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
+	}
+	R:= r		... restore rounded mode
+	return sqrt(x):=z.
+
+	If multiplication is cheaper then the foregoing red tape, the 
+	Inexact flag can be evaluated by
+
+	    I := i;
+	    I := (z*z!=x) or I.
+
+	Note that z*z can overwrite I; this value must be sensed if it is 
+	True.
+
+	Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
+	zero.
+
+		    --------------------
+		z1: |        f2        | 
+		    --------------------
+		bit 31		   bit 0
+
+	Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
+	or even of logb(x) have the following relations:
+
+	-------------------------------------------------
+	bit 27,26 of z1		bit 1,0 of x1	logb(x)
+	-------------------------------------------------
+	00			00		odd and even
+	01			01		even
+	10			10		odd
+	10			00		even
+	11			01		even
+	-------------------------------------------------
+
+    (4)	Special cases (see (4) of Section A).	
+ 
+ */
+ 

lib/msun/src/e_sqrtf.c

@@ -0,0 +1,97 @@
+/* e_sqrtf.c -- float version of e_sqrt.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_sqrtf.c,v 1.2 1994/08/18 23:06:07 jtc Exp $";
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static	const float	one	= 1.0, tiny=1.0e-30;
+#else
+static	float	one	= 1.0, tiny=1.0e-30;
+#endif
+
+#ifdef __STDC__
+	float __ieee754_sqrtf(float x)
+#else
+	float __ieee754_sqrtf(x)
+	float x;
+#endif
+{
+	float z;
+	int32_t sign = (int)0x80000000; 
+	int32_t ix,s,q,m,t,i;
+	u_int32_t r;
+
+	GET_FLOAT_WORD(ix,x);
+
+    /* take care of Inf and NaN */
+	if((ix&0x7f800000)==0x7f800000) {			
+	    return x*x+x;		/* sqrt(NaN)=NaN, sqrt(+inf)=+inf
+					   sqrt(-inf)=sNaN */
+	} 
+    /* take care of zero */
+	if(ix<=0) {
+	    if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
+	    else if(ix<0)
+		return (x-x)/(x-x);		/* sqrt(-ve) = sNaN */
+	}
+    /* normalize x */
+	m = (ix>>23);
+	if(m==0) {				/* subnormal x */
+	    for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
+	    m -= i-1;
+	}
+	m -= 127;	/* unbias exponent */
+	ix = (ix&0x007fffff)|0x00800000;
+	if(m&1)	/* odd m, double x to make it even */
+	    ix += ix;
+	m >>= 1;	/* m = [m/2] */
+
+    /* generate sqrt(x) bit by bit */
+	ix += ix;
+	q = s = 0;		/* q = sqrt(x) */
+	r = 0x01000000;		/* r = moving bit from right to left */
+
+	while(r!=0) {
+	    t = s+r; 
+	    if(t<=ix) { 
+		s    = t+r; 
+		ix  -= t; 
+		q   += r; 
+	    } 
+	    ix += ix;
+	    r>>=1;
+	}
+
+    /* use floating add to find out rounding direction */
+	if(ix!=0) {
+	    z = one-tiny; /* trigger inexact flag */
+	    if (z>=one) {
+	        z = one+tiny;
+		if (z>one)
+		    q += 2;
+		else
+		    q += (q&1);
+	    }
+	}
+	ix = (q>>1)+0x3f000000;
+	ix += (m <<23);
+	SET_FLOAT_WORD(z,ix);
+	return z;
+}