* Makefile:

. Hook coshl, sinhl, and tanhl into libm.
  . Create symbolic links for corresponding manpages.
  . While here remove a nearby extraneous space.

* Symbol.map:
* src/math.h:
  . Move coshl, sinhl, and tanhl to their proper locations.

* man/cosh.3:
* man/sinh.3:
* man/tanh.3:
  . Update the manpages.

* src/e_cosh.c:
* src/e_sinh.c:
* src/s_tanh.c:
  . Add weak reference for LBDL_MANT_DIG==53 targets.

* src/imprecise.c:
  . Remove the coshl, sinhl, and tanhl kludge.

* src/e_coshl.c:
  . ld80 and ld128 implementation of coshl().

* src/e_sinhl.c:
  . ld80 and ld128 implementation of sinhl().

* src/s_tanhl.c:
  . ld80 and ld128 implementation of tanhl().

Obtained from:	bde (mostly), das and kargl

lib/msun/Makefile

@@ -96,13 +96,14 @@ COMMON_SRCS+=	s_copysignl.c s_fabsl.c s_llrintl.c s_lrintl.c s_modfl.c
 .if ${LDBL_PREC} != 53
 # If long double != double use these; otherwise, we alias the double versions.
 COMMON_SRCS+=	e_acoshl.c e_acosl.c e_asinl.c e_atan2l.c e_atanhl.c \
-	e_fmodl.c e_hypotl.c e_remainderl.c e_sqrtl.c \
+	e_coshl.c e_fmodl.c e_hypotl.c \
+	e_remainderl.c e_sinhl.c e_sqrtl.c \
 	invtrig.c k_cosl.c k_sinl.c k_tanl.c \
 	s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c s_cprojl.c \
 	s_csqrtl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \
 	s_frexpl.c s_logbl.c s_logl.c s_nanl.c s_nextafterl.c \
-	s_nexttoward.c s_remquol.c s_rintl.c  s_roundl.c s_scalbnl.c \
+	s_nexttoward.c s_remquol.c s_rintl.c s_roundl.c s_scalbnl.c \
-	s_sinl.c s_tanl.c s_truncl.c w_cabsl.c
+	s_sinl.c s_tanhl.c s_tanl.c s_truncl.c w_cabsl.c
 .endif
 
 # C99 complex functions
@@ -160,7 +161,7 @@ MLINKS+=cimag.3 cimagf.3 cimag.3 cimagl.3 \
 	cimag.3 creal.3 cimag.3 crealf.3 cimag.3 creall.3
 MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3
 MLINKS+=cos.3 cosf.3 cos.3 cosl.3
-MLINKS+=cosh.3 coshf.3
+MLINKS+=cosh.3 coshf.3 cosh.3 coshl.3
 MLINKS+=csqrt.3 csqrtf.3 csqrt.3 csqrtl.3
 MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3
 MLINKS+=exp.3 expm1.3 exp.3 expm1f.3 exp.3 expm1l.3 exp.3 pow.3 exp.3 powf.3 \
@@ -208,11 +209,11 @@ MLINKS+=round.3 roundf.3 round.3 roundl.3
 MLINKS+=scalbn.3 scalbln.3 scalbn.3 scalblnf.3 scalbn.3 scalblnl.3
 MLINKS+=scalbn.3 scalbnf.3 scalbn.3 scalbnl.3
 MLINKS+=sin.3 sinf.3 sin.3 sinl.3
-MLINKS+=sinh.3 sinhf.3
+MLINKS+=sinh.3 sinhf.3 sinh.3 sinhl.3
 MLINKS+=sqrt.3 cbrt.3 sqrt.3 cbrtf.3 sqrt.3 cbrtl.3 sqrt.3 sqrtf.3 \
 	sqrt.3 sqrtl.3
 MLINKS+=tan.3 tanf.3 tan.3 tanl.3
-MLINKS+=tanh.3 tanhf.3
+MLINKS+=tanh.3 tanhf.3 tanh.3 tanhl.3
 MLINKS+=trunc.3 truncf.3 trunc.3 truncl.3
 
 .include <bsd.lib.mk>

lib/msun/Symbol.map

@@ -260,6 +260,7 @@ FBSD_1.3 {
 	ccosf;
 	ccosh;
 	ccoshf;
+	coshl;
 	ctan;
 	ctanf;
 	ctanh;
@@ -270,13 +271,12 @@ FBSD_1.3 {
 	log1pl;
 	log2l;
 	logl;
+	sinhl;
+	tanhl;
 	/* Implemented as weak aliases for imprecise versions */
-	coshl;
 	erfcl;
 	erfl;
 	lgammal;
 	powl;
-	sinhl;
-	tanhl;
 	tgammal;
 };

lib/msun/man/cosh.3

@@ -28,12 +28,13 @@
 .\"     from: @(#)cosh.3	5.1 (Berkeley) 5/2/91
 .\" $FreeBSD$
 .\"
-.Dd January 14, 2005
+.Dd August 17, 2013
 .Dt COSH 3
 .Os
 .Sh NAME
 .Nm cosh ,
-.Nm coshf
+.Nm coshf ,
+.Nm coshl
 .Nd hyperbolic cosine functions
 .Sh LIBRARY
 .Lb libm
@@ -43,11 +44,14 @@
 .Fn cosh "double x"
 .Ft float
 .Fn coshf "float x"
+.Ft long double
+.Fn coshl "long double x"
 .Sh DESCRIPTION
 The
-.Fn cosh
+.Fn cosh ,
+.Fn coshf ,
 and the
-.Fn coshf
+.Fn coshl
 functions compute the hyperbolic cosine of
 .Fa x .
 .Sh SEE ALSO

lib/msun/man/sinh.3

@@ -42,11 +42,14 @@
 .Fn sinh "double x"
 .Ft float
 .Fn sinhf "float x"
+.Ft long double
+.Fn sinhl "long double x"
 .Sh DESCRIPTION
 The
-.Fn sinh
+.Fn sinh ,
+.Fn sinhf ,
 and the
-.Fn sinhf
+.Fn sinhl
 functions compute the hyperbolic sine of
 .Fa x .
 .Sh SEE ALSO

lib/msun/man/tanh.3

@@ -28,12 +28,13 @@
 .\"     from: @(#)tanh.3	5.1 (Berkeley) 5/2/91
 .\" $FreeBSD$
 .\"
-.Dd May 2, 1991
+.Dd August 17, 2013
 .Dt TANH 3
 .Os
 .Sh NAME
 .Nm tanh ,
-.Nm tanhf
+.Nm tanhf ,
+.Nm tanhl
 .Nd hyperbolic tangent functions
 .Sh LIBRARY
 .Lb libm
@@ -43,20 +44,24 @@
 .Fn tanh "double x"
 .Ft float
 .Fn tanhf "float x"
+.Ft long double
+.Fn tanhl "long double x"
 .Sh DESCRIPTION
 The
-.Fn tanh
+.Fn tanh ,
+.Fn tanhf ,
 and the
-.Fn tanhf
+.Fn tanhl
 functions compute the hyperbolic tangent of
 .Fa x .
 For a discussion of error due to roundoff, see
 .Xr math 3 .
 .Sh RETURN VALUES
 The
-.Fn tanh
+.Fn tanh ,
+.Fn tanhf ,
 and the
-.Fn tanhf
+.Fn tanhl
 functions return the hyperbolic tangent value.
 .Sh SEE ALSO
 .Xr acos 3 ,

lib/msun/src/e_cosh.c

@@ -35,6 +35,8 @@ __FBSDID("$FreeBSD$");
  *	only cosh(0)=1 is exact for finite x.
  */
 
+#include <float.h>
+
 #include "math.h"
 #include "math_private.h"
 
@@ -77,3 +79,7 @@ __ieee754_cosh(double x)
     /* |x| > overflowthresold, cosh(x) overflow */
 	return huge*huge;
 }
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(cosh, coshl);
+#endif

lib/msun/src/e_coshl.c

@@ -0,0 +1,130 @@
+/* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See e_cosh.c for complete comments.
+ *
+ * Converted to long double by Bruce D. Evans.
+ */
+
+#include <float.h>
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+#include "k_expl.h"
+
+#if LDBL_MAX_EXP != 0x4000
+/* We also require the usual expsign encoding. */
+#error "Unsupported long double format"
+#endif
+
+#define	BIAS	(LDBL_MAX_EXP - 1)
+
+static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L;
+#if LDBL_MANT_DIG == 64
+/*
+ * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]:
+ * |cosh(x) - c(x)| < 2**-68.8
+ */
+static const union IEEEl2bits
+C4u = LD80C(0xaaaaaaaaaaaaac78, -5,  4.16666666666666682297e-2L);
+#define	C4	C4u.e
+static const double
+C2  =  0.5,
+C6  =  1.3888888888888616e-3,		/*  0x16c16c16c16b99.0p-62 */
+C8  =  2.4801587301767953e-5,		/*  0x1a01a01a027061.0p-68 */
+C10 =  2.7557319163300398e-7,		/*  0x127e4fb6c9b55f.0p-74 */
+C12 =  2.0876768371393075e-9,		/*  0x11eed99406a3f4.0p-81 */
+C14 =  1.1469537039374480e-11,		/*  0x1938c67cd18c48.0p-89 */
+C16 =  4.8473490896852041e-14;		/*  0x1b49c429701e45.0p-97 */
+#elif LDBL_MANT_DIG == 113
+/*
+ * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]:
+ * |cosh(x) - c(x)| < 2**-121.69
+ */
+static const long double
+C4  =  4.16666666666666666666666666666666225e-2L,	/*  0x1555555555555555555555555554e.0p-117L */
+C6  =  1.38888888888888888888888888889434831e-3L,	/*  0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */
+C8  =  2.48015873015873015873015871870962089e-5L,	/*  0x1a01a01a01a01a01a01a017af2756.0p-128L */
+C10 =  2.75573192239858906525574318600800201e-7L,	/*  0x127e4fb7789f5c72ef01c8a040640.0p-134L */
+C12 =  2.08767569878680989791444691755468269e-9L,	/*  0x11eed8eff8d897b543d0679607399.0p-141L */
+C14=  1.14707455977297247387801189650495351e-11L,	/*  0x193974a8c07c9d24ae169a7fa9b54.0p-149L */
+C16 =  4.77947733238737883626416876486279985e-14L;	/*  0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */
+static const double
+C2  =  0.5,
+C18 =  1.5619206968597871e-16,		/*  0x16827863b9900b.0p-105 */
+C20 =  4.1103176218528049e-19,		/*  0x1e542ba3d3c269.0p-114 */
+C22 =  8.8967926401641701e-22,		/*  0x10ce399542a014.0p-122 */
+C24 =  1.6116681626523904e-24,		/*  0x1f2c981d1f0cb7.0p-132 */
+C26 =  2.5022374732804632e-27;		/*  0x18c7ecf8b2c4a0.0p-141 */
+#else
+#error "Unsupported long double format"
+#endif /* LDBL_MANT_DIG == 64 */
+
+/* log(2**16385 - 0.5) rounded towards up: */
+static const float
+o_threshold =  1.13572168e4;		/*  0xb174de.0p-10 */
+
+long double
+coshl(long double x)
+{
+	long double hi,lo,x2,x4;
+	double dx2;
+	uint16_t ix;
+
+	GET_LDBL_EXPSIGN(ix,x);
+	ix &= 0x7fff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7fff) return x*x;
+
+	ENTERI();
+
+    /* |x| < 1, return 1 or c(x) */
+	if(ix<0x3fff) {
+	    if (ix<BIAS-(LDBL_MANT_DIG+1)/2) 	/* |x| < TINY */
+		RETURNI(1+tiny);	/* cosh(tiny) = 1(+) with inexact */
+	    x2 = x*x;
+#if LDBL_MANT_DIG == 64
+	    x4 = x2*x2;
+	    RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) +
+		((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1);
+#elif LDBL_MANT_DIG == 113
+	    dx2 = x2;
+	    RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 +
+		C20)*x2 + C18)*x2 +
+		C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 +
+		C4)*(x2*x2) + C2*x2 + 1);
+#endif
+	}
+
+    /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */
+	if (ix < 0x4005) {
+	    k_hexpl(fabsl(x), &hi, &lo);
+	    RETURNI(lo + 0.25/(hi + lo) + hi);
+	}
+
+    /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */
+	if (fabsl(x) <= o_threshold)
+	    RETURNI(hexpl(fabsl(x)));
+
+    /* |x| > o_threshold, cosh(x) overflow */
+	RETURNI(huge*huge);
+}

lib/msun/src/e_sinh.c

@@ -32,6 +32,8 @@ __FBSDID("$FreeBSD$");
  *	only sinh(0)=0 is exact for finite x.
  */
 
+#include <float.h>
+
 #include "math.h"
 #include "math_private.h"
 
@@ -71,3 +73,7 @@ __ieee754_sinh(double x)
     /* |x| > overflowthresold, sinh(x) overflow */
 	return x*shuge;
 }
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(sinh, sinhl);
+#endif

lib/msun/src/e_sinhl.c

@@ -0,0 +1,131 @@
+/* from: FreeBSD: head/lib/msun/src/e_sinhl.c XXX */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See e_sinh.c for complete comments.
+ *
+ * Converted to long double by Bruce D. Evans.
+ */
+
+#include <float.h>
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+#include "k_expl.h"
+
+#if LDBL_MAX_EXP != 0x4000
+/* We also require the usual expsign encoding. */
+#error "Unsupported long double format"
+#endif
+
+#define	BIAS	(LDBL_MAX_EXP - 1)
+
+static const long double shuge = 0x1p16383L;
+#if LDBL_MANT_DIG == 64
+/*
+ * Domain [-1, 1], range ~[-6.6749e-22, 6.6749e-22]:
+ * |sinh(x)/x - s(x)| < 2**-70.3
+ */
+static const union IEEEl2bits
+S3u = LD80C(0xaaaaaaaaaaaaaaaa, -3,  1.66666666666666666658e-1L);
+#define	S3	S3u.e
+static const double
+S5  =  8.3333333333333332e-3,		/*  0x11111111111111.0p-59 */
+S7  =  1.9841269841270074e-4,		/*  0x1a01a01a01a070.0p-65 */
+S9  =  2.7557319223873889e-6,		/*  0x171de3a5565fe6.0p-71 */
+S11 =  2.5052108406704084e-8,		/*  0x1ae6456857530f.0p-78 */
+S13 =  1.6059042748655297e-10,		/*  0x161245fa910697.0p-85 */
+S15 =  7.6470006914396920e-13,		/*  0x1ae7ce4eff2792.0p-93 */
+S17 =  2.8346142308424267e-15;		/*  0x19882ce789ffc6.0p-101 */
+#elif LDBL_MANT_DIG == 113
+/*
+ * Domain [-1, 1], range ~[-2.9673e-36, 2.9673e-36]:
+ * |sinh(x)/x - s(x)| < 2**-118.0
+ */
+static const long double
+S3  =  1.66666666666666666666666666666666033e-1L,	/*  0x1555555555555555555555555553b.0p-115L */
+S5  =  8.33333333333333333333333333337643193e-3L,	/*  0x111111111111111111111111180f5.0p-119L */
+S7  =  1.98412698412698412698412697391263199e-4L,	/*  0x1a01a01a01a01a01a01a0176aad11.0p-125L */
+S9  =  2.75573192239858906525574406205464218e-6L,	/*  0x171de3a556c7338faac243aaa9592.0p-131L */
+S11 =  2.50521083854417187749675637460977997e-8L,	/*  0x1ae64567f544e38fe59b3380d7413.0p-138L */
+S13 =  1.60590438368216146368737762431552702e-10L,	/*  0x16124613a86d098059c7620850fc2.0p-145L */
+S15 =  7.64716373181980539786802470969096440e-13L,	/*  0x1ae7f3e733b814193af09ce723043.0p-153L */
+S17 =  2.81145725434775409870584280722701574e-15L;	/*  0x1952c77030c36898c3fd0b6dfc562.0p-161L */
+static const double
+S19=  8.2206352435411005e-18,		/*  0x12f49b4662b86d.0p-109 */
+S21=  1.9572943931418891e-20,		/*  0x171b8f2fab9628.0p-118 */
+S23 =  3.8679983530666939e-23,		/*  0x17617002b73afc.0p-127 */
+S25 =  6.5067867911512749e-26;		/*  0x1423352626048a.0p-136 */
+#else
+#error "Unsupported long double format"
+#endif /* LDBL_MANT_DIG == 64 */
+
+/* log(2**16385 - 0.5) rounded towards up: */
+static const float
+o_threshold =  1.13572168e4;		/*  0xb174de.0p-10 */
+
+long double
+sinhl(long double x)
+{
+	long double hi,lo,x2,x4;
+	double dx2,s;
+	int16_t ix,jx;
+
+	GET_LDBL_EXPSIGN(jx,x);
+	ix = jx&0x7fff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7fff) return x+x;
+
+	ENTERI();
+
+	s = 1;
+	if (jx<0) s = -1;
+
+    /* |x| < 64, return x, s(x), or accurate s*(exp(|x|)/2-1/exp(|x|)/2) */
+	if (ix<0x4005) {		/* |x|<64 */
+	    if (ix<BIAS-(LDBL_MANT_DIG+1)/2) 	/* |x|<TINY */
+		if(shuge+x>1) RETURNI(x);  /* sinh(tiny) = tiny with inexact */
+	    if (ix<0x3fff) {		/* |x|<1 */
+		x2 = x*x;
+#if LDBL_MANT_DIG == 64
+		x4 = x2*x2;
+		RETURNI(((S17*x2 + S15)*x4 + (S13*x2 + S11))*(x2*x*x4*x4) +
+		    ((S9*x2 + S7)*x2 + S5)*(x2*x*x2) + S3*(x2*x) + x);
+#elif LDBL_MANT_DIG == 113
+		dx2 = x2;
+		RETURNI(((((((((((S25*dx2 + S23)*dx2 +
+		    S21)*x2 + S19)*x2 +
+		    S17)*x2 + S15)*x2 + S13)*x2 + S11)*x2 + S9)*x2 + S7)*x2 +
+		    S5)* (x2*x*x2) +
+		    S3*(x2*x) + x);
+#endif
+	    }
+	    k_hexpl(fabsl(x), &hi, &lo);
+	    RETURNI(s*(lo - 0.25/(hi + lo) + hi));
+	}
+
+    /* |x| in [64, o_threshold], return correctly-overflowing s*exp(|x|)/2 */
+	if (fabsl(x) <= o_threshold)
+	    RETURNI(s*hexpl(fabsl(x)));
+
+    /* |x| > o_threshold, sinh(x) overflow */
+	return x*shuge;
+}

lib/msun/src/imprecise.c

@@ -60,10 +60,7 @@ DECLARE_WEAK(powl);
 	long double imprecise_ ## f ## l(long double v) { return f(v); }\
 	DECLARE_WEAK(f ## l)
 
-DECLARE_IMPRECISE(cosh);
 DECLARE_IMPRECISE(erfc);
 DECLARE_IMPRECISE(erf);
 DECLARE_IMPRECISE(lgamma);
-DECLARE_IMPRECISE(sinh);
-DECLARE_IMPRECISE(tanh);
 DECLARE_IMPRECISE(tgamma);

lib/msun/src/math.h

@@ -451,6 +451,7 @@ long double	atanl(long double);
 long double	cbrtl(long double);
 long double	ceill(long double);
 long double	copysignl(long double, long double) __pure2;
+long double	coshl(long double);
 long double	cosl(long double);
 long double	exp2l(long double);
 long double	expl(long double);
@@ -488,8 +489,10 @@ long double	rintl(long double);
 long double	roundl(long double);
 long double	scalblnl(long double, long);
 long double	scalbnl(long double, int);
+long double	sinhl(long double);
 long double	sinl(long double);
 long double	sqrtl(long double);
+long double	tanhl(long double);
 long double	tanl(long double);
 long double	truncl(long double);
 
@@ -510,13 +513,10 @@ __END_DECLS
  */
 __BEGIN_DECLS
 
-long double	coshl(long double);
 long double	erfcl(long double);
 long double	erfl(long double);
 long double	lgammal(long double);
 long double	powl(long double, long double);
-long double	sinhl(long double);
-long double	tanhl(long double);
 long double	tgammal(long double);
 
 __END_DECLS

lib/msun/src/s_tanh.c

@@ -37,6 +37,8 @@ __FBSDID("$FreeBSD$");
  *	only tanh(0)=0 is exact for finite argument.
  */
 
+#include <float.h>
+
 #include "math.h"
 #include "math_private.h"
 
@@ -75,3 +77,7 @@ tanh(double x)
 	}
 	return (jx>=0)? z: -z;
 }
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(tanh, tanhl);
+#endif

lib/msun/src/s_tanhl.c

@@ -0,0 +1,164 @@
+/* from: FreeBSD: head/lib/msun/src/s_tanhl.c XXX */
+
+/* @(#)s_tanh.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.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See s_tanh.c for complete comments.
+ *
+ * Converted to long double by Bruce D. Evans.
+ */
+
+#include <float.h>
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+
+#include "math.h"
+#include "math_private.h"
+#include "fpmath.h"
+#include "k_expl.h"
+
+#if LDBL_MAX_EXP != 0x4000
+/* We also require the usual expsign encoding. */
+#error "Unsupported long double format"
+#endif
+
+#define	BIAS	(LDBL_MAX_EXP - 1)
+
+static const volatile double tiny = 1.0e-300;
+static const double one = 1.0;
+#if LDBL_MANT_DIG == 64
+/*
+ * Domain [-0.25, 0.25], range ~[-1.6304e-22, 1.6304e-22]:
+ * |tanh(x)/x - t(x)| < 2**-72.3
+ */
+static const union IEEEl2bits
+T3u = LD80C(0xaaaaaaaaaaaaaa9f, -2, -3.33333333333333333017e-1L);
+#define	T3	T3u.e
+static const double
+T5  =  1.3333333333333314e-1,		/*  0x1111111111110a.0p-55 */
+T7  = -5.3968253968210485e-2,		/* -0x1ba1ba1ba1a1a1.0p-57 */
+T9  =  2.1869488531393817e-2,		/*  0x1664f488172022.0p-58 */
+T11 = -8.8632352345964591e-3,		/* -0x1226e34bc138d5.0p-59 */
+T13 =  3.5921169709993771e-3,		/*  0x1d6d371d3e400f.0p-61 */
+T15 = -1.4555786415756001e-3,		/* -0x17d923aa63814d.0p-62 */
+T17 =  5.8645267876296793e-4,		/*  0x13378589b85aa7.0p-63 */
+T19 = -2.1121033571392224e-4;		/* -0x1baf0af80c4090.0p-65 */
+#elif LDBL_MANT_DIG == 113
+/*
+ * Domain [-0.25, 0.25], range ~[-2.4211e-37, 2.4211e-37]:
+ * |tanh(x)/x - t(x)| < 2**121.6
+ */
+static const long double
+T3 = -3.33333333333333333333333333333332980e-1L,	/* -0x1555555555555555555555555554e.0p-114L */
+T5  =  1.33333333333333333333333333332707260e-1L,	/*  0x1111111111111111111111110ab7b.0p-115L */
+T7  = -5.39682539682539682539682535723482314e-2L,	/* -0x1ba1ba1ba1ba1ba1ba1ba17b5fc98.0p-117L */
+T9  =  2.18694885361552028218693591149061717e-2L,	/*  0x1664f4882c10f9f32d6b1a12a25e5.0p-118L */
+T11 = -8.86323552990219656883762347736381851e-3L,	/* -0x1226e355e6c23c8f5a5a0f386cb4d.0p-119L */
+T13 =  3.59212803657248101358314398220822722e-3L,	/*  0x1d6d3d0e157ddfb403ad3637442c6.0p-121L */
+T15 = -1.45583438705131796512568010348874662e-3L;	/* -0x17da36452b75e150c44cc34253b34.0p-122L */
+static const double
+T17 =  5.9002744094556621e-4,		/*  0x1355824803668e.0p-63 */
+T19 = -2.3912911424260516e-4,		/* -0x1f57d7734c8dde.0p-65 */
+T21 =  9.6915379535512898e-5,		/*  0x1967e18ad6a6ca.0p-66 */
+T23 = -3.9278322983156353e-5,		/* -0x1497d8e6b75729.0p-67 */
+T25 =  1.5918887220143869e-5,		/*  0x10b1319998cafa.0p-68 */
+T27 = -6.4514295231630956e-6,		/* -0x1b0f2b71b218eb.0p-70 */
+T29 =  2.6120754043964365e-6,		/*  0x15e963a3cf3a39.0p-71 */
+T31 = -1.0407567231003314e-6,		/* -0x1176041e656869.0p-72 */
+T33 =  3.4744117554063574e-7;		/*  0x1750fe732cab9c.0p-74 */
+#endif /* LDBL_MANT_DIG == 64 */
+
+static inline long double
+divl(long double a, long double b, long double c, long double d,
+    long double e, long double f)
+{
+	long double inv, r, w;
+	float fr, fw;
+	uint32_t hx;
+
+	_2sumF(a, c);
+	b = b + c;
+	_2sumF(d, f);
+	e = e + f;
+
+	inv = 1 / (d + e);
+
+	r = (a + b) * inv;
+	fr = r;
+	r = fr;
+
+	fw = d + e;
+	e = d - fw + e;
+	d = fw;
+
+	r = r + (a - d * r + b - e * r) * inv;
+
+	return r;
+}
+
+long double
+tanhl(long double x)
+{
+	long double hi,lo,s,x2,x4,z;
+	double dx2;
+	int16_t jx,ix;
+
+	GET_LDBL_EXPSIGN(jx,x);
+	ix = jx&0x7fff;
+
+    /* x is INF or NaN */
+	if(ix>=0x7fff) {
+	    if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
+	    else       return one/x-one;    /* tanh(NaN) = NaN */
+	}
+
+	ENTERI();
+
+	if (fabsl(x) < 40) {	/* |x|<40 */
+	    if (__predict_false(ix<BIAS-(LDBL_MANT_DIG+1)/2)) {	/* |x|<TINY */
+		/* tanh(+-0) = +0; tanh(tiny) = tiny(-+) with inexact: */
+		return (x == 0 ? x : (0x1p200 * x - x) * 0x1p-200);
+	    }
+	    if (fabsl(x) < 0.25) {		/* |x|<0.25 */
+		x2 = x*x;
+#if LDBL_MANT_DIG == 64
+		x4 = x2*x2;
+		RETURNI(((T19*x2 + T17)*x4 + (T15*x2 + T13))*(x2*x*x2*x4*x4) +
+		    ((T11*x2 + T9)*x4 + (T7*x2 + T5))*(x2*x*x2) +
+		    T3*(x2*x) + x);
+#elif LDBL_MANT_DIG == 113
+		dx2 = x2;
+		RETURNI(((((((((((((((T33*dx2 + T31)*dx2 + T29)*dx2 + T27)*dx2 +
+		    T25)*x2 + T23)*x2 + T21)*x2 + T19)*x2 + T17)*x2 +
+		    T15)*x2 + T13)*x2 + T11)*x2 + T9)*x2 + T7)*x2 + T5)*
+		    (x2*x*x2) +
+		    T3*(x2*x) + x);
+#endif
+	    }
+	    k_hexpl(2*fabsl(x), &hi, &lo);
+	    if (fabsl(x) < 1.5)	/* |x|<1.5 */
+		z = divl(hi, lo, -0.5, hi, lo, 0.5);
+	    else
+		z = one - one/(lo+0.5+hi);
+    /* |x| >= 40, return +-1 */
+	} else {
+	    z = one - tiny;		/* raise inexact flag */
+	}
+	s = 1;
+	if (jx<0) s = -1;
+	RETURNI(s*z);
+}