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freebsd-nq/lib/msun/i387/e_acos.S

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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
1994-08-19 09:40:01 +00:00
/*
* 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> instead of kernel-only <machine/asmacros.h>.
1997-03-09 14:01:11 +00:00
#include <machine/asm.h>
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
1994-08-19 09:40:01 +00:00
$Id$ -> $FreeBSD$
1999-08-28 00:22:10 +00:00
RCSID("$FreeBSD$")
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
1994-08-19 09:40:01 +00:00
Compute (1 - x^2) as ((1 - x) * (1 + x)) instead of as (1 - x * x) to avoid easily avoidable loss of precision when |x| is nearly 1. Extended (64-bit) precision only moves the meaning of "nearly" here. This probably could be done better by splitting up the range into |x| <= 0.5 and |x| > 0.5 like the C version. However, ucbtest does't report any errors in this version. Perhaps the C version should be used anyway. It's only 25% slower now on a P5, provided the C version of sqrt() isn't used, and the C version could be optimized better. Errors checked by: ucbtest
1997-02-20 12:37:49 +00:00
/*
* acos(x) = atan2(sqrt(1 - x^2, x).
* Actually evaluate (1 - x^2) as (1 - x) * (1 + x) to avoid loss of
* precision when |x| is nearly 1.
*/
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
1994-08-19 09:40:01 +00:00
ENTRY(__ieee754_acos)
fldl 4(%esp) /* x */
Compute (1 - x^2) as ((1 - x) * (1 + x)) instead of as (1 - x * x) to avoid easily avoidable loss of precision when |x| is nearly 1. Extended (64-bit) precision only moves the meaning of "nearly" here. This probably could be done better by splitting up the range into |x| <= 0.5 and |x| > 0.5 like the C version. However, ucbtest does't report any errors in this version. Perhaps the C version should be used anyway. It's only 25% slower now on a P5, provided the C version of sqrt() isn't used, and the C version could be optimized better. Errors checked by: ucbtest
1997-02-20 12:37:49 +00:00
fld1
fld %st(0)
fsub %st(2) /* 1 - x */
fxch %st(1)
fadd %st(2) /* 1 + x */
fmulp %st(1) /* (1 - x) * (1 + x) */
fsqrt
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
1994-08-19 09:40:01 +00:00
fxch %st(1)
fpatan
ret
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