8cc821405a
k_tanf.c but with different details. The polynomial is odd with degree 13 for tanf() and odd with degree 9 for sinf(), so the details are not very different for sinf() -- the term with the x**11 and x**13 coefficients goes awaym and (mysteriously) it helps to do the evaluation of w = z*z early although moving it later was a key optimization for tanf(). The details are different but simpler for cosf() because the polynomial is even and of lower degree. On Athlons, for uniformly distributed args in [-2pi, 2pi], this gives an optimization of about 4 cycles (10%) in most cases (13% for sinf() on AXP, but 0% for cosf() with gcc-3.3 -O1 on AXP). The best case (sinf() with gcc-3.4 -O1 -fcaller-saves on A64) now takes 33-39 cycles (was 37-45 cycles). Hardware sinf takes 74-129 cycles. Despite being fine tuned for Athlons, the optimization is even larger on some other arches (about 15% on ia64 (pluto2) and 20% on alpha (beast) with gcc -O2 -fomit-frame-pointer).
48 lines
1.2 KiB
C
48 lines
1.2 KiB
C
/* k_sinf.c -- float version of k_sin.c
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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* Optimized by Bruce D. Evans.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#ifndef INLINE_KERNEL_SINDF
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#ifndef lint
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static char rcsid[] = "$FreeBSD$";
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#endif
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#endif
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#include "math.h"
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#include "math_private.h"
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/* |sin(x)/x - s(x)| < 2**-37.5 (~[-4.89e-12, 4.824e-12]). */
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static const double
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S1 = -0x15555554cbac77.0p-55, /* -0.166666666416265235595 */
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S2 = 0x111110896efbb2.0p-59, /* 0.0083333293858894631756 */
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S3 = -0x1a00f9e2cae774.0p-65, /* -0.000198393348360966317347 */
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S4 = 0x16cd878c3b46a7.0p-71; /* 0.0000027183114939898219064 */
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#ifdef INLINE_KERNEL_SINDF
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extern inline
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#endif
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float
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__kernel_sindf(double x)
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{
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double r, s, w, z;
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/* Try to optimize for parallel evaluation as in k_tanf.c. */
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z = x*x;
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w = z*z;
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r = S3+z*S4;
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s = z*x;
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return (x + s*(S1+z*S2)) + s*w*r;
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}
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