1dd21062e5
Instead of echoing the code in a comment, try to describe why we split up the evaluation in a special way. The new optimization is mostly to move the evaluation of w = z*z later so that everything else (except z = x*x) doesn't have to wait for w. On Athlons, FP multiplication has a latency of 4 cycles so this optimization saves 4 cycles per call provided no new dependencies are introduced. Tweaking the other terms in to reduce dependencies saves a couple more cycles in some cases (more on AXP than on A64; up to 8 cycles out of 56 altogether in some cases). The previous version had a similar optimization for s = z*x. Special optimizations like these probably have a larger effect than the simple 2-way vectorization permitted (but not activated by gcc) in the old version, since 2-way vectorization is not enough and the polynomial's degree is so small in the float case that non-vectorizable dependencies dominate. On an AXP, tanf() on uniformly distributed args in [-2pi, 2pi] now takes 34-55 cycles (was 39-59 cycles).
68 lines
2.0 KiB
C
68 lines
2.0 KiB
C
/* k_tanf.c -- float version of k_tan.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 2004 Sun Microsystems, Inc. All Rights Reserved.
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*
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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_TANDF
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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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/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
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static const double
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T[] = {
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0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
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0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
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0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
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0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
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0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
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0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
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};
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#ifdef INLINE_KERNEL_TANDF
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extern inline
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#endif
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float
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__kernel_tandf(double x, int iy)
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{
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double z,r,w,s,t,u;
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z = x*x;
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/*
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* Split up the polynomial into small independent terms to give
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* opportunities for parallel evaluation. The chosen splitting is
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* micro-optimized for Athlons (XP, X64). It costs 2 multiplications
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* relative to Horner's method on sequential machines.
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*
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* We add the small terms from lowest degree up for efficiency on
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* non-sequential machines (the lowest degree terms tend to be ready
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* earlier). Apart from this, we don't care about order of
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* operations, and don't need to to care since we have precision to
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* spare. However, the chosen splitting is good for accuracy too,
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* and would give results as accurate as Horner's method if the
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* small terms were added from highest degree down.
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*/
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r = T[4]+z*T[5];
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t = T[2]+z*T[3];
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w = z*z;
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s = z*x;
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u = T[0]+z*T[1];
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r = (x+s*u)+(s*w)*(t+w*r);
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if(iy==1) return r;
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else return -1.0/r;
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}
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