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e216951f50
When FLT_EVAL_METHOD!=0 (only i386 with x87 fp) the excess
precision of an expression must be removed in an assignment.
(gcc needs -fexcess-precision=standard or -std=c99 for this)
This is done by extra load/store instructions which adds code
bloat when lot of temporaries are used and it makes the result
less precise in many cases.
Using double_t and float_t avoids these issues on i386 and
it makes no difference on other archs.
For now only a few functions are modified where the excess
precision is clearly beneficial (mostly polynomial evaluations
with temporaries).
object size differences on i386, gcc-4.8:
old new
__cosdf.o 123 95
__cos.o 199 169
__sindf.o 131 95
__sin.o 225 203
__tandf.o 207 151
__tan.o 605 499
erff.o 1470 1416
erf.o 1703 1649
j0f.o 1779 1745
j0.o 2308 2274
j1f.o 1602 1568
j1.o 2286 2252
tgamma.o 1431 1424
math/*.o 64164 63635
56 lines
1.8 KiB
C
56 lines
1.8 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/src/k_tanf.c */
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/*
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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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#include "libm.h"
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/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
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static const double 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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float __tandf(double x, int iy)
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{
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double_t 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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