c273267e83
on i386-class hardware for sinl and cosl. The hand-rolled argument
reduction have been replaced by e_rem_pio2l() implementations. To
preserve history the following commands have been executed:
svn cp src/e_rem_pio2.c ld80/e_rem_pio2l.h
mv ${HOME}/bde/ld80/e_rem_pio2l.c ld80/e_rem_pio2l.h
svn cp src/e_rem_pio2.c ld128/e_rem_pio2l.h
mv ${HOME}/bde/ld128/e_rem_pio2l.c ld128/e_rem_pio2l.h
The ld80 version has been tested by bde, das, and kargl over the
last few years (bde, das) and few months (kargl). An older ld128
version was tested by das. The committed version has only been
compiled tested via 'make universe'.
Approved by: das (mentor)
Obtained from: bde
153 lines
4.5 KiB
C
153 lines
4.5 KiB
C
/* From: @(#)e_rem_pio2.c 1.4 95/01/18 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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* Optimized by Bruce D. Evans.
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/* ld80 version of __ieee754_rem_pio2l(x,y)
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*
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* return the remainder of x rem pi/2 in y[0]+y[1]
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* use __kernel_rem_pio2()
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*/
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#include <float.h>
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#include "math.h"
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#include "math_private.h"
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#include "fpmath.h"
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#define BIAS (LDBL_MAX_EXP - 1)
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/*
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* invpio2: 64 bits of 2/pi
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* pio2_1: first 39 bits of pi/2
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* pio2_1t: pi/2 - pio2_1
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* pio2_2: second 39 bits of pi/2
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* pio2_2t: pi/2 - (pio2_1+pio2_2)
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* pio2_3: third 39 bits of pi/2
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* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
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*/
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static const double
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zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
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two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
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pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
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pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
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#if defined(__amd64__) || defined(__i386__)
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/* Long double constants are slow on these arches, and broken on i386. */
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static const volatile double
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invpio2hi = 6.3661977236758138e-01, /* 0x145f306dc9c883.0p-53 */
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invpio2lo = -3.9356538861223811e-17, /* -0x16b00000000000.0p-107 */
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pio2_1thi = -1.0746346554971943e-12, /* -0x12e7b9676733af.0p-92 */
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pio2_1tlo = 8.8451028997905949e-29, /* 0x1c080000000000.0p-146 */
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pio2_2thi = 6.3683171635109499e-25, /* 0x18a2e03707344a.0p-133 */
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pio2_2tlo = 2.3183081793789774e-41, /* 0x10280000000000.0p-187 */
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pio2_3thi = -2.7529965190440717e-37, /* -0x176b7ed8fbbacc.0p-174 */
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pio2_3tlo = -4.2006647512740502e-54; /* -0x19c00000000000.0p-230 */
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#define invpio2 ((long double)invpio2hi + invpio2lo)
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#define pio2_1t ((long double)pio2_1thi + pio2_1tlo)
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#define pio2_2t ((long double)pio2_2thi + pio2_2tlo)
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#define pio2_3t ((long double)pio2_3thi + pio2_3tlo)
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#else
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static const long double
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invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
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pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
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pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
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pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
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#endif
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#ifdef INLINE_REM_PIO2L
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static inline __always_inline
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#endif
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int
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__ieee754_rem_pio2l(long double x, long double *y)
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{
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union IEEEl2bits u,u1;
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long double z,w,t,r,fn;
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double tx[3],ty[2];
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int e0,ex,i,j,nx,n;
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int16_t expsign;
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u.e = x;
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expsign = u.xbits.expsign;
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ex = expsign & 0x7fff;
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if (ex < BIAS + 25 || ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2) {
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/* |x| ~< 2^25*(pi/2), medium size */
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/* Use a specialized rint() to get fn. Assume round-to-nearest. */
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fn = x*invpio2+0x1.8p63;
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fn = fn-0x1.8p63;
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#ifdef HAVE_EFFICIENT_IRINT
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n = irint(fn);
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#else
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n = fn;
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#endif
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r = x-fn*pio2_1;
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w = fn*pio2_1t; /* 1st round good to 102 bit */
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{
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union IEEEl2bits u2;
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int ex1;
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j = ex;
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y[0] = r-w;
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u2.e = y[0];
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ex1 = u2.xbits.expsign & 0x7fff;
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i = j-ex1;
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if(i>22) { /* 2nd iteration needed, good to 141 */
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t = r;
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w = fn*pio2_2;
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r = t-w;
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w = fn*pio2_2t-((t-r)-w);
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y[0] = r-w;
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u2.e = y[0];
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ex1 = u2.xbits.expsign & 0x7fff;
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i = j-ex1;
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if(i>61) { /* 3rd iteration need, 180 bits acc */
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t = r; /* will cover all possible cases */
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w = fn*pio2_3;
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r = t-w;
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w = fn*pio2_3t-((t-r)-w);
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y[0] = r-w;
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}
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}
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}
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y[1] = (r-y[0])-w;
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return n;
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}
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/*
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* all other (large) arguments
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*/
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if(ex==0x7fff) { /* x is inf or NaN */
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y[0]=y[1]=x-x; return 0;
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}
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/* set z = scalbn(|x|,ilogb(x)-23) */
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u1.e = x;
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e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */
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u1.xbits.expsign = ex - e0;
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z = u1.e;
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for(i=0;i<2;i++) {
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tx[i] = (double)((int32_t)(z));
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z = (z-tx[i])*two24;
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}
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tx[2] = z;
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nx = 3;
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while(tx[nx-1]==zero) nx--; /* skip zero term */
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n = __kernel_rem_pio2(tx,ty,e0,nx,2);
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r = (long double)ty[0] + ty[1];
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w = ty[1] - (r - ty[0]);
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if(expsign<0) {y[0] = -r; y[1] = -w; return -n;}
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y[0] = r; y[1] = w; return n;
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}
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