mirror of
git://sourceware.org/git/newlib-cygwin.git
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048ebea981
Rename s_nearbyint.c, s_fdim.c and s_scalbln.c to remove conflicts
Remove functions that are not needed from above files
Modify include paths
Add includes missing in cygwin build
Add missing types
Create Makefiles
Create header files to resolve dependencies between directories
Modify some instances of unsigned long to uint64_t for 32 bit platforms
Add HAVE_FPMATH_H
144 lines
4.3 KiB
C
144 lines
4.3 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 "../ld/math_private.h"
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#include "../ld/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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static inline __always_inline 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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fn = rnintl(x*invpio2);
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n = irint(fn);
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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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