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
136 lines
3.9 KiB
C
136 lines
3.9 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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/* ld128 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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* XXX need to verify that nonzero integer multiples of pi/2 within the
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* range get no closer to a long double than 2**-140, or that
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* ilogb(x) + ilogb(min_delta) < 45 - -140.
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*/
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/*
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* invpio2: 113 bits of 2/pi
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* pio2_1: first 68 bits of pi/2
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* pio2_1t: pi/2 - pio2_1
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* pio2_2: second 68 bits of pi/2
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* pio2_2t: pi/2 - (pio2_1+pio2_2)
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* pio2_3: third 68 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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static const long double
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invpio2 = 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113 */
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pio2_1 = 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112 */
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pio2_1t = 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181 */
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pio2_2 = 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181 */
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pio2_2t = 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254 */
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pio2_3 = 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254 */
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pio2_3t = -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */
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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[5],ty[3];
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int64_t n;
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int e0,ex,i,j,nx;
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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 + 45 || ex == BIAS + 45 &&
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u.bits.manh < 0x921fb54442d1LL) {
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/* |x| ~< 2^45*(pi/2), medium size */
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/* TODO: use only double precision for fn, as in expl(). */
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fn = rnintl(x * invpio2);
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n = i64rint(fn);
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r = x-fn*pio2_1;
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w = fn*pio2_1t; /* 1st round good to 180 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>51) { /* 2nd iteration needed, good to 248 */
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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>119) { /* 3rd iteration need, 316 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<4;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[4] = z;
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nx = 5;
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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,3);
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t = (long double)ty[2] + ty[1];
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r = t + ty[0];
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w = ty[0] - (r - t);
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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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