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/* $MidnightBSD$ */ |
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/* 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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|
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#include <sys/cdefs.h> |
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__FBSDID("$FreeBSD: stable/10/lib/msun/ld80/e_rem_pio2l.h 223262 2011-06-18 13:56:33Z benl $"); |
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|
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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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|
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#include <float.h> |
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|
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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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|
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#define BIAS (LDBL_MAX_EXP - 1) |
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|
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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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|
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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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|
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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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|
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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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|
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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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} |
