142 lines
4.4 KiB
C
142 lines
4.4 KiB
C
/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */
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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 "libc/math/libm.h"
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#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
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/* ld80 and ld128 version of __rem_pio2(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 __rem_pio2_large() for large x
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*/
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static const long double toint = 1.5/LDBL_EPSILON;
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#if LDBL_MANT_DIG == 64
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/* u ~< 0x1p25*pi/2 */
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#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x921f>>1 | 0x8000))
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#define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff)
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#define ROUND1 22
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#define ROUND2 61
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#define NX 3
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#define NY 2
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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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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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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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#elif LDBL_MANT_DIG == 113
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/* u ~< 0x1p45*pi/2 */
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#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x921f))
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#define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff)
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#define ROUND1 51
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#define ROUND2 119
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#define NX 5
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#define NY 3
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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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#endif
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int __rem_pio2l(long double x, long double *y)
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{
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union ldshape u,uz;
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long double z,w,t,r,fn;
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double tx[NX],ty[NY];
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int ex,ey,n,i;
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u.f = x;
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ex = u.i.se & 0x7fff;
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if (SMALL(u)) {
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/* rint(x/(pi/2)), Assume round-to-nearest. */
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fn = x*invpio2 + toint - toint;
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n = QUOBITS(fn);
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r = x-fn*pio2_1;
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w = fn*pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */
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y[0] = r-w;
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u.f = y[0];
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ey = u.i.se & 0x7fff;
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if (ex - ey > ROUND1) { /* 2nd iteration needed, good to 141/248 (ld80/ld128) */
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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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u.f = y[0];
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ey = u.i.se & 0x7fff;
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if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/316 bits */
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t = r; /* will cover all possible cases (not verified for ld128) */
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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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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;
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return 0;
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}
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/* set z = scalbn(|x|,-ilogb(x)+23) */
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uz.f = x;
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uz.i.se = 0x3fff + 23;
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z = uz.f;
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for (i=0; i < NX - 1; i++) {
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tx[i] = (double)(int32_t)z;
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z = (z-tx[i])*0x1p24;
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}
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tx[i] = z;
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while (tx[i] == 0)
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i--;
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n = __rem_pio2_large(tx, ty, ex-0x3fff-23, i+1, NY);
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w = ty[1];
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if (NY == 3)
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w += ty[2];
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r = ty[0] + w;
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/* TODO: for ld128 this does not follow the recommendation of the
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comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */
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w -= r - ty[0];
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if (u.i.se >> 15) {
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y[0] = -r;
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y[1] = -w;
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return -n;
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}
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y[0] = r;
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y[1] = w;
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return n;
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}
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#endif
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