mirror of
https://github.com/jart/cosmopolitan.git
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226 lines
7.3 KiB
C
226 lines
7.3 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/intrin/likely.h"
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#include "libc/math.h"
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#include "libc/tinymath/kernel.internal.h"
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asm(".ident\t\"\\n\\n\
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fdlibm (fdlibm license)\\n\
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Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2014 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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/* clang-format off */
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/* origin: FreeBSD /usr/src/lib/msun/src/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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*
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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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/* __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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#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
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#define EPS DBL_EPSILON
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#elif FLT_EVAL_METHOD==2
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#define EPS LDBL_EPSILON
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#endif
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/*
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* invpio2: 53 bits of 2/pi
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* pio2_1: first 33 bit of pi/2
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* pio2_1t: pi/2 - pio2_1
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* pio2_2: second 33 bit of pi/2
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* pio2_2t: pi/2 - (pio2_1+pio2_2)
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* pio2_3: third 33 bit 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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#define toint (1.5/EPS)
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#define pio4 0x1.921fb54442d18p-1
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#define invpio2 6.36619772367581382433e-01
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#define pio2_1 1.57079632673412561417e+00
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#define pio2_1t 6.07710050650619224932e-11
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#define pio2_2 6.07710050630396597660e-11
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#define pio2_2t 2.02226624879595063154e-21
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#define pio2_3 2.02226624871116645580e-21
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#define pio2_3t 8.47842766036889956997e-32
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/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
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int __rem_pio2(double x, double *y)
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{
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union {double f; uint64_t i;} u = {x};
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double_t z,w,t,r,fn;
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double tx[3],ty[2];
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uint32_t ix;
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int sign, n, ex, ey, i;
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sign = u.i>>63;
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ix = u.i>>32 & 0x7fffffff;
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if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
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if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
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goto medium; /* cancellation -- use medium case */
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if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
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if (!sign) {
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z = x - pio2_1; /* one round good to 85 bits */
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y[0] = z - pio2_1t;
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y[1] = (z-y[0]) - pio2_1t;
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return 1;
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} else {
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z = x + pio2_1;
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y[0] = z + pio2_1t;
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y[1] = (z-y[0]) + pio2_1t;
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return -1;
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}
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} else {
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if (!sign) {
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z = x - 2*pio2_1;
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y[0] = z - 2*pio2_1t;
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y[1] = (z-y[0]) - 2*pio2_1t;
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return 2;
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} else {
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z = x + 2*pio2_1;
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y[0] = z + 2*pio2_1t;
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y[1] = (z-y[0]) + 2*pio2_1t;
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return -2;
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}
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}
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}
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if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
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if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
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if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
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goto medium;
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if (!sign) {
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z = x - 3*pio2_1;
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y[0] = z - 3*pio2_1t;
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y[1] = (z-y[0]) - 3*pio2_1t;
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return 3;
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} else {
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z = x + 3*pio2_1;
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y[0] = z + 3*pio2_1t;
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y[1] = (z-y[0]) + 3*pio2_1t;
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return -3;
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}
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} else {
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if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
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goto medium;
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if (!sign) {
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z = x - 4*pio2_1;
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y[0] = z - 4*pio2_1t;
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y[1] = (z-y[0]) - 4*pio2_1t;
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return 4;
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} else {
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z = x + 4*pio2_1;
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y[0] = z + 4*pio2_1t;
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y[1] = (z-y[0]) + 4*pio2_1t;
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return -4;
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}
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}
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}
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if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
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medium:
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/* rint(x/(pi/2)) */
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fn = (double_t)x*invpio2 + toint - toint;
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n = (int32_t)fn;
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r = x - fn*pio2_1;
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w = fn*pio2_1t; /* 1st round, good to 85 bits */
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/* Matters with directed rounding. */
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if (UNLIKELY(r - w < -pio4)) {
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n--;
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fn--;
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r = x - fn*pio2_1;
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w = fn*pio2_1t;
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} else if (UNLIKELY(r - w > pio4)) {
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n++;
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fn++;
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r = x - fn*pio2_1;
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w = fn*pio2_1t;
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}
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y[0] = r - w;
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u.f = y[0];
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ey = u.i>>52 & 0x7ff;
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ex = ix>>20;
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if (ex - ey > 16) { /* 2nd round, good to 118 bits */
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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>>52 & 0x7ff;
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if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */
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t = r;
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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 (ix >= 0x7ff00000) { /* 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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u.f = x;
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u.i &= (uint64_t)-1>>12;
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u.i |= (uint64_t)(0x3ff + 23)<<52;
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z = u.f;
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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])*0x1p24;
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}
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tx[i] = z;
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/* skip zero terms, first term is non-zero */
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while (tx[i] == 0.0)
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i--;
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n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1);
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if (sign) {
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y[0] = -ty[0];
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y[1] = -ty[1];
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return -n;
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}
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y[0] = ty[0];
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y[1] = ty[1];
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return n;
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}
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