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* C3_MATH feature This feature allows the usage of noclib math files even when libc is in use. If a nolibc symbol exists, it will be used in place of libc, otherwise it will default to libc. * Added MIT License notices to atan.c3
538 lines
12 KiB
Plaintext
538 lines
12 KiB
Plaintext
module std::math::nolibc @if(env::NO_LIBC || $feature(C3_MATH));
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import std::math;
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/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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* Debugged and optimized by Bruce D. Evans.
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*/
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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 SunPro, 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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/* __rem_pio2f(x,y)
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*
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* return the remainder of x rem pi/2 in *y
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* use double precision for everything except passing x
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* use __rem_pio2_large() for large x
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*/
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/*
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* invpio2: 53 bits of 2/pi
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* pio2_1: first 25 bits of pi/2
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* pio2_1t: pi/2 - pio2_1
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*/
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fn int __rem_pio2f(float x, double *y)
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{
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const double PIO4 = 0x1.921fb6p-1;
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const double INVPIO2 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
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const double PIO2_1 = 1.57079631090164184570e+00; /* 0x3FF921FB, 0x50000000 */
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const double PIO2_1T = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
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uint ux = bitcast(x, uint);
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uint ix = ux & 0x7fffffff;
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/* 25+53 bit pi is good enough for medium size */
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if (ix < 0x4dc90fdb)
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{
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// |x| ~< 2^28*(pi/2), medium size
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// Use a specialized rint() to get f.
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uint f = (uint)(((double)x * INVPIO2 + TOINT15) - TOINT15);
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int n = (int)f;
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*y = x - f * PIO2_1 - f * PIO2_1T;
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/* Matters with directed rounding. */
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if (*y < -PIO4) // likely false
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{
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n--;
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f--;
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*y = x - f * PIO2_1 - f * PIO2_1T;
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}
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else if (*y > PIO4) // likely false
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{
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n++;
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f++;
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*y = x - f * PIO2_1 - f * PIO2_1T;
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}
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return n;
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}
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if (ix >= 0x7f800000)
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{
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// x is inf or NaN
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*y = x - (double)x;
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return 0;
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}
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/* scale x into [2^23, 2^24-1] */
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int sign = ux >> 31;
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int e0 = (ix >> 23) - (0x7f + 23); /* e0 = ilogb(|x|)-23, positive */
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ux = ix - e0 << 23;
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double tx = bitcast(ux, float);
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double ty @noinit;
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int n = __rem_pio2_large(&tx,&ty, e0, 1, 0);
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if (sign)
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{
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*y = (float)-ty;
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return -n;
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}
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*y = (float)ty;
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return n;
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}
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/* origin: FreeBSD /usr/src/lib/msun/src/k_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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const int[*] INIT_JK = {3,4,4,6}; /* initial value for jk */
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const int[*] IPIO2 = {
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
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0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
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0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
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0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
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0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
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0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
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0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
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0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
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0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
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0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, };
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const double[*] PIO2 = {
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1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
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7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
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5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
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3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
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1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
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1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
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2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
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2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
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};
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fn int __rem_pio2_large(double* x, double* y, int e0, int nx, int prec)
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{
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double[20] f @noinit;
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double[20] fq @noinit;
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double[20] q @noinit;
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int[20] iq @noinit;
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double fw @noinit;
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/* initialize jk*/
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int jk = INIT_JK[prec];
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int jp = jk;
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/* determine jx,jv,q0, note that 3>q0 */
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int jx = nx - 1;
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int jv = (e0 - 3) / 24;
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if (jv < 0) jv = 0;
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int q0 = e0 - 24 * (jv + 1);
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// set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk]
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int j = jv - jx;
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int m = jx + jk;
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for (int i = 0; i <= m; i++, j++)
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{
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f[i] = j < 0 ? 0.0 : (double)IPIO2[j];
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}
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// compute q[0],q[1],...q[jk]
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for (int i = 0; i <= jk; i++)
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{
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for (j = 0, fw = 0.0; j <= jx; j++) fw += x[j] * f[jx + i - j];
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q[i] = fw;
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}
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int jz = jk;
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double z @noinit;
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int ih = 0;
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int n @noinit;
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while (1)
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{
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/* distill q[] into iq[] reversingly */
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z = q[jz];
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j = jz;
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for (int i = 0; j > 0; i++, j--)
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{
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fw = (double)(int)(0x1p-24 * z);
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iq[i] = (int)(z - 0x1p24 * fw);
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z = q[j - 1] + fw;
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}
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// compute n
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z = nolibc::_scalbn(z, q0); /* actual value of z */
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z -= 8.0 * nolibc::_floor(z * 0.125); /* trim off integer >= 8 */
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n = (int)z;
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z -= (double)n;
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switch
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{
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case q0 > 0:
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// need iq[jz-1] to determine n
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int i = iq[jz - 1] >> (24 - q0);
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n += i;
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iq[jz - 1] -= i << (24 - q0);
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ih = iq[jz - 1] >> (23 - q0);
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case q0 == 0:
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ih = iq[jz - 1] >> 23;
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case z >= 0.5:
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ih = 2;
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}
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if (ih > 0)
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{
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/* q > 0.5 */
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n += 1;
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int carry = 0;
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for (int i = 0; i < jz; i++)
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{
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/* compute 1-q */
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j = iq[i];
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if (carry == 0)
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{
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if (j != 0)
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{
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carry = 1;
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iq[i] = 0x1000000 - j;
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}
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}
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else
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{
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iq[i] = 0xffffff - j;
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}
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}
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if (q0 > 0)
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{
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/* rare case: chance is 1 in 12 */
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switch (q0)
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{
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case 1: iq[jz - 1] &= 0x7fffff;
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case 2: iq[jz - 1] &= 0x3fffff;
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}
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}
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if (ih == 2)
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{
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z = 1.0 - z;
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if (carry != 0) z -= nolibc::_scalbn(1.0, q0);
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}
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}
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// check if recomputation is needed
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if (z == 0.0)
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{
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j = 0;
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for (int i = jz - 1; i >= jk; i--) j |= iq[i];
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if (j == 0)
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{
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/* need recomputation */
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int k = 1;
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for (; iq[jk - k] == 0; k++); /* k = no. of terms needed */
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for (int i = jz + 1; i <= jz + k; i++)
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{
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/* add q[jz+1] to q[jz+k] */
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f[jx + i] = (double)IPIO2[jv + i];
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for (j = 0, fw = 0.0; j <= jx; j++)
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fw += x[j] * f[jx + i - j];
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q[i] = fw;
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}
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jz += k;
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continue;
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}
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}
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break;
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}
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/* chop off zero terms */
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if (z == 0.0)
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{
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jz -= 1;
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q0 -= 24;
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while (iq[jz] == 0)
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{
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jz--;
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q0 -= 24;
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}
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}
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else
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{
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/* break z into 24-bit if necessary */
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z = _scalbn(z,-q0);
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if (z >= 0x1p24)
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{
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fw = (double)(int)(0x1p-24 * z);
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iq[jz] = (int)(z - 0x1p24 * fw);
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jz += 1;
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q0 += 24;
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iq[jz] = (int)fw;
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}
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else
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{
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iq[jz] = (int)z;
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}
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}
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/* convert integer "bit" chunk to floating-point value */
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fw = nolibc::_scalbn(1.0 , q0);
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for (int i = jz; i >= 0; i --)
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{
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q[i] = fw * (double)iq[i];
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fw *= 0x1p-24;
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}
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/* compute PIO2[0,...,jp]*q[jz,...,0] */
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for (int i = jz; i >= 0; i--)
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{
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for (fw = 0.0, int k = 0; k <= jp && k <= jz-i; k++) fw += PIO2[k] * q[i + k];
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fq[jz - i] = fw;
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}
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/* compress fq[] into y[] */
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switch (prec)
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{
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case 0:
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fw = 0.0;
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for (int i = jz; i >= 0; i--) fw += fq[i];
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y[0] = ih == 0 ? fw : -fw;
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case 1:
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case 2:
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fw = 0.0;
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for (int i = jz; i >= 0; i--)
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fw += fq[i];
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// TODO: drop excess precision here once double_t is used
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fw = (double)fw;
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y[0] = ih == 0 ? fw : -fw;
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fw = fq[0]-fw;
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for (int i = 1; i <= jz; i++) fw += fq[i];
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y[1] = ih == 0 ? fw : -fw;
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case 3: /* painful */
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for (int i = jz; i > 0; i--)
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{
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fw = fq[i - 1] + fq[i];
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fq[i] += fq[i - 1] - fw;
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fq[i - 1] = fw;
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}
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for (int i = jz; i > 1; i--)
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{
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fw = fq[i-1] + fq[i];
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fq[i] += fq[i - 1] - fw;
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fq[i - 1] = fw;
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}
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for (fw = 0.0, int i = jz; i >= 2; i--)
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fw += fq[i];
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if (ih == 0)
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{
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y[0] = fq[0];
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y[1] = fq[1];
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y[2] = fw;
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}
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else
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{
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y[0] = -fq[0];
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y[1] = -fq[1];
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y[2] = -fw;
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}
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}
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return n & 7;
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}
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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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/*
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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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<* caller must handle the case when reduction is not needed: |x| ~<= pi/4 *>
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fn int __rem_pio2(double x, double *y)
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{
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const double PIO4 = 0x1.921fb54442d18p-1;
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const double INVPIO2 = 6.36619772367581382433e-01; /* 0x3FE45F30, 0x6DC9C883 */
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const double PIO2_1 = 1.57079632673412561417e+00; /* 0x3FF921FB, 0x54400000 */
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const double PIO2_1T = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
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const double PIO2_2 = 6.07710050630396597660e-11; /* 0x3DD0B461, 0x1A600000 */
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const double PIO2_2T = 2.02226624879595063154e-21; /* 0x3BA3198A, 0x2E037073 */
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const double PIO2_3 = 2.02226624871116645580e-21; /* 0x3BA3198A, 0x2E000000 */
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const double PIO2_3T = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
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ulong u = bitcast(x, ulong);
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int sign = (int)(u >> 63);
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uint ix = (uint)(u >> 32 & 0x7fffffff);
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switch
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{
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// |x| ~<= 5pi/4
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case ix <= 0x400f6a7a:
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// |x| ~= pi/2 or 2pi/2
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if ((ix & 0xfffff) == 0x921fb)
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{
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// cancellation -- use medium case
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break;
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}
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// |x| ~<= 3pi/4
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if (ix <= 0x4002d97c)
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{
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if (!sign)
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{
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double 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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}
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double 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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if (!sign)
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{
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double 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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double 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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// |x| ~<= 9pi/4
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case ix <= 0x401c463b:
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// |x| ~<= 7pi/4
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if (ix <= 0x4015fdbc)
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{
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// |x| ~= 3pi/2
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if (ix == 0x4012d97c) break; // Use medium
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if (!sign)
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{
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double 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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double 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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// |x| ~= 4pi/2
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if (ix == 0x401921fb) break; // Use medium
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if (!sign)
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{
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double 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;
|
|
return 4;
|
|
}
|
|
double z = x + 4*PIO2_1;
|
|
y[0] = z + 4 * PIO2_1T;
|
|
y[1] = (z - y[0]) + 4 * PIO2_1T;
|
|
return -4;
|
|
case ix < 0x413921fb:
|
|
break; // medium
|
|
case ix >= 0x7ff00000:
|
|
// x is inf or NaN
|
|
y[0] = y[1] = x - x;
|
|
return 0;
|
|
default:
|
|
// all other (large) arguments
|
|
// set z = scalbn(|x|,-ilogb(x)+23)
|
|
u = bitcast(x, ulong);
|
|
u &= ((ulong)-1) >> 12;
|
|
u |= (ulong)(0x3ff + 23) << 52;
|
|
double z = bitcast(u, double);
|
|
double[3] tx;
|
|
int i;
|
|
for (i = 0; i < 2; i++)
|
|
{
|
|
tx[i] = (double)(int)z;
|
|
z = (z - tx[i]) * 0x1p24;
|
|
}
|
|
tx[i] = z;
|
|
// skip zero terms, first term is non-zero
|
|
while (tx[i] == 0.0) i--;
|
|
double[2] ty;
|
|
int n = __rem_pio2_large(&tx, &ty, (int)(ix >> 20) - (0x3ff + 23), i + 1, 1);
|
|
if (sign)
|
|
{
|
|
y[0] = -ty[0];
|
|
y[1] = -ty[1];
|
|
return -n;
|
|
}
|
|
y[0] = ty[0];
|
|
y[1] = ty[1];
|
|
return n;
|
|
}
|
|
|
|
// |x| ~< 2^20*(pi/2), medium size
|
|
// rint(x/(pi/2))
|
|
double fnn = (double)x * INVPIO2 + TOINT15 - TOINT15;
|
|
int n = (int)fnn;
|
|
double r = x - fnn * PIO2_1;
|
|
double w = fnn * PIO2_1T; // 1st round, good to 85 bits
|
|
// Matters with directed rounding.
|
|
if (r - w < -PIO4) /*@unlikely*/
|
|
{
|
|
n--;
|
|
fnn--;
|
|
r = x - fnn * PIO2_1;
|
|
w = fnn * PIO2_1T;
|
|
}
|
|
else if (r - w > PIO4) /*@unlikely*/
|
|
{
|
|
n++;
|
|
fnn++;
|
|
r = x - fnn * PIO2_1;
|
|
w = fnn * PIO2_1T;
|
|
}
|
|
y[0] = r - w;
|
|
u = bitcast(y[0], ulong);
|
|
int ey = (int)(u >> 52 & 0x7ff);
|
|
int ex = (int)(ix >> 20);
|
|
if (ex - ey > 16)
|
|
{
|
|
// 2nd round, good to 118 bits
|
|
double t = r;
|
|
w = fnn * PIO2_2;
|
|
r = t - w;
|
|
w = fnn * PIO2_2T - ((t - r) - w);
|
|
y[0] = r - w;
|
|
u = bitcast(y[0], ulong);
|
|
ey = (int)(u >> 52 & 0x7ff);
|
|
if (ex - ey > 49)
|
|
{
|
|
// 3rd round, good to 151 bits, covers all cases
|
|
t = r;
|
|
w = fnn * PIO2_3;
|
|
r = t - w;
|
|
w = fnn * PIO2_3T - ((t - r) - w);
|
|
y[0] = r - w;
|
|
}
|
|
}
|
|
y[1] = (r - y[0]) - w;
|
|
return n;
|
|
|
|
|
|
}
|