src/libm/e_rem_pio2.c
author Philipp Wiesemann <philipp.wiesemann@arcor.de>
Sun, 28 Dec 2014 22:00:24 +0100
changeset 9301 7377a9a3aed6
parent 6044 35448a5ea044
child 10650 b6ec7005ca15
permissions -rw-r--r--
Renamed README-emscripten.txt to README-emscripten.md.
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/* @(#)e_rem_pio2.c 5.1 93/09/24 */
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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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#if defined(LIBM_SCCS) && !defined(lint)
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static const char rcsid[] =
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    "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
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#endif
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/* __ieee754_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 __kernel_rem_pio2()
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 */
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#include "math_libm.h"
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#include "math_private.h"
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libm_hidden_proto(fabs)
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/*
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 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
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 */
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#ifdef __STDC__
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     static const int32_t two_over_pi[] = {
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#else
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     static int32_t two_over_pi[] = {
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#endif
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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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     };
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#ifdef __STDC__
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static const int32_t npio2_hw[] = {
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#else
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static int32_t npio2_hw[] = {
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#endif
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    0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
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    0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
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    0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
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    0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
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    0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
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    0x404858EB, 0x404921FB,
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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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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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  zero = 0.00000000000000000000e+00,    /* 0x00000000, 0x00000000 */
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    half = 5.00000000000000000000e-01,  /* 0x3FE00000, 0x00000000 */
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    two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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    invpio2 = 6.36619772367581382433e-01,       /* 0x3FE45F30, 0x6DC9C883 */
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    pio2_1 = 1.57079632673412561417e+00,        /* 0x3FF921FB, 0x54400000 */
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    pio2_1t = 6.07710050650619224932e-11,       /* 0x3DD0B461, 0x1A626331 */
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    pio2_2 = 6.07710050630396597660e-11,        /* 0x3DD0B461, 0x1A600000 */
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    pio2_2t = 2.02226624879595063154e-21,       /* 0x3BA3198A, 0x2E037073 */
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    pio2_3 = 2.02226624871116645580e-21,        /* 0x3BA3198A, 0x2E000000 */
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    pio2_3t = 8.47842766036889956997e-32;       /* 0x397B839A, 0x252049C1 */
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#ifdef __STDC__
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int32_t attribute_hidden
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__ieee754_rem_pio2(double x, double *y)
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#else
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int32_t attribute_hidden
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__ieee754_rem_pio2(x, y)
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     double x, y[];
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#endif
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{
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    double z = 0.0, w, t, r, fn;
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    double tx[3];
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    int32_t e0, i, j, nx, n, ix, hx;
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    u_int32_t low;
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    GET_HIGH_WORD(hx, x);       /* high word of x */
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    ix = hx & 0x7fffffff;
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    if (ix <= 0x3fe921fb) {     /* |x| ~<= pi/4 , no need for reduction */
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        y[0] = x;
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        y[1] = 0;
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        return 0;
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    }
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    if (ix < 0x4002d97c) {      /* |x| < 3pi/4, special case with n=+-1 */
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        if (hx > 0) {
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            z = x - pio2_1;
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            if (ix != 0x3ff921fb) {     /* 33+53 bit pi is good enough */
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                y[0] = z - pio2_1t;
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                y[1] = (z - y[0]) - pio2_1t;
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            } else {            /* near pi/2, use 33+33+53 bit pi */
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                z -= pio2_2;
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                y[0] = z - pio2_2t;
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                y[1] = (z - y[0]) - pio2_2t;
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            }
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            return 1;
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        } else {                /* negative x */
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            z = x + pio2_1;
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            if (ix != 0x3ff921fb) {     /* 33+53 bit pi is good enough */
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                y[0] = z + pio2_1t;
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                y[1] = (z - y[0]) + pio2_1t;
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            } else {            /* near pi/2, use 33+33+53 bit pi */
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                z += pio2_2;
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                y[0] = z + pio2_2t;
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                y[1] = (z - y[0]) + pio2_2t;
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            }
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            return -1;
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        }
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    }
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    if (ix <= 0x413921fb) {     /* |x| ~<= 2^19*(pi/2), medium size */
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        t = fabs(x);
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        n = (int32_t) (t * invpio2 + half);
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        fn = (double) n;
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        r = t - fn * pio2_1;
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        w = fn * pio2_1t;       /* 1st round good to 85 bit */
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        if (n < 32 && ix != npio2_hw[n - 1]) {
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            y[0] = r - w;       /* quick check no cancellation */
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        } else {
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            u_int32_t high;
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            j = ix >> 20;
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            y[0] = r - w;
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            GET_HIGH_WORD(high, y[0]);
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            i = j - ((high >> 20) & 0x7ff);
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            if (i > 16) {       /* 2nd iteration needed, good to 118 */
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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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                GET_HIGH_WORD(high, y[0]);
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                i = j - ((high >> 20) & 0x7ff);
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                if (i > 49) {   /* 3rd iteration need, 151 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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        if (hx < 0) {
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            y[0] = -y[0];
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            y[1] = -y[1];
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            return -n;
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        } else
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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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    GET_LOW_WORD(low, x);
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    SET_LOW_WORD(z, low);
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    e0 = (ix >> 20) - 1046;     /* e0 = ilogb(z)-23; */
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    SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20)));
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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)
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        nx--;                   /* skip zero term */
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    n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi);
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    if (hx < 0) {
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        y[0] = -y[0];
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        y[1] = -y[1];
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        return -n;
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    }
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    return n;
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}