src/libm/e_rem_pio2.c
changeset 2756 a98604b691c8
child 3162 dc1eb82ffdaa
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/libm/e_rem_pio2.c	Mon Sep 15 06:33:23 2008 +0000
     1.3 @@ -0,0 +1,201 @@
     1.4 +/* @(#)e_rem_pio2.c 5.1 93/09/24 */
     1.5 +/*
     1.6 + * ====================================================
     1.7 + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     1.8 + *
     1.9 + * Developed at SunPro, a Sun Microsystems, Inc. business.
    1.10 + * Permission to use, copy, modify, and distribute this
    1.11 + * software is freely granted, provided that this notice
    1.12 + * is preserved.
    1.13 + * ====================================================
    1.14 + */
    1.15 +
    1.16 +#if defined(LIBM_SCCS) && !defined(lint)
    1.17 +static char rcsid[] =
    1.18 +    "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
    1.19 +#endif
    1.20 +
    1.21 +/* __ieee754_rem_pio2(x,y)
    1.22 + *
    1.23 + * return the remainder of x rem pi/2 in y[0]+y[1]
    1.24 + * use __kernel_rem_pio2()
    1.25 + */
    1.26 +
    1.27 +#include "math.h"
    1.28 +#include "math_private.h"
    1.29 +
    1.30 +libm_hidden_proto(fabs)
    1.31 +
    1.32 +/*
    1.33 + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
    1.34 + */
    1.35 +#ifdef __STDC__
    1.36 +     static const int32_t two_over_pi[] = {
    1.37 +#else
    1.38 +     static int32_t two_over_pi[] = {
    1.39 +#endif
    1.40 +         0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
    1.41 +         0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
    1.42 +         0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
    1.43 +         0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
    1.44 +         0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
    1.45 +         0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
    1.46 +         0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
    1.47 +         0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
    1.48 +         0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
    1.49 +         0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
    1.50 +         0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
    1.51 +     };
    1.52 +
    1.53 +#ifdef __STDC__
    1.54 +static const int32_t npio2_hw[] = {
    1.55 +#else
    1.56 +static int32_t npio2_hw[] = {
    1.57 +#endif
    1.58 +    0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
    1.59 +    0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
    1.60 +    0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
    1.61 +    0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
    1.62 +    0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
    1.63 +    0x404858EB, 0x404921FB,
    1.64 +};
    1.65 +
    1.66 +/*
    1.67 + * invpio2:  53 bits of 2/pi
    1.68 + * pio2_1:   first  33 bit of pi/2
    1.69 + * pio2_1t:  pi/2 - pio2_1
    1.70 + * pio2_2:   second 33 bit of pi/2
    1.71 + * pio2_2t:  pi/2 - (pio2_1+pio2_2)
    1.72 + * pio2_3:   third  33 bit of pi/2
    1.73 + * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
    1.74 + */
    1.75 +
    1.76 +#ifdef __STDC__
    1.77 +static const double
    1.78 +#else
    1.79 +static double
    1.80 +#endif
    1.81 +  zero = 0.00000000000000000000e+00,    /* 0x00000000, 0x00000000 */
    1.82 +    half = 5.00000000000000000000e-01,  /* 0x3FE00000, 0x00000000 */
    1.83 +    two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
    1.84 +    invpio2 = 6.36619772367581382433e-01,       /* 0x3FE45F30, 0x6DC9C883 */
    1.85 +    pio2_1 = 1.57079632673412561417e+00,        /* 0x3FF921FB, 0x54400000 */
    1.86 +    pio2_1t = 6.07710050650619224932e-11,       /* 0x3DD0B461, 0x1A626331 */
    1.87 +    pio2_2 = 6.07710050630396597660e-11,        /* 0x3DD0B461, 0x1A600000 */
    1.88 +    pio2_2t = 2.02226624879595063154e-21,       /* 0x3BA3198A, 0x2E037073 */
    1.89 +    pio2_3 = 2.02226624871116645580e-21,        /* 0x3BA3198A, 0x2E000000 */
    1.90 +    pio2_3t = 8.47842766036889956997e-32;       /* 0x397B839A, 0x252049C1 */
    1.91 +
    1.92 +#ifdef __STDC__
    1.93 +int32_t attribute_hidden
    1.94 +__ieee754_rem_pio2(double x, double *y)
    1.95 +#else
    1.96 +int32_t attribute_hidden
    1.97 +__ieee754_rem_pio2(x, y)
    1.98 +     double x, y[];
    1.99 +#endif
   1.100 +{
   1.101 +    double z = 0.0, w, t, r, fn;
   1.102 +    double tx[3];
   1.103 +    int32_t e0, i, j, nx, n, ix, hx;
   1.104 +    u_int32_t low;
   1.105 +
   1.106 +    GET_HIGH_WORD(hx, x);       /* high word of x */
   1.107 +    ix = hx & 0x7fffffff;
   1.108 +    if (ix <= 0x3fe921fb) {     /* |x| ~<= pi/4 , no need for reduction */
   1.109 +        y[0] = x;
   1.110 +        y[1] = 0;
   1.111 +        return 0;
   1.112 +    }
   1.113 +    if (ix < 0x4002d97c) {      /* |x| < 3pi/4, special case with n=+-1 */
   1.114 +        if (hx > 0) {
   1.115 +            z = x - pio2_1;
   1.116 +            if (ix != 0x3ff921fb) {     /* 33+53 bit pi is good enough */
   1.117 +                y[0] = z - pio2_1t;
   1.118 +                y[1] = (z - y[0]) - pio2_1t;
   1.119 +            } else {            /* near pi/2, use 33+33+53 bit pi */
   1.120 +                z -= pio2_2;
   1.121 +                y[0] = z - pio2_2t;
   1.122 +                y[1] = (z - y[0]) - pio2_2t;
   1.123 +            }
   1.124 +            return 1;
   1.125 +        } else {                /* negative x */
   1.126 +            z = x + pio2_1;
   1.127 +            if (ix != 0x3ff921fb) {     /* 33+53 bit pi is good enough */
   1.128 +                y[0] = z + pio2_1t;
   1.129 +                y[1] = (z - y[0]) + pio2_1t;
   1.130 +            } else {            /* near pi/2, use 33+33+53 bit pi */
   1.131 +                z += pio2_2;
   1.132 +                y[0] = z + pio2_2t;
   1.133 +                y[1] = (z - y[0]) + pio2_2t;
   1.134 +            }
   1.135 +            return -1;
   1.136 +        }
   1.137 +    }
   1.138 +    if (ix <= 0x413921fb) {     /* |x| ~<= 2^19*(pi/2), medium size */
   1.139 +        t = fabs(x);
   1.140 +        n = (int32_t) (t * invpio2 + half);
   1.141 +        fn = (double) n;
   1.142 +        r = t - fn * pio2_1;
   1.143 +        w = fn * pio2_1t;       /* 1st round good to 85 bit */
   1.144 +        if (n < 32 && ix != npio2_hw[n - 1]) {
   1.145 +            y[0] = r - w;       /* quick check no cancellation */
   1.146 +        } else {
   1.147 +            u_int32_t high;
   1.148 +            j = ix >> 20;
   1.149 +            y[0] = r - w;
   1.150 +            GET_HIGH_WORD(high, y[0]);
   1.151 +            i = j - ((high >> 20) & 0x7ff);
   1.152 +            if (i > 16) {       /* 2nd iteration needed, good to 118 */
   1.153 +                t = r;
   1.154 +                w = fn * pio2_2;
   1.155 +                r = t - w;
   1.156 +                w = fn * pio2_2t - ((t - r) - w);
   1.157 +                y[0] = r - w;
   1.158 +                GET_HIGH_WORD(high, y[0]);
   1.159 +                i = j - ((high >> 20) & 0x7ff);
   1.160 +                if (i > 49) {   /* 3rd iteration need, 151 bits acc */
   1.161 +                    t = r;      /* will cover all possible cases */
   1.162 +                    w = fn * pio2_3;
   1.163 +                    r = t - w;
   1.164 +                    w = fn * pio2_3t - ((t - r) - w);
   1.165 +                    y[0] = r - w;
   1.166 +                }
   1.167 +            }
   1.168 +        }
   1.169 +        y[1] = (r - y[0]) - w;
   1.170 +        if (hx < 0) {
   1.171 +            y[0] = -y[0];
   1.172 +            y[1] = -y[1];
   1.173 +            return -n;
   1.174 +        } else
   1.175 +            return n;
   1.176 +    }
   1.177 +    /*
   1.178 +     * all other (large) arguments
   1.179 +     */
   1.180 +    if (ix >= 0x7ff00000) {     /* x is inf or NaN */
   1.181 +        y[0] = y[1] = x - x;
   1.182 +        return 0;
   1.183 +    }
   1.184 +    /* set z = scalbn(|x|,ilogb(x)-23) */
   1.185 +    GET_LOW_WORD(low, x);
   1.186 +    SET_LOW_WORD(z, low);
   1.187 +    e0 = (ix >> 20) - 1046;     /* e0 = ilogb(z)-23; */
   1.188 +    SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20)));
   1.189 +    for (i = 0; i < 2; i++) {
   1.190 +        tx[i] = (double) ((int32_t) (z));
   1.191 +        z = (z - tx[i]) * two24;
   1.192 +    }
   1.193 +    tx[2] = z;
   1.194 +    nx = 3;
   1.195 +    while (tx[nx - 1] == zero)
   1.196 +        nx--;                   /* skip zero term */
   1.197 +    n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi);
   1.198 +    if (hx < 0) {
   1.199 +        y[0] = -y[0];
   1.200 +        y[1] = -y[1];
   1.201 +        return -n;
   1.202 +    }
   1.203 +    return n;
   1.204 +}