e_rem_pio2.c

/*
 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

/* __ieee754_rem_pio2(x,y)
 *
 * return the remainder of x rem pi/2 in y[0]+y[1]
 * use __kernel_rem_pio2()
 */

#include "fdlibm.h"

/*
 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
 */
#ifdef __STDC__
static const int two_over_pi[] = {
#else
static int two_over_pi[] = {
#endif
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
};

#ifdef __STDC__
static const int npio2_hw[] = {
#else
static int npio2_hw[] = {
#endif
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 0x404921FB,
};

/*
 * invpio2:  53 bits of 2/pi
 * pio2_1:   first  33 bit of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 33 bit of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  33 bit of pi/2
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */

#ifdef __STDC__
static const double
#else
static double
#endif
zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */

#ifdef __STDC__
        int __ieee754_rem_pio2(double x, double *y)
#else
        int __ieee754_rem_pio2(x,y)
        double x,y[];
#endif
{
        double z,w,t,r,fn;
        double tx[3];
        int e0,i,j,nx,n,ix,hx;

        hx = __HI(x);           /* high word of x */
        ix = hx&0x7fffffff;
        if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
            {y[0] = x; y[1] = 0; return 0;}
        if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
            if(hx>0) {
                z = x - pio2_1;
                if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
                    y[0] = z - pio2_1t;
                    y[1] = (z-y[0])-pio2_1t;
                } else {                /* near pi/2, use 33+33+53 bit pi */
                    z -= pio2_2;
                    y[0] = z - pio2_2t;
                    y[1] = (z-y[0])-pio2_2t;
                }
                return 1;
            } else {    /* negative x */
                z = x + pio2_1;
                if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
                    y[0] = z + pio2_1t;
                    y[1] = (z-y[0])+pio2_1t;
                } else {                /* near pi/2, use 33+33+53 bit pi */
                    z += pio2_2;
                    y[0] = z + pio2_2t;
                    y[1] = (z-y[0])+pio2_2t;
                }
                return -1;
            }
        }
        if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
            t  = fabs(x);
            n  = (int) (t*invpio2+half);
            fn = (double)n;
            r  = t-fn*pio2_1;
            w  = fn*pio2_1t;    /* 1st round good to 85 bit */
            if(n<32&&ix!=npio2_hw[n-1]) {
                y[0] = r-w;     /* quick check no cancellation */
            } else {
                j  = ix>>20;
                y[0] = r-w;
                i = j-(((__HI(y[0]))>>20)&0x7ff);
                if(i>16) {  /* 2nd iteration needed, good to 118 */
                    t  = r;
                    w  = fn*pio2_2;
                    r  = t-w;
                    w  = fn*pio2_2t-((t-r)-w);
                    y[0] = r-w;
                    i = j-(((__HI(y[0]))>>20)&0x7ff);
                    if(i>49)  { /* 3rd iteration need, 151 bits acc */
                        t  = r; /* will cover all possible cases */
                        w  = fn*pio2_3;
                        r  = t-w;
                        w  = fn*pio2_3t-((t-r)-w);
                        y[0] = r-w;
                    }
                }
            }
            y[1] = (r-y[0])-w;
            if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
            else         return n;
        }
    /*
     * all other (large) arguments
     */
        if(ix>=0x7ff00000) {            /* x is inf or NaN */
            y[0]=y[1]=x-x; return 0;
        }
    /* set z = scalbn(|x|,ilogb(x)-23) */
        __LO(z) = __LO(x);
        e0      = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
        __HI(z) = ix - (e0<<20);
        for(i=0;i<2;i++) {
                tx[i] = (double)((int)(z));
                z     = (z-tx[i])*two24;
        }
        tx[2] = z;
        nx = 3;
        while(tx[nx-1]==zero) nx--;     /* skip zero term */
        n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
        if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
        return n;
}