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Annotation of src/lib/libm/src/e_rem_pio2.c, Revision 1.2

1.1       jtc         1:
                      2: /* @(#)e_rem_pio2.c 5.1 93/09/24 */
                      3: /*
                      4:  * ====================================================
                      5:  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
                      6:  *
                      7:  * Developed at SunPro, a Sun Microsystems, Inc. business.
                      8:  * Permission to use, copy, modify, and distribute this
                      9:  * software is freely granted, provided that this notice
                     10:  * is preserved.
                     11:  * ====================================================
                     12:  *
                     13:  */
                     14:
                     15: /* __ieee754_rem_pio2(x,y)
                     16:  *
                     17:  * return the remainder of x rem pi/2 in y[0]+y[1]
                     18:  * use __kernel_rem_pio2()
                     19:  */
                     20:
1.2     ! jtc        21: #include <math.h>
1.1       jtc        22:
                     23: /*
                     24:  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
                     25:  */
                     26: #ifdef __STDC__
                     27: static const int two_over_pi[] = {
                     28: #else
                     29: static int two_over_pi[] = {
                     30: #endif
                     31: 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
                     32: 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
                     33: 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
                     34: 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
                     35: 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
                     36: 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
                     37: 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
                     38: 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
                     39: 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
                     40: 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
                     41: 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
                     42: };
                     43:
                     44: #ifdef __STDC__
                     45: static const int npio2_hw[] = {
                     46: #else
                     47: static int npio2_hw[] = {
                     48: #endif
                     49: 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
                     50: 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
                     51: 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
                     52: 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
                     53: 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
                     54: 0x404858EB, 0x404921FB,
                     55: };
                     56:
                     57: /*
                     58:  * invpio2:  53 bits of 2/pi
                     59:  * pio2_1:   first  33 bit of pi/2
                     60:  * pio2_1t:  pi/2 - pio2_1
                     61:  * pio2_2:   second 33 bit of pi/2
                     62:  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
                     63:  * pio2_3:   third  33 bit of pi/2
                     64:  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
                     65:  */
                     66:
                     67: #ifdef __STDC__
                     68: static const double
                     69: #else
                     70: static double
                     71: #endif
                     72: zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
                     73: half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
                     74: two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
                     75: invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
                     76: pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
                     77: pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
                     78: pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
                     79: pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
                     80: pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
                     81: pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
                     82:
                     83: #ifdef __STDC__
                     84:        int __ieee754_rem_pio2(double x, double *y)
                     85: #else
                     86:        int __ieee754_rem_pio2(x,y)
                     87:        double x,y[];
                     88: #endif
                     89: {
                     90:        double z,w,t,r,fn;
                     91:        double tx[3];
                     92:        int e0,i,j,nx,n,ix,hx,i0;
                     93:
                     94:        i0 = ((*(int*)&two24)>>30)^1;   /* high word index */
                     95:        hx = *(i0+(int*)&x);            /* high word of x */
                     96:        ix = hx&0x7fffffff;
                     97:        if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
                     98:            {y[0] = x; y[1] = 0; return 0;}
                     99:        if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
                    100:            t  = fabs(x);
                    101:            n  = (int) (t*invpio2+half);
                    102:            fn = (double)n;
                    103:            r  = t-fn*pio2_1;
                    104:            w  = fn*pio2_1t;    /* 1st round good to 85 bit */
                    105:            if(n<32&&ix!=npio2_hw[n-1]) {
                    106:                y[0] = r-w;     /* quick check no cancellation */
                    107:            } else {
                    108:                j  = ix>>20;
                    109:                y[0] = r-w;
                    110:                i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff);
                    111:                if(i>16) {  /* 2nd iteration needed, good to 118 */
                    112:                    t  = r;
                    113:                    w  = fn*pio2_2;
                    114:                    r  = t-w;
                    115:                    w  = fn*pio2_2t-((t-r)-w);
                    116:                    y[0] = r-w;
                    117:                    i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff);
                    118:                    if(i>49)  { /* 3rd iteration need, 151 bits acc */
                    119:                        t  = r; /* will cover all possible cases */
                    120:                        w  = fn*pio2_3;
                    121:                        r  = t-w;
                    122:                        w  = fn*pio2_3t-((t-r)-w);
                    123:                        y[0] = r-w;
                    124:                    }
                    125:                }
                    126:            }
                    127:            y[1] = (r-y[0])-w;
                    128:            if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
                    129:            else         return n;
                    130:        }
                    131:     /*
                    132:      * all other (large) arguments
                    133:      */
                    134:        if(ix>=0x7ff00000) {            /* x is inf or NaN */
                    135:            y[0]=y[1]=x-x; return 0;
                    136:        }
                    137:     /* set z = scalbn(|x|,ilogb(x)-23) */
                    138:        *(1-i0+(int*)&z) = *(1-i0+(int*)&x);
                    139:        e0      = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
                    140:        *(i0+(int*)&z) = ix - (e0<<20);
                    141:        for(i=0;i<2;i++) {
                    142:                tx[i] = (double)((int)(z));
                    143:                z     = (z-tx[i])*two24;
                    144:        }
                    145:        tx[2] = z;
                    146:        nx = 3;
                    147:        while(tx[nx-1]==zero) nx--;     /* skip zero term */
                    148:        n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
                    149:        if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
                    150:        return n;
                    151: }