js/src/fdlibm/e_rem_pio2.c

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  39
  40 /* @(#)e_rem_pio2.c 1.4 95/01/18 */
  41 /*
  42  * ====================================================
  43  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  44  *
  45  * Developed at SunSoft, a Sun Microsystems, Inc. business.
  46  * Permission to use, copy, modify, and distribute this
  47  * software is freely granted, provided that this notice
  48  * is preserved.
  49  * ====================================================
  50  *
  51  */
  52
  53 /* __ieee754_rem_pio2(x,y)
  54  *
  55  * return the remainder of x rem pi/2 in y[0]+y[1]
  56  * use __kernel_rem_pio2()
  57  */
  58
  59 #include "fdlibm.h"
  60
  61 /*
  62  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
  63  */
  64 #ifdef __STDC__
  65 static const int two_over_pi[] = {
  66 #else
  67 static int two_over_pi[] = {
  68 #endif
  69 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
  70 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
  71 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
  72 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
  73 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
  74 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
  75 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
  76 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
  77 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
  78 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
  79 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
  80 };
  81
  82 #ifdef __STDC__
  83 static const int npio2_hw[] = {
  84 #else
  85 static int npio2_hw[] = {
  86 #endif
  87 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
  88 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
  89 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
  90 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
  91 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
  92 0x404858EB, 0x404921FB,
  93 };
  94
  95 /*
  96  * invpio2:  53 bits of 2/pi
  97  * pio2_1:   first  33 bit of pi/2
  98  * pio2_1t:  pi/2 - pio2_1
  99  * pio2_2:   second 33 bit of pi/2
 100  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 101  * pio2_3:   third  33 bit of pi/2
 102  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 103  */
 104
 105 #ifdef __STDC__
 106 static const double
 107 #else
 108 static double
 109 #endif
 110 zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
 111 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
 112 two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
 113 invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
 114 pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
 115 pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
 116 pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
 117 pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
 118 pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
 119 pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
 120
 121 #ifdef __STDC__
 122         int __ieee754_rem_pio2(double x, double *y)
 123 #else
 124         int __ieee754_rem_pio2(x,y)
 125         double x,y[];
 126 #endif
 127 {
 128         fd_twoints u, ux, uz;
 129         double z = 0;
 130         double w,t,r,fn;
 131         double tx[3];
 132         int e0,i,j,nx,n,ix,hx;
 133
 134         u.d = x;
 135         hx = __HI(u);           /* high word of x */
 136         ix = hx&0x7fffffff;
 137         if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
 138             {y[0] = x; y[1] = 0; return 0;}
 139         if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
 140             if(hx>0) {
 141                 z = x - pio2_1;
 142                 if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
 143                     y[0] = z - pio2_1t;
 144                     y[1] = (z-y[0])-pio2_1t;
 145                 } else {                /* near pi/2, use 33+33+53 bit pi */
 146                     z -= pio2_2;
 147                     y[0] = z - pio2_2t;
 148                     y[1] = (z-y[0])-pio2_2t;
 149                 }
 150                 return 1;
 151             } else {    /* negative x */
 152                 z = x + pio2_1;
 153                 if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
 154                     y[0] = z + pio2_1t;
 155                     y[1] = (z-y[0])+pio2_1t;
 156                 } else {                /* near pi/2, use 33+33+53 bit pi */
 157                     z += pio2_2;
 158                     y[0] = z + pio2_2t;
 159                     y[1] = (z-y[0])+pio2_2t;
 160                 }
 161                 return -1;
 162             }
 163         }
 164         if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
 165             t  = fd_fabs(x);
 166             n  = (int) (t*invpio2+half);
 167             fn = (double)n;
 168             r  = t-fn*pio2_1;
 169             w  = fn*pio2_1t;    /* 1st round good to 85 bit */
 170             if(n<32&&ix!=npio2_hw[n-1]) {
 171                 y[0] = r-w;     /* quick check no cancellation */
 172             } else {
 173                 j  = ix>>20;
 174                 y[0] = r-w;
 175                 u.d = y[0];
 176                 i = j-(((__HI(u))>>20)&0x7ff);
 177                 if(i>16) {  /* 2nd iteration needed, good to 118 */
 178                     t  = r;
 179                     w  = fn*pio2_2;
 180                     r  = t-w;
 181                     w  = fn*pio2_2t-((t-r)-w);
 182                     y[0] = r-w;
 183                     u.d = y[0];
 184                     i = j-(((__HI(u))>>20)&0x7ff);
 185                     if(i>49)  { /* 3rd iteration need, 151 bits acc */
 186                         t  = r; /* will cover all possible cases */
 187                         w  = fn*pio2_3;
 188                         r  = t-w;
 189                         w  = fn*pio2_3t-((t-r)-w);
 190                         y[0] = r-w;
 191                     }
 192                 }
 193             }
 194             y[1] = (r-y[0])-w;
 195             if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 196             else         return n;
 197         }
 198     /*
 199      * all other (large) arguments
 200      */
 201         if(ix>=0x7ff00000) {            /* x is inf or NaN */
 202             y[0]=y[1]=x-x; return 0;
 203         }
 204     /* set z = scalbn(|x|,ilogb(x)-23) */
 205         ux.d = x; uz.d = z;
 206         __LO(uz) = __LO(ux);
 207         z = uz.d;
 208         e0      = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
 209         uz.d = z;
 210         __HI(uz) = ix - (e0<<20);
 211         z = uz.d;
 212         for(i=0;i<2;i++) {
 213                 tx[i] = (double)((int)(z));
 214                 z     = (z-tx[i])*two24;
 215         }
 216         tx[2] = z;
 217         nx = 3;
 218         while(tx[nx-1]==zero) nx--;     /* skip zero term */
 219         n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
 220         if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 221         return n;
 222 }