sysdeps/libm-ieee754/e_rem_pio2.c

   1 /* @(#)e_rem_pio2.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
  15 #endif
  16
  17 /* __ieee754_rem_pio2(x,y)
  18  *
  19  * return the remainder of x rem pi/2 in y[0]+y[1]
  20  * use __kernel_rem_pio2()
  21  */
  22
  23 #include "math.h"
  24 #include "math_private.h"
  25
  26 /*
  27  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
  28  */
  29 #ifdef __STDC__
  30 static const int32_t two_over_pi[] = {
  31 #else
  32 static int32_t two_over_pi[] = {
  33 #endif
  34 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
  35 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
  36 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
  37 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
  38 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
  39 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
  40 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
  41 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
  42 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
  43 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
  44 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
  45 };
  46
  47 #ifdef __STDC__
  48 static const int32_t npio2_hw[] = {
  49 #else
  50 static int32_t npio2_hw[] = {
  51 #endif
  52 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
  53 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
  54 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
  55 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
  56 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
  57 0x404858EB, 0x404921FB,
  58 };
  59
  60 /*
  61  * invpio2:  53 bits of 2/pi
  62  * pio2_1:   first  33 bit of pi/2
  63  * pio2_1t:  pi/2 - pio2_1
  64  * pio2_2:   second 33 bit of pi/2
  65  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
  66  * pio2_3:   third  33 bit of pi/2
  67  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
  68  */
  69
  70 #ifdef __STDC__
  71 static const double
  72 #else
  73 static double
  74 #endif
  75 zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  76 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  77 two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
  78 invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  79 pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
  80 pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
  81 pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
  82 pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
  83 pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
  84 pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
  85
  86 #ifdef __STDC__
  87         int32_t __ieee754_rem_pio2(double x, double *y)
  88 #else
  89         int32_t __ieee754_rem_pio2(x,y)
  90         double x,y[];
  91 #endif
  92 {
  93         double z,w,t,r,fn;
  94         double tx[3];
  95         int32_t e0,i,j,nx,n,ix,hx;
  96         u_int32_t low;
  97
  98         GET_HIGH_WORD(hx,x);            /* high word of x */
  99         ix = hx&0x7fffffff;
 100         if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
 101             {y[0] = x; y[1] = 0; return 0;}
 102         if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
 103             if(hx>0) {
 104                 z = x - pio2_1;
 105                 if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
 106                     y[0] = z - pio2_1t;
 107                     y[1] = (z-y[0])-pio2_1t;
 108                 } else {                /* near pi/2, use 33+33+53 bit pi */
 109                     z -= pio2_2;
 110                     y[0] = z - pio2_2t;
 111                     y[1] = (z-y[0])-pio2_2t;
 112                 }
 113                 return 1;
 114             } else {    /* negative x */
 115                 z = x + pio2_1;
 116                 if(ix!=0x3ff921fb) {    /* 33+53 bit pi is good enough */
 117                     y[0] = z + pio2_1t;
 118                     y[1] = (z-y[0])+pio2_1t;
 119                 } else {                /* near pi/2, use 33+33+53 bit pi */
 120                     z += pio2_2;
 121                     y[0] = z + pio2_2t;
 122                     y[1] = (z-y[0])+pio2_2t;
 123                 }
 124                 return -1;
 125             }
 126         }
 127         if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
 128             t  = fabs(x);
 129             n  = (int32_t) (t*invpio2+half);
 130             fn = (double)n;
 131             r  = t-fn*pio2_1;
 132             w  = fn*pio2_1t;    /* 1st round good to 85 bit */
 133             if(n<32&&ix!=npio2_hw[n-1]) {
 134                 y[0] = r-w;     /* quick check no cancellation */
 135             } else {
 136                 u_int32_t high;
 137                 j  = ix>>20;
 138                 y[0] = r-w;
 139                 GET_HIGH_WORD(high,y[0]);
 140                 i = j-((high>>20)&0x7ff);
 141                 if(i>16) {  /* 2nd iteration needed, good to 118 */
 142                     t  = r;
 143                     w  = fn*pio2_2;
 144                     r  = t-w;
 145                     w  = fn*pio2_2t-((t-r)-w);
 146                     y[0] = r-w;
 147                     GET_HIGH_WORD(high,y[0]);
 148                     i = j-((high>>20)&0x7ff);
 149                     if(i>49)  { /* 3rd iteration need, 151 bits acc */
 150                         t  = r; /* will cover all possible cases */
 151                         w  = fn*pio2_3;
 152                         r  = t-w;
 153                         w  = fn*pio2_3t-((t-r)-w);
 154                         y[0] = r-w;
 155                     }
 156                 }
 157             }
 158             y[1] = (r-y[0])-w;
 159             if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 160             else         return n;
 161         }
 162     /*
 163      * all other (large) arguments
 164      */
 165         if(ix>=0x7ff00000) {            /* x is inf or NaN */
 166             y[0]=y[1]=x-x; return 0;
 167         }
 168     /* set z = scalbn(|x|,ilogb(x)-23) */
 169         GET_LOW_WORD(low,x);
 170         SET_LOW_WORD(z,low);
 171         e0      = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
 172         SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
 173         for(i=0;i<2;i++) {
 174                 tx[i] = (double)((int32_t)(z));
 175                 z     = (z-tx[i])*two24;
 176         }
 177         tx[2] = z;
 178         nx = 3;
 179         while(tx[nx-1]==zero) nx--;     /* skip zero term */
 180         n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
 181         if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 182         return n;
 183 }