nsz Git - libm/blob - src/math/__rem_pio2.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunSoft, 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  * Optimized by Bruce D. Evans.
  13  */
  14 /* __rem_pio2(x,y)
  15  *
  16  * return the remainder of x rem pi/2 in y[0]+y[1]
  17  * use __rem_pio2_slow()
  18  */
  19
  20 #include "libm.h"
  21
  22 /*
  23  * invpio2:  53 bits of 2/pi
  24  * pio2_1:   first  33 bit of pi/2
  25  * pio2_1t:  pi/2 - pio2_1
  26  * pio2_2:   second 33 bit of pi/2
  27  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
  28  * pio2_3:   third  33 bit of pi/2
  29  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
  30  */
  31 static const double
  32 zero    = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  33 two24   = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
  34 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  35 pio2_1  = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
  36 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
  37 pio2_2  = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
  38 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
  39 pio2_3  = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
  40 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
  41
  42 /* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
  43 int __rem_pio2(double x, double *y)
  44 {
  45         double z,w,t,r,fn;
  46         double tx[3],ty[2];
  47         int32_t e0,i,j,nx,n,ix,hx;
  48         uint32_t low;
  49
  50         GET_HIGH_WORD(hx,x);
  51         ix = hx & 0x7fffffff;
  52         if (ix <= 0x400f6a7a) {  /* |x| ~<= 5pi/4 */
  53                 if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
  54                         goto medium;  /* cancellation -- use medium case */
  55                 if (ix <= 0x4002d97c) {  /* |x| ~<= 3pi/4 */
  56                         if (hx > 0) {
  57                                 z = x - pio2_1;  /* one round good to 85 bits */
  58                                 y[0] = z - pio2_1t;
  59                                 y[1] = (z-y[0]) - pio2_1t;
  60                                 return 1;
  61                         } else {
  62                                 z = x + pio2_1;
  63                                 y[0] = z + pio2_1t;
  64                                 y[1] = (z-y[0]) + pio2_1t;
  65                                 return -1;
  66                         }
  67                 } else {
  68                         if (hx > 0) {
  69                                 z = x - 2*pio2_1;
  70                                 y[0] = z - 2*pio2_1t;
  71                                 y[1] = (z-y[0]) - 2*pio2_1t;
  72                                 return 2;
  73                         } else {
  74                                 z = x + 2*pio2_1;
  75                                 y[0] = z + 2*pio2_1t;
  76                                 y[1] = (z-y[0]) + 2*pio2_1t;
  77                                 return -2;
  78                         }
  79                 }
  80         }
  81         if (ix <= 0x401c463b) {  /* |x| ~<= 9pi/4 */
  82                 if (ix <= 0x4015fdbc) {  /* |x| ~<= 7pi/4 */
  83                         if (ix == 0x4012d97c)  /* |x| ~= 3pi/2 */
  84                                 goto medium;
  85                         if (hx > 0) {
  86                                 z = x - 3*pio2_1;
  87                                 y[0] = z - 3*pio2_1t;
  88                                 y[1] = (z-y[0]) - 3*pio2_1t;
  89                                 return 3;
  90                         } else {
  91                                 z = x + 3*pio2_1;
  92                                 y[0] = z + 3*pio2_1t;
  93                                 y[1] = (z-y[0]) + 3*pio2_1t;
  94                                 return -3;
  95                         }
  96                 } else {
  97                         if (ix == 0x401921fb)  /* |x| ~= 4pi/2 */
  98                                 goto medium;
  99                         if (hx > 0) {
 100                                 z = x - 4*pio2_1;
 101                                 y[0] = z - 4*pio2_1t;
 102                                 y[1] = (z-y[0]) - 4*pio2_1t;
 103                                 return 4;
 104                         } else {
 105                                 z = x + 4*pio2_1;
 106                                 y[0] = z + 4*pio2_1t;
 107                                 y[1] = (z-y[0]) + 4*pio2_1t;
 108                                 return -4;
 109                         }
 110                 }
 111         }
 112         if (ix < 0x413921fb) {  /* |x| ~< 2^20*(pi/2), medium size */
 113                 uint32_t high;
 114 medium:
 115                 /* Use a specialized rint() to get fn.  Assume round-to-nearest. */
 116                 STRICT_ASSIGN(double, fn, x*invpio2 + 0x1.8p52);
 117                 fn = fn - 0x1.8p52;
 118 // FIXME
 119 #ifdef HAVE_EFFICIENT_IRINT
 120                 n = irint(fn);
 121 #else
 122                 n = (int32_t)fn;
 123 #endif
 124                 r = x - fn*pio2_1;
 125                 w = fn*pio2_1t;  /* 1st round, good to 85 bits */
 126                 j = ix>>20;
 127                 y[0] = r - w;
 128                 GET_HIGH_WORD(high,y[0]);
 129                 i = j - ((high>>20)&0x7ff);
 130                 if (i > 16) {  /* 2nd round, good to 118 bits */
 131                         t = r;
 132                         w = fn*pio2_2;
 133                         r = t - w;
 134                         w = fn*pio2_2t - ((t-r)-w);
 135                         y[0] = r - w;
 136                         GET_HIGH_WORD(high,y[0]);
 137                         i = j - ((high>>20)&0x7ff);
 138                         if (i > 49) {  /* 3rd round, good to 151 bits, covers all cases */
 139                                 t = r;
 140                                 w = fn*pio2_3;
 141                                 r = t - w;
 142                                 w = fn*pio2_3t - ((t-r)-w);
 143                                 y[0] = r - w;
 144                         }
 145                 }
 146                 y[1] = (r-y[0]) - w;
 147                 return n;
 148         }
 149         /*
 150          * all other (large) arguments
 151          */
 152         if (ix >= 0x7ff00000) {  /* x is inf or NaN */
 153                 y[0] = y[1] = x - x;
 154                 return 0;
 155         }
 156         /* set z = scalbn(|x|,ilogb(x)-23) */
 157         GET_LOW_WORD(low,x);
 158         e0 = (ix>>20) - 1046;  /* e0 = ilogb(z)-23; */
 159         INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low);
 160         for (i=0; i<2; i++) {
 161                 tx[i] = (double)((int32_t)(z));
 162                 z = (z-tx[i])*two24;
 163         }
 164         tx[2] = z;
 165         nx = 3;
 166         while (tx[nx-1] == zero) nx--;  /* skip zero term */
 167         n = __rem_pio2_slow(tx,ty,e0,nx,1);
 168         if (hx < 0) {
 169                 y[0] = -ty[0];
 170                 y[1] = -ty[1];
 171                 return -n;
 172         }
 173         y[0] = ty[0];
 174         y[1] = ty[1];
 175         return n;
 176 }