lib/msun/src/e_rem_pio2.c

   1
   2 /* @(#)e_rem_pio2.c 1.4 95/01/18 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunSoft, 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 #include <sys/cdefs.h>
  16 __FBSDID("$FreeBSD$");
  17
  18 /* __ieee754_rem_pio2(x,y)
  19  *
  20  * return the remainder of x rem pi/2 in y[0]+y[1]
  21  * use __kernel_rem_pio2()
  22  */
  23
  24 #include <float.h>
  25
  26 #include "math.h"
  27 #include "math_private.h"
  28
  29 static const int32_t npio2_hw[] = {
  30 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
  31 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
  32 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
  33 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
  34 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
  35 0x404858EB, 0x404921FB,
  36 };
  37
  38 /*
  39  * invpio2:  53 bits of 2/pi
  40  * pio2_1:   first  33 bit of pi/2
  41  * pio2_1t:  pi/2 - pio2_1
  42  * pio2_2:   second 33 bit of pi/2
  43  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
  44  * pio2_3:   third  33 bit of pi/2
  45  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
  46  */
  47
  48 static const double
  49 zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  50 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  51 two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
  52 invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  53 pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
  54 pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
  55 pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
  56 pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
  57 pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
  58 pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
  59
  60 #ifdef INLINE_REM_PIO2
  61 extern inline
  62 #endif
  63 int
  64 __ieee754_rem_pio2(double x, double *y)
  65 {
  66         double z,w,t,r,fn;
  67         double tx[3];
  68         int32_t e0,i,j,nx,n,ix,hx;
  69         u_int32_t low;
  70
  71         GET_HIGH_WORD(hx,x);            /* high word of x */
  72         ix = hx&0x7fffffff;
  73 #if 0 /* Must be handled in caller. */
  74         if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
  75             {y[0] = x; y[1] = 0; return 0;}
  76 #endif
  77         if (ix <= 0x400f6a7a) {         /* |x| ~<= 5pi/4 */
  78             if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
  79                 goto medium;            /* cancellation -- use medium case */
  80             if (ix <= 0x4002d97c) {     /* |x| ~<= 3pi/4 */
  81                 if (hx > 0) {
  82                     z = x - pio2_1;     /* one round good to 85 bits */
  83                     y[0] = z - pio2_1t;
  84                     y[1] = (z-y[0])-pio2_1t;
  85                     return 1;
  86                 } else {
  87                     z = x + pio2_1;
  88                     y[0] = z + pio2_1t;
  89                     y[1] = (z-y[0])+pio2_1t;
  90                     return -1;
  91                 }
  92             } else {
  93                 if (hx > 0) {
  94                     z = x - 2*pio2_1;
  95                     y[0] = z - 2*pio2_1t;
  96                     y[1] = (z-y[0])-2*pio2_1t;
  97                     return 2;
  98                 } else {
  99                     z = x + 2*pio2_1;
 100                     y[0] = z + 2*pio2_1t;
 101                     y[1] = (z-y[0])+2*pio2_1t;
 102                     return -2;
 103                 }
 104             }
 105         }
 106         if (ix <= 0x401c463b) {         /* |x| ~<= 9pi/4 */
 107             if (ix <= 0x4015fdbc) {     /* |x| ~<= 7pi/4 */
 108                 if (ix == 0x4012d97c)   /* |x| ~= 3pi/2 */
 109                     goto medium;
 110                 if (hx > 0) {
 111                     z = x - 3*pio2_1;
 112                     y[0] = z - 3*pio2_1t;
 113                     y[1] = (z-y[0])-3*pio2_1t;
 114                     return 3;
 115                 } else {
 116                     z = x + 3*pio2_1;
 117                     y[0] = z + 3*pio2_1t;
 118                     y[1] = (z-y[0])+3*pio2_1t;
 119                     return -3;
 120                 }
 121             } else {
 122                 if (ix == 0x401921fb)   /* |x| ~= 4pi/2 */
 123                     goto medium;
 124                 if (hx > 0) {
 125                     z = x - 4*pio2_1;
 126                     y[0] = z - 4*pio2_1t;
 127                     y[1] = (z-y[0])-4*pio2_1t;
 128                     return 4;
 129                 } else {
 130                     z = x + 4*pio2_1;
 131                     y[0] = z + 4*pio2_1t;
 132                     y[1] = (z-y[0])+4*pio2_1t;
 133                     return -4;
 134                 }
 135             }
 136         }
 137         if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
 138 medium:
 139             t  = fabs(x);
 140 #ifdef HAVE_EFFICIENT_IRINT
 141             /* Use a specialized rint() to get fn.  Assume round-to-nearest. */
 142             STRICT_ASSIGN(double,fn,t*invpio2+0x1.8p52);
 143             fn = fn-0x1.8p52;
 144             n  = irint(fn);
 145 #else
 146             n  = (int32_t) (t*invpio2+half);
 147             fn = (double)n;
 148 #endif
 149             r  = t-fn*pio2_1;
 150             w  = fn*pio2_1t;    /* 1st round good to 85 bit */
 151             if(n<32&&ix!=npio2_hw[n-1]) {
 152                 y[0] = r-w;     /* quick check no cancellation */
 153             } else {
 154                 u_int32_t high;
 155                 j  = ix>>20;
 156                 y[0] = r-w;
 157                 GET_HIGH_WORD(high,y[0]);
 158                 i = j-((high>>20)&0x7ff);
 159                 if(i>16) {  /* 2nd iteration needed, good to 118 */
 160                     t  = r;
 161                     w  = fn*pio2_2;
 162                     r  = t-w;
 163                     w  = fn*pio2_2t-((t-r)-w);
 164                     y[0] = r-w;
 165                     GET_HIGH_WORD(high,y[0]);
 166                     i = j-((high>>20)&0x7ff);
 167                     if(i>49)  { /* 3rd iteration need, 151 bits acc */
 168                         t  = r; /* will cover all possible cases */
 169                         w  = fn*pio2_3;
 170                         r  = t-w;
 171                         w  = fn*pio2_3t-((t-r)-w);
 172                         y[0] = r-w;
 173                     }
 174                 }
 175             }
 176             y[1] = (r-y[0])-w;
 177             if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 178             else         return n;
 179         }
 180     /*
 181      * all other (large) arguments
 182      */
 183         if(ix>=0x7ff00000) {            /* x is inf or NaN */
 184             y[0]=y[1]=x-x; return 0;
 185         }
 186     /* set z = scalbn(|x|,ilogb(x)-23) */
 187         GET_LOW_WORD(low,x);
 188         SET_LOW_WORD(z,low);
 189         e0      = (ix>>20)-1046;        /* e0 = ilogb(z)-23; */
 190         SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
 191         for(i=0;i<2;i++) {
 192                 tx[i] = (double)((int32_t)(z));
 193                 z     = (z-tx[i])*two24;
 194         }
 195         tx[2] = z;
 196         nx = 3;
 197         while(tx[nx-1]==zero) nx--;     /* skip zero term */
 198         n  =  __kernel_rem_pio2(tx,y,e0,nx,2);
 199         if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 200         return n;
 201 }