lib/libm/src/e_rem_pio2f.c

   1 /* e_rem_pio2f.c -- float version of e_rem_pio2.c
   2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 /* __ieee754_rem_pio2f(x,y)
  17  *
  18  * return the remainder of x rem pi/2 in y[0]+y[1]
  19  * use __kernel_rem_pio2f()
  20  */
  21
  22 #include "math.h"
  23 #include "math_private.h"
  24
  25 /*
  26  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
  27  */
  28 static const int32_t two_over_pi[] = {
  29 0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
  30 0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
  31 0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
  32 0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
  33 0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
  34 0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
  35 0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
  36 0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
  37 0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
  38 0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
  39 0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
  40 0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
  41 0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
  42 0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
  43 0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
  44 0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
  45 0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
  46 0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
  47 0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
  48 0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
  49 0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
  50 0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
  51 };
  52
  53 /* This array is like the one in e_rem_pio2.c, but the numbers are
  54    single precision and the last 8 bits are forced to 0.  */
  55 static const int32_t npio2_hw[] = {
  56 0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
  57 0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
  58 0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
  59 0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
  60 0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
  61 0x4242c700, 0x42490f00
  62 };
  63
  64 /*
  65  * invpio2:  24 bits of 2/pi
  66  * pio2_1:   first  17 bit of pi/2
  67  * pio2_1t:  pi/2 - pio2_1
  68  * pio2_2:   second 17 bit of pi/2
  69  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
  70  * pio2_3:   third  17 bit of pi/2
  71  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
  72  */
  73
  74 static const float
  75 zero =  0.0000000000e+00, /* 0x00000000 */
  76 half =  5.0000000000e-01, /* 0x3f000000 */
  77 two8 =  2.5600000000e+02, /* 0x43800000 */
  78 invpio2 =  6.3661980629e-01, /* 0x3f22f984 */
  79 pio2_1  =  1.5707855225e+00, /* 0x3fc90f80 */
  80 pio2_1t =  1.0804334124e-05, /* 0x37354443 */
  81 pio2_2  =  1.0804273188e-05, /* 0x37354400 */
  82 pio2_2t =  6.0770999344e-11, /* 0x2e85a308 */
  83 pio2_3  =  6.0770943833e-11, /* 0x2e85a300 */
  84 pio2_3t =  6.1232342629e-17; /* 0x248d3132 */
  85
  86 int32_t
  87 __ieee754_rem_pio2f(float x, float *y)
  88 {
  89         float z,w,t,r,fn;
  90         float tx[3];
  91         int32_t e0,i,j,nx,n,ix,hx;
  92
  93         GET_FLOAT_WORD(hx,x);
  94         ix = hx&0x7fffffff;
  95         if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
  96             {y[0] = x; y[1] = 0; return 0;}
  97         if(ix<0x4016cbe4) {  /* |x| < 3pi/4, special case with n=+-1 */
  98             if(hx>0) {
  99                 z = x - pio2_1;
 100                 if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
 101                     y[0] = z - pio2_1t;
 102                     y[1] = (z-y[0])-pio2_1t;
 103                 } else {                /* near pi/2, use 24+24+24 bit pi */
 104                     z -= pio2_2;
 105                     y[0] = z - pio2_2t;
 106                     y[1] = (z-y[0])-pio2_2t;
 107                 }
 108                 return 1;
 109             } else {    /* negative x */
 110                 z = x + pio2_1;
 111                 if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
 112                     y[0] = z + pio2_1t;
 113                     y[1] = (z-y[0])+pio2_1t;
 114                 } else {                /* near pi/2, use 24+24+24 bit pi */
 115                     z += pio2_2;
 116                     y[0] = z + pio2_2t;
 117                     y[1] = (z-y[0])+pio2_2t;
 118                 }
 119                 return -1;
 120             }
 121         }
 122         if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
 123             t  = fabsf(x);
 124             n  = (int32_t) (t*invpio2+half);
 125             fn = (float)n;
 126             r  = t-fn*pio2_1;
 127             w  = fn*pio2_1t;    /* 1st round good to 40 bit */
 128             if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {
 129                 y[0] = r-w;     /* quick check no cancellation */
 130             } else {
 131                 u_int32_t high;
 132                 j  = ix>>23;
 133                 y[0] = r-w;
 134                 GET_FLOAT_WORD(high,y[0]);
 135                 i = j-((high>>23)&0xff);
 136                 if(i>8) {  /* 2nd iteration needed, good to 57 */
 137                     t  = r;
 138                     w  = fn*pio2_2;
 139                     r  = t-w;
 140                     w  = fn*pio2_2t-((t-r)-w);
 141                     y[0] = r-w;
 142                     GET_FLOAT_WORD(high,y[0]);
 143                     i = j-((high>>23)&0xff);
 144                     if(i>25)  { /* 3rd iteration need, 74 bits acc */
 145                         t  = r; /* will cover all possible cases */
 146                         w  = fn*pio2_3;
 147                         r  = t-w;
 148                         w  = fn*pio2_3t-((t-r)-w);
 149                         y[0] = r-w;
 150                     }
 151                 }
 152             }
 153             y[1] = (r-y[0])-w;
 154             if(hx<0)    {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 155             else         return n;
 156         }
 157     /*
 158      * all other (large) arguments
 159      */
 160         if(ix>=0x7f800000) {            /* x is inf or NaN */
 161             y[0]=y[1]=x-x; return 0;
 162         }
 163     /* set z = scalbn(|x|,ilogb(x)-7) */
 164         e0      = (ix>>23)-134;         /* e0 = ilogb(z)-7; */
 165         SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23)));
 166         for(i=0;i<2;i++) {
 167                 tx[i] = (float)((int32_t)(z));
 168                 z     = (z-tx[i])*two8;
 169         }
 170         tx[2] = z;
 171         nx = 3;
 172         while(tx[nx-1]==zero) nx--;     /* skip zero term */
 173         n  =  __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
 174         if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
 175         return n;
 176 }