gonzui

    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: }