gonzui

    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: /* __ieee754_rem_pio2(x,y)
   14:  * 
   15:  * return the remainder of x rem pi/2 in y[0]+y[1] 
   16:  * use __kernel_rem_pio2()
   17:  */
   18: 
   19: #include "math.h"
   20: #include "math_private.h"
   21: 
   22: static const int32_t npio2_hw[] = {
   23: 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
   24: 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
   25: 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
   26: 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
   27: 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
   28: 0x404858EB, 0x404921FB,
   29: };
   30: 
   31: /*
   32:  * invpio2:  53 bits of 2/pi
   33:  * pio2_1:   first  33 bit of pi/2
   34:  * pio2_1t:  pi/2 - pio2_1
   35:  * pio2_2:   second 33 bit of pi/2
   36:  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
   37:  * pio2_3:   third  33 bit of pi/2
   38:  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
   39:  */
   40: 
   41: static const double 
   42: zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
   43: half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
   44: two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
   45: invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
   46: pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
   47: pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
   48: pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
   49: pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
   50: pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
   51: pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
   52: 
   53: int32_t
   54: __ieee754_rem_pio2(double x, double *y)
   55: {
   56:         double z,w,t,r,fn;
   57:         double tx[3];
   58:         int32_t e0,i,j,nx,n,ix,hx;
   59:         u_int32_t low;
   60: 
   61:         GET_HIGH_WORD(hx,x);           /* high word of x */
   62:         ix = hx&0x7fffffff;
   63:         if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
   64:             {y[0] = x; y[1] = 0; return 0;}
   65:         if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
   66:             if(hx>0) { 
   67:                 z = x - pio2_1;
   68:                 if(ix!=0x3ff921fb) {  /* 33+53 bit pi is good enough */
   69:                     y[0] = z - pio2_1t;
   70:                     y[1] = (z-y[0])-pio2_1t;
   71:                 } else {              /* near pi/2, use 33+33+53 bit pi */
   72:                     z -= pio2_2;
   73:                     y[0] = z - pio2_2t;
   74:                     y[1] = (z-y[0])-pio2_2t;
   75:                 }
   76:                 return 1;
   77:             } else {   /* negative x */
   78:                 z = x + pio2_1;
   79:                 if(ix!=0x3ff921fb) {  /* 33+53 bit pi is good enough */
   80:                     y[0] = z + pio2_1t;
   81:                     y[1] = (z-y[0])+pio2_1t;
   82:                 } else {              /* near pi/2, use 33+33+53 bit pi */
   83:                     z += pio2_2;
   84:                     y[0] = z + pio2_2t;
   85:                     y[1] = (z-y[0])+pio2_2t;
   86:                 }
   87:                 return -1;
   88:             }
   89:         }
   90:         if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
   91:             t  = fabs(x);
   92:             n  = (int32_t) (t*invpio2+half);
   93:             fn = (double)n;
   94:             r  = t-fn*pio2_1;
   95:             w  = fn*pio2_1t;   /* 1st round good to 85 bit */
   96:             if(n<32&&ix!=npio2_hw[n-1]) {      
   97:                 y[0] = r-w;   /* quick check no cancellation */
   98:             } else {
   99:                 u_int32_t high;
  100:                 j  = ix>>20;
  101:                 y[0] = r-w; 
  102:                 GET_HIGH_WORD(high,y[0]);
  103:                 i = j-((high>>20)&0x7ff);
  104:                 if(i>16) {  /* 2nd iteration needed, good to 118 */
  105:                     t  = r;
  106:                     w  = fn*pio2_2;   
  107:                     r  = t-w;
  108:                     w  = fn*pio2_2t-((t-r)-w);        
  109:                     y[0] = r-w;
  110:                     GET_HIGH_WORD(high,y[0]);
  111:                     i = j-((high>>20)&0x7ff);
  112:                     if(i>49)  {       /* 3rd iteration need, 151 bits acc */
  113:                       t  = r;  /* will cover all possible cases */
  114:                       w  = fn*pio2_3;  
  115:                       r  = t-w;
  116:                       w  = fn*pio2_3t-((t-r)-w);       
  117:                       y[0] = r-w;
  118:                     }
  119:                 }
  120:             }
  121:             y[1] = (r-y[0])-w;
  122:             if(hx<0)   {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  123:             else        return n;
  124:         }
  125:     /* 
  126:      * all other (large) arguments
  127:      */
  128:         if(ix>=0x7ff00000) {           /* x is inf or NaN */
  129:             y[0]=y[1]=x-x; return 0;
  130:         }
  131:     /* set z = scalbn(|x|,ilogb(x)-23) */
  132:         GET_LOW_WORD(low,x);
  133:         SET_LOW_WORD(z,low);
  134:         e0     = (ix>>20)-1046;   /* e0 = ilogb(z)-23; */
  135:         SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
  136:         for(i=0;i<2;i++) {
  137:                 tx[i] = (double)((int32_t)(z));
  138:                 z     = (z-tx[i])*two24;
  139:         }
  140:         tx[2] = z;
  141:         nx = 3;
  142:         while(tx[nx-1]==zero) nx--;    /* skip zero term */
  143:         n  =  __kernel_rem_pio2(tx,y,e0,nx,2);
  144:         if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
  145:         return n;
  146: }