gonzui

    1: /* @(#)e_hypot.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: /* LINTLIBRARY */
   14: 
   15: /* hypot(x,y)
   16:  *
   17:  * Method :                  
   18:  *      If (assume round-to-nearest) z=x*x+y*y 
   19:  *      has error less than sqrt(2)/2 ulp, than 
   20:  *      sqrt(z) has error less than 1 ulp (exercise).
   21:  *
   22:  *      So, compute sqrt(x*x+y*y) with some care as 
   23:  *      follows to get the error below 1 ulp:
   24:  *
   25:  *      Assume x>y>0;
   26:  *      (if possible, set rounding to round-to-nearest)
   27:  *      1. if x > 2y  use
   28:  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
   29:  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
   30:  *      2. if x <= 2y use
   31:  *              t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
   32:  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 
   33:  *      yy1= y with lower 32 bits chopped, y2 = y-yy1.
   34:  *              
   35:  *      NOTE: scaling may be necessary if some argument is too 
   36:  *            large or too tiny
   37:  *
   38:  * Special cases:
   39:  *      hypot(x,y) is INF if x or y is +INF or -INF; else
   40:  *      hypot(x,y) is NAN if x or y is NAN.
   41:  *
   42:  * Accuracy:
   43:  *      hypot(x,y) returns sqrt(x^2+y^2) with error less 
   44:  *      than 1 ulps (units in the last place) 
   45:  */
   46: 
   47: #include <sys/cdefs.h>
   48: #include <float.h>
   49: #include <math.h>
   50: 
   51: #include "math_private.h"
   52: 
   53: double
   54: hypot(double x, double y)
   55: {
   56:         double a=x,b=y,t1,t2,yy1,y2,w;
   57:         int32_t j,k,ha,hb;
   58: 
   59:         GET_HIGH_WORD(ha,x);
   60:         ha &= 0x7fffffff;
   61:         GET_HIGH_WORD(hb,y);
   62:         hb &= 0x7fffffff;
   63:         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
   64:         SET_HIGH_WORD(a,ha);   /* a <- |a| */
   65:         SET_HIGH_WORD(b,hb);   /* b <- |b| */
   66:         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
   67:         k=0;
   68:         if(ha > 0x5f300000) {  /* a>2**500 */
   69:            if(ha >= 0x7ff00000) {      /* Inf or NaN */
   70:                u_int32_t low;
   71:                w = a+b;                        /* for sNaN */
   72:                GET_LOW_WORD(low,a);
   73:                if(((ha&0xfffff)|low)==0) w = a;
   74:                GET_LOW_WORD(low,b);
   75:                if(((hb^0x7ff00000)|low)==0) w = b;
   76:                return w;
   77:            }
   78:            /* scale a and b by 2**-600 */
   79:            ha -= 0x25800000; hb -= 0x25800000; k += 600;
   80:            SET_HIGH_WORD(a,ha);
   81:            SET_HIGH_WORD(b,hb);
   82:         }
   83:         if(hb < 0x20b00000) {  /* b < 2**-500 */
   84:             if(hb <= 0x000fffff) {     /* subnormal b or 0 */      
   85:                 u_int32_t low;
   86:                 GET_LOW_WORD(low,b);
   87:                 if((hb|low)==0) return a;
   88:                 t1=0;
   89:                 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
   90:                 b *= t1;
   91:                 a *= t1;
   92:                 k -= 1022;
   93:             } else {           /* scale a and b by 2^600 */
   94:                 ha += 0x25800000;      /* a *= 2^600 */
   95:                 hb += 0x25800000;     /* b *= 2^600 */
   96:                 k -= 600;
   97:                 SET_HIGH_WORD(a,ha);
   98:                 SET_HIGH_WORD(b,hb);
   99:             }
  100:         }
  101:     /* medium size a and b */
  102:         w = a-b;
  103:         if (w>b) {
  104:             t1 = 0;
  105:             SET_HIGH_WORD(t1,ha);
  106:             t2 = a-t1;
  107:             w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
  108:         } else {
  109:             a  = a+a;
  110:             yy1 = 0;
  111:             SET_HIGH_WORD(yy1,hb);
  112:             y2 = b - yy1;
  113:             t1 = 0;
  114:             SET_HIGH_WORD(t1,ha+0x00100000);
  115:             t2 = a - t1;
  116:             w  = sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
  117:         }
  118:         if(k!=0) {
  119:             u_int32_t high;
  120:             t1 = 1.0;
  121:             GET_HIGH_WORD(high,t1);
  122:             SET_HIGH_WORD(t1,high+(k<<20));
  123:             return t1*w;
  124:         } else return w;
  125: }
  126: 
  127: #if     LDBL_MANT_DIG == 53
  128: #ifdef  lint
  129: /* PROTOLIB1 */
  130: long double hypotl(long double, long double);
  131: #else   /* lint */
  132: __weak_alias(hypotl, hypot);
  133: #endif  /* lint */
  134: #endif  /* LDBL_MANT_DIG == 53 */