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  1.  
  2. /* @(#)e_hypot.c 5.1 93/09/24 */
  3. /*
  4.  * ====================================================
  5.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  6.  *
  7.  * Developed at SunPro, 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. /* __ieee754_hypot(x,y)
  15.  *
  16.  * Method :                  
  17.  *      If (assume round-to-nearest) z=x*x+y*y
  18.  *      has error less than sqrt(2)/2 ulp, than
  19.  *      sqrt(z) has error less than 1 ulp (exercise).
  20.  *
  21.  *      So, compute sqrt(x*x+y*y) with some care as
  22.  *      follows to get the error below 1 ulp:
  23.  *
  24.  *      Assume x>y>0;
  25.  *      (if possible, set rounding to round-to-nearest)
  26.  *      1. if x > 2y  use
  27.  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  28.  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  29.  *      2. if x <= 2y use
  30.  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  31.  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  32.  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  33.  *             
  34.  *      NOTE: scaling may be necessary if some argument is too
  35.  *            large or too tiny
  36.  *
  37.  * Special cases:
  38.  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  39.  *      hypot(x,y) is NAN if x or y is NAN.
  40.  *
  41.  * Accuracy:
  42.  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  43.  *      than 1 ulps (units in the last place)
  44.  */
  45.  
  46. #include "fdlibm.h"
  47.  
  48. #ifndef _DOUBLE_IS_32BITS
  49.  
  50. #ifdef __STDC__
  51.         double __ieee754_hypot(double x, double y)
  52. #else
  53.         double __ieee754_hypot(x,y)
  54.         double x, y;
  55. #endif
  56. {
  57.         double a=x,b=y,t1,t2,y1,y2,w;
  58.         __int32_t j,k,ha,hb;
  59.  
  60.         GET_HIGH_WORD(ha,x);
  61.         ha &= 0x7fffffff;
  62.         GET_HIGH_WORD(hb,y);
  63.         hb &= 0x7fffffff;
  64.         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  65.         SET_HIGH_WORD(a,ha);    /* a <- |a| */
  66.         SET_HIGH_WORD(b,hb);    /* b <- |b| */
  67.         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  68.         k=0;
  69.         if(ha > 0x5f300000) {   /* a>2**500 */
  70.            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  71.                __uint32_t low;
  72.                w = a+b;                 /* for sNaN */
  73.                GET_LOW_WORD(low,a);
  74.                if(((ha&0xfffff)|low)==0) w = a;
  75.                GET_LOW_WORD(low,b);
  76.                if(((hb^0x7ff00000)|low)==0) w = b;
  77.                return w;
  78.            }
  79.            /* scale a and b by 2**-600 */
  80.            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  81.            SET_HIGH_WORD(a,ha);
  82.            SET_HIGH_WORD(b,hb);
  83.         }
  84.         if(hb < 0x20b00000) {   /* b < 2**-500 */
  85.             if(hb <= 0x000fffff) {      /* subnormal b or 0 */ 
  86.                 __uint32_t low;
  87.                 GET_LOW_WORD(low,b);
  88.                 if((hb|low)==0) return a;
  89.                 t1=0;
  90.                 SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
  91.                 b *= t1;
  92.                 a *= t1;
  93.                 k -= 1022;
  94.             } else {            /* scale a and b by 2^600 */
  95.                 ha += 0x25800000;       /* a *= 2^600 */
  96.                 hb += 0x25800000;       /* b *= 2^600 */
  97.                 k -= 600;
  98.                 SET_HIGH_WORD(a,ha);
  99.                 SET_HIGH_WORD(b,hb);
  100.             }
  101.         }
  102.     /* medium size a and b */
  103.         w = a-b;
  104.         if (w>b) {
  105.             t1 = 0;
  106.             SET_HIGH_WORD(t1,ha);
  107.             t2 = a-t1;
  108.             w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
  109.         } else {
  110.             a  = a+a;
  111.             y1 = 0;
  112.             SET_HIGH_WORD(y1,hb);
  113.             y2 = b - y1;
  114.             t1 = 0;
  115.             SET_HIGH_WORD(t1,ha+0x00100000);
  116.             t2 = a - t1;
  117.             w  = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
  118.         }
  119.         if(k!=0) {
  120.             __uint32_t high;
  121.             t1 = 1.0;
  122.             GET_HIGH_WORD(high,t1);
  123.             SET_HIGH_WORD(t1,high+(k<<20));
  124.             return t1*w;
  125.         } else return w;
  126. }
  127.  
  128. #endif /* defined(_DOUBLE_IS_32BITS) */
  129.