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  1. /* Copyright (C) 1995 DJ Delorie, see COPYING.DJ for details */
  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. #if defined(LIBM_SCCS) && !defined(lint)
  15. static char rcsid[] = "$Id: e_hypot.c,v 1.6 1994/08/18 23:05:24 jtc Exp $";
  16. #endif
  17.  
  18. /* __ieee754_hypot(x,y)
  19.  *
  20.  * Method :                  
  21.  *      If (assume round-to-nearest) z=x*x+y*y
  22.  *      has error less than sqrt(2)/2 ulp, than
  23.  *      sqrt(z) has error less than 1 ulp (exercise).
  24.  *
  25.  *      So, compute sqrt(x*x+y*y) with some care as
  26.  *      follows to get the error below 1 ulp:
  27.  *
  28.  *      Assume x>y>0;
  29.  *      (if possible, set rounding to round-to-nearest)
  30.  *      1. if x > 2y  use
  31.  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  32.  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  33.  *      2. if x <= 2y use
  34.  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  35.  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  36.  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  37.  *             
  38.  *      NOTE: scaling may be necessary if some argument is too
  39.  *            large or too tiny
  40.  *
  41.  * Special cases:
  42.  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  43.  *      hypot(x,y) is NAN if x or y is NAN.
  44.  *
  45.  * Accuracy:
  46.  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  47.  *      than 1 ulps (units in the last place)
  48.  */
  49.  
  50. #include "math.h"
  51. #include "math_private.h"
  52.  
  53. #ifdef __STDC__
  54.         double __ieee754_hypot(double x, double y)
  55. #else
  56.         double __ieee754_hypot(x,y)
  57.         double x, y;
  58. #endif
  59. {
  60.         double a=x,b=y,t1,t2,y1a,y2,w;
  61.         int32_t j,k,ha,hb;
  62.  
  63.         GET_HIGH_WORD(ha,x);
  64.         ha &= 0x7fffffff;
  65.         GET_HIGH_WORD(hb,y);
  66.         hb &= 0x7fffffff;
  67.         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  68.         SET_HIGH_WORD(a,ha);    /* a <- |a| */
  69.         SET_HIGH_WORD(b,hb);    /* b <- |b| */
  70.         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  71.         k=0;
  72.         if(ha > 0x5f300000) {   /* a>2**500 */
  73.            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  74.                u_int32_t low;
  75.                w = a+b;                 /* for sNaN */
  76.                GET_LOW_WORD(low,a);
  77.                if(((ha&0xfffff)|low)==0) w = a;
  78.                GET_LOW_WORD(low,b);
  79.                if(((hb^0x7ff00000)|low)==0) w = b;
  80.                return w;
  81.            }
  82.            /* scale a and b by 2**-600 */
  83.            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  84.            SET_HIGH_WORD(a,ha);
  85.            SET_HIGH_WORD(b,hb);
  86.         }
  87.         if(hb < 0x20b00000) {   /* b < 2**-500 */
  88.             if(hb <= 0x000fffff) {      /* subnormal b or 0 */ 
  89.                 u_int32_t low;
  90.                 GET_LOW_WORD(low,b);
  91.                 if((hb|low)==0) return a;
  92.                 t1=0;
  93.                 SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
  94.                 b *= t1;
  95.                 a *= t1;
  96.                 k -= 1022;
  97.             } else {            /* scale a and b by 2^600 */
  98.                 ha += 0x25800000;       /* a *= 2^600 */
  99.                 hb += 0x25800000;       /* b *= 2^600 */
  100.                 k -= 600;
  101.                 SET_HIGH_WORD(a,ha);
  102.                 SET_HIGH_WORD(b,hb);
  103.             }
  104.         }
  105.     /* medium size a and b */
  106.         w = a-b;
  107.         if (w>b) {
  108.             t1 = 0;
  109.             SET_HIGH_WORD(t1,ha);
  110.             t2 = a-t1;
  111.             w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
  112.         } else {
  113.             a  = a+a;
  114.             y1a = 0;
  115.             SET_HIGH_WORD(y1a,hb);
  116.             y2 = b - y1a;
  117.             t1 = 0;
  118.             SET_HIGH_WORD(t1,ha+0x00100000);
  119.             t2 = a - t1;
  120.             w  = sqrt(t1*y1a-(w*(-w)-(t1*y2+t2*b)));
  121.         }
  122.         if(k!=0) {
  123.             u_int32_t high;
  124.             t1 = 1.0;
  125.             GET_HIGH_WORD(high,t1);
  126.             SET_HIGH_WORD(t1,high+(k<<20));
  127.             return t1*w;
  128.         } else return w;
  129. }
  130.