src/math/hypot.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/e_hypot.c */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunSoft, 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 /* hypot(x,y)
  13  *
  14  * Method :
  15  *      If (assume round-to-nearest) z=x*x+y*y
  16  *      has error less than sqrt(2)/2 ulp, then
  17  *      sqrt(z) has error less than 1 ulp (exercise).
  18  *
  19  *      So, compute sqrt(x*x+y*y) with some care as
  20  *      follows to get the error below 1 ulp:
  21  *
  22  *      Assume x>y>0;
  23  *      (if possible, set rounding to round-to-nearest)
  24  *      1. if x > 2y  use
  25  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  26  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  27  *      2. if x <= 2y use
  28  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  29  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  30  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  31  *
  32  *      NOTE: scaling may be necessary if some argument is too
  33  *            large or too tiny
  34  *
  35  * Special cases:
  36  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  37  *      hypot(x,y) is NAN if x or y is NAN.
  38  *
  39  * Accuracy:
  40  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  41  *      than 1 ulps (units in the last place)
  42  */
  43
  44 #include "libm.h"
  45
  46 double hypot(double x, double y)
  47 {
  48         double a,b,t1,t2,y1,y2,w;
  49         int32_t j,k,ha,hb;
  50
  51         GET_HIGH_WORD(ha, x);
  52         ha &= 0x7fffffff;
  53         GET_HIGH_WORD(hb, y);
  54         hb &= 0x7fffffff;
  55         if (hb > ha) {
  56                 a = y;
  57                 b = x;
  58                 j=ha; ha=hb; hb=j;
  59         } else {
  60                 a = x;
  61                 b = y;
  62         }
  63         a = fabs(a);
  64         b = fabs(b);
  65         if (ha - hb > 0x3c00000)  /* x/y > 2**60 */
  66                 return a+b;
  67         k = 0;
  68         if (ha > 0x5f300000) {    /* a > 2**500 */
  69                 if(ha >= 0x7ff00000) {  /* Inf or NaN */
  70                         uint32_t low;
  71                         /* Use original arg order iff result is NaN; quieten sNaNs. */
  72                         w = fabs(x+0.0) - fabs(y+0.0);
  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)
  89                                 return a;
  90                         t1 = 0;
  91                         SET_HIGH_WORD(t1, 0x7fd00000);  /* t1 = 2^1022 */
  92                         b *= t1;
  93                         a *= t1;
  94                         k -= 1022;
  95                 } else {            /* scale a and b by 2^600 */
  96                         ha += 0x25800000;  /* a *= 2^600 */
  97                         hb += 0x25800000;  /* b *= 2^600 */
  98                         k -= 600;
  99                         SET_HIGH_WORD(a, ha);
 100                         SET_HIGH_WORD(b, hb);
 101                 }
 102         }
 103         /* medium size a and b */
 104         w = a - b;
 105         if (w > b) {
 106                 t1 = 0;
 107                 SET_HIGH_WORD(t1, ha);
 108                 t2 = a-t1;
 109                 w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 110         } else {
 111                 a  = a + a;
 112                 y1 = 0;
 113                 SET_HIGH_WORD(y1, hb);
 114                 y2 = b - y1;
 115                 t1 = 0;
 116                 SET_HIGH_WORD(t1, ha+0x00100000);
 117                 t2 = a - t1;
 118                 w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 119         }
 120         if (k)
 121                 w = scalbn(w, k);
 122         return w;
 123 }