nsz Git - musl/blob - src/math/e_hypot.c

   1
   2 /* @(#)e_hypot.c 1.3 95/01/18 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunSoft, 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 /* 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 <math.h>
  47 #include "math_private.h"
  48
  49 double
  50 hypot(double x, double y)
  51 {
  52         double a=x,b=y,t1,t2,y1,y2,w;
  53         int32_t j,k,ha,hb;
  54
  55         GET_HIGH_WORD(ha,x);
  56         ha &= 0x7fffffff;
  57         GET_HIGH_WORD(hb,y);
  58         hb &= 0x7fffffff;
  59         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  60         SET_HIGH_WORD(a,ha);    /* a <- |a| */
  61         SET_HIGH_WORD(b,hb);    /* b <- |b| */
  62         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  63         k=0;
  64         if(ha > 0x5f300000) {   /* a>2**500 */
  65            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  66                uint32_t low;
  67                w = a+b;                 /* for sNaN */
  68                GET_LOW_WORD(low,a);
  69                if(((ha&0xfffff)|low)==0) w = a;
  70                GET_LOW_WORD(low,b);
  71                if(((hb^0x7ff00000)|low)==0) w = b;
  72                return w;
  73            }
  74            /* scale a and b by 2**-600 */
  75            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  76            SET_HIGH_WORD(a,ha);
  77            SET_HIGH_WORD(b,hb);
  78         }
  79         if(hb < 0x20b00000) {   /* b < 2**-500 */
  80             if(hb <= 0x000fffff) {      /* subnormal b or 0 */
  81                 uint32_t low;
  82                 GET_LOW_WORD(low,b);
  83                 if((hb|low)==0) return a;
  84                 t1=0;
  85                 SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
  86                 b *= t1;
  87                 a *= t1;
  88                 k -= 1022;
  89             } else {            /* scale a and b by 2^600 */
  90                 ha += 0x25800000;       /* a *= 2^600 */
  91                 hb += 0x25800000;       /* b *= 2^600 */
  92                 k -= 600;
  93                 SET_HIGH_WORD(a,ha);
  94                 SET_HIGH_WORD(b,hb);
  95             }
  96         }
  97     /* medium size a and b */
  98         w = a-b;
  99         if (w>b) {
 100             t1 = 0;
 101             SET_HIGH_WORD(t1,ha);
 102             t2 = a-t1;
 103             w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 104         } else {
 105             a  = a+a;
 106             y1 = 0;
 107             SET_HIGH_WORD(y1,hb);
 108             y2 = b - y1;
 109             t1 = 0;
 110             SET_HIGH_WORD(t1,ha+0x00100000);
 111             t2 = a - t1;
 112             w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 113         }
 114         if(k!=0) {
 115             uint32_t high;
 116             t1 = 1.0;
 117             GET_HIGH_WORD(high,t1);
 118             SET_HIGH_WORD(t1,high+(k<<20));
 119             return t1*w;
 120         } else return w;
 121 }