lib/msun/src/e_hypot.c

   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 #ifndef lint
  14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_hypot.c,v 1.6 1999/08/28 00:06:31 peter Exp $";
  15 #endif
  16
  17 /* __ieee754_hypot(x,y)
  18  *
  19  * Method :
  20  *      If (assume round-to-nearest) z=x*x+y*y
  21  *      has error less than sqrt(2)/2 ulp, than
  22  *      sqrt(z) has error less than 1 ulp (exercise).
  23  *
  24  *      So, compute sqrt(x*x+y*y) with some care as
  25  *      follows to get the error below 1 ulp:
  26  *
  27  *      Assume x>y>0;
  28  *      (if possible, set rounding to round-to-nearest)
  29  *      1. if x > 2y  use
  30  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  31  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  32  *      2. if x <= 2y use
  33  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  34  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  35  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  36  *
  37  *      NOTE: scaling may be necessary if some argument is too
  38  *            large or too tiny
  39  *
  40  * Special cases:
  41  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  42  *      hypot(x,y) is NAN if x or y is NAN.
  43  *
  44  * Accuracy:
  45  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  46  *      than 1 ulps (units in the last place)
  47  */
  48
  49 #include "math.h"
  50 #include "math_private.h"
  51
  52 #ifdef __STDC__
  53         double __ieee754_hypot(double x, double y)
  54 #else
  55         double __ieee754_hypot(x,y)
  56         double x, y;
  57 #endif
  58 {
  59         double a=x,b=y,t1,t2,y1,y2,w;
  60         int32_t j,k,ha,hb;
  61
  62         GET_HIGH_WORD(ha,x);
  63         ha &= 0x7fffffff;
  64         GET_HIGH_WORD(hb,y);
  65         hb &= 0x7fffffff;
  66         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  67         SET_HIGH_WORD(a,ha);    /* a <- |a| */
  68         SET_HIGH_WORD(b,hb);    /* b <- |b| */
  69         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  70         k=0;
  71         if(ha > 0x5f300000) {   /* a>2**500 */
  72            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  73                u_int32_t low;
  74                w = a+b;                 /* for sNaN */
  75                GET_LOW_WORD(low,a);
  76                if(((ha&0xfffff)|low)==0) w = a;
  77                GET_LOW_WORD(low,b);
  78                if(((hb^0x7ff00000)|low)==0) w = b;
  79                return w;
  80            }
  81            /* scale a and b by 2**-600 */
  82            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  83            SET_HIGH_WORD(a,ha);
  84            SET_HIGH_WORD(b,hb);
  85         }
  86         if(hb < 0x20b00000) {   /* b < 2**-500 */
  87             if(hb <= 0x000fffff) {      /* subnormal b or 0 */
  88                 u_int32_t low;
  89                 GET_LOW_WORD(low,b);
  90                 if((hb|low)==0) return a;
  91                 t1=0;
  92                 SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
  93                 b *= t1;
  94                 a *= t1;
  95                 k -= 1022;
  96             } else {            /* scale a and b by 2^600 */
  97                 ha += 0x25800000;       /* a *= 2^600 */
  98                 hb += 0x25800000;       /* b *= 2^600 */
  99                 k -= 600;
 100                 SET_HIGH_WORD(a,ha);
 101                 SET_HIGH_WORD(b,hb);
 102             }
 103         }
 104     /* medium size a and b */
 105         w = a-b;
 106         if (w>b) {
 107             t1 = 0;
 108             SET_HIGH_WORD(t1,ha);
 109             t2 = a-t1;
 110             w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 111         } else {
 112             a  = a+a;
 113             y1 = 0;
 114             SET_HIGH_WORD(y1,hb);
 115             y2 = b - y1;
 116             t1 = 0;
 117             SET_HIGH_WORD(t1,ha+0x00100000);
 118             t2 = a - t1;
 119             w  = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 120         }
 121         if(k!=0) {
 122             u_int32_t high;
 123             t1 = 1.0;
 124             GET_HIGH_WORD(high,t1);
 125             SET_HIGH_WORD(t1,high+(k<<20));
 126             return t1*w;
 127         } else return w;
 128 }