lib/libm/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  * $NetBSD: e_hypot.c,v 1.12 2002/05/26 22:01:50 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/e_hypot.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16 /* hypot(x,y)
  17  *
  18  * Method :
  19  *      If (assume round-to-nearest) z=x*x+y*y
  20  *      has error less than sqrt(2)/2 ulp, than
  21  *      sqrt(z) has error less than 1 ulp (exercise).
  22  *
  23  *      So, compute sqrt(x*x+y*y) with some care as
  24  *      follows to get the error below 1 ulp:
  25  *
  26  *      Assume x>y>0;
  27  *      (if possible, set rounding to round-to-nearest)
  28  *      1. if x > 2y  use
  29  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  30  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  31  *      2. if x <= 2y use
  32  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  33  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  34  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  35  *
  36  *      NOTE: scaling may be necessary if some argument is too
  37  *            large or too tiny
  38  *
  39  * Special cases:
  40  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  41  *      hypot(x,y) is NAN if x or y is NAN.
  42  *
  43  * Accuracy:
  44  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  45  *      than 1 ulps (units in the last place)
  46  */
  47
  48 #include <math.h>
  49 #include "math_private.h"
  50
  51 double
  52 hypot(double x, double y)
  53 {
  54         double a=x,b=y,t1,t2,y1_,y2,w;
  55         int32_t j,k,ha,hb;
  56
  57         GET_HIGH_WORD(ha,x);
  58         ha &= 0x7fffffff;
  59         GET_HIGH_WORD(hb,y);
  60         hb &= 0x7fffffff;
  61         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  62         SET_HIGH_WORD(a,ha);    /* a <- |a| */
  63         SET_HIGH_WORD(b,hb);    /* b <- |b| */
  64         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  65         k=0;
  66         if(ha > 0x5f300000) {   /* a>2**500 */
  67            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  68                u_int32_t low;
  69                w = a+b;                 /* for sNaN */
  70                GET_LOW_WORD(low,a);
  71                if(((ha&0xfffff)|low)==0) w = a;
  72                GET_LOW_WORD(low,b);
  73                if(((hb^0x7ff00000)|low)==0) w = b;
  74                return w;
  75            }
  76            /* scale a and b by 2**-600 */
  77            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  78            SET_HIGH_WORD(a,ha);
  79            SET_HIGH_WORD(b,hb);
  80         }
  81         if(hb < 0x20b00000) {   /* b < 2**-500 */
  82             if(hb <= 0x000fffff) {      /* subnormal b or 0 */
  83                 u_int32_t low;
  84                 GET_LOW_WORD(low,b);
  85                 if((hb|low)==0) return a;
  86                 t1=0;
  87                 SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
  88                 b *= t1;
  89                 a *= t1;
  90                 k -= 1022;
  91             } else {            /* scale a and b by 2^600 */
  92                 ha += 0x25800000;       /* a *= 2^600 */
  93                 hb += 0x25800000;       /* b *= 2^600 */
  94                 k -= 600;
  95                 SET_HIGH_WORD(a,ha);
  96                 SET_HIGH_WORD(b,hb);
  97             }
  98         }
  99     /* medium size a and b */
 100         w = a-b;
 101         if (w>b) {
 102             t1 = 0;
 103             SET_HIGH_WORD(t1,ha);
 104             t2 = a-t1;
 105             w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 106         } else {
 107             a  = a+a;
 108             y1_ = 0;
 109             SET_HIGH_WORD(y1_,hb);
 110             y2 = b - y1_;
 111             t1 = 0;
 112             SET_HIGH_WORD(t1,ha+0x00100000);
 113             t2 = a - t1;
 114             w  = sqrt(t1*y1_-(w*(-w)-(t1*y2+t2*b)));
 115         }
 116         if(k!=0) {
 117             u_int32_t high;
 118             t1 = 1.0;
 119             GET_HIGH_WORD(high,t1);
 120             SET_HIGH_WORD(t1,high+(k<<20));
 121             return t1*w;
 122         } else return w;
 123 }