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
  13 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: e_hypot.c,v 1.13 2008/04/25 22:21:53 christos 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*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
  35  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  36  *      yy1= y with lower 32 bits chopped, y2 = y-yy1.
  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 double
  54 __ieee754_hypot(double x, double y)
  55 {
  56         double a=x,b=y,t1,t2,yy1,y2,w;
  57         int32_t j,k,ha,hb;
  58
  59         GET_HIGH_WORD(ha,x);
  60         ha &= 0x7fffffff;
  61         GET_HIGH_WORD(hb,y);
  62         hb &= 0x7fffffff;
  63         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  64         SET_HIGH_WORD(a,ha);    /* a <- |a| */
  65         SET_HIGH_WORD(b,hb);    /* b <- |b| */
  66         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  67         k=0;
  68         if(ha > 0x5f300000) {   /* a>2**500 */
  69            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  70                u_int32_t low;
  71                w = a+b;                 /* for sNaN */
  72                GET_LOW_WORD(low,a);
  73                if(((ha&0xfffff)|low)==0) w = a;
  74                GET_LOW_WORD(low,b);
  75                if(((hb^0x7ff00000)|low)==0) w = b;
  76                return w;
  77            }
  78            /* scale a and b by 2**-600 */
  79            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  80            SET_HIGH_WORD(a,ha);
  81            SET_HIGH_WORD(b,hb);
  82         }
  83         if(hb < 0x20b00000) {   /* b < 2**-500 */
  84             if(hb <= 0x000fffff) {      /* subnormal b or 0 */
  85                 u_int32_t low;
  86                 GET_LOW_WORD(low,b);
  87                 if((hb|low)==0) return a;
  88                 t1=0;
  89                 SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
  90                 b *= t1;
  91                 a *= t1;
  92                 k -= 1022;
  93             } else {            /* scale a and b by 2^600 */
  94                 ha += 0x25800000;       /* a *= 2^600 */
  95                 hb += 0x25800000;       /* b *= 2^600 */
  96                 k -= 600;
  97                 SET_HIGH_WORD(a,ha);
  98                 SET_HIGH_WORD(b,hb);
  99             }
 100         }
 101     /* medium size a and b */
 102         w = a-b;
 103         if (w>b) {
 104             t1 = 0;
 105             SET_HIGH_WORD(t1,ha);
 106             t2 = a-t1;
 107             w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 108         } else {
 109             a  = a+a;
 110             yy1 = 0;
 111             SET_HIGH_WORD(yy1,hb);
 112             y2 = b - yy1;
 113             t1 = 0;
 114             SET_HIGH_WORD(t1,ha+0x00100000);
 115             t2 = a - t1;
 116             w  = __ieee754_sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
 117         }
 118         if(k!=0) {
 119             u_int32_t high;
 120             t1 = 1.0;
 121             GET_HIGH_WORD(high,t1);
 122             SET_HIGH_WORD(t1,high+(k<<20));
 123             return t1*w;
 124         } else return w;
 125 }