lib/libm/src/e_hypot.c

   1
   2 /* @(#)e_hypot.c 1.3 95/01/18 */
   3 /* $FreeBSD: head/lib/msun/src/e_hypot.c 226380 2011-10-15 07:00:28Z das $ */
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 /* __ieee754_hypot(x,y)
  16  *
  17  * Method :
  18  *      If (assume round-to-nearest) z=x*x+y*y
  19  *      has error less than sqrt(2)/2 ulp, than
  20  *      sqrt(z) has error less than 1 ulp (exercise).
  21  *
  22  *      So, compute sqrt(x*x+y*y) with some care as
  23  *      follows to get the error below 1 ulp:
  24  *
  25  *      Assume x>y>0;
  26  *      (if possible, set rounding to round-to-nearest)
  27  *      1. if x > 2y  use
  28  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  29  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  30  *      2. if x <= 2y use
  31  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  32  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  33  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  34  *
  35  *      NOTE: scaling may be necessary if some argument is too
  36  *            large or too tiny
  37  *
  38  * Special cases:
  39  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  40  *      hypot(x,y) is NAN if x or y is NAN.
  41  *
  42  * Accuracy:
  43  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  44  *      than 1 ulps (units in the last place)
  45  */
  46
  47 #include <float.h>
  48
  49 #include "math.h"
  50 #include "math_private.h"
  51
  52 double
  53 __ieee754_hypot(double x, double y)
  54 {
  55         double a,b,t1,t2,y1,y2,w;
  56         int32_t j,k,ha,hb;
  57
  58         GET_HIGH_WORD(ha,x);
  59         ha &= 0x7fffffff;
  60         GET_HIGH_WORD(hb,y);
  61         hb &= 0x7fffffff;
  62         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  63         a = fabs(a);
  64         b = fabs(b);
  65         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  66         k=0;
  67         if(ha > 0x5f300000) {   /* a>2**500 */
  68            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  69                u_int32_t low;
  70                /* Use original arg order iff result is NaN; quieten sNaNs. */
  71                w = fabs(x+0.0)-fabs(y+0.0);
  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  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 108         } else {
 109             a  = a+a;
 110             y1 = 0;
 111             SET_HIGH_WORD(y1,hb);
 112             y2 = b - y1;
 113             t1 = 0;
 114             SET_HIGH_WORD(t1,ha+0x00100000);
 115             t2 = a - t1;
 116             w  = sqrt(t1*y1-(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 }
 126
 127 #if LDBL_MANT_DIG == 53
 128 __weak_reference(hypot, hypotl);
 129 #endif