lib/msun/src/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 #include <sys/cdefs.h>
  15 __FBSDID("$FreeBSD$");
  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 <float.h>
  50
  51 #include "math.h"
  52 #include "math_private.h"
  53
  54 double
  55 __ieee754_hypot(double x, double y)
  56 {
  57         double a,b,t1,t2,y1,y2,w;
  58         int32_t j,k,ha,hb;
  59
  60         GET_HIGH_WORD(ha,x);
  61         ha &= 0x7fffffff;
  62         GET_HIGH_WORD(hb,y);
  63         hb &= 0x7fffffff;
  64         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  65         a = fabs(a);
  66         b = fabs(b);
  67         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  68         k=0;
  69         if(ha > 0x5f300000) {   /* a>2**500 */
  70            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  71                u_int32_t low;
  72                /* Use original arg order iff result is NaN; quieten sNaNs. */
  73                w = fabs(x+0.0)-fabs(y+0.0);
  74                GET_LOW_WORD(low,a);
  75                if(((ha&0xfffff)|low)==0) w = a;
  76                GET_LOW_WORD(low,b);
  77                if(((hb^0x7ff00000)|low)==0) w = b;
  78                return w;
  79            }
  80            /* scale a and b by 2**-600 */
  81            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  82            SET_HIGH_WORD(a,ha);
  83            SET_HIGH_WORD(b,hb);
  84         }
  85         if(hb < 0x20b00000) {   /* b < 2**-500 */
  86             if(hb <= 0x000fffff) {      /* subnormal b or 0 */
  87                 u_int32_t low;
  88                 GET_LOW_WORD(low,b);
  89                 if((hb|low)==0) return a;
  90                 t1=0;
  91                 SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
  92                 b *= t1;
  93                 a *= t1;
  94                 k -= 1022;
  95             } else {            /* scale a and b by 2^600 */
  96                 ha += 0x25800000;       /* a *= 2^600 */
  97                 hb += 0x25800000;       /* b *= 2^600 */
  98                 k -= 600;
  99                 SET_HIGH_WORD(a,ha);
 100                 SET_HIGH_WORD(b,hb);
 101             }
 102         }
 103     /* medium size a and b */
 104         w = a-b;
 105         if (w>b) {
 106             t1 = 0;
 107             SET_HIGH_WORD(t1,ha);
 108             t2 = a-t1;
 109             w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 110         } else {
 111             a  = a+a;
 112             y1 = 0;
 113             SET_HIGH_WORD(y1,hb);
 114             y2 = b - y1;
 115             t1 = 0;
 116             SET_HIGH_WORD(t1,ha+0x00100000);
 117             t2 = a - t1;
 118             w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 119         }
 120         if(k!=0) {
 121             t1 = 0.0;
 122             SET_HIGH_WORD(t1,(1023+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