sysdeps/ieee754/dbl-64/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 /* __ieee754_hypot(x,y)
  14  *
  15  * Method :
  16  *      If (assume round-to-nearest) z=x*x+y*y
  17  *      has error less than sqrt(2)/2 ulp, than
  18  *      sqrt(z) has error less than 1 ulp (exercise).
  19  *
  20  *      So, compute sqrt(x*x+y*y) with some care as
  21  *      follows to get the error below 1 ulp:
  22  *
  23  *      Assume x>y>0;
  24  *      (if possible, set rounding to round-to-nearest)
  25  *      1. if x > 2y  use
  26  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  27  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  28  *      2. if x <= 2y use
  29  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  30  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  31  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  32  *
  33  *      NOTE: scaling may be necessary if some argument is too
  34  *            large or too tiny
  35  *
  36  * Special cases:
  37  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  38  *      hypot(x,y) is NAN if x or y is NAN.
  39  *
  40  * Accuracy:
  41  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  42  *      than 1 ulps (units in the last place)
  43  */
  44
  45 #include "math.h"
  46 #include "math_private.h"
  47
  48 double
  49 __ieee754_hypot(double x, double y)
  50 {
  51         double a,b,t1,t2,y1,y2,w;
  52         int32_t j,k,ha,hb;
  53
  54         GET_HIGH_WORD(ha,x);
  55         ha &= 0x7fffffff;
  56         GET_HIGH_WORD(hb,y);
  57         hb &= 0x7fffffff;
  58         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  59         SET_HIGH_WORD(a,ha);    /* a <- |a| */
  60         SET_HIGH_WORD(b,hb);    /* b <- |b| */
  61         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
  62         k=0;
  63         if(__builtin_expect(ha > 0x5f300000, 0)) {      /* a>2**500 */
  64            if(ha >= 0x7ff00000) {       /* Inf or NaN */
  65                u_int32_t low;
  66                w = a+b;                 /* for sNaN */
  67                GET_LOW_WORD(low,a);
  68                if(((ha&0xfffff)|low)==0) w = a;
  69                GET_LOW_WORD(low,b);
  70                if(((hb^0x7ff00000)|low)==0) w = b;
  71                return w;
  72            }
  73            /* scale a and b by 2**-600 */
  74            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  75            SET_HIGH_WORD(a,ha);
  76            SET_HIGH_WORD(b,hb);
  77         }
  78         if(__builtin_expect(hb < 0x20b00000, 0)) {      /* b < 2**-500 */
  79             if(hb <= 0x000fffff) {      /* subnormal b or 0 */
  80                 u_int32_t low;
  81                 GET_LOW_WORD(low,b);
  82                 if((hb|low)==0) return a;
  83                 t1=0;
  84                 SET_HIGH_WORD(t1,0x7fd00000);   /* t1=2^1022 */
  85                 b *= t1;
  86                 a *= t1;
  87                 k -= 1022;
  88             } else {            /* scale a and b by 2^600 */
  89                 ha += 0x25800000;       /* a *= 2^600 */
  90                 hb += 0x25800000;       /* b *= 2^600 */
  91                 k -= 600;
  92                 SET_HIGH_WORD(a,ha);
  93                 SET_HIGH_WORD(b,hb);
  94             }
  95         }
  96     /* medium size a and b */
  97         w = a-b;
  98         if (w>b) {
  99             t1 = 0;
 100             SET_HIGH_WORD(t1,ha);
 101             t2 = a-t1;
 102             w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 103         } else {
 104             a  = a+a;
 105             y1 = 0;
 106             SET_HIGH_WORD(y1,hb);
 107             y2 = b - y1;
 108             t1 = 0;
 109             SET_HIGH_WORD(t1,ha+0x00100000);
 110             t2 = a - t1;
 111             w  = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 112         }
 113         if(k!=0) {
 114             u_int32_t high;
 115             t1 = 1.0;
 116             GET_HIGH_WORD(high,t1);
 117             SET_HIGH_WORD(t1,high+(k<<20));
 118             return t1*w;
 119         } else return w;
 120 }
 121 strong_alias (__ieee754_hypot, __hypot_finite)