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)
  59     {
  60       a = y; b = x; j = ha; ha = hb; hb = j;
  61     }
  62   else
  63     {
  64       a = x; b = y;
  65     }
  66   SET_HIGH_WORD (a, ha);        /* a <- |a| */
  67   SET_HIGH_WORD (b, hb);        /* b <- |b| */
  68   if ((ha - hb) > 0x3c00000)
  69     {
  70       return a + b;
  71     }                                       /* x/y > 2**60 */
  72   k = 0;
  73   if (__glibc_unlikely (ha > 0x5f300000))                  /* a>2**500 */
  74     {
  75       if (ha >= 0x7ff00000)             /* Inf or NaN */
  76         {
  77           u_int32_t low;
  78           w = a + b;                    /* for sNaN */
  79           GET_LOW_WORD (low, a);
  80           if (((ha & 0xfffff) | low) == 0)
  81             w = a;
  82           GET_LOW_WORD (low, b);
  83           if (((hb ^ 0x7ff00000) | low) == 0)
  84             w = b;
  85           return w;
  86         }
  87       /* scale a and b by 2**-600 */
  88       ha -= 0x25800000; hb -= 0x25800000;  k += 600;
  89       SET_HIGH_WORD (a, ha);
  90       SET_HIGH_WORD (b, hb);
  91     }
  92   if (__builtin_expect (hb < 0x23d00000, 0))            /* b < 2**-450 */
  93     {
  94       if (hb <= 0x000fffff)             /* subnormal b or 0 */
  95         {
  96           u_int32_t low;
  97           GET_LOW_WORD (low, b);
  98           if ((hb | low) == 0)
  99             return a;
 100           t1 = 0;
 101           SET_HIGH_WORD (t1, 0x7fd00000);       /* t1=2^1022 */
 102           b *= t1;
 103           a *= t1;
 104           k -= 1022;
 105           GET_HIGH_WORD (ha, a);
 106           GET_HIGH_WORD (hb, b);
 107           if (hb > ha)
 108             {
 109               t1 = a;
 110               a = b;
 111               b = t1;
 112               j = ha;
 113               ha = hb;
 114               hb = j;
 115             }
 116         }
 117       else                      /* scale a and b by 2^600 */
 118         {
 119           ha += 0x25800000;             /* a *= 2^600 */
 120           hb += 0x25800000;             /* b *= 2^600 */
 121           k -= 600;
 122           SET_HIGH_WORD (a, ha);
 123           SET_HIGH_WORD (b, hb);
 124         }
 125     }
 126   /* medium size a and b */
 127   w = a - b;
 128   if (w > b)
 129     {
 130       t1 = 0;
 131       SET_HIGH_WORD (t1, ha);
 132       t2 = a - t1;
 133       w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));
 134     }
 135   else
 136     {
 137       a = a + a;
 138       y1 = 0;
 139       SET_HIGH_WORD (y1, hb);
 140       y2 = b - y1;
 141       t1 = 0;
 142       SET_HIGH_WORD (t1, ha + 0x00100000);
 143       t2 = a - t1;
 144       w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
 145     }
 146   if (k != 0)
 147     {
 148       u_int32_t high;
 149       t1 = 1.0;
 150       GET_HIGH_WORD (high, t1);
 151       SET_HIGH_WORD (t1, high + (k << 20));
 152       return t1 * w;
 153     }
 154   else
 155     return w;
 156 }
 157 strong_alias (__ieee754_hypot, __hypot_finite)