lib/libm/src/ld80/e_hypotl.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 /* hypotl(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*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
  30  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  31  *      yy1= y with lower 32 bits chopped, y2 = y-yy1.
  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
  47 #include "math_private.h"
  48
  49 long double
  50 hypotl(long double x, long double y)
  51 {
  52         long double a,b,t1,t2,yy1,y2,w;
  53         u_int32_t j,k,ea,eb;
  54
  55         GET_LDOUBLE_EXP(ea,x);
  56         ea &= 0x7fff;
  57         GET_LDOUBLE_EXP(eb,y);
  58         eb &= 0x7fff;
  59         if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
  60         SET_LDOUBLE_EXP(a,ea);  /* a <- |a| */
  61         SET_LDOUBLE_EXP(b,eb);  /* b <- |b| */
  62         if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
  63         k=0;
  64         if(ea > 0x5f3f) {       /* a>2**8000 */
  65            if(ea == 0x7fff) {   /* Inf or NaN */
  66                u_int32_t es,high,low;
  67                w = a+b;                 /* for sNaN */
  68                GET_LDOUBLE_WORDS(es,high,low,a);
  69                if(((high&0x7fffffff)|low)==0) w = a;
  70                GET_LDOUBLE_WORDS(es,high,low,b);
  71                if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
  72                return w;
  73            }
  74            /* scale a and b by 2**-9600 */
  75            ea -= 0x2580; eb -= 0x2580;  k += 9600;
  76            SET_LDOUBLE_EXP(a,ea);
  77            SET_LDOUBLE_EXP(b,eb);
  78         }
  79         if(eb < 0x20bf) {       /* b < 2**-8000 */
  80             if(eb == 0) {       /* subnormal b or 0 */
  81                 u_int32_t es,high,low;
  82                 GET_LDOUBLE_WORDS(es,high,low,b);
  83                 if((high|low)==0) return a;
  84                 SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0);    /* t1=2^16382 */
  85                 b *= t1;
  86                 a *= t1;
  87                 k -= 16382;
  88             } else {            /* scale a and b by 2^9600 */
  89                 ea += 0x2580;   /* a *= 2^9600 */
  90                 eb += 0x2580;   /* b *= 2^9600 */
  91                 k -= 9600;
  92                 SET_LDOUBLE_EXP(a,ea);
  93                 SET_LDOUBLE_EXP(b,eb);
  94             }
  95         }
  96     /* medium size a and b */
  97         w = a-b;
  98         if (w>b) {
  99             u_int32_t high;
 100             GET_LDOUBLE_MSW(high,a);
 101             SET_LDOUBLE_WORDS(t1,ea,high,0);
 102             t2 = a-t1;
 103             w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
 104         } else {
 105             u_int32_t high;
 106             GET_LDOUBLE_MSW(high,b);
 107             a  = a+a;
 108             SET_LDOUBLE_WORDS(yy1,eb,high,0);
 109             y2 = b - yy1;
 110             GET_LDOUBLE_MSW(high,a);
 111             SET_LDOUBLE_WORDS(t1,ea+1,high,0);
 112             t2 = a - t1;
 113             w  = sqrtl(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
 114         }
 115         if(k!=0) {
 116             u_int32_t es;
 117             t1 = 1.0;
 118             GET_LDOUBLE_EXP(es,t1);
 119             SET_LDOUBLE_EXP(t1,es+k);
 120             return t1*w;
 121         } else return w;
 122 }