sysdeps/ieee754/ldbl-96/e_hypotl.c

   1 /* e_hypotl.c -- long double version of e_hypot.c.
   2  * Conversion to long double by Ulrich Drepper,
   3  * Cygnus Support, drepper@cygnus.com.
   4  */
   5
   6 /*
   7  * ====================================================
   8  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   9  *
  10  * Developed at SunPro, a Sun Microsystems, Inc. business.
  11  * Permission to use, copy, modify, and distribute this
  12  * software is freely granted, provided that this notice
  13  * is preserved.
  14  * ====================================================
  15  */
  16
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 static char rcsid[] = "$NetBSD: $";
  19 #endif
  20
  21 /* __ieee754_hypotl(x,y)
  22  *
  23  * Method :
  24  *      If (assume round-to-nearest) z=x*x+y*y
  25  *      has error less than sqrt(2)/2 ulp, than
  26  *      sqrt(z) has error less than 1 ulp (exercise).
  27  *
  28  *      So, compute sqrt(x*x+y*y) with some care as
  29  *      follows to get the error below 1 ulp:
  30  *
  31  *      Assume x>y>0;
  32  *      (if possible, set rounding to round-to-nearest)
  33  *      1. if x > 2y  use
  34  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  35  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  36  *      2. if x <= 2y use
  37  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  38  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  39  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  40  *
  41  *      NOTE: scaling may be necessary if some argument is too
  42  *            large or too tiny
  43  *
  44  * Special cases:
  45  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  46  *      hypot(x,y) is NAN if x or y is NAN.
  47  *
  48  * Accuracy:
  49  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  50  *      than 1 ulps (units in the last place)
  51  */
  52
  53 #include "math.h"
  54 #include "math_private.h"
  55
  56 #ifdef __STDC__
  57         long double __ieee754_hypotl(long double x, long double y)
  58 #else
  59         long double __ieee754_hypotl(x,y)
  60         long double x, y;
  61 #endif
  62 {
  63         long double a,b,t1,t2,y1,y2,w;
  64         u_int32_t j,k,ea,eb;
  65
  66         GET_LDOUBLE_EXP(ea,x);
  67         ea &= 0x7fff;
  68         GET_LDOUBLE_EXP(eb,y);
  69         eb &= 0x7fff;
  70         if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
  71         SET_LDOUBLE_EXP(a,ea);  /* a <- |a| */
  72         SET_LDOUBLE_EXP(b,eb);  /* b <- |b| */
  73         if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
  74         k=0;
  75         if(ea > 0x5f3f) {       /* a>2**8000 */
  76            if(ea == 0x7fff) {   /* Inf or NaN */
  77                u_int32_t exp,high,low;
  78                w = a+b;                 /* for sNaN */
  79                GET_LDOUBLE_WORDS(exp,high,low,a);
  80                if(((high&0x7fffffff)|low)==0) w = a;
  81                GET_LDOUBLE_WORDS(exp,high,low,b);
  82                if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
  83                return w;
  84            }
  85            /* scale a and b by 2**-9600 */
  86            ea -= 0x2580; eb -= 0x2580;  k += 9600;
  87            SET_LDOUBLE_EXP(a,ea);
  88            SET_LDOUBLE_EXP(b,eb);
  89         }
  90         if(eb < 0x20bf) {       /* b < 2**-8000 */
  91             if(eb == 0) {       /* subnormal b or 0 */
  92                 u_int32_t exp,high,low;
  93                 GET_LDOUBLE_WORDS(exp,high,low,b);
  94                 if((high|low)==0) return a;
  95                 SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0);    /* t1=2^16382 */
  96                 b *= t1;
  97                 a *= t1;
  98                 k -= 16382;
  99             } else {            /* scale a and b by 2^9600 */
 100                 ea += 0x2580;   /* a *= 2^9600 */
 101                 eb += 0x2580;   /* b *= 2^9600 */
 102                 k -= 9600;
 103                 SET_LDOUBLE_EXP(a,ea);
 104                 SET_LDOUBLE_EXP(b,eb);
 105             }
 106         }
 107     /* medium size a and b */
 108         w = a-b;
 109         if (w>b) {
 110             u_int32_t high;
 111             GET_LDOUBLE_MSW(high,a);
 112             SET_LDOUBLE_WORDS(t1,ea,high,0);
 113             t2 = a-t1;
 114             w  = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
 115         } else {
 116             u_int32_t high;
 117             GET_LDOUBLE_MSW(high,b);
 118             a  = a+a;
 119             SET_LDOUBLE_WORDS(y1,eb,high,0);
 120             y2 = b - y1;
 121             GET_LDOUBLE_MSW(high,a);
 122             SET_LDOUBLE_WORDS(t1,ea+1,high,0);
 123             t2 = a - t1;
 124             w  = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 125         }
 126         if(k!=0) {
 127             u_int32_t exp;
 128             t1 = 1.0;
 129             GET_LDOUBLE_EXP(exp,t1);
 130             SET_LDOUBLE_EXP(t1,exp+k);
 131             return t1*w;
 132         } else return w;
 133 }