sysdeps/ieee754/ldbl-128/e_hypotl.c

   1 /* e_hypotl.c -- long double version of e_hypot.c.
   2  * Conversion to long double by Jakub Jelinek, jakub@redhat.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 #if defined(LIBM_SCCS) && !defined(lint)
  17 static char rcsid[] = "$NetBSD: e_hypotl.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
  18 #endif
  19
  20 /* __ieee754_hypotl(x,y)
  21  *
  22  * Method :
  23  *      If (assume round-to-nearest) z=x*x+y*y
  24  *      has error less than sqrtl(2)/2 ulp, than
  25  *      sqrtl(z) has error less than 1 ulp (exercise).
  26  *
  27  *      So, compute sqrtl(x*x+y*y) with some care as
  28  *      follows to get the error below 1 ulp:
  29  *
  30  *      Assume x>y>0;
  31  *      (if possible, set rounding to round-to-nearest)
  32  *      1. if x > 2y  use
  33  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  34  *      where x1 = x with lower 64 bits cleared, x2 = x-x1; else
  35  *      2. if x <= 2y use
  36  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  37  *      where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1,
  38  *      y1= y with lower 64 bits chopped, y2 = y-y1.
  39  *
  40  *      NOTE: scaling may be necessary if some argument is too
  41  *            large or too tiny
  42  *
  43  * Special cases:
  44  *      hypotl(x,y) is INF if x or y is +INF or -INF; else
  45  *      hypotl(x,y) is NAN if x or y is NAN.
  46  *
  47  * Accuracy:
  48  *      hypotl(x,y) returns sqrtl(x^2+y^2) with error less
  49  *      than 1 ulps (units in the last place)
  50  */
  51
  52 #include "math.h"
  53 #include "math_private.h"
  54
  55 #ifdef __STDC__
  56         long double __ieee754_hypotl(long double x, long double y)
  57 #else
  58         long double __ieee754_hypotl(x,y)
  59         long double x, y;
  60 #endif
  61 {
  62         long double a,b,t1,t2,y1,y2,w;
  63         int64_t j,k,ha,hb;
  64
  65         GET_LDOUBLE_MSW64(ha,x);
  66         ha &= 0x7fffffffffffffffLL;
  67         GET_LDOUBLE_MSW64(hb,y);
  68         hb &= 0x7fffffffffffffffLL;
  69         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  70         SET_LDOUBLE_MSW64(a,ha);        /* a <- |a| */
  71         SET_LDOUBLE_MSW64(b,hb);        /* b <- |b| */
  72         if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
  73         k=0;
  74         if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
  75            if(ha >= 0x7fff000000000000LL) {     /* Inf or NaN */
  76                u_int64_t low;
  77                w = a+b;                 /* for sNaN */
  78                GET_LDOUBLE_LSW64(low,a);
  79                if(((ha&0xffffffffffffLL)|low)==0) w = a;
  80                GET_LDOUBLE_LSW64(low,b);
  81                if(((hb^0x7fff000000000000LL)|low)==0) w = b;
  82                return w;
  83            }
  84            /* scale a and b by 2**-9600 */
  85            ha -= 0x2580000000000000LL;
  86            hb -= 0x2580000000000000LL;  k += 9600;
  87            SET_LDOUBLE_MSW64(a,ha);
  88            SET_LDOUBLE_MSW64(b,hb);
  89         }
  90         if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
  91             if(hb <= 0x0000ffffffffffffLL) {    /* subnormal b or 0 */
  92                 u_int64_t low;
  93                 GET_LDOUBLE_LSW64(low,b);
  94                 if((hb|low)==0) return a;
  95                 t1=0;
  96                 SET_LDOUBLE_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
  97                 b *= t1;
  98                 a *= t1;
  99                 k -= 16382;
 100             } else {            /* scale a and b by 2^9600 */
 101                 ha += 0x2580000000000000LL;     /* a *= 2^9600 */
 102                 hb += 0x2580000000000000LL;     /* b *= 2^9600 */
 103                 k -= 9600;
 104                 SET_LDOUBLE_MSW64(a,ha);
 105                 SET_LDOUBLE_MSW64(b,hb);
 106             }
 107         }
 108     /* medium size a and b */
 109         w = a-b;
 110         if (w>b) {
 111             t1 = 0;
 112             SET_LDOUBLE_MSW64(t1,ha);
 113             t2 = a-t1;
 114             w  = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
 115         } else {
 116             a  = a+a;
 117             y1 = 0;
 118             SET_LDOUBLE_MSW64(y1,hb);
 119             y2 = b - y1;
 120             t1 = 0;
 121             SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL);
 122             t2 = a - t1;
 123             w  = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 124         }
 125         if(k!=0) {
 126             u_int64_t high;
 127             t1 = 1.0L;
 128             GET_LDOUBLE_MSW64(high,t1);
 129             SET_LDOUBLE_MSW64(t1,high+(k<<48));
 130             return t1*w;
 131         } else return w;
 132 }