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/* @(#)e_hypotl.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_hypotl.c,v 1.9 1995/05/12 04:57:27 jtc Exp $";
#endif
/* __ieee754_hypotl(x,y)
*
* Method :
* If (assume round-to-nearest) z=x*x+y*y
* has error less than sqrtl(2)/2 ulp, than
* sqrtl(z) has error less than 1 ulp (exercise).
*
* So, compute sqrtl(x*x+y*y) with some care as
* follows to get the error below 1 ulp:
*
* Assume x>y>0;
* (if possible, set rounding to round-to-nearest)
* 1. if x > 2y use
* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
* where x1 = x with lower 53 bits cleared, x2 = x-x1; else
* 2. if x <= 2y use
* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
* where t1 = 2x with lower 53 bits cleared, t2 = 2x-t1,
* y1= y with lower 53 bits chopped, y2 = y-y1.
*
* NOTE: scaling may be necessary if some argument is too
* large or too tiny
*
* Special cases:
* hypotl(x,y) is INF if x or y is +INF or -INF; else
* hypotl(x,y) is NAN if x or y is NAN.
*
* Accuracy:
* hypotl(x,y) returns sqrtl(x^2+y^2) with error less
* than 1 ulps (units in the last place)
*/
#include "math.h"
#include "math_private.h"
static const long double two600 = 0x1.0p+600L;
static const long double two1022 = 0x1.0p+1022L;
#ifdef __STDC__
long double __ieee754_hypotl(long double x, long double y)
#else
long double __ieee754_hypotl(x,y)
long double x, y;
#endif
{
long double a,b,t1,t2,y1,y2,w,kld;
int64_t j,k,ha,hb;
GET_LDOUBLE_MSW64(ha,x);
ha &= 0x7fffffffffffffffLL;
GET_LDOUBLE_MSW64(hb,y);
hb &= 0x7fffffffffffffffLL;
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
a = fabsl(a); /* a <- |a| */
b = fabsl(b); /* b <- |b| */
if((ha-hb)>0x3c0000000000000LL) {return a+b;} /* x/y > 2**60 */
k=0;
kld = 1.0L;
if(ha > 0x5f30000000000000LL) { /* a>2**500 */
if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */
u_int64_t low;
w = a+b; /* for sNaN */
GET_LDOUBLE_LSW64(low,a);
if(((ha&0xfffffffffffffLL)|(low&0x7fffffffffffffffLL))==0)
w = a;
GET_LDOUBLE_LSW64(low,b);
if(((hb^0x7ff0000000000000LL)|(low&0x7fffffffffffffffLL))==0)
w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x2580000000000000LL; hb -= 0x2580000000000000LL; k += 600;
a /= two600;
b /= two600;
k += 600;
kld = two600;
}
if(hb < 0x20b0000000000000LL) { /* b < 2**-500 */
if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */
u_int64_t low;
GET_LDOUBLE_LSW64(low,b);
if((hb|(low&0x7fffffffffffffffLL))==0) return a;
t1=two1022; /* t1=2^1022 */
b *= t1;
a *= t1;
k -= 1022;
kld = kld / two1022;
} else { /* scale a and b by 2^600 */
ha += 0x2580000000000000LL; /* a *= 2^600 */
hb += 0x2580000000000000LL; /* b *= 2^600 */
k -= 600;
a *= two600;
b *= two600;
kld = kld / two600;
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
SET_LDOUBLE_WORDS64(t1,ha,0);
t2 = a-t1;
w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a = a+a;
SET_LDOUBLE_WORDS64(y1,hb,0);
y2 = b - y1;
SET_LDOUBLE_WORDS64(t1,ha+0x0010000000000000LL,0);
t2 = a - t1;
w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0)
return w*kld;
else
return w;
}
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