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/* e_hypotl.c -- long double version of e_hypot.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
/*
* ====================================================
* 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: $";
#endif
/* __ieee754_hypotl(x,y)
*
* Method :
* If (assume round-to-nearest) z=x*x+y*y
* has error less than sqrt(2)/2 ulp, than
* sqrt(z) has error less than 1 ulp (exercise).
*
* So, compute sqrt(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 32 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 32 bits cleared, t2 = 2x-t1,
* y1= y with lower 32 bits chopped, y2 = y-y1.
*
* NOTE: scaling may be necessary if some argument is too
* large or too tiny
*
* Special cases:
* hypot(x,y) is INF if x or y is +INF or -INF; else
* hypot(x,y) is NAN if x or y is NAN.
*
* Accuracy:
* hypot(x,y) returns sqrt(x^2+y^2) with error less
* than 1 ulps (units in the last place)
*/
#include "math.h"
#include "math_private.h"
#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;
u_int32_t j,k,ea,eb;
GET_LDOUBLE_EXP(ea,x);
ea &= 0x7fff;
GET_LDOUBLE_EXP(eb,y);
eb &= 0x7fff;
if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
k=0;
if(ea > 0x5f3f) { /* a>2**8000 */
if(ea == 0x7fff) { /* Inf or NaN */
u_int32_t exp,high,low;
w = a+b; /* for sNaN */
GET_LDOUBLE_WORDS(exp,high,low,a);
if(((high&0x7fffffff)|low)==0) w = a;
GET_LDOUBLE_WORDS(exp,high,low,b);
if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
return w;
}
/* scale a and b by 2**-9600 */
ea -= 0x2580; eb -= 0x2580; k += 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
if(eb < 0x20bf) { /* b < 2**-8000 */
if(eb == 0) { /* subnormal b or 0 */
u_int32_t exp,high,low;
GET_LDOUBLE_WORDS(exp,high,low,b);
if((high|low)==0) return a;
SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0); /* t1=2^16382 */
b *= t1;
a *= t1;
k -= 16382;
} else { /* scale a and b by 2^9600 */
ea += 0x2580; /* a *= 2^9600 */
eb += 0x2580; /* b *= 2^9600 */
k -= 9600;
SET_LDOUBLE_EXP(a,ea);
SET_LDOUBLE_EXP(b,eb);
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
u_int32_t high;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea,high,0);
t2 = a-t1;
w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
u_int32_t high;
GET_LDOUBLE_MSW(high,b);
a = a+a;
SET_LDOUBLE_WORDS(y1,eb,high,0);
y2 = b - y1;
GET_LDOUBLE_MSW(high,a);
SET_LDOUBLE_WORDS(t1,ea+1,high,0);
t2 = a - t1;
w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
u_int32_t exp;
t1 = 1.0;
GET_LDOUBLE_EXP(exp,t1);
SET_LDOUBLE_EXP(t1,exp+k);
return t1*w;
} else return w;
}
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