mirror of
https://sourceware.org/git/glibc.git
synced 2025-10-30 10:45:40 +03:00
125 lines
3.4 KiB
C
125 lines
3.4 KiB
C
/* @(#)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.
|
|
* ====================================================
|
|
*/
|
|
|
|
/* __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;
|
|
|
|
long double
|
|
__ieee754_hypotl(long double x, long double y)
|
|
{
|
|
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;
|
|
}
|
|
strong_alias (__ieee754_hypotl, __hypotl_finite)
|