# shithub: 9ferno

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```/* derived from /netlib/fdlibm */

/* @(#)e_hypot.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

/* __ieee754_hypot(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 "fdlibm.h"

double __ieee754_hypot(double x, double y)
{
double a=x,b=y,t1,t2,y1,y2,w;
int j,k,ha,hb;

ha = __HI(x)&0x7fffffff;	/* high word of  x */
hb = __HI(y)&0x7fffffff;	/* high word of  y */
if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
__HI(a) = ha;	/* a <- |a| */
__HI(b) = hb;	/* b <- |b| */
if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
k=0;
if(ha > 0x5f300000) {	/* a>2**500 */
if(ha >= 0x7ff00000) {	/* Inf or NaN */
w = a+b;			/* for sNaN */
if(((ha&0xfffff)|__LO(a))==0) w = a;
if(((hb^0x7ff00000)|__LO(b))==0) w = b;
return w;
}
/* scale a and b by 2**-600 */
ha -= 0x25800000; hb -= 0x25800000;	k += 600;
__HI(a) = ha;
__HI(b) = hb;
}
if(hb < 0x20b00000) {	/* b < 2**-500 */
if(hb <= 0x000fffff) {	/* subnormal b or 0 */
if((hb|(__LO(b)))==0) return a;
t1=0;
__HI(t1) = 0x7fd00000;	/* t1=2^1022 */
b *= t1;
a *= t1;
k -= 1022;
} else {		/* scale a and b by 2^600 */
ha += 0x25800000; 	/* a *= 2^600 */
hb += 0x25800000;	/* b *= 2^600 */
k -= 600;
__HI(a) = ha;
__HI(b) = hb;
}
}
/* medium size a and b */
w = a-b;
if (w>b) {
t1 = 0;
__HI(t1) = ha;
t2 = a-t1;
w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
} else {
a  = a+a;
y1 = 0;
__HI(y1) = hb;
y2 = b - y1;
t1 = 0;
__HI(t1) = ha+0x00100000;
t2 = a - t1;
w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
}
if(k!=0) {
t1 = 1.0;
__HI(t1) += (k<<20);
return t1*w;
} else return w;
}
```