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/* @(#)e_hypot.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.
* ====================================================
*/
#ifndef lint
static char rcsid
[] = "$\Id: e_hypot.c,v 1.2 1995/05/30 05:48:16 rgrimes Exp $";
#endif
/* __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 "math.h"
#include "math_private.h"
#ifdef __STDC__
double __ieee754_hypot
(double x
, double y
)
#else
double __ieee754_hypot
(x
,y
)
double x
, y
;
#endif
{
double a
=x
,b
=y
,t1
,t2
,y1
,y2
,w
;
int32_t j
,k
,ha
,hb
;
GET_HIGH_WORD
(ha
,x
);
ha
&= 0x7fffffff;
GET_HIGH_WORD
(hb
,y
);
hb
&= 0x7fffffff;
if(hb
> ha
) {a
=y
;b
=x
;j
=ha
; ha
=hb
;hb
=j
;} else {a
=x
;b
=y
;}
SET_HIGH_WORD
(a
,ha
); /* a <- |a| */
SET_HIGH_WORD
(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 */
u_int32_t low
;
w
= a
+b
; /* for sNaN */
GET_LOW_WORD
(low
,a
);
if(((ha
&0xfffff)|low
)==0) w
= a
;
GET_LOW_WORD
(low
,b
);
if(((hb
^0x7ff00000)|low
)==0) w
= b
;
return w
;
}
/* scale a and b by 2**-600 */
ha
-= 0x25800000; hb
-= 0x25800000; k
+= 600;
SET_HIGH_WORD
(a
,ha
);
SET_HIGH_WORD
(b
,hb
);
}
if(hb
< 0x20b00000) { /* b < 2**-500 */
if(hb
<= 0x000fffff) { /* subnormal b or 0 */
u_int32_t low
;
GET_LOW_WORD
(low
,b
);
if((hb
|low
)==0) return a
;
t1
=0;
SET_HIGH_WORD
(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;
SET_HIGH_WORD
(a
,ha
);
SET_HIGH_WORD
(b
,hb
);
}
}
/* medium size a and b */
w
= a
-b
;
if (w
>b
) {
t1
= 0;
SET_HIGH_WORD
(t1
,ha
);
t2
= a
-t1
;
w
= sqrt(t1
*t1
-(b
*(-b
)-t2
*(a
+t1
)));
} else {
a
= a
+a
;
y1
= 0;
SET_HIGH_WORD
(y1
,hb
);
y2
= b
- y1
;
t1
= 0;
SET_HIGH_WORD
(t1
,ha
+0x00100000);
t2
= a
- t1
;
w
= sqrt(t1
*y1
-(w
*(-w
)-(t1
*y2
+t2
*b
)));
}
if(k
!=0) {
u_int32_t high
;
t1
= 1.0;
GET_HIGH_WORD
(high
,t1
);
SET_HIGH_WORD
(t1
,high
+(k
<<20));
return t1
*w
;
} else return w
;
}