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/* origin: FreeBSD /usr/src/lib/msun/src/e_hypot.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/* hypot(x,y)
*
* Method :
* If (assume round-to-nearest) z=x*x+y*y
* has error less than sqrt(2)/2 ulp, then
* 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 "libm.h"
double hypot(double x, double y)
{
double a,b,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;
}
a = fabs(a);
b = fabs(b);
if (ha - hb > 0x3c00000) /* x/y > 2**60 */
return a+b;
k = 0;
if (ha > 0x5f300000) { /* a > 2**500 */
if(ha >= 0x7ff00000) { /* Inf or NaN */
uint32_t low;
/* Use original arg order iff result is NaN; quieten sNaNs. */
w = fabs(x+0.0) - fabs(y+0.0);
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 */
uint32_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)
w = scalbn(w, k);
return w;
}
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