mirror of
https://gitea.nishi.boats/pyrite-dev/milsko
synced 2025-12-31 06:30:52 +00:00
7f523a3d76
git-svn-id: http://svn2.nishi.boats/svn/milsko/trunk@557 b9cfdab3-6d41-4d17-bbe4-086880011989
124 lines
2.9 KiB
C
124 lines
2.9 KiB
C
|
|
/* @(#)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.
|
|
* ====================================================
|
|
*/
|
|
|
|
/* __math.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 tinyv
|
|
*
|
|
* 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"
|
|
|
|
double __fdlibm_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;
|
|
}
|