0,0 → 1,129 |
/* Copyright (C) 1995 DJ Delorie, see COPYING.DJ for details */ |
/* @(#)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. |
* ==================================================== |
*/ |
|
#if defined(LIBM_SCCS) && !defined(lint) |
static char rcsid[] = "$Id: e_hypot.c,v 1.6 1994/08/18 23:05:24 jtc 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,y1a,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; |
y1a = 0; |
SET_HIGH_WORD(y1a,hb); |
y2 = b - y1a; |
t1 = 0; |
SET_HIGH_WORD(t1,ha+0x00100000); |
t2 = a - t1; |
w = sqrt(t1*y1a-(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; |
} |