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122 lines
3.2 KiB
C
122 lines
3.2 KiB
C
/* @(#)e_hypot.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* hypotl(x,y)
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*
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* Method :
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* If (assume round-to-nearest) z=x*x+y*y
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* has error less than sqrt(2)/2 ulp, than
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* sqrt(z) has error less than 1 ulp (exercise).
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*
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* So, compute sqrt(x*x+y*y) with some care as
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* follows to get the error below 1 ulp:
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*
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* Assume x>y>0;
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* (if possible, set rounding to round-to-nearest)
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* 1. if x > 2y use
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* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
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* where x1 = x with lower 32 bits cleared, x2 = x-x1; else
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* 2. if x <= 2y use
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* t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
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* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
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* yy1= y with lower 32 bits chopped, y2 = y-yy1.
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*
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* NOTE: scaling may be necessary if some argument is too
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* large or too tiny
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*
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* Special cases:
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* hypot(x,y) is INF if x or y is +INF or -INF; else
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* hypot(x,y) is NAN if x or y is NAN.
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*
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* Accuracy:
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* hypot(x,y) returns sqrt(x^2+y^2) with error less
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* than 1 ulps (units in the last place)
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*/
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#include <openlibm.h>
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#include "math_private.h"
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long double
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hypotl(long double x, long double y)
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{
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long double a,b,t1,t2,yy1,y2,w;
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u_int32_t j,k,ea,eb;
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GET_LDOUBLE_EXP(ea,x);
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ea &= 0x7fff;
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GET_LDOUBLE_EXP(eb,y);
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eb &= 0x7fff;
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if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
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SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
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SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
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if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
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k=0;
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if(ea > 0x5f3f) { /* a>2**8000 */
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if(ea == 0x7fff) { /* Inf or NaN */
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u_int32_t es,high,low;
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w = a+b; /* for sNaN */
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GET_LDOUBLE_WORDS(es,high,low,a);
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if(((high&0x7fffffff)|low)==0) w = a;
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GET_LDOUBLE_WORDS(es,high,low,b);
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if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
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return w;
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}
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/* scale a and b by 2**-9600 */
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ea -= 0x2580; eb -= 0x2580; k += 9600;
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SET_LDOUBLE_EXP(a,ea);
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SET_LDOUBLE_EXP(b,eb);
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}
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if(eb < 0x20bf) { /* b < 2**-8000 */
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if(eb == 0) { /* subnormal b or 0 */
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u_int32_t es,high,low;
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GET_LDOUBLE_WORDS(es,high,low,b);
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if((high|low)==0) return a;
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SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0); /* t1=2^16382 */
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b *= t1;
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a *= t1;
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k -= 16382;
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} else { /* scale a and b by 2^9600 */
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ea += 0x2580; /* a *= 2^9600 */
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eb += 0x2580; /* b *= 2^9600 */
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k -= 9600;
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SET_LDOUBLE_EXP(a,ea);
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SET_LDOUBLE_EXP(b,eb);
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}
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}
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/* medium size a and b */
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w = a-b;
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if (w>b) {
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u_int32_t high;
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GET_LDOUBLE_MSW(high,a);
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SET_LDOUBLE_WORDS(t1,ea,high,0);
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t2 = a-t1;
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w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
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} else {
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u_int32_t high;
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GET_LDOUBLE_MSW(high,b);
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a = a+a;
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SET_LDOUBLE_WORDS(yy1,eb,high,0);
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y2 = b - yy1;
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GET_LDOUBLE_MSW(high,a);
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SET_LDOUBLE_WORDS(t1,ea+1,high,0);
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t2 = a - t1;
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w = sqrtl(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
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}
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if(k!=0) {
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u_int32_t es;
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t1 = 1.0;
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GET_LDOUBLE_EXP(es,t1);
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SET_LDOUBLE_EXP(t1,es+k);
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return t1*w;
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} else return w;
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}
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