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/* @(#)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 <math.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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DEF_STD(hypotl); |