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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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/* hypot(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 <float.h> |
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#include <math.h> |
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#include "math_private.h" |
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double |
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hypot(double x, double y) |
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{ |
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double a=x,b=y,t1,t2,yy1,y2,w; |
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int32_t j,k,ha,hb; |
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GET_HIGH_WORD(ha,x); |
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ha &= 0x7fffffff; |
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GET_HIGH_WORD(hb,y); |
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hb &= 0x7fffffff; |
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if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
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SET_HIGH_WORD(a,ha); /* a <- |a| */ |
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SET_HIGH_WORD(b,hb); /* b <- |b| */ |
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if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ |
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k=0; |
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if(ha > 0x5f300000) { /* a>2**500 */ |
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if(ha >= 0x7ff00000) { /* Inf or NaN */ |
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u_int32_t low; |
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w = a+b; /* for sNaN */ |
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GET_LOW_WORD(low,a); |
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if(((ha&0xfffff)|low)==0) w = a; |
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GET_LOW_WORD(low,b); |
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if(((hb^0x7ff00000)|low)==0) w = b; |
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return w; |
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} |
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/* scale a and b by 2**-600 */ |
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ha -= 0x25800000; hb -= 0x25800000; k += 600; |
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SET_HIGH_WORD(a,ha); |
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SET_HIGH_WORD(b,hb); |
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} |
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if(hb < 0x20b00000) { /* b < 2**-500 */ |
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if(hb <= 0x000fffff) { /* subnormal b or 0 */ |
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u_int32_t low; |
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GET_LOW_WORD(low,b); |
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if((hb|low)==0) return a; |
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t1=0; |
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SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ |
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b *= t1; |
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a *= t1; |
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k -= 1022; |
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} else { /* scale a and b by 2^600 */ |
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ha += 0x25800000; /* a *= 2^600 */ |
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hb += 0x25800000; /* b *= 2^600 */ |
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k -= 600; |
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SET_HIGH_WORD(a,ha); |
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SET_HIGH_WORD(b,hb); |
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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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t1 = 0; |
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SET_HIGH_WORD(t1,ha); |
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t2 = a-t1; |
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w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); |
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} else { |
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a = a+a; |
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yy1 = 0; |
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SET_HIGH_WORD(yy1,hb); |
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y2 = b - yy1; |
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t1 = 0; |
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SET_HIGH_WORD(t1,ha+0x00100000); |
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t2 = a - t1; |
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w = sqrt(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 high; |
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t1 = 1.0; |
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GET_HIGH_WORD(high,t1); |
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SET_HIGH_WORD(t1,high+(k<<20)); |
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return t1*w; |
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} else return w; |
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} |
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DEF_STD(hypot); |
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LDBL_MAYBE_CLONE(hypot); |