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125 lines
3.5 KiB
C
125 lines
3.5 KiB
C
/*
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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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/* From e_hypotl.c -- long double version of e_hypot.c.
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* Conversion to long double by Jakub Jelinek, jakub@redhat.com.
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* Conversion to __float128 by FX Coudert, fxcoudert@gcc.gnu.org.
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*/
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/* hypotq(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 sqrtl(2)/2 ulp, than
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* sqrtl(z) has error less than 1 ulp (exercise).
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*
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* So, compute sqrtl(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 64 bits cleared, x2 = x-x1; else
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* 2. if x <= 2y use
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* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
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* where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1,
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* y1= y with lower 64 bits chopped, y2 = y-y1.
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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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* hypotq(x,y) is INF if x or y is +INF or -INF; else
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* hypotq(x,y) is NAN if x or y is NAN.
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*
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* Accuracy:
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* hypotq(x,y) returns sqrtl(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 "quadmath-imp.h"
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__float128
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hypotq (__float128 x, __float128 y)
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{
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__float128 a, b, t1, t2, y1, y2, w;
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int64_t j, k, ha, hb;
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GET_FLT128_MSW64(ha,x);
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ha &= 0x7fffffffffffffffLL;
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GET_FLT128_MSW64(hb,y);
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hb &= 0x7fffffffffffffffLL;
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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_FLT128_MSW64(a,ha); /* a <- |a| */
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SET_FLT128_MSW64(b,hb); /* b <- |b| */
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if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
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k=0;
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if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
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if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
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uint64_t low;
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w = a+b; /* for sNaN */
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GET_FLT128_LSW64(low,a);
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if(((ha&0xffffffffffffLL)|low)==0) w = a;
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GET_FLT128_LSW64(low,b);
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if(((hb^0x7fff000000000000LL)|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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ha -= 0x2580000000000000LL;
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hb -= 0x2580000000000000LL; k += 9600;
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SET_FLT128_MSW64(a,ha);
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SET_FLT128_MSW64(b,hb);
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}
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if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
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if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
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uint64_t low;
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GET_FLT128_LSW64(low,b);
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if((hb|low)==0) return a;
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t1=0;
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SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* 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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ha += 0x2580000000000000LL; /* a *= 2^9600 */
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hb += 0x2580000000000000LL; /* b *= 2^9600 */
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k -= 9600;
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SET_FLT128_MSW64(a,ha);
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SET_FLT128_MSW64(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_FLT128_MSW64(t1,ha);
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t2 = a-t1;
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w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1)));
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} else {
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a = a+a;
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y1 = 0;
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SET_FLT128_MSW64(y1,hb);
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y2 = b - y1;
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t1 = 0;
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SET_FLT128_MSW64(t1,ha+0x0001000000000000LL);
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t2 = a - t1;
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w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b)));
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}
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if(k!=0) {
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uint64_t high;
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t1 = 1.0Q;
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GET_FLT128_MSW64(high,t1);
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SET_FLT128_MSW64(t1,high+(k<<48));
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return t1*w;
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} else return w;
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}
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