141 lines
3.6 KiB
C
141 lines
3.6 KiB
C
/* @(#)e_hypotl.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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/* __ieee754_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 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 53 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 53 bits cleared, t2 = 2x-t1,
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* y1= y with lower 53 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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* hypotl(x,y) is INF if x or y is +INF or -INF; else
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* hypotl(x,y) is NAN if x or y is NAN.
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*
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* Accuracy:
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* hypotl(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 <math.h>
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#include <math_private.h>
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#include <math-underflow.h>
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#include <libm-alias-finite.h>
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long double
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__ieee754_hypotl(long double x, long double y)
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{
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long double a,b,a1,a2,b1,b2,w,kld;
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int64_t j,k,ha,hb;
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double xhi, yhi, hi, lo;
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xhi = ldbl_high (x);
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EXTRACT_WORDS64 (ha, xhi);
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yhi = ldbl_high (y);
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EXTRACT_WORDS64 (hb, yhi);
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ha &= 0x7fffffffffffffffLL;
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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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a = fabsl(a); /* a <- |a| */
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b = fabsl(b); /* b <- |b| */
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if((ha-hb)>0x0780000000000000LL) {return a+b;} /* x/y > 2**120 */
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k=0;
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kld = 1.0L;
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if(ha > 0x5f30000000000000LL) { /* a>2**500 */
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if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */
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w = a+b; /* for sNaN */
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if (issignaling (a) || issignaling (b))
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return w;
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if(ha == 0x7ff0000000000000LL)
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w = a;
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if(hb == 0x7ff0000000000000LL)
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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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a *= 0x1p-600L;
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b *= 0x1p-600L;
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k = 600;
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kld = 0x1p+600L;
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}
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else if(hb < 0x23d0000000000000LL) { /* b < 2**-450 */
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if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */
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if(hb==0) return a;
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a *= 0x1p+1022L;
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b *= 0x1p+1022L;
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k = -1022;
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kld = 0x1p-1022L;
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} else { /* scale a and b by 2^600 */
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a *= 0x1p+600L;
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b *= 0x1p+600L;
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k = -600;
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kld = 0x1p-600L;
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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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ldbl_unpack (a, &hi, &lo);
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a1 = hi;
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a2 = lo;
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/* a*a + b*b
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= (a1+a2)*a + b*b
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= a1*a + a2*a + b*b
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= a1*(a1+a2) + a2*a + b*b
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= a1*a1 + a1*a2 + a2*a + b*b
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= a1*a1 + a2*(a+a1) + b*b */
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w = sqrtl(a1*a1-(b*(-b)-a2*(a+a1)));
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} else {
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a = a+a;
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ldbl_unpack (b, &hi, &lo);
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b1 = hi;
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b2 = lo;
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ldbl_unpack (a, &hi, &lo);
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a1 = hi;
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a2 = lo;
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/* a*a + b*b
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= a*a + (a-b)*(a-b) - (a-b)*(a-b) + b*b
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= a*a + w*w - (a*a - 2*a*b + b*b) + b*b
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= w*w + 2*a*b
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= w*w + (a1+a2)*b
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= w*w + a1*b + a2*b
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= w*w + a1*(b1+b2) + a2*b
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= w*w + a1*b1 + a1*b2 + a2*b */
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w = sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b)));
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}
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if(k!=0)
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{
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w *= kld;
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math_check_force_underflow_nonneg (w);
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return w;
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}
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else
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return w;
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}
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libm_alias_finite (__ieee754_hypotl, __hypotl)
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