| /* @(#)e_hypotl.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| /* __ieee754_hypotl(x,y) |
| * |
| * Method : |
| * If (assume round-to-nearest) z=x*x+y*y |
| * has error less than sqrtl(2)/2 ulp, than |
| * sqrtl(z) has error less than 1 ulp (exercise). |
| * |
| * So, compute sqrtl(x*x+y*y) with some care as |
| * follows to get the error below 1 ulp: |
| * |
| * Assume x>y>0; |
| * (if possible, set rounding to round-to-nearest) |
| * 1. if x > 2y use |
| * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y |
| * where x1 = x with lower 53 bits cleared, x2 = x-x1; else |
| * 2. if x <= 2y use |
| * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) |
| * where t1 = 2x with lower 53 bits cleared, t2 = 2x-t1, |
| * y1= y with lower 53 bits chopped, y2 = y-y1. |
| * |
| * NOTE: scaling may be necessary if some argument is too |
| * large or too tiny |
| * |
| * Special cases: |
| * hypotl(x,y) is INF if x or y is +INF or -INF; else |
| * hypotl(x,y) is NAN if x or y is NAN. |
| * |
| * Accuracy: |
| * hypotl(x,y) returns sqrtl(x^2+y^2) with error less |
| * than 1 ulps (units in the last place) |
| */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| |
| long double |
| __ieee754_hypotl(long double x, long double y) |
| { |
| long double a,b,a1,a2,b1,b2,w,kld; |
| int64_t j,k,ha,hb; |
| double xhi, yhi, hi, lo; |
| |
| xhi = ldbl_high (x); |
| EXTRACT_WORDS64 (ha, xhi); |
| yhi = ldbl_high (y); |
| EXTRACT_WORDS64 (hb, yhi); |
| ha &= 0x7fffffffffffffffLL; |
| hb &= 0x7fffffffffffffffLL; |
| if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
| a = fabsl(a); /* a <- |a| */ |
| b = fabsl(b); /* b <- |b| */ |
| if((ha-hb)>0x0780000000000000LL) {return a+b;} /* x/y > 2**120 */ |
| k=0; |
| kld = 1.0L; |
| if(ha > 0x5f30000000000000LL) { /* a>2**500 */ |
| if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */ |
| w = a+b; /* for sNaN */ |
| if(ha == 0x7ff0000000000000LL) |
| w = a; |
| if(hb == 0x7ff0000000000000LL) |
| w = b; |
| return w; |
| } |
| /* scale a and b by 2**-600 */ |
| a *= 0x1p-600L; |
| b *= 0x1p-600L; |
| k = 600; |
| kld = 0x1p+600L; |
| } |
| else if(hb < 0x23d0000000000000LL) { /* b < 2**-450 */ |
| if(hb <= 0x000fffffffffffffLL) { /* subnormal b or 0 */ |
| if(hb==0) return a; |
| a *= 0x1p+1022L; |
| b *= 0x1p+1022L; |
| k = -1022; |
| kld = 0x1p-1022L; |
| } else { /* scale a and b by 2^600 */ |
| a *= 0x1p+600L; |
| b *= 0x1p+600L; |
| k = -600; |
| kld = 0x1p-600L; |
| } |
| } |
| /* medium size a and b */ |
| w = a-b; |
| if (w>b) { |
| ldbl_unpack (a, &hi, &lo); |
| a1 = hi; |
| a2 = lo; |
| /* a*a + b*b |
| = (a1+a2)*a + b*b |
| = a1*a + a2*a + b*b |
| = a1*(a1+a2) + a2*a + b*b |
| = a1*a1 + a1*a2 + a2*a + b*b |
| = a1*a1 + a2*(a+a1) + b*b */ |
| w = __ieee754_sqrtl(a1*a1-(b*(-b)-a2*(a+a1))); |
| } else { |
| a = a+a; |
| ldbl_unpack (b, &hi, &lo); |
| b1 = hi; |
| b2 = lo; |
| ldbl_unpack (a, &hi, &lo); |
| a1 = hi; |
| a2 = lo; |
| /* a*a + b*b |
| = a*a + (a-b)*(a-b) - (a-b)*(a-b) + b*b |
| = a*a + w*w - (a*a - 2*a*b + b*b) + b*b |
| = w*w + 2*a*b |
| = w*w + (a1+a2)*b |
| = w*w + a1*b + a2*b |
| = w*w + a1*(b1+b2) + a2*b |
| = w*w + a1*b1 + a1*b2 + a2*b */ |
| w = __ieee754_sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b))); |
| } |
| if(k!=0) |
| return w*kld; |
| else |
| return w; |
| } |
| strong_alias (__ieee754_hypotl, __hypotl_finite) |
