diff options
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c')
| -rw-r--r-- | REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c | 138 |
1 files changed, 138 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c new file mode 100644 index 0000000000..de5a66ab05 --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c @@ -0,0 +1,138 @@ +/* @(#)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 (issignaling (a) || issignaling (b)) + return w; + 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) + { + w *= kld; + math_check_force_underflow_nonneg (w); + return w; + } + else + return w; +} +strong_alias (__ieee754_hypotl, __hypotl_finite) |