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Diffstat (limited to 'gcc-4.9/libquadmath/math/hypotq.c')
| -rw-r--r-- | gcc-4.9/libquadmath/math/hypotq.c | 124 |
1 files changed, 124 insertions, 0 deletions
diff --git a/gcc-4.9/libquadmath/math/hypotq.c b/gcc-4.9/libquadmath/math/hypotq.c new file mode 100644 index 000000000..2df317f36 --- /dev/null +++ b/gcc-4.9/libquadmath/math/hypotq.c @@ -0,0 +1,124 @@ +/* + * ==================================================== + * 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. + * ==================================================== + */ + +/* From e_hypotl.c -- long double version of e_hypot.c. + * Conversion to long double by Jakub Jelinek, jakub@redhat.com. + * Conversion to __float128 by FX Coudert, fxcoudert@gcc.gnu.org. + */ + +/* hypotq(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 64 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 64 bits cleared, t2 = 2x-t1, + * y1= y with lower 64 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypotq(x,y) is INF if x or y is +INF or -INF; else + * hypotq(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypotq(x,y) returns sqrtl(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include "quadmath-imp.h" + +__float128 +hypotq (__float128 x, __float128 y) +{ + __float128 a, b, t1, t2, y1, y2, w; + int64_t j, k, ha, hb; + + GET_FLT128_MSW64(ha,x); + ha &= 0x7fffffffffffffffLL; + GET_FLT128_MSW64(hb,y); + hb &= 0x7fffffffffffffffLL; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_FLT128_MSW64(a,ha); /* a <- |a| */ + SET_FLT128_MSW64(b,hb); /* b <- |b| */ + if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */ + k=0; + if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */ + if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */ + uint64_t low; + w = a+b; /* for sNaN */ + GET_FLT128_LSW64(low,a); + if(((ha&0xffffffffffffLL)|low)==0) w = a; + GET_FLT128_LSW64(low,b); + if(((hb^0x7fff000000000000LL)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-9600 */ + ha -= 0x2580000000000000LL; + hb -= 0x2580000000000000LL; k += 9600; + SET_FLT128_MSW64(a,ha); + SET_FLT128_MSW64(b,hb); + } + if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */ + if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */ + uint64_t low; + GET_FLT128_LSW64(low,b); + if((hb|low)==0) return a; + t1=0; + SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */ + b *= t1; + a *= t1; + k -= 16382; + } else { /* scale a and b by 2^9600 */ + ha += 0x2580000000000000LL; /* a *= 2^9600 */ + hb += 0x2580000000000000LL; /* b *= 2^9600 */ + k -= 9600; + SET_FLT128_MSW64(a,ha); + SET_FLT128_MSW64(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_FLT128_MSW64(t1,ha); + t2 = a-t1; + w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = 0; + SET_FLT128_MSW64(y1,hb); + y2 = b - y1; + t1 = 0; + SET_FLT128_MSW64(t1,ha+0x0001000000000000LL); + t2 = a - t1; + w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + uint64_t high; + t1 = 1.0Q; + GET_FLT128_MSW64(high,t1); + SET_FLT128_MSW64(t1,high+(k<<48)); + return t1*w; + } else return w; +} |