| /* |
| * ==================================================== |
| * 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; |
| GET_FLT128_MSW64 (ha, a); |
| GET_FLT128_MSW64 (hb, b); |
| if (hb > ha) |
| { |
| t1 = a; |
| a = b; |
| b = t1; |
| j = ha; |
| ha = hb; |
| hb = j; |
| } |
| } 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)); |
| w *= t1; |
| math_check_force_underflow_nonneg (w); |
| return w; |
| } else return w; |
| } |