2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
9 * ====================================================
12 /* From e_hypotl.c -- long double version of e_hypot.c.
13 * Conversion to long double by Jakub Jelinek, jakub@redhat.com.
14 * Conversion to __float128 by FX Coudert, fxcoudert@gcc.gnu.org.
20 * If (assume round-to-nearest) z=x*x+y*y
21 * has error less than sqrtl(2)/2 ulp, than
22 * sqrtl(z) has error less than 1 ulp (exercise).
24 * So, compute sqrtl(x*x+y*y) with some care as
25 * follows to get the error below 1 ulp:
28 * (if possible, set rounding to round-to-nearest)
30 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
31 * where x1 = x with lower 64 bits cleared, x2 = x-x1; else
33 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
34 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1,
35 * y1= y with lower 64 bits chopped, y2 = y-y1.
37 * NOTE: scaling may be necessary if some argument is too
41 * hypotq(x,y) is INF if x or y is +INF or -INF; else
42 * hypotq(x,y) is NAN if x or y is NAN.
45 * hypotq(x,y) returns sqrtl(x^2+y^2) with error less
46 * than 1 ulps (units in the last place)
49 #include "quadmath-imp.h"
52 hypotq (__float128 x, __float128 y)
54 __float128 a, b, t1, t2, y1, y2, w;
57 GET_FLT128_MSW64(ha,x);
58 ha &= 0x7fffffffffffffffLL;
59 GET_FLT128_MSW64(hb,y);
60 hb &= 0x7fffffffffffffffLL;
61 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
62 SET_FLT128_MSW64(a,ha); /* a <- |a| */
63 SET_FLT128_MSW64(b,hb); /* b <- |b| */
64 if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
66 if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
67 if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
69 w = a+b; /* for sNaN */
70 GET_FLT128_LSW64(low,a);
71 if(((ha&0xffffffffffffLL)|low)==0) w = a;
72 GET_FLT128_LSW64(low,b);
73 if(((hb^0x7fff000000000000LL)|low)==0) w = b;
76 /* scale a and b by 2**-9600 */
77 ha -= 0x2580000000000000LL;
78 hb -= 0x2580000000000000LL; k += 9600;
79 SET_FLT128_MSW64(a,ha);
80 SET_FLT128_MSW64(b,hb);
82 if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
83 if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
85 GET_FLT128_LSW64(low,b);
86 if((hb|low)==0) return a;
88 SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
92 } else { /* scale a and b by 2^9600 */
93 ha += 0x2580000000000000LL; /* a *= 2^9600 */
94 hb += 0x2580000000000000LL; /* b *= 2^9600 */
96 SET_FLT128_MSW64(a,ha);
97 SET_FLT128_MSW64(b,hb);
100 /* medium size a and b */
104 SET_FLT128_MSW64(t1,ha);
106 w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1)));
110 SET_FLT128_MSW64(y1,hb);
113 SET_FLT128_MSW64(t1,ha+0x0001000000000000LL);
115 w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b)));
120 GET_FLT128_MSW64(high,t1);
121 SET_FLT128_MSW64(t1,high+(k<<48));