1/*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
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
8 * is preserved.
9 * ====================================================
10 */
11
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.
15 */
16
17/* hypotq(x,y)
18 *
19 * Method :
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).
23 *
24 * So, compute sqrtl(x*x+y*y) with some care as
25 * follows to get the error below 1 ulp:
26 *
27 * Assume x>y>0;
28 * (if possible, set rounding to round-to-nearest)
29 * 1. if x > 2y use
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
32 * 2. if x <= 2y use
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.
36 *
37 * NOTE: scaling may be necessary if some argument is too
38 * large or too tiny
39 *
40 * Special cases:
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.
43 *
44 * Accuracy:
45 * hypotq(x,y) returns sqrtl(x^2+y^2) with error less
46 * than 1 ulps (units in the last place)
47 */
48
49#include "quadmath-imp.h"
50
51__float128
52hypotq (__float128 x, __float128 y)
53{
54 __float128 a, b, t1, t2, y1, y2, w;
55 int64_t j, k, ha, hb;
56
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 */
65 k=0;
66 if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
67 if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
68 uint64_t low;
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;
74 return w;
75 }
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);
81 }
82 if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
83 if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
84 uint64_t low;
85 GET_FLT128_LSW64(low,b);
86 if((hb|low)==0) return a;
87 t1=0;
88 SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
89 b *= t1;
90 a *= t1;
91 k -= 16382;
92 GET_FLT128_MSW64 (ha, a);
93 GET_FLT128_MSW64 (hb, b);
94 if (hb > ha)
95 {
96 t1 = a;
97 a = b;
98 b = t1;
99 j = ha;
100 ha = hb;
101 hb = j;
102 }
103 } else { /* scale a and b by 2^9600 */
104 ha += 0x2580000000000000LL; /* a *= 2^9600 */
105 hb += 0x2580000000000000LL; /* b *= 2^9600 */
106 k -= 9600;
107 SET_FLT128_MSW64(a,ha);
108 SET_FLT128_MSW64(b,hb);
109 }
110 }
111 /* medium size a and b */
112 w = a-b;
113 if (w>b) {
114 t1 = 0;
115 SET_FLT128_MSW64(t1,ha);
116 t2 = a-t1;
117 w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1)));
118 } else {
119 a = a+a;
120 y1 = 0;
121 SET_FLT128_MSW64(y1,hb);
122 y2 = b - y1;
123 t1 = 0;
124 SET_FLT128_MSW64(t1,ha+0x0001000000000000LL);
125 t2 = a - t1;
126 w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b)));
127 }
128 if(k!=0) {
129 uint64_t high;
130 t1 = 1.0Q;
131 GET_FLT128_MSW64(high,t1);
132 SET_FLT128_MSW64(t1,high+(k<<48));
133 w *= t1;
134 math_check_force_underflow_nonneg (w);
135 return w;
136 } else return w;
137}
138