1 /* e_hypotl.c -- long double version of e_hypot.c.
2 * Conversion to long double by Jakub Jelinek, jakub@redhat.com.
3 */
4
5 /*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16 /* hypotq(x,y)
17 *
18 * Method :
19 * If (assume round-to-nearest) z=x*x+y*y
20 * has error less than sqrtq(2)/2 ulp, than
21 * sqrtq(z) has error less than 1 ulp (exercise).
22 *
23 * So, compute sqrtq(x*x+y*y) with some care as
24 * follows to get the error below 1 ulp:
25 *
26 * Assume x>y>0;
27 * (if possible, set rounding to round-to-nearest)
28 * 1. if x > 2y use
29 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
30 * where x1 = x with lower 64 bits cleared, x2 = x-x1; else
31 * 2. if x <= 2y use
32 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
33 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1,
34 * y1= y with lower 64 bits chopped, y2 = y-y1.
35 *
36 * NOTE: scaling may be necessary if some argument is too
37 * large or too tiny
38 *
39 * Special cases:
40 * hypotl(x,y) is INF if x or y is +INF or -INF; else
41 * hypotl(x,y) is NAN if x or y is NAN.
42 *
43 * Accuracy:
44 * hypotl(x,y) returns sqrtq(x^2+y^2) with error less
45 * than 1 ulps (units in the last place)
46 */
47
48 #include "quadmath-imp.h"
49
50 __float128
51 hypotq(__float128 x, __float128 y)
52 {
53 __float128 a,b,t1,t2,y1,y2,w;
54 int64_t j,k,ha,hb;
55
56 GET_FLT128_MSW64(ha,x);
57 ha &= 0x7fffffffffffffffLL;
58 GET_FLT128_MSW64(hb,y);
59 hb &= 0x7fffffffffffffffLL;
60 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
61 SET_FLT128_MSW64(a,ha); /* a <- |a| */
62 SET_FLT128_MSW64(b,hb); /* b <- |b| */
63 if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
64 k=0;
65 if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
66 if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
67 uint64_t low;
68 w = a+b; /* for sNaN */
69 if (issignalingq (a) || issignalingq (b))
70 return w;
71 GET_FLT128_LSW64(low,a);
72 if(((ha&0xffffffffffffLL)|low)==0) w = a;
73 GET_FLT128_LSW64(low,b);
74 if(((hb^0x7fff000000000000LL)|low)==0) w = b;
75 return w;
76 }
77 /* scale a and b by 2**-9600 */
78 ha -= 0x2580000000000000LL;
79 hb -= 0x2580000000000000LL; k += 9600;
80 SET_FLT128_MSW64(a,ha);
81 SET_FLT128_MSW64(b,hb);
82 }
83 if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
84 if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
85 uint64_t low;
86 GET_FLT128_LSW64(low,b);
87 if((hb|low)==0) return a;
88 t1=0;
89 SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
90 b *= t1;
91 a *= t1;
92 k -= 16382;
93 GET_FLT128_MSW64 (ha, a);
94 GET_FLT128_MSW64 (hb, b);
95 if (hb > ha)
96 {
97 t1 = a;
98 a = b;
99 b = t1;
100 j = ha;
101 ha = hb;
102 hb = j;
103 }
104 } else { /* scale a and b by 2^9600 */
105 ha += 0x2580000000000000LL; /* a *= 2^9600 */
106 hb += 0x2580000000000000LL; /* b *= 2^9600 */
107 k -= 9600;
108 SET_FLT128_MSW64(a,ha);
109 SET_FLT128_MSW64(b,hb);
110 }
111 }
112 /* medium size a and b */
113 w = a-b;
114 if (w>b) {
115 t1 = 0;
116 SET_FLT128_MSW64(t1,ha);
117 t2 = a-t1;
118 w = sqrtq(t1*t1-(b*(-b)-t2*(a+t1)));
119 } else {
120 a = a+a;
121 y1 = 0;
122 SET_FLT128_MSW64(y1,hb);
123 y2 = b - y1;
124 t1 = 0;
125 SET_FLT128_MSW64(t1,ha+0x0001000000000000LL);
126 t2 = a - t1;
127 w = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b)));
128 }
129 if(k!=0) {
130 uint64_t high;
131 t1 = 1;
132 GET_FLT128_MSW64(high,t1);
133 SET_FLT128_MSW64(t1,high+(k<<48));
134 w *= t1;
135 math_check_force_underflow_nonneg (w);
136 return w;
137 } else return w;
138 }