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/* __ieee754_hypotl(x,y)
17 *
18 * Method :
19 * If (assume round-to-nearest) z=x*x+y*y
20 * has error less than sqrtl(2)/2 ulp, than
21 * sqrtl(z) has error less than 1 ulp (exercise).
22 *
23 * So, compute sqrtl(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 sqrtl(x^2+y^2) with error less
45 * than 1 ulps (units in the last place)
46 */
47
48#include <math.h>
49#include <math_private.h>
50
51_Float128
52__ieee754_hypotl(_Float128 x, _Float128 y)
53{
54 _Float128 a,b,t1,t2,y1,y2,w;
55 int64_t j,k,ha,hb;
56
57 GET_LDOUBLE_MSW64(ha,x);
58 ha &= 0x7fffffffffffffffLL;
59 GET_LDOUBLE_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_LDOUBLE_MSW64(a,ha); /* a <- |a| */
63 SET_LDOUBLE_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 u_int64_t low;
69 w = a+b; /* for sNaN */
70 if (issignaling (a) || issignaling (b))
71 return w;
72 GET_LDOUBLE_LSW64(low,a);
73 if(((ha&0xffffffffffffLL)|low)==0) w = a;
74 GET_LDOUBLE_LSW64(low,b);
75 if(((hb^0x7fff000000000000LL)|low)==0) w = b;
76 return w;
77 }
78 /* scale a and b by 2**-9600 */
79 ha -= 0x2580000000000000LL;
80 hb -= 0x2580000000000000LL; k += 9600;
81 SET_LDOUBLE_MSW64(a,ha);
82 SET_LDOUBLE_MSW64(b,hb);
83 }
84 if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
85 if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
86 u_int64_t low;
87 GET_LDOUBLE_LSW64(low,b);
88 if((hb|low)==0) return a;
89 t1=0;
90 SET_LDOUBLE_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
91 b *= t1;
92 a *= t1;
93 k -= 16382;
94 GET_LDOUBLE_MSW64 (ha, a);
95 GET_LDOUBLE_MSW64 (hb, b);
96 if (hb > ha)
97 {
98 t1 = a;
99 a = b;
100 b = t1;
101 j = ha;
102 ha = hb;
103 hb = j;
104 }
105 } else { /* scale a and b by 2^9600 */
106 ha += 0x2580000000000000LL; /* a *= 2^9600 */
107 hb += 0x2580000000000000LL; /* b *= 2^9600 */
108 k -= 9600;
109 SET_LDOUBLE_MSW64(a,ha);
110 SET_LDOUBLE_MSW64(b,hb);
111 }
112 }
113 /* medium size a and b */
114 w = a-b;
115 if (w>b) {
116 t1 = 0;
117 SET_LDOUBLE_MSW64(t1,ha);
118 t2 = a-t1;
119 w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
120 } else {
121 a = a+a;
122 y1 = 0;
123 SET_LDOUBLE_MSW64(y1,hb);
124 y2 = b - y1;
125 t1 = 0;
126 SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL);
127 t2 = a - t1;
128 w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
129 }
130 if(k!=0) {
131 u_int64_t high;
132 t1 = 1;
133 GET_LDOUBLE_MSW64(high,t1);
134 SET_LDOUBLE_MSW64(t1,high+(k<<48));
135 w *= t1;
136 math_check_force_underflow_nonneg (w);
137 return w;
138 } else return w;
139}
140strong_alias (__ieee754_hypotl, __hypotl_finite)
141