1/* @(#)e_hypot.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13/* __ieee754_hypot(x,y)
14 *
15 * Method :
16 * If (assume round-to-nearest) z=x*x+y*y
17 * has error less than sqrt(2)/2 ulp, than
18 * sqrt(z) has error less than 1 ulp (exercise).
19 *
20 * So, compute sqrt(x*x+y*y) with some care as
21 * follows to get the error below 1 ulp:
22 *
23 * Assume x>y>0;
24 * (if possible, set rounding to round-to-nearest)
25 * 1. if x > 2y use
26 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
27 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
28 * 2. if x <= 2y use
29 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
30 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
31 * y1= y with lower 32 bits chopped, y2 = y-y1.
32 *
33 * NOTE: scaling may be necessary if some argument is too
34 * large or too tiny
35 *
36 * Special cases:
37 * hypot(x,y) is INF if x or y is +INF or -INF; else
38 * hypot(x,y) is NAN if x or y is NAN.
39 *
40 * Accuracy:
41 * hypot(x,y) returns sqrt(x^2+y^2) with error less
42 * than 1 ulps (units in the last place)
43 */
44
45#include <math.h>
46#include <math_private.h>
47
48double
49__ieee754_hypot (double x, double y)
50{
51 double a, b, t1, t2, y1, y2, w;
52 int32_t j, k, ha, hb;
53
54 GET_HIGH_WORD (ha, x);
55 ha &= 0x7fffffff;
56 GET_HIGH_WORD (hb, y);
57 hb &= 0x7fffffff;
58 if (hb > ha)
59 {
60 a = y; b = x; j = ha; ha = hb; hb = j;
61 }
62 else
63 {
64 a = x; b = y;
65 }
66 SET_HIGH_WORD (a, ha); /* a <- |a| */
67 SET_HIGH_WORD (b, hb); /* b <- |b| */
68 if ((ha - hb) > 0x3c00000)
69 {
70 return a + b;
71 } /* x/y > 2**60 */
72 k = 0;
73 if (__glibc_unlikely (ha > 0x5f300000)) /* a>2**500 */
74 {
75 if (ha >= 0x7ff00000) /* Inf or NaN */
76 {
77 uint32_t low;
78 w = a + b; /* for sNaN */
79 if (issignaling (a) || issignaling (b))
80 return w;
81 GET_LOW_WORD (low, a);
82 if (((ha & 0xfffff) | low) == 0)
83 w = a;
84 GET_LOW_WORD (low, b);
85 if (((hb ^ 0x7ff00000) | low) == 0)
86 w = b;
87 return w;
88 }
89 /* scale a and b by 2**-600 */
90 ha -= 0x25800000; hb -= 0x25800000; k += 600;
91 SET_HIGH_WORD (a, ha);
92 SET_HIGH_WORD (b, hb);
93 }
94 if (__builtin_expect (hb < 0x23d00000, 0)) /* b < 2**-450 */
95 {
96 if (hb <= 0x000fffff) /* subnormal b or 0 */
97 {
98 uint32_t low;
99 GET_LOW_WORD (low, b);
100 if ((hb | low) == 0)
101 return a;
102 t1 = 0;
103 SET_HIGH_WORD (t1, 0x7fd00000); /* t1=2^1022 */
104 b *= t1;
105 a *= t1;
106 k -= 1022;
107 GET_HIGH_WORD (ha, a);
108 GET_HIGH_WORD (hb, b);
109 if (hb > ha)
110 {
111 t1 = a;
112 a = b;
113 b = t1;
114 j = ha;
115 ha = hb;
116 hb = j;
117 }
118 }
119 else /* scale a and b by 2^600 */
120 {
121 ha += 0x25800000; /* a *= 2^600 */
122 hb += 0x25800000; /* b *= 2^600 */
123 k -= 600;
124 SET_HIGH_WORD (a, ha);
125 SET_HIGH_WORD (b, hb);
126 }
127 }
128 /* medium size a and b */
129 w = a - b;
130 if (w > b)
131 {
132 t1 = 0;
133 SET_HIGH_WORD (t1, ha);
134 t2 = a - t1;
135 w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));
136 }
137 else
138 {
139 a = a + a;
140 y1 = 0;
141 SET_HIGH_WORD (y1, hb);
142 y2 = b - y1;
143 t1 = 0;
144 SET_HIGH_WORD (t1, ha + 0x00100000);
145 t2 = a - t1;
146 w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
147 }
148 if (k != 0)
149 {
150 uint32_t high;
151 t1 = 1.0;
152 GET_HIGH_WORD (high, t1);
153 SET_HIGH_WORD (t1, high + (k << 20));
154 w *= t1;
155 math_check_force_underflow_nonneg (w);
156 return w;
157 }
158 else
159 return w;
160}
161strong_alias (__ieee754_hypot, __hypot_finite)
162