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#include <math-underflow.h>
48
49double
50__ieee754_hypot (double x, double y)
51{
52 double a, b, t1, t2, y1, y2, w;
53 int32_t j, k, ha, hb;
54
55 GET_HIGH_WORD (ha, x);
56 ha &= 0x7fffffff;
57 GET_HIGH_WORD (hb, y);
58 hb &= 0x7fffffff;
59 if (hb > ha)
60 {
61 a = y; b = x; j = ha; ha = hb; hb = j;
62 }
63 else
64 {
65 a = x; b = y;
66 }
67 SET_HIGH_WORD (a, ha); /* a <- |a| */
68 SET_HIGH_WORD (b, hb); /* b <- |b| */
69 if ((ha - hb) > 0x3c00000)
70 {
71 return a + b;
72 } /* x/y > 2**60 */
73 k = 0;
74 if (__glibc_unlikely (ha > 0x5f300000)) /* a>2**500 */
75 {
76 if (ha >= 0x7ff00000) /* Inf or NaN */
77 {
78 uint32_t low;
79 w = a + b; /* for sNaN */
80 if (issignaling (a) || issignaling (b))
81 return w;
82 GET_LOW_WORD (low, a);
83 if (((ha & 0xfffff) | low) == 0)
84 w = a;
85 GET_LOW_WORD (low, b);
86 if (((hb ^ 0x7ff00000) | low) == 0)
87 w = b;
88 return w;
89 }
90 /* scale a and b by 2**-600 */
91 ha -= 0x25800000; hb -= 0x25800000; k += 600;
92 SET_HIGH_WORD (a, ha);
93 SET_HIGH_WORD (b, hb);
94 }
95 if (__builtin_expect (hb < 0x23d00000, 0)) /* b < 2**-450 */
96 {
97 if (hb <= 0x000fffff) /* subnormal b or 0 */
98 {
99 uint32_t low;
100 GET_LOW_WORD (low, b);
101 if ((hb | low) == 0)
102 return a;
103 t1 = 0;
104 SET_HIGH_WORD (t1, 0x7fd00000); /* t1=2^1022 */
105 b *= t1;
106 a *= t1;
107 k -= 1022;
108 GET_HIGH_WORD (ha, a);
109 GET_HIGH_WORD (hb, b);
110 if (hb > ha)
111 {
112 t1 = a;
113 a = b;
114 b = t1;
115 j = ha;
116 ha = hb;
117 hb = j;
118 }
119 }
120 else /* scale a and b by 2^600 */
121 {
122 ha += 0x25800000; /* a *= 2^600 */
123 hb += 0x25800000; /* b *= 2^600 */
124 k -= 600;
125 SET_HIGH_WORD (a, ha);
126 SET_HIGH_WORD (b, hb);
127 }
128 }
129 /* medium size a and b */
130 w = a - b;
131 if (w > b)
132 {
133 t1 = 0;
134 SET_HIGH_WORD (t1, ha);
135 t2 = a - t1;
136 w = sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));
137 }
138 else
139 {
140 a = a + a;
141 y1 = 0;
142 SET_HIGH_WORD (y1, hb);
143 y2 = b - y1;
144 t1 = 0;
145 SET_HIGH_WORD (t1, ha + 0x00100000);
146 t2 = a - t1;
147 w = sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
148 }
149 if (k != 0)
150 {
151 uint32_t high;
152 t1 = 1.0;
153 GET_HIGH_WORD (high, t1);
154 SET_HIGH_WORD (t1, high + (k << 20));
155 w *= t1;
156 math_check_force_underflow_nonneg (w);
157 return w;
158 }
159 else
160 return w;
161}
162strong_alias (__ieee754_hypot, __hypot_finite)
163