1 /*
2 * Copyright (c) 1998, 2015, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 /**
27 * A transliteration of the "Freely Distributable Math Library"
28 * algorithms from C into Java. That is, this port of the algorithms
29 * is as close to the C originals as possible while still being
30 * readable legal Java.
31 */
32 public class FdlibmTranslit {
33 private FdlibmTranslit() {
34 throw new UnsupportedOperationException("No FdLibmTranslit instances for you.");
35 }
36
37 /**
38 * Return the low-order 32 bits of the double argument as an int.
39 */
40 private static int __LO(double x) {
41 long transducer = Double.doubleToRawLongBits(x);
42 return (int)transducer;
43 }
44
45 /**
46 * Return a double with its low-order bits of the second argument
47 * and the high-order bits of the first argument..
48 */
49 private static double __LO(double x, int low) {
50 long transX = Double.doubleToRawLongBits(x);
51 return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low );
52 }
53
54 /**
55 * Return the high-order 32 bits of the double argument as an int.
56 */
57 private static int __HI(double x) {
58 long transducer = Double.doubleToRawLongBits(x);
59 return (int)(transducer >> 32);
60 }
61
62 /**
63 * Return a double with its high-order bits of the second argument
64 * and the low-order bits of the first argument..
65 */
66 private static double __HI(double x, int high) {
67 long transX = Double.doubleToRawLongBits(x);
68 return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 );
69 }
70
71 public static double hypot(double x, double y) {
72 return Hypot.compute(x, y);
73 }
74
75 /**
76 * hypot(x,y)
77 *
78 * Method :
79 * If (assume round-to-nearest) z = x*x + y*y
80 * has error less than sqrt(2)/2 ulp, than
81 * sqrt(z) has error less than 1 ulp (exercise).
82 *
83 * So, compute sqrt(x*x + y*y) with some care as
84 * follows to get the error below 1 ulp:
85 *
86 * Assume x > y > 0;
87 * (if possible, set rounding to round-to-nearest)
88 * 1. if x > 2y use
89 * x1*x1 + (y*y + (x2*(x + x1))) for x*x + y*y
90 * where x1 = x with lower 32 bits cleared, x2 = x - x1; else
91 * 2. if x <= 2y use
92 * t1*y1 + ((x-y) * (x-y) + (t1*y2 + t2*y))
93 * where t1 = 2x with lower 32 bits cleared, t2 = 2x - t1,
94 * y1= y with lower 32 bits chopped, y2 = y - y1.
95 *
96 * NOTE: scaling may be necessary if some argument is too
97 * large or too tiny
98 *
99 * Special cases:
100 * hypot(x,y) is INF if x or y is +INF or -INF; else
101 * hypot(x,y) is NAN if x or y is NAN.
102 *
103 * Accuracy:
104 * hypot(x,y) returns sqrt(x^2 + y^2) with error less
105 * than 1 ulps (units in the last place)
106 */
107 static class Hypot {
108 public static double compute(double x, double y) {
109 double a = x;
110 double b = y;
111 double t1, t2, y1, y2, w;
112 int j, k, ha, hb;
113
114 ha = __HI(x) & 0x7fffffff; // high word of x
115 hb = __HI(y) & 0x7fffffff; // high word of y
116 if(hb > ha) {
117 a = y;
118 b = x;
119 j = ha;
120 ha = hb;
121 hb = j;
122 } else {
123 a = x;
124 b = y;
125 }
126 a = __HI(a, ha); // a <- |a|
127 b = __HI(b, hb); // b <- |b|
128 if ((ha - hb) > 0x3c00000) {
129 return a + b; // x / y > 2**60
130 }
131 k=0;
132 if (ha > 0x5f300000) { // a>2**500
133 if (ha >= 0x7ff00000) { // Inf or NaN
134 w = a + b; // for sNaN
135 if (((ha & 0xfffff) | __LO(a)) == 0)
136 w = a;
137 if (((hb ^ 0x7ff00000) | __LO(b)) == 0)
138 w = b;
139 return w;
140 }
141 // scale a and b by 2**-600
142 ha -= 0x25800000;
143 hb -= 0x25800000;
144 k += 600;
145 a = __HI(a, ha);
146 b = __HI(b, hb);
147 }
148 if (hb < 0x20b00000) { // b < 2**-500
149 if (hb <= 0x000fffff) { // subnormal b or 0 */
150 if ((hb | (__LO(b))) == 0)
151 return a;
152 t1 = 0;
153 t1 = __HI(t1, 0x7fd00000); // t1=2^1022
154 b *= t1;
155 a *= t1;
156 k -= 1022;
157 } else { // scale a and b by 2^600
158 ha += 0x25800000; // a *= 2^600
159 hb += 0x25800000; // b *= 2^600
160 k -= 600;
161 a = __HI(a, ha);
162 b = __HI(b, hb);
163 }
164 }
165 // medium size a and b
166 w = a - b;
167 if (w > b) {
168 t1 = 0;
169 t1 = __HI(t1, ha);
170 t2 = a - t1;
171 w = Math.sqrt(t1*t1 - (b*(-b) - t2 * (a + t1)));
172 } else {
173 a = a + a;
174 y1 = 0;
175 y1 = __HI(y1, hb);
176 y2 = b - y1;
177 t1 = 0;
178 t1 = __HI(t1, ha + 0x00100000);
179 t2 = a - t1;
180 w = Math.sqrt(t1*y1 - (w*(-w) - (t1*y2 + t2*b)));
181 }
182 if (k != 0) {
183 t1 = 1.0;
184 int t1_hi = __HI(t1);
185 t1_hi += (k << 20);
186 t1 = __HI(t1, t1_hi);
187 return t1 * w;
188 } else
189 return w;
190 }
191 }
192 }