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 * cbrt(x)
77 * Return cube root of x
78 */
79 public static class Cbrt {
80 // unsigned
81 private static final int B1 = 715094163; /* B1 = (682-0.03306235651)*2**20 */
82 private static final int B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
83
84 private static final double C = 5.42857142857142815906e-01; /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
85 private static final double D = -7.05306122448979611050e-01; /* -864/1225 = 0xBFE691DE, 0x2532C834 */
86 private static final double E = 1.41428571428571436819e+00; /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
87 private static final double F = 1.60714285714285720630e+00; /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
88 private static final double G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
89
90 public static strictfp double compute(double x) {
91 int hx;
92 double r, s, t=0.0, w;
93 int sign; // unsigned
94
95 hx = __HI(x); // high word of x
96 sign = hx & 0x80000000; // sign= sign(x)
97 hx ^= sign;
98 if (hx >= 0x7ff00000)
99 return (x+x); // cbrt(NaN,INF) is itself
100 if ((hx | __LO(x)) == 0)
101 return(x); // cbrt(0) is itself
102
103 x = __HI(x, hx); // x <- |x|
104 // rough cbrt to 5 bits
105 if (hx < 0x00100000) { // subnormal number
106 t = __HI(t, 0x43500000); // set t= 2**54
107 t *= x;
108 t = __HI(t, __HI(t)/3+B2);
109 } else {
110 t = __HI(t, hx/3+B1);
111 }
112
113 // new cbrt to 23 bits, may be implemented in single precision
114 r = t * t/x;
115 s = C + r*t;
116 t *= G + F/(s + E + D/s);
117
118 // chopped to 20 bits and make it larger than cbrt(x)
119 t = __LO(t, 0);
120 t = __HI(t, __HI(t)+0x00000001);
121
122
123 // one step newton iteration to 53 bits with error less than 0.667 ulps
124 s = t * t; // t*t is exact
125 r = x / s;
126 w = t + t;
127 r= (r - t)/(w + r); // r-s is exact
128 t= t + t*r;
129
130 // retore the sign bit
131 t = __HI(t, __HI(t) | sign);
132 return(t);
133 }
134 }
135
136 /**
137 * hypot(x,y)
138 *
139 * Method :
140 * If (assume round-to-nearest) z = x*x + y*y
141 * has error less than sqrt(2)/2 ulp, than
142 * sqrt(z) has error less than 1 ulp (exercise).
143 *
144 * So, compute sqrt(x*x + y*y) with some care as
145 * follows to get the error below 1 ulp:
146 *
147 * Assume x > y > 0;
148 * (if possible, set rounding to round-to-nearest)
149 * 1. if x > 2y use
150 * x1*x1 + (y*y + (x2*(x + x1))) for x*x + y*y
151 * where x1 = x with lower 32 bits cleared, x2 = x - x1; else
152 * 2. if x <= 2y use
153 * t1*y1 + ((x-y) * (x-y) + (t1*y2 + t2*y))
154 * where t1 = 2x with lower 32 bits cleared, t2 = 2x - t1,
155 * y1= y with lower 32 bits chopped, y2 = y - y1.
156 *
157 * NOTE: scaling may be necessary if some argument is too
158 * large or too tiny
159 *
160 * Special cases:
161 * hypot(x,y) is INF if x or y is +INF or -INF; else
162 * hypot(x,y) is NAN if x or y is NAN.
163 *
164 * Accuracy:
165 * hypot(x,y) returns sqrt(x^2 + y^2) with error less
166 * than 1 ulps (units in the last place)
167 */
168 static class Hypot {
169 public static double compute(double x, double y) {
170 double a = x;
171 double b = y;
172 double t1, t2, y1, y2, w;
173 int j, k, ha, hb;
174
175 ha = __HI(x) & 0x7fffffff; // high word of x
176 hb = __HI(y) & 0x7fffffff; // high word of y
177 if(hb > ha) {
178 a = y;
179 b = x;
180 j = ha;
181 ha = hb;
182 hb = j;
183 } else {
184 a = x;
185 b = y;
186 }
187 a = __HI(a, ha); // a <- |a|
188 b = __HI(b, hb); // b <- |b|
189 if ((ha - hb) > 0x3c00000) {
190 return a + b; // x / y > 2**60
191 }
192 k=0;
193 if (ha > 0x5f300000) { // a>2**500
194 if (ha >= 0x7ff00000) { // Inf or NaN
195 w = a + b; // for sNaN
196 if (((ha & 0xfffff) | __LO(a)) == 0)
197 w = a;
198 if (((hb ^ 0x7ff00000) | __LO(b)) == 0)
199 w = b;
200 return w;
201 }
202 // scale a and b by 2**-600
203 ha -= 0x25800000;
204 hb -= 0x25800000;
205 k += 600;
206 a = __HI(a, ha);
207 b = __HI(b, hb);
208 }
209 if (hb < 0x20b00000) { // b < 2**-500
210 if (hb <= 0x000fffff) { // subnormal b or 0 */
211 if ((hb | (__LO(b))) == 0)
212 return a;
213 t1 = 0;
214 t1 = __HI(t1, 0x7fd00000); // t1=2^1022
215 b *= t1;
216 a *= t1;
217 k -= 1022;
218 } else { // scale a and b by 2^600
219 ha += 0x25800000; // a *= 2^600
220 hb += 0x25800000; // b *= 2^600
221 k -= 600;
222 a = __HI(a, ha);
223 b = __HI(b, hb);
224 }
225 }
226 // medium size a and b
227 w = a - b;
228 if (w > b) {
229 t1 = 0;
230 t1 = __HI(t1, ha);
231 t2 = a - t1;
232 w = Math.sqrt(t1*t1 - (b*(-b) - t2 * (a + t1)));
233 } else {
234 a = a + a;
235 y1 = 0;
236 y1 = __HI(y1, hb);
237 y2 = b - y1;
238 t1 = 0;
239 t1 = __HI(t1, ha + 0x00100000);
240 t2 = a - t1;
241 w = Math.sqrt(t1*y1 - (w*(-w) - (t1*y2 + t2*b)));
242 }
243 if (k != 0) {
244 t1 = 1.0;
245 int t1_hi = __HI(t1);
246 t1_hi += (k << 20);
247 t1 = __HI(t1, t1_hi);
248 return t1 * w;
249 } else
250 return w;
251 }
252 }
253 }