samples/fixed_point.js

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1 /*
2 * Copyright (c) 2015, Oracle and/or its affiliates. All rights reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 *
8 * - Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 *
11 * - Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * - Neither the name of Oracle nor the names of its
16 * contributors may be used to endorse or promote products derived
17 * from this software without specific prior written permission.
18 *
19 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
20 * IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
21 * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
22 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
23 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
24 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
25 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
26 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
27 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
28 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
29 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
30 */
31
32 // Simple sample demonstrating "fixed point" computation with Streams
33
34 // See also https://mitpress.mit.edu/sicp/chapter1/node21.html#secprocgeneralmethods
35 var Stream = Java.type("java.util.stream.Stream");
36
37 // generic fixed point procedure
38 function fixed_point(f, init_guess) {
39 var tolerance = 0.00001;
40 function close_enough(v1, v2) Math.abs(v1 - v2) < tolerance;
41
42 var prev;
43 return Stream.iterate(init_guess, f)
44 .filter(function(x) {
45 try {
46 return prev == undefined? false : close_enough(prev, x);
47 } finally {
48 prev = x;
49 }
50 })
51 .findFirst()
52 .get();
53 }
54
55 // solution to x = cos(x)
56 print(fixed_point(Math.cos, 1.0))
57
58 // solution to x = sin(x) + cos(x)
59 print(fixed_point(function(x) Math.sin(x) + Math.cos(x), 1.0));
60
61 // square root by Newton's method
62 // http://en.wikipedia.org/wiki/Newton's_method
63 function sqrt(n)
64 fixed_point(function(x) (x + n/x) / 2, 2.0);
65
66 print(sqrt(2))
67 print(sqrt(3))
68
69

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