fixed_point.js revision 1412:bfe6bd5d57bf 
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31
32// Simple sample demonstrating "fixed point" computation with Streams
33
34// See also https://mitpress.mit.edu/sicp/chapter1/node21.html#secprocgeneralmethods
35var Stream = Java.type("java.util.stream.Stream");
36
37// generic fixed point procedure
38function 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)
56print(fixed_point(Math.cos, 1.0))
57
58// solution to x = sin(x) + cos(x)
59print(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
63function sqrt(n)
64  fixed_point(function(x) (x + n/x) / 2, 2.0);
65
66print(sqrt(2))
67print(sqrt(3))
68
69
70