fixed_point.js

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// Simple sample demonstrating "fixed point" computation with Streams

// See also https://mitpress.mit.edu/sicp/chapter1/node21.html#secprocgeneralmethods
var Stream = Java.type("java.util.stream.Stream");

// generic fixed point procedure
function fixed_point(f, init_guess) {
  var tolerance = 0.00001;
  function close_enough(v1, v2) Math.abs(v1 - v2) < tolerance;
 
  var prev; 
  return Stream.iterate(init_guess, f)
      .filter(function(x) {
          try {
              return prev == undefined? false : close_enough(prev, x);
          } finally {
              prev = x;
          }
      })
      .findFirst()
      .get();
}

// solution to x = cos(x)
print(fixed_point(Math.cos, 1.0))

// solution to x = sin(x) + cos(x)
print(fixed_point(function(x) Math.sin(x) + Math.cos(x), 1.0));

// square root by Newton's method
// http://en.wikipedia.org/wiki/Newton's_method
function sqrt(n)
  fixed_point(function(x) (x + n/x) / 2, 2.0);

print(sqrt(2))
print(sqrt(3))