sundar@1524: /*
sundar@1524:  * Copyright (c) 2015, Oracle and/or its affiliates. All rights reserved.
sundar@1524:  *
sundar@1524:  * Redistribution and use in source and binary forms, with or without
sundar@1524:  * modification, are permitted provided that the following conditions
sundar@1524:  * are met:
sundar@1524:  *
sundar@1524:  *   - Redistributions of source code must retain the above copyright
sundar@1524:  *     notice, this list of conditions and the following disclaimer.
sundar@1524:  *
sundar@1524:  *   - Redistributions in binary form must reproduce the above copyright
sundar@1524:  *     notice, this list of conditions and the following disclaimer in the
sundar@1524:  *     documentation and/or other materials provided with the distribution.
sundar@1524:  *
sundar@1524:  *   - Neither the name of Oracle nor the names of its
sundar@1524:  *     contributors may be used to endorse or promote products derived
sundar@1524:  *     from this software without specific prior written permission.
sundar@1524:  *
sundar@1524:  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
sundar@1524:  * IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
sundar@1524:  * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
sundar@1524:  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
sundar@1524:  * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
sundar@1524:  * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
sundar@1524:  * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
sundar@1524:  * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
sundar@1524:  * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
sundar@1524:  * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
sundar@1524:  * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
sundar@1524:  */
sundar@1524: 
sundar@1524: // Simple sample demonstrating "fixed point" computation with Streams
sundar@1524: 
sundar@1524: // See also https://mitpress.mit.edu/sicp/chapter1/node21.html#secprocgeneralmethods
sundar@1524: var Stream = Java.type("java.util.stream.Stream");
sundar@1524: 
sundar@1524: // generic fixed point procedure
sundar@1524: function fixed_point(f, init_guess) {
sundar@1524:   var tolerance = 0.00001;
sundar@1524:   function close_enough(v1, v2) Math.abs(v1 - v2) < tolerance;
sundar@1524:  
sundar@1524:   var prev; 
sundar@1524:   return Stream.iterate(init_guess, f)
sundar@1524:       .filter(function(x) {
sundar@1524:           try {
sundar@1524:               return prev == undefined? false : close_enough(prev, x);
sundar@1524:           } finally {
sundar@1524:               prev = x;
sundar@1524:           }
sundar@1524:       })
sundar@1524:       .findFirst()
sundar@1524:       .get();
sundar@1524: }
sundar@1524: 
sundar@1524: // solution to x = cos(x)
sundar@1524: print(fixed_point(Math.cos, 1.0))
sundar@1524: 
sundar@1524: // solution to x = sin(x) + cos(x)
sundar@1524: print(fixed_point(function(x) Math.sin(x) + Math.cos(x), 1.0));
sundar@1524: 
sundar@1524: // square root by Newton's method
sundar@1524: // http://en.wikipedia.org/wiki/Newton's_method
sundar@1524: function sqrt(n)
sundar@1524:   fixed_point(function(x) (x + n/x) / 2, 2.0);
sundar@1524: 
sundar@1524: print(sqrt(2))
sundar@1524: print(sqrt(3))
sundar@1524: 
sundar@1524: