source: Dev/trunk/src/client/dojox/calc/toFrac.js

define([
        "dojo/_base/lang",
        "dojox/calc/_Executor"
], function(lang, calc) {

        var multiples;

        function _fracHashInit(){
                var sqrts = [
                        5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,
                        30,31,33,34,35,37,38,39,41,42,43,46,47,51,53,55,57,58,59,
                        61,62,65,66,67,69,70,71,73,74,77,78,79,82,83,85,86,87,89,91,93,94,95,97
                ];
                multiples = { "1":1, "\u221A(2)":Math.sqrt(2), "\u221A(3)":Math.sqrt(3), "pi":Math.PI };
                // populate the rest of the multiples array
                for(var i in sqrts){
                        var n = sqrts[i];
                        multiples["\u221A("+n+")"] = Math.sqrt(n);
                }
                multiples["\u221A(pi)"] = Math.sqrt(Math.PI);
        }

        function _fracLookup(number){
                function findSimpleFraction(fraction){
                        var denom1Low = Math.floor(1 / fraction);
                        // fraction <= 1/denom1Low 
                        var quotient = calc.approx(1 / denom1Low);
                        if(quotient == fraction){ return { n:1, d:denom1Low }; }
                        var denom1High = denom1Low + 1;
                        // 1/denom1High <= fraction < 1/denom1Low 
                        quotient = calc.approx(1 / denom1High);
                        if(quotient == fraction){ return { n:1, d:denom1High }; }
                        if(denom1Low >= 50){ return null; } // only 1's in the numerator beyond this point
                        // 1/denom1High < fraction < 1/denom1Low 
                        var denom2 = denom1Low + denom1High;
                        quotient = calc.approx(2 / denom2);
                        // 1/denom1High < 2/(denom1Low+denom1High) < 1/denom1Low 
                        if(quotient == fraction){ return { n:2, d:denom2 }; }
                        if(denom1Low >= 34){ return null; } // only 1's and 2's in the numerator beyond this point
                        var less2 = fraction < quotient;
                        // if less2
                        //      1/denom1High < fraction < 2/(denom1Low+denom1High)
                        // else
                        //      2/(denom1Low+denom1High) < fraction < 1/denom1Low
                        var denom4 = denom2 * 2 + (less2 ? 1 : -1);
                        quotient = calc.approx(4 / denom4);
                        // 1/denom1High < 4/(2*denom1Low+2*denom1High+1) < 2/(denom1Low+denom1High) < 4/(2*denom1Low+2*denom1High-1) < 1/denom1Low 
                        if(quotient == fraction){ return { n:4, d:denom4 }; }
                        var less4 = fraction < quotient;
                        // we've already checked for 1, 2 and 4, but now see if we need to check for 3 in the numerator
                        if((less2 && !less4) || (!less2 && less4)){
                                var denom3 = (denom2 + denom4) >> 1;
                                quotient = calc.approx(3 / denom3);
                                // 1/denom1High < 4/(2*denom1Low+2*denom1High+1) < 3/((3*denom1Low+3*denom1High+1)/2) < 2/(denom1Low+denom1High) < 3/((3*denom1Low+3*denom1High-1)/2) < 4/(2*denom1Low+2*denom1High-1) < 1/denom1Low 
                                if(quotient == fraction){ return { n:3, d:denom3 }; }
                        }
                        if(denom1Low >= 20){ return null; } // only 1's, 2's, 3's, and 4's in the numerator beyond this point
                        // if less2
                        //      if less4
                        //              1/denom1High < fraction < 4/(2*denom1Low+2*denom1High+1)
                        //      else
                        //              4/(2*denom1Low+2*denom1High+1) < fraction < 2/(denom1Low+denom1High)
                        // else
                        //      if less4
                        //              2/(denom1Low+denom1High) < fraction < 4/(2*denom1Low+2*denom1High-1)
                        //      else
                        //              4/(2*denom1Low+2*denom1High-1) < fraction < 1/denom1Low
                        var smallestDenom = denom2 + denom1Low * 2;
                        var largestDenom = smallestDenom + 2;
                        for(var numerator = 5; smallestDenom <= 100; numerator++){ // start with 5 in the numerator
                                smallestDenom += denom1Low;
                                largestDenom += denom1High;
                                var startDenom = less2 ? ((largestDenom + smallestDenom + 1) >> 1) : smallestDenom;
                                var stopDenom = less2 ? largestDenom : ((largestDenom + smallestDenom - 1) >> 1);
                                startDenom = less4 ? ((startDenom + stopDenom) >> 1) : startDenom;
                                stopDenom = less4 ? stopDenom : ((startDenom + stopDenom) >> 1);
                                for(var thisDenom = startDenom; thisDenom <= stopDenom; thisDenom++){
                                        if(numerator & 1 == 0 && thisDenom & 1 == 0){ continue; } // skip where n and d are both even
                                        quotient = calc.approx(numerator / thisDenom);
                                        if(quotient == fraction){ return { n:numerator, d:thisDenom }; }
                                        if(quotient < fraction){ break; } // stop since the values will just get smaller
                                }
                        }
                        return null;
                }
                number = Math.abs(number);
                for(var mt in multiples){
                        var multiple = multiples[mt];
                        var simpleFraction = number / multiple;
                        var wholeNumber = Math.floor(simpleFraction);
                        simpleFraction = calc.approx(simpleFraction - wholeNumber);
                        if(simpleFraction == 0){
                                return { mt:mt, m:multiple, n:wholeNumber, d:1 };
                        }else{
                                var a = findSimpleFraction(simpleFraction);
                                if(!a){ continue; }
                                return { mt:mt, m:multiple, n:(wholeNumber * a.d + a.n), d:a.d };
                        }
                }
                return null;
        }

        // make the hash
        _fracHashInit();

        // add toFrac to the calculator
        return lang.mixin(calc, {
                toFrac: function(number){// get a string fraction for a decimal with a set range of numbers, based on the hash
                        var f = _fracLookup(number);
                        return f ? ((number < 0 ? '-' : '') + (f.m == 1 ? '' : (f.n == 1 ? '' : (f.n + '*'))) + (f.m == 1 ? f.n : f.mt) + ((f.d == 1 ? '' : '/' + f.d))) : number;
                        //return f ? ((number < 0 ? '-' : '') + (f.m == 1 ? '' : (f.n == 1 ? '' : (f.n + '*'))) + (f.m == 1 ? f.n : f.mt) + '/' + f.d) : number;
                },
                pow: function(base, exponent){// pow benefits from toFrac because it can overcome many of the limitations set before the standard Math.pow
                        // summary:
                        //              Computes base ^ exponent

                        //      Wrapper to Math.pow(base, exponent) to handle (-27) ^ (1/3)
                        function isInt(n){
                                return Math.floor(n) == n;
                        }

                        if(base>0||isInt(exponent)){
                                return Math.pow(base, exponent);
                        }else{
                                var f = _fracLookup(exponent);
                                if(base >= 0){
                                        return (f && f.m == 1)
                                                ? Math.pow(Math.pow(base, 1 / f.d), exponent < 0 ? -f.n : f.n) // 32 ^ (2/5) is much more accurate if done as (32 ^ (1/5)) ^ 2
                                                : Math.pow(base, exponent);
                                }else{  // e.g. (1/3) root of -27 = -3, 1 / exponent must be an odd integer for a negative base
                                        return (f && f.d & 1) ? Math.pow(Math.pow(-Math.pow(-base, 1 / f.d), exponent < 0 ? -f.n : f.n), f.m) : NaN;
                                }
                        }
                }
        });
/*
        function reduceError(number){
                var f = _fracLookup(number);
                if(!f){ f = _fracLookup(number); }
                return f ? ((number < 0 ? -1 : 1) * f.n * f.m / f.d) : number;
        }
*/
});