/
toFrac.js
143 lines (136 loc) · 5.84 KB
/
toFrac.js
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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;
}
*/
});