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v.0.8.2
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* fibonacci, bell, catalan numbers computations
* fix tuples counting method (used arguments in wrong order)
* use additive recursive relation to compute binomial
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Nikos M committed Jan 30, 2017
1 parent e0be248 commit 45ca8ee
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2 changes: 1 addition & 1 deletion README.md
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Expand Up @@ -5,7 +5,7 @@ A combinatorics library for Node/XPCOM/JS, PHP, Python, C/C++, Java
(php/python/java/c implementations in progress)


**version 0.8.1** (~ 49kB minified, ~ 16kB zipped)
**version 0.8.2** (~ 49kB minified, ~ 16kB zipped)

![abacus combinatorial numbers](/abacus.jpg)

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62 changes: 55 additions & 7 deletions src/js/Abacus.js
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Expand Up @@ -2,7 +2,7 @@
*
* Abacus
* A combinatorics library for Node/XPCOM/JS, PHP, Python, Java, C/C++
* @version: 0.8.1
* @version: 0.8.2
* https://github.com/foo123/Abacus
**/
!function( root, name, factory ){
Expand All @@ -22,7 +22,7 @@ else if ( !(name in root) ) /* Browser/WebWorker/.. */
/* module factory */ function ModuleFactory__Abacus( undef ){
"use strict";

var Abacus = {VERSION: "0.8.1"}, stdMath = Math, PROTO = 'prototype', CLASS = 'constructor'
var Abacus = {VERSION: "0.8.2"}, stdMath = Math, PROTO = 'prototype', CLASS = 'constructor'
,slice = Array.prototype.slice, HAS = Object[PROTO].hasOwnProperty, toString = Object[PROTO].toString
,log2 = stdMath.log2 || function(x) { return stdMath.log(x) / stdMath.LN2; }
,trim_re = /^\s+|\s+$/g
Expand Down Expand Up @@ -601,7 +601,8 @@ function factorial( n, m )
if ( null == m )
{
// http://www.luschny.de/math/factorial/index.html
// simple factorial = n! = n (n-1)!
// https://en.wikipedia.org/wiki/Factorial
// simple factorial = F(n) = n F(n-1) = n!
if ( 10 >= n ) return 0 > n ? O : (0 === n ? I : NUM(([1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800])[n-1]));
key = String(n)/*+'!'*/;
if ( null == factorial.mem1[key] )
Expand All @@ -611,7 +612,9 @@ function factorial( n, m )
}
else if ( false === m )
{
// derangement sub-factorial !n = D(n) = n D(n-1) + (-1)^n = [(n!+1)/e]
// http://mathworld.wolfram.com/Subfactorial.html
// https://en.wikipedia.org/wiki/Derangement
// derangement sub-factorial D(n) = n D(n-1) + (-1)^n = !n = [(n!+1)/e]
if ( 10 >= n ) return 2 > n ? O : NUM(([1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961])[n-2]);
key = '!'+String(n);
if ( null == factorial.mem2[key] )
Expand All @@ -633,6 +636,7 @@ function factorial( n, m )
}
else if ( is_array(m) )
{
// https://en.wikipedia.org/wiki/Multinomial_theorem
// multinomial = n!/m1!..mk!
if ( !m.length ) return 0 > n ? O : factorial(n);
else if ( 0 > n ) return O;
Expand All @@ -654,7 +658,8 @@ function factorial( n, m )
factorial.mem3[key] = operate(mul, I, null, n+m+1, n);
return factorial.mem3[key];
}
// binomial = n!/m!(n-m)!
// https://en.wikipedia.org/wiki/Binomial_coefficient
// binomial = C(n,m) = C(n-1,m-1)+C(n-1,m) = n!/m!(n-m)!
if ( m+m > n ) m = n-m; // take advantage of symmetry
if ( (0 > m) || (1 > n) ) return O;
else if ( (0 === m) || (1 === n) ) return I;
Expand All @@ -664,7 +669,7 @@ function factorial( n, m )
factorial.mem3[key] = Arithmetic.isDefault() ? stdMath.round(operate(function(Cnm, i){
// this is faster and will not overflow unnecesarily for default arithmetic
return Cnm*(1+n/i);
}, (n=n-m)+1, null, 2, m)) : div(factorial(n,-m), factorial(m));
}, (n=n-m)+1, null, 2, m)) : add(factorial(n-1,m-1),factorial(n-1,m))/*div(factorial(n,-m), factorial(m))*/;
return factorial.mem3[key];
}
return O;
Expand Down Expand Up @@ -768,6 +773,46 @@ function compositions( n, K /*exactly K parts or null*/, M /*max part is M or nu
return compositions.mem[key];
}
compositions.mem = {};
function catalan( n )
{
var Arithmetic = Abacus.Arithmetic, O = Arithmetic.O,
NUM = Arithmetic.N, div = Arithmetic.div, mul = Arithmetic.mul, key;
// https://en.wikipedia.org/wiki/Catalan_number
// catalan numbers C(n) = (4n+2)C(n-1)/(n+1)
if ( 14 >= n ) return 0 > n ? O : NUM(([1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900])[n]);
key = String(n);
if ( null == catalan.mem[key] )
/*catalan.mem[key] = operate(function(c,i){return add(c,mul(catalan(i),catalan(n-1-i)));},O,null,0,n-1,1);*/
catalan.mem[key] = div(mul(catalan(n-1),4*n-2),n+1);/* n -> n-1 */
return catalan.mem[key];
}
catalan.mem = {};
function bell( n )
{
var Arithmetic = Abacus.Arithmetic, O = Arithmetic.O,
NUM = Arithmetic.N, add = Arithmetic.add, mul = Arithmetic.mul, key;
// https://en.wikipedia.org/wiki/Bell_number
// bell numbers B(n) = SUM[k:0->n-1] ( C(n-1,k) B(k) )
if ( 12 >= n ) return 0 > n ? O : NUM(([1,1,2,5,15,52,203,877,4140,21147,115975,678570])[n]);
key = String(n);
if ( null == bell.mem[key] )
bell.mem[key] = operate(function(b,k){return add(b,mul(factorial(n-1,k),bell(k)));},O,null,0,n-1,1);
return bell.mem[key];
}
bell.mem = {};
function fibonacci( n )
{
var Arithmetic = Abacus.Arithmetic, O = Arithmetic.O,
NUM = Arithmetic.N, add = Arithmetic.add, key;
// http://en.wikipedia.org/wiki/Fibonacci_number
// fibonacci numbers F(n) = F(n-1) + F(n-2)
if ( 29 >= n ) return 0 > n ? O : NUM(([0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765, 10946,17711,28657,46368,75025,121393,196418,317811])[n]);
key = String(n);
if ( null == fibonacci.mem[key] )
fibonacci.mem[key] = add(fibonacci(n-1),fibonacci(n-2));
return fibonacci.mem[key];
}
fibonacci.mem = {};


Abacus.Class = Class;
Expand Down Expand Up @@ -861,6 +906,9 @@ Abacus.Math = {
,factorial: factorial
,partitions: partitions
,compositions: compositions
,bell: bell
,catalan: catalan
,fibonacci: fibonacci
};

// pluggable arithmetics, eg biginteger Arithmetic
Expand Down Expand Up @@ -2267,7 +2315,7 @@ Tensor = Abacus.Tensor = Class(CombinatorialIterator, {
,DUAL: CombinatorialIterator.DUAL
,count: function( n, $ ) {
var O = Abacus.Arithmetic.O, type = $ && $.type ? $.type : "tensor";
return "tuple"===type ? (!n || (0 >= n[0]) ? O : Abacus.Math.exp(n[0], n[1])) : (!n || !n.length ? O : Abacus.Math.product(n));
return "tuple"===type ? (!n || (0 >= n[0]) ? O : Abacus.Math.exp(n[1], n[0])) : (!n || !n.length ? O : Abacus.Math.product(n));
}
,initial: function( n, $, dir ) {
// some C-P-T dualities, symmetries & processes at play here
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