mirror of
https://scm.univ-tours.fr/22107988t/rappaurio-sae501_502.git
synced 2025-11-04 05:25:22 +01:00
506 lines
25 KiB
JavaScript
506 lines
25 KiB
JavaScript
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/**
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* @name CeL quotient function
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* @fileoverview
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* 本檔案包含了 quotient 的 functions。
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* @since 2010/3/11 16:59:59
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* @example
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* <code>
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* CeL.run('data.math');
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* // TODO: bug
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* CeL.run('data.math.quotient');
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* var q1 = new CeL.quotient(2,3);
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* // 數字基底的轉換:
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* CeL.log(CeL.quotient.parse_base('4877.6'.toLowerCase(),10).to_base(16).replace(/_([^\(]+)/,'_<i style="text-decoration:overline">$1</i>'));
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* </code>
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*/
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/*
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TODO:
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use {String} value + {Number} exponent
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http://www.leemon.com/crypto/BigInt.html
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http://www-cs-students.stanford.edu/~tjw/jsbn/
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http://java.sun.com/javase/6/docs/api/java/math/BigInteger.html
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*/
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'use strict';
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if (typeof CeL === 'function')
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CeL.run(
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{
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name:'data.math.quotient',
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require : 'data.math.to_rational_number|data.math.GCD|data.math.factorization',
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code : function(library_namespace) {
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// requiring
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var to_rational_number = this.r('to_rational_number'), GCD = this.r('GCD'), factorization = this.r('factorization');
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//library_namespace.debug(to_rational_number);
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//library_namespace.debug(GCD);
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//============================================================================
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// definition of module quotient
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var
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/*
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整數部分
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分數 fraction
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真分數 proper fraction
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vinculum = "divide by"
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*/
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/**
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* 有理數 rational number，有理数全体のつくる集合はしばしば、商を意味する integer の頭文字をとり、太字の Q で表す。<br />
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* 若要輸入不同基底的數值，請用 parse_base()
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*
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* @param numerator 分子
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* @param [denominator] 分母
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* @param {Boolean}[approximate] 取近似值
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*
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* @example
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* <code>
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* CeL.log((new CeL.integer(3,4)).count('*',new CeL.integer(2,7)).reduce().to_print_mode());
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* </code>
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*
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* @class integer 的 functions
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* @constructor
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*/
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_// JSDT:_module_
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= function(numerator, denominator, approximate) {
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if (typeof numerator === 'object' && numerator instanceof _
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//&& numerator.Class === 'quotient'
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)
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return numerator;
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if (isNaN(numerator))
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numerator = 0;
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if (!denominator || isNaN(denominator))
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denominator = 1;
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else if (denominator < 0)
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denominator = -denominator, numerator = -numerator;
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// to_rational_number 需 test，並回傳(分子,分母,誤差)！
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var q = to_rational_number(numerator);
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//library_namespace.debug(numerator + ' → ' + q);
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if (!q)
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numerator = 0;
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else if (approximate || !q[2])
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// 無誤差時使用之
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numerator = q[0], denominator *= q[1] || 1;
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else
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while (numerator % 1 || denominator % 1)
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// 化為整數
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numerator *= 10, denominator *= 10;
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// value
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this.n = numerator, this.d = denominator;
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// this.type='quotient';
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//library_namespace.debug(this.n + ' / ' + this.d);
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return this;
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};
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//class public interface ---------------------------
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_// JSDT:_module_
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.
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/**
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* 循環節分隔符號： {String} 整數.小數__repetend_separator__循環節
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* @_memberOf _module_
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*/
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repetend_separator = '_';//' '
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_// JSDT:_module_
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.
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/**
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* 數字集
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* @_memberOf _module_
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* @see
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* <a href="http://en.wikipedia.org/wiki/Numerical_digit" accessdate="2010/4/16 20:47">Numerical digit</a>
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*/
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digit_char = '0123456789abcdefghijklmnopqrstuvwxyz';//.split('')
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_// JSDT:_module_
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.
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/**
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* 轉換指定進位的數字成為 quotient 物件
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* @since 2004/7/9 16:13
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* @param number 數字
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* @param base 基底
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* @param {String}[digit_chars] 循環小數 digit 字集。
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* @return 回傳 quotient 物件，請用 quotient.to_base() 傳回所欲之 base
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* @_memberOf _module_
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* @example
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* var q=parse_base('10000.'+_.repetend_separator+'3',11);
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* if(!q)
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* alert('bad input!');
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* else
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* library_namespace.debug('<br />'+q.base(8)+','+q.base()+' , '+q.to_print_mode()+','+q.print(1)+','+q.to_print_mode(2)+','+q.to_print_mode(3,0,'',5));
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*/
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parse_base = function(number, base, digit_char) {
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// if(!num) num = 0;
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if ((!(base = Math.floor(base)) || base < 2) && digit_char)
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base = digit_char.length;
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if (!digit_char)
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digit_char = _.digit_char;
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if (isNaN(base) || base < 2 || digit_char.length < base)
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base = 10;
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if (!number || base === 10
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&& ('' + number).indexOf(_.repetend_separator) === -1)
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// 可能有循環小數，所以不能放過僅僅 base === 10
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return new _(number);
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var i = 0, n = new _(0, 1), m = 0, t = 0, p, c = {}, r = new _(0, 1);
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for (; i < digit_char.length; i++)
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c[digit_char.charAt(i)] = i; // 字集
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number += '', i = -1, n.d = r.d = 1;
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//library_namespace.debug('<br />'+i+','+num.length+','+t+','+num+','+n.to_print_mode());
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if (number.charAt(0) === '-')
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i = 0, m = 1;
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while (++i < number.length && (p = number.charAt(i)) != '.')
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// 整數
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if (isNaN(p = c[p]) || p >= base)
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// error!
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return;
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else
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t = t * base + p;
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//library_namespace.debug('<br />'+i+','+num.length+','+t+','+num+','+n.to_print_mode());
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while (++i < number.length
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&& (p = number.charAt(i)) != _.repetend_separator)
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// 小數
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if (isNaN(p = c[p]) || p >= base)
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// error!
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return;
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else
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n.n = n.n * base + p, n.d *= base;
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while (++i < number.length)
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// 循環節
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if (isNaN(p = c[number.charAt(i)]) || p >= base)
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return; // error!
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else
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r.n = r.n * base + p, r.d *= base;
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//library_namespace.debug('<br />**'+n.to_print_mode());
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// 善後
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n = n.count('+=', t);
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if (r.n)
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r.d = (r.d - 1) * n.d, n.count('+=', r);
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n.reduce();
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//library_namespace.debug('<br />*'+n.to_print_mode());
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if (m)
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n.n = -n.n;
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return n;
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};
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_// JSDT:_module_
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.prototype = {
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// instance public interface -------------------
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/**
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* 最簡分數/化簡, 約分 reduction
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* @return 化簡後的
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* @_name _module_.prototype.reduce
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*/
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reduce : function() {
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var g = GCD(this.n, this.d);
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if (g && g > 1)
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this.n /= g, this.d /= g;
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return this;
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},
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/**
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* 四則運算/算數運算 + - * / (+-×÷), **, ^, [=]
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* @param op operator
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* @param q2 the second quotient
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* @return 計算後的結果
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* @see
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* <a href="http://www.javaworld.com.tw/jute/post/view?bid=35&id=30169&tpg=1&ppg=1&sty=1&age=0#30169" accessdate="2010/4/16 20:47">JavaWorld@TW Java論壇 - post.view</a>
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* @_name _module_.prototype.count
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*/
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count : function(op, q2) {
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var q;
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if (op.slice(-1) === '=')
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q = this, op = op.slice(0, -1);
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else
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q = new _(this);
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q2 = new _(q2);
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//library_namespace.debug('<br />'+this.type+','+q.to_print_mode()+' , '+q2.to_print_mode());
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if (op === '-')
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q2.n = -q2.n, op = '+';
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else if (op === '/') {
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var t = q2.n;
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q2.n = q2.d, q2.d = t, op = '*';
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}
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//library_namespace.debug('<br />'+q.to_print_mode(1)+','+q2.to_print_mode(1));
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if (op === '+')
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q.n = q.n * q2.d + q.d * q2.n, q.d *= q2.d;
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else if (op === '*')
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q.n *= q2.n, q.d *= q2.d;
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// N! 是指 N的階乘 (Factorial,power)
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else if ((op === '**' || op === '^') && q2.reduce().d === 1) {
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q.reduce(), q.n = Math.pow(q.n, q2.n), q.d = Math.pow(q.d, q2.n);
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return q;
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} else {
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library_namespace.error('illegal operator [' + op + ']!');
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return this;
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}
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//library_namespace.debug('<br />'+q.to_print_mode(1)+','+q2.to_print_mode(1));
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// other: error
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//library_namespace.debug('<br />_'+q.reduce().to_print_mode());
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try {
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return q.reduce();
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} catch (e) {
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}
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return q;
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},
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/**
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* 依指定基底轉成循環小數 circulating decimal / repeating decimal。
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* 特殊情況可以考慮使用 .toString()，會快很多。
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* TODO: 小數
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* @since 2004/7/9 13:28
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* @param base 基底
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* @param digit_char 循環小數 digit 字集
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* @return (decimal/數字部分string,repunitIndex/循環節Repetend出現在)
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* @see
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* <a href="http://mathworld.wolfram.com/RepeatingDecimal.html" accessdate="2010/4/16 20:47">Repeating Decimal -- from Wolfram MathWorld</a>
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* <a href="http://hk.geocities.com/goodprimes/OFrp.htm">循環小數與素數。素之異類。</a>
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* @_name _module_.prototype.to_base
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*/
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to_base : function(base, digit_char) {
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//if (!isNaN(digit_char)) digit_char += '';
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if (typeof digit_char !== 'string' || digit_char.length < 2)
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// 字集
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digit_char = _.digit_char;
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// 基底預設為 10 進位
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if (!(base = Math.floor(base)) || base == 10 ||
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// illegal base
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base < 2 || base > digit_char.length)
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return this.to_decimal();
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this.reduce();
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var d = this.d, o = this.n, i, t, m = 0,
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// find base 的因數(factor)
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f = factorization(base);
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if (o < 0)
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// 負數
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o = -o, m = 1;
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// find 分母的因數(factor)與基底 base 之交集(不能用GCD)
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for (var i = 0, g = 1, t = d; i < f.length; i += 2)
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while (t % f[i] === 0)
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g *= f[i], t /= f[i];
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// get 整數 integer 部分 → out
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f = o % d;
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i = (o - f) / d;
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o = '';
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while (i)
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t = i % base, i = (i - t) / base, o = digit_char.charAt(t) + o;
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if (!o)
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o = '0', m = 0;
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//library_namespace.debug('<br />_' + typeof o + ',' + (o || '(null)') + ',' + o);
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if (!f)
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return m ? '-' + o : o;
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// 進入小數
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o += '.';
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// set 餘數f/分母d, 餘數residue mark r=f, 循環節 Repetend location of out:l, 已解決的因數 s
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var r = f, l = o.length, s = 1;
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// do main loop
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// while(o.length-l<d){ // 限制?位: debug用
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while (true) {
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//library_namespace.debug('<br />.'+r+','+f+'/'+d+'('+base+'),'+s+':'+g+','+o);
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if (!f) {
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// 可以整除，無循環。
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l = 0;
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break;
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}
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f *= base;
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if (s === g) {
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// 分母與 base 已互質
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t = f, f %= d, o += digit_char.charAt((t - f) / d);
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if (f === r)
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// bingo! 餘數重複出現，循環節結束。
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break;
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} else {
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// f 與 d 已互質
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t = GCD(base, d), s *= t, f /= t, d /= t,
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// do the same thing
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t = f, f %= d, o += digit_char.charAt((t - f) / d),
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// r 需重設..此處有否可能出問題? maybe not?
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r = f, l = o.length;
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}
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}
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// 善後
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if (l)
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o += '(' + (o.length - l) + ')', o = o.slice(0, l)
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+ _.repetend_separator + o.substr(l);
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if (m)
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o = '-' + o;
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return o;
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},
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/**
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* 為十進位最佳化的 to_base()<br />
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* 以結論來說，好像快不了多少?
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* @since 2004/7/9 13:47
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* @return
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* @_name _module_.prototype.to_decimal
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*/
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to_decimal : function() {
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this.reduce();
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var d = this.d, t = d, g = 1, m = 0, f, o = this.n;
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if (o < 0)
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o = -o, m = 1; // 負數
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// find 分母的 2,5 因數
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while (t % 2 === 0)
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// 使用下面這行會造成 bug: 輸出 .110011001100110011001100110011001100(2) 會導致 g===t===0, 掛掉
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// 以結論來說，好像快不了多少?
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//g <<= 1, t >>= 1;
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g *= 2, t /= 2;
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while (t % 5 === 0)
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g *= 5, t /= 5;
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// get 整數 integer 部分 → out
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f = o % d, o = (o - f) / d;
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//library_namespace.debug('<br />_'+typeof o+','+(o||'(null)')+','+o);
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if (!f)
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// 留下+-
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return (m ? '-' : '') + o;
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// 進入小數
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o += '.';
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// set 餘數f/分母d, 餘數 residue mark r=f, 循環節 Repetend location of out:l, 已解決的因數 s
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var r = f, l = o.length, s = 1;
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// do main loop
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// while(o.length-l<d){// 限制?位:debug用
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while (true) {
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//library_namespace.debug('<br />.'+r+','+f+'/'+d+','+s+':'+g+','+o);
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if (!f) {
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// 可以整除，無循環。
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l = 0;
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break;
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}
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f *= 10;
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if (s === g) {
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// 分母與 base 已互質
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t = f, f %= d, o += (t - f) / d;
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if (f === r)
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// bingo! 循環節結束
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break;
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} else {
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t = d % 5 === 0 ? d % 2 === 0 ? 10 : 5 : 2, s *= t, f /= t, d /= t,
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// do the same thing
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t = f, f %= d, o += (t - f) / d,
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// r 需重設..此處有否可能出問題? maybe not?
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r = f, l = o.length;
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}
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}
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// 善後
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if (l)
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o += '(' + (o.length - l) + ')',
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o = o.slice(0, l) + _.repetend_separator + o.substr(l);
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if (m)
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o = '-' + o;
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return o;
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},
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/*
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有效位數、小數位數 http://technet.microsoft.com/zh-tw/library/ms190476.aspx
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Precision, Scale
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有效位數是數字的位數。小數位數是數字中在小數點右側的位數。例如，123.45 這個數字的有效位數是 5，小數位數是 2。
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Precision is the number of digits in a number. Scale is the number of digits to the right of the decimal point in a number. For example, the number 123.45 has a precision of 5 and a scale of 2.
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*/
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/**
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* 顯示成各種不同模式的數字
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* @since 2004/7/9 14:23
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* @param mode 顯示模式
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* 0 真分數 proper fraction、假分數 improper fraction (U.S., British or Australian) or top-heavy fraction (British, occasionally North America),
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* 1 帶分數 mixed numeral (often called a mixed number, also called a mixed fraction),
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* 2 直接除(10進位),
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||
* 3 轉成循環小數 repeating decimal,除至小數點下digit位數（非四捨五入！）.
|
||
* @param base 基底
|
||
* @param sum_char 顯示帶分數時代表整數與真分數之間的分隔。多為' '或'+'或''。
|
||
* @param digit 轉成循環小數時，代表循環小數 digit 字集
|
||
* @return {String} 顯示模式數字
|
||
* @_name _module_.prototype.to_print_mode
|
||
*/
|
||
to_print_mode : function(mode, base, sum_char, digit) {
|
||
if (mode < 3 || !mode) {
|
||
if (mode === 2)
|
||
return this.n / this.d;
|
||
var p, f;
|
||
if (!mode || this.n < this.d)
|
||
p = this.n + '/' + this.d;
|
||
else
|
||
f = this.n % this.d,
|
||
p = (this.n - f) / this.d
|
||
+ (f ? (sum_char || '+') + f + '/' + this.d : '');
|
||
return p;
|
||
}
|
||
|
||
if (mode === 3) {
|
||
var n = this.to_base(base, sum_char);
|
||
if (isNaN(digit))
|
||
return n;
|
||
var f = n.indexOf(_.repetend_separator), b = n.indexOf('.');
|
||
if (f === -1 || !digit)
|
||
return b === -1 ? n :
|
||
digit ? n.slice(0, b + digit + 1) : n.slice(0, b);
|
||
digit += b + 1,
|
||
// 循環節
|
||
b = n.substr(f + 1),
|
||
n = n.slice(0, f);
|
||
while (n.length < digit)
|
||
n += b;
|
||
return n.slice(0, digit);
|
||
}
|
||
},
|
||
|
||
/**
|
||
* 測試大小/比大小
|
||
* @param q2 the second quotient
|
||
* @return {Number} 0:==, <0:<, >0:>
|
||
* @_name _module_.prototype.compare_to
|
||
*/
|
||
compare_to : function(q2) {
|
||
q2 = new _(q2);
|
||
return this.n * q2.d - this.d * q2.n;
|
||
}
|
||
|
||
};
|
||
|
||
// setup toString function
|
||
_.prototype.toString = _.prototype.to_print_mode;
|
||
|
||
|
||
|
||
return (
|
||
_// JSDT:_module_
|
||
);
|
||
}
|
||
|
||
|
||
});
|
||
|