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303 lines
15 KiB
HTML
303 lines
15 KiB
HTML
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<body style="background-color:#333333; color:#EEEEEE; font-family:arial, inconsolata, monospace, sans-serif; font-size:24px;">
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<div>
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Division algorithm with repeating decimal detection test<br><br>
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<input id="num1" type="text" onchange="divide();" oninput='this.onchange()' onfocus='this.select();' style="width:100px; background-color:#555555; color:#EEEEEE; font-size:20px; text-align:center;" /> ÷
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<input id="num2" type="text" onchange="divide();" oninput='this.onchange()' onfocus='this.select();' style="width:100px; background-color:#555555; color:#EEEEEE; font-size:20px; text-align:center;" />
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</div><br>
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<table style="font-size:20px;">
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<tr>
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<td>long_division(A, B):</td>
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<td id='long_div_result'></td>
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</tr>
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<tr>
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<td>(A / B):</td>
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<td id='standard_result'></td>
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</tr>
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</table>
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<br>
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<table>
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<tr>
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<td>p_max:</td>
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<td>
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<input type="button" value="−" onclick="document.getElementById('p_max').value = parseInt(document.getElementById('p_max').value) - 1; divide();" >
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<input id="p_max" value="4" type="text" onchange="divide();" oninput="this.onchange();" onfocus="this.select();" style="width:40px; background-color:#555555; color:#EEEEEE; font-size:16px; text-align:center;" />
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<input type="button" value="+" onclick="document.getElementById('p_max').value = parseInt(document.getElementById('p_max').value) + 1; divide();" >
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</td>
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<td>(Maximum precision)</td>
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</tr>
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<tr>
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<td>p_min:</td>
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<td>
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<input type="button" value="−" onclick="document.getElementById('p_min').value = parseInt(document.getElementById('p_min').value) - 1; divide();" >
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<input id="p_min" value="0" type="text" onchange="divide();" oninput="this.onchange();" onfocus="this.select();" style="width:40px; background-color:#555555; color:#EEEEEE; font-size:16px; text-align:center;" />
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<input type="button" value="+" onclick="document.getElementById('p_min').value = parseInt(document.getElementById('p_min').value) + 1; divide();" >
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</td>
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<td>(Minimum precision)</td>
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</tr>
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<tr>
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<td>Repeat singles twice:<br>(i.e. 1.<span style="text-decoration:overline;">33</span> instead of 1.<span style="text-decoration:overline;">3</span>)</td>
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<td style="text-align:center;"><input id="singles" type="checkbox" onchange="divide();" checked /></td>
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</tr>
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<tr>
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<td>Use ≈ symbol for non-exact output:</td>
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<td style="text-align:center;"><input id="approx" type="checkbox" onchange="divide();" checked /></td>
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</tr>
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</table>
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<br>
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<table>
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<tr><td>Quick Tests:</td></tr>
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<tr><td></td></tr>
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<tr><td><input type="button" value="4 ÷ 3" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(4, 3);" /> (1-digit repeating pattern)</td></tr>
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<tr><td><input type="button" value="16 ÷ 9" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(16, 9);" /> (1-digit repeating pattern)</td></tr>
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<tr><td><input type="button" value="64 ÷ 27" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(64, 27);" /> (3-digit repeating pattern)</td></tr>
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<tr><td><input type="button" value="30 ÷ 13" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(30, 13);" /> (6-digit repeating pattern)</td></tr>
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<tr><td><input type="button" value="43 ÷ 18" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(43, 18);" /> (1 non-repeating + 1-digit repeating pattern)</td></tr>
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<tr><td><input type="button" value="256 ÷ 135" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(256, 135);" /> (1 non-repeating + 3-digit repeating pattern)</td></tr>
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<tr><td> </td></tr>
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<tr><td><input type="button" value="8 ÷ 4" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(8, 4);" /> (integer result)</td></tr>
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<tr><td><input type="button" value="8 ÷ 5" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(8, 5);" /> (1-decimal evenly-divisible result)</td></tr>
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<tr><td><input type="button" value="1 ÷ 64" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(1, 64);" /> (6-decimal evenly-divisible result)</td></tr>
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<tr><td><input type="button" value="−256 ÷ 135" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(-256, 135);" /> (negative A)</td></tr>
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<tr><td><input type="button" value="256 ÷ −135" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(256, -135);" /> (negative B)</td></tr>
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<tr><td><input type="button" value="−256 ÷ −135" style="background-color:#555555; color:#EEEEEE; font-size:16px;" onclick="divide(-256, -135);" /> (negative A and B)</td></tr>
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</table>
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</body>
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<script>
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function divide(A, B) {
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if(A) { document.getElementById('num1').value = A; }
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if(B) { document.getElementById('num2').value = B; }
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console.log('A:', A, 'B:', B);
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A = A || parseFloat(document.getElementById('num1').value);
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B = B || parseFloat(document.getElementById('num2').value);
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var p_max = document.getElementById('p_max').value;
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var p_min = document.getElementById('p_min').value;
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var singles = document.getElementById('singles').checked;
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if (document.getElementById('approx').checked) { var approx = '≈'; } else { var approx = ''; }
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var options = {
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'p_max': p_max,
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'p_min': p_min,
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'repeat_singles': singles,
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'approx': approx,
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//'OL_open': '{{overline|',
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//'OL_close': '}}',
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}
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//var result = long_division_core(A, B);
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var result = long_division(A, B, options);
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document.getElementById('long_div_result').innerHTML = result;
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document.getElementById('standard_result').innerHTML = (A / B);
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}
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function long_division_core(A, B) {
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if (isNaN(A / B)) { return NaN; }
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var Max_Depth = 32; // maximum number of decimal places
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var Radix_Point = '.';
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var Base = 10;
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var Sign = '';
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if ((A / B) < 0) { Sign = '-'; }
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var Dividend = Math.abs(parseFloat(A));
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var Divisor = Math.abs(parseFloat(B));
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var Quotient = Dividend / Divisor;
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var Remainder = Dividend % Divisor;
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var Result = Math.floor(Quotient).toString() + Radix_Point; // Use floor division to determine the front part of the number immediately
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Dividend = Remainder * Base;
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var i = 0;
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while (i < Max_Depth) {
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Quotient = Dividend / Divisor;
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Remainder = Dividend % Divisor;
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Dividend = Remainder * 10;
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Result += Math.floor(Quotient).toString();
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i += 1;
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}
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return Sign.concat(Result);
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}
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function long_division(A, B, options) {
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console.log('BEGIN:', A, '÷', B)
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if (isNaN(A / B) || !isFinite(A / B)) { console.log('Answer is NaN or Infinity. Function aborted.'); return ''; }
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var OL_open = '<span style="text-decoration:overline;">'; // Overline markup opening tag
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var OL_close = '</span>'; // Overline markup closing tag. Used in conjunction with OL_open to surround the repeating numbers. May be set to control markup, separate it with parentheses, or simply left blank, etc.
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var p_max = 8; // Maximum number of decimal places
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var p_min = 3; // Minimum number of decimal places
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var Approx = '≈'; // Symbol to be used for "approximately equal to". Can be set to '~' or blank if desired, etc.
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var Radix_Point = '.'; // Character to use for the radix point ("decimal point")
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var Base = 10; // Number base system to use
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var Minus_Sign = '−'; // Character to preceed negative numbers
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var Plus_Sign = ''; // Character to preceed positive numbers
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var RepeatSinglesFlag = true; // Display single-digit repeating patterns as 1.(33) instead of 1.(3)
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if (typeof(options) === 'number') { // If 3rd argument is a number rather than a dictionary, use it as the p_max value
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p_max = options;
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}
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else if(options) {
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if ('OL_open' in options) { OL_open = options['OL_open']; }
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if ('OL_close' in options) { OL_close = options['OL_close']; }
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if ('p_max' in options) { p_max = options['p_max']; }
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if ('p_min' in options) { p_min = options['p_min']; }
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if ('radix' in options) { Radix_Point = options['radix']; }
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if ('approx' in options) { Approx = options['approx']; }
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if ('minus' in options) { Minus_Sign = options['minus']; }
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if ('plus' in options) { Plus_Sign = options['plus']; }
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if ('base' in options) { Base = options['base']; }
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if ('repeat_singles' in options) { RepeatSinglesFlag = options['repeat_singles']; }
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}
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p_max = parseInt(p_max);
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p_min = parseInt(p_min);
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Base = parseInt(Base);
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if (p_max < 0 || p_min < 0 || p_max < p_min || isNaN(p_max) || isNaN(p_min) || !isFinite(p_max) || !isFinite(p_min)) {
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console.log('Invalid p_max and p_min values. Both values must be non-negative numbers, and p_min cannot be greater than p_max. p_max:', p_max, 'p_min', p_min)
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return '';
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}
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if (isNaN(Base)) {
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console.log('Invalid Base value. Must be an integer number. Base:', Base);
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return '';
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}
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if (p_max == 0) {
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var Result = Math.round(A / B).toFixed(0);
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if (Result != (A / B)) { Result = '≈'.concat(Result); }
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return Result;
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}
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var Max_Depth = 32; // Depth of internal calculations, regardless of p_max or p_min settings
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var Decimal_Digits = '';
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var Previous_Dividends = {};
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var Prefix = '';
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var Repetend = '';
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var RepeatFlag = false;
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var ApproxFlag = true;
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var Sign = Plus_Sign;
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// Determine if answer will be negative, then use the absolute value of inputs for the rest of the calculations.
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if ((A < 0) ? !(B < 0) : (B < 0)) { Sign = Minus_Sign; } // If (A is negative) XOR (B is negative) then final result will be negative.
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var Dividend = Math.abs(parseFloat(A));
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var Divisor = Math.abs(parseFloat(B));
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var Quotient = Dividend / Divisor;
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var Remainder = Dividend % Divisor;
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var Result = Math.floor(Quotient).toString() + Radix_Point; // Use floor division to determine the front part of the number immediately
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Dividend = Remainder * Base;
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// Use long division for the decimal places, so that repeating decimals can be detected
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var i = 0;
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while (i < p_max + 2) {
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if (!(Dividend in Previous_Dividends)) {
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Previous_Dividends[Dividend] = i;
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Quotient = Dividend / Divisor;
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Remainder = Dividend % Divisor;
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Dividend = Remainder * Base;
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//if (i < p_max) {
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Decimal_Digits += Math.floor(Quotient).toString();
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//}
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console.log('i:', i, 'Quotient:', Quotient, 'Remainder:', Remainder, 'Dividend:', Dividend, 'Result:', Result, 'Decimal_Digits:', Decimal_Digits);
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}
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else {
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RepeatFlag = true;
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ApproxFlag = false;
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console.log('Repetition Detected');
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Prefix = Decimal_Digits.substring(0, Previous_Dividends[Dividend]);
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Repetend = Decimal_Digits.substring(Previous_Dividends[Dividend], Decimal_Digits.length);
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console.log('Prefix:', Prefix, 'Repetend:', Repetend);
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if (Repetend == '0') { // A "repeating" dividend of 0 signals a non-repeating result
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console.log('Removing Repetend of 0...');
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Repetend = '';
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RepeatFlag = false;
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Decimal_Digits = Prefix;
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}
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//Decimal_Digits = Prefix + Repetend;
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break;
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}
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i += 1;
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}
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if (RepeatFlag == false) {
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if (Decimal_Digits.length > p_max) {
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console.log('Truncating decimals.');
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//Decimal_Digits = Decimal_Digits.substr(0, p_max);
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Decimal_Digits = Math.round(parseFloat(Decimal_Digits.substr(0, p_max) + '.' + Decimal_Digits.substr(p_max))).toString();
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if (p_max - Decimal_Digits.length >= 0) {
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Decimal_Digits = '0'.repeat(p_max - Decimal_Digits.length) + Decimal_Digits;
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}
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ApproxFlag = true;
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}
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if (Decimal_Digits.length < p_min) {
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console.log('Padding end with zeroes. Decimal Digits:', Decimal_Digits.length, 'p_min:', p_min);
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if (p_min - Decimal_Digits.length >= 0) {
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Decimal_Digits += '0'.repeat(p_min - Decimal_Digits.length);
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}
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}
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}
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console.log('Prefix:', Prefix, 'Repetend:', Repetend);
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if (RepeatFlag == true) {
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if (Prefix.length + Repetend.length > p_max) {
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if (Prefix.length > p_max) {
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Prefix = Math.round(parseFloat(Prefix.substr(0, p_max) + '.' + Prefix.substr(p_max))).toString();
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if (p_max - Prefix.length >= 0) {
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Prefix = '0'.repeat(p_max - Prefix.length) + Prefix;
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}
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}
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else {
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Prefix = Prefix + Repetend.substr(0, p_max - Prefix.length);
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}
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Decimal_Digits = Prefix;
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RepeatFlag = false;
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ApproxFlag = true;
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}
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if (Prefix.length + Repetend.length < p_min) {
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console.log('Decimal Count is lower than p_min. Prefix length:', Prefix.length, 'Repetend length:', Repetend.length);
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if ((p_min - (Prefix.length + Repetend.length)) >= Repetend.length) {
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console.log('Multiplying repetend. Remaining space:', p_min - (Prefix.length + Repetend.length), 'Repetend length:', Repetend.length, 'Multiply by:', Math.floor((p_min - (Prefix.length + Repetend.length)) / Repetend.length));
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Repetend += Repetend.repeat(Math.floor((p_min - (Prefix.length + Repetend.length)) / Repetend.length));
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console.log('New Repetend:', Repetend);
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}
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while (Prefix.length + Repetend.length < p_min) {
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Prefix = Prefix.concat(Repetend[0]);
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Repetend = Repetend.slice(1).concat(Repetend[0]);
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}
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}
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}
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console.log('Prefix:', Prefix, 'Repetend:', Repetend);
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if (RepeatFlag == true) {
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if (Repetend.length == 1 && (Prefix.length + Repetend.length < p_max) && RepeatSinglesFlag == true) { Repetend = Repetend.repeat(2); } // Single-digit repetitions will be displayed twice, i.e. 4/3 will result in 1.(33) rather than 1.(3)
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Result += Prefix + OL_open + Repetend + OL_close;
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}
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else {
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Result += Decimal_Digits;
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}
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Result = Sign.concat(Result);
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if (ApproxFlag == true) {
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Result = Approx.concat(Result);
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}
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if (Result[Result.length - 1] == Radix_Point) { Result = Result.replace(Radix_Point, ''); }
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return Result;
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//return Result * Sign;
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}
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</script> |