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@@ -0,0 +1,1146 @@
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+/* big.js v3.1.3 https://github.com/MikeMcl/big.js/LICENCE */
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+;(function (global) {
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+ 'use strict';
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+
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+/*
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+ big.js v3.1.3
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+ A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic.
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+ https://github.com/MikeMcl/big.js/
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+ Copyright (c) 2014 Michael Mclaughlin <M8ch88l@gmail.com>
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+ MIT Expat Licence
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+*/
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+
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+/***************************** EDITABLE DEFAULTS ******************************/
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+
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+ // The default values below must be integers within the stated ranges.
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+
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+ /*
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+ * The maximum number of decimal places of the results of operations
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+ * involving division: div and sqrt, and pow with negative exponents.
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+ */
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+ var DP = 20, // 0 to MAX_DP
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+
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+ /*
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+ * The rounding mode used when rounding to the above decimal places.
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+ *
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+ * 0 Towards zero (i.e. truncate, no rounding). (ROUND_DOWN)
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+ * 1 To nearest neighbour. If equidistant, round up. (ROUND_HALF_UP)
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+ * 2 To nearest neighbour. If equidistant, to even. (ROUND_HALF_EVEN)
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+ * 3 Away from zero. (ROUND_UP)
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+ */
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+ RM = 1, // 0, 1, 2 or 3
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+
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+ // The maximum value of DP and Big.DP.
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+ MAX_DP = 1E6, // 0 to 1000000
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+
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+ // The maximum magnitude of the exponent argument to the pow method.
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+ MAX_POWER = 1E6, // 1 to 1000000
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+
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+ /*
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+ * The exponent value at and beneath which toString returns exponential
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+ * notation.
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+ * JavaScript's Number type: -7
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+ * -1000000 is the minimum recommended exponent value of a Big.
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+ */
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+ E_NEG = -7, // 0 to -1000000
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+
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+ /*
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+ * The exponent value at and above which toString returns exponential
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+ * notation.
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+ * JavaScript's Number type: 21
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+ * 1000000 is the maximum recommended exponent value of a Big.
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+ * (This limit is not enforced or checked.)
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+ */
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+ E_POS = 21, // 0 to 1000000
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+
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+/******************************************************************************/
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+
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+ // The shared prototype object.
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+ P = {},
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+ isValid = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
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+ Big;
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+
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+
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+ /*
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+ * Create and return a Big constructor.
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+ *
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+ */
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+ function bigFactory() {
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+
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+ /*
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+ * The Big constructor and exported function.
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+ * Create and return a new instance of a Big number object.
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+ *
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+ * n {number|string|Big} A numeric value.
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+ */
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+ function Big(n) {
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+ var x = this;
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+
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+ // Enable constructor usage without new.
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+ if (!(x instanceof Big)) {
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+ return n === void 0 ? bigFactory() : new Big(n);
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+ }
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+
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+ // Duplicate.
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+ if (n instanceof Big) {
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+ x.s = n.s;
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+ x.e = n.e;
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+ x.c = n.c.slice();
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+ } else {
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+ parse(x, n);
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+ }
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+
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+ /*
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+ * Retain a reference to this Big constructor, and shadow
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+ * Big.prototype.constructor which points to Object.
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+ */
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+ x.constructor = Big;
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+ }
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+
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+ Big.prototype = P;
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+ Big.DP = DP;
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+ Big.RM = RM;
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+ Big.E_NEG = E_NEG;
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+ Big.E_POS = E_POS;
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+
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+ return Big;
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+ }
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+
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+
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+ // Private functions
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+
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+
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+ /*
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+ * Return a string representing the value of Big x in normal or exponential
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+ * notation to dp fixed decimal places or significant digits.
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+ *
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+ * x {Big} The Big to format.
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+ * dp {number} Integer, 0 to MAX_DP inclusive.
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+ * toE {number} 1 (toExponential), 2 (toPrecision) or undefined (toFixed).
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+ */
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+ function format(x, dp, toE) {
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+ var Big = x.constructor,
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+
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+ // The index (normal notation) of the digit that may be rounded up.
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+ i = dp - (x = new Big(x)).e,
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+ c = x.c;
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+
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+ // Round?
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+ if (c.length > ++dp) {
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+ rnd(x, i, Big.RM);
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+ }
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+
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+ if (!c[0]) {
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+ ++i;
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+ } else if (toE) {
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+ i = dp;
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+
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+ // toFixed
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+ } else {
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+ c = x.c;
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+
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+ // Recalculate i as x.e may have changed if value rounded up.
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+ i = x.e + i + 1;
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+ }
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+
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+ // Append zeros?
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+ for (; c.length < i; c.push(0)) {
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+ }
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+ i = x.e;
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+
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+ /*
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+ * toPrecision returns exponential notation if the number of
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+ * significant digits specified is less than the number of digits
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+ * necessary to represent the integer part of the value in normal
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+ * notation.
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+ */
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+ return toE === 1 || toE && (dp <= i || i <= Big.E_NEG) ?
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+
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+ // Exponential notation.
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+ (x.s < 0 && c[0] ? '-' : '') +
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+ (c.length > 1 ? c[0] + '.' + c.join('').slice(1) : c[0]) +
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+ (i < 0 ? 'e' : 'e+') + i
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+
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+ // Normal notation.
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+ : x.toString();
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+ }
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+
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+
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+ /*
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+ * Parse the number or string value passed to a Big constructor.
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+ *
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+ * x {Big} A Big number instance.
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+ * n {number|string} A numeric value.
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+ */
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+ function parse(x, n) {
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+ var e, i, nL;
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+
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+ // Minus zero?
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+ if (n === 0 && 1 / n < 0) {
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+ n = '-0';
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+
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+ // Ensure n is string and check validity.
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+ } else if (!isValid.test(n += '')) {
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+ throwErr(NaN);
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+ }
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+
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+ // Determine sign.
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+ x.s = n.charAt(0) == '-' ? (n = n.slice(1), -1) : 1;
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+
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+ // Decimal point?
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+ if ((e = n.indexOf('.')) > -1) {
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+ n = n.replace('.', '');
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+ }
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+
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+ // Exponential form?
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+ if ((i = n.search(/e/i)) > 0) {
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+
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+ // Determine exponent.
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+ if (e < 0) {
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+ e = i;
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+ }
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+ e += +n.slice(i + 1);
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+ n = n.substring(0, i);
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+
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+ } else if (e < 0) {
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+
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+ // Integer.
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+ e = n.length;
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+ }
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+
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+ // Determine leading zeros.
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+ for (i = 0; n.charAt(i) == '0'; i++) {
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+ }
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+
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+ if (i == (nL = n.length)) {
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+
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+ // Zero.
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+ x.c = [ x.e = 0 ];
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+ } else {
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+
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+ // Determine trailing zeros.
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+ for (; n.charAt(--nL) == '0';) {
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+ }
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+
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+ x.e = e - i - 1;
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+ x.c = [];
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+
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+ // Convert string to array of digits without leading/trailing zeros.
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+ for (e = 0; i <= nL; x.c[e++] = +n.charAt(i++)) {
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+ }
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+ }
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+
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+ return x;
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+ }
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+
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+
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+ /*
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+ * Round Big x to a maximum of dp decimal places using rounding mode rm.
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+ * Called by div, sqrt and round.
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+ *
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+ * x {Big} The Big to round.
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+ * dp {number} Integer, 0 to MAX_DP inclusive.
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+ * rm {number} 0, 1, 2 or 3 (DOWN, HALF_UP, HALF_EVEN, UP)
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+ * [more] {boolean} Whether the result of division was truncated.
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+ */
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+ function rnd(x, dp, rm, more) {
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+ var u,
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+ xc = x.c,
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+ i = x.e + dp + 1;
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+
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+ if (rm === 1) {
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+
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+ // xc[i] is the digit after the digit that may be rounded up.
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+ more = xc[i] >= 5;
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+ } else if (rm === 2) {
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+ more = xc[i] > 5 || xc[i] == 5 &&
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+ (more || i < 0 || xc[i + 1] !== u || xc[i - 1] & 1);
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+ } else if (rm === 3) {
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+ more = more || xc[i] !== u || i < 0;
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+ } else {
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+ more = false;
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+
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+ if (rm !== 0) {
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+ throwErr('!Big.RM!');
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+ }
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+ }
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+
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+ if (i < 1 || !xc[0]) {
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+
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+ if (more) {
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+
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+ // 1, 0.1, 0.01, 0.001, 0.0001 etc.
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+ x.e = -dp;
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+ x.c = [1];
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+ } else {
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+
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+ // Zero.
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+ x.c = [x.e = 0];
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+ }
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+ } else {
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+
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+ // Remove any digits after the required decimal places.
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+ xc.length = i--;
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+
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+ // Round up?
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+ if (more) {
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+
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+ // Rounding up may mean the previous digit has to be rounded up.
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+ for (; ++xc[i] > 9;) {
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+ xc[i] = 0;
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+
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+ if (!i--) {
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+ ++x.e;
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+ xc.unshift(1);
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+ }
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+ }
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+ }
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+
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+ // Remove trailing zeros.
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+ for (i = xc.length; !xc[--i]; xc.pop()) {
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+ }
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+ }
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+
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+ return x;
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+ }
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+
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+ P.rnd = function(dp, rm, more) {
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+ return rnd(this, dp, rm, more)
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+ }
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+
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+
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+ /*
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+ * Throw a BigError.
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+ *
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+ * message {string} The error message.
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+ */
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+ function throwErr(message) {
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+ var err = new Error(message);
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+ err.name = 'BigError';
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+
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+ throw err;
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+ }
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+
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+
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+ // Prototype/instance methods
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+
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+
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+ /*
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+ * Return a new Big whose value is the absolute value of this Big.
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+ */
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+ P.abs = function () {
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+ var x = new this.constructor(this);
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+ x.s = 1;
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+
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+ return x;
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+ };
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+
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+
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+ /*
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+ * Return
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+ * 1 if the value of this Big is greater than the value of Big y,
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+ * -1 if the value of this Big is less than the value of Big y, or
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+ * 0 if they have the same value.
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+ */
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+ P.cmp = function (y) {
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+ var xNeg,
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+ x = this,
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+ xc = x.c,
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+ yc = (y = new x.constructor(y)).c,
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+ i = x.s,
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+ j = y.s,
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+ k = x.e,
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+ l = y.e;
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+
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+ // Either zero?
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+ if (!xc[0] || !yc[0]) {
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+ return !xc[0] ? !yc[0] ? 0 : -j : i;
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+ }
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+
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+ // Signs differ?
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+ if (i != j) {
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+ return i;
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+ }
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+ xNeg = i < 0;
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+
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+ // Compare exponents.
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+ if (k != l) {
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+ return k > l ^ xNeg ? 1 : -1;
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+ }
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+
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+ i = -1;
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+ j = (k = xc.length) < (l = yc.length) ? k : l;
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+
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+ // Compare digit by digit.
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+ for (; ++i < j;) {
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+
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+ if (xc[i] != yc[i]) {
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+ return xc[i] > yc[i] ^ xNeg ? 1 : -1;
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+ }
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+ }
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+
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+ // Compare lengths.
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+ return k == l ? 0 : k > l ^ xNeg ? 1 : -1;
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+ };
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+
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+
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+ /*
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+ * Return a new Big whose value is the value of this Big divided by the
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+ * value of Big y, rounded, if necessary, to a maximum of Big.DP decimal
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+ * places using rounding mode Big.RM.
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+ */
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+ P.div = function (y) {
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+ var x = this,
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+ Big = x.constructor,
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+ // dividend
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+ dvd = x.c,
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+ //divisor
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+ dvs = (y = new Big(y)).c,
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+ s = x.s == y.s ? 1 : -1,
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+ dp = Big.DP;
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+
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+ if (dp !== ~~dp || dp < 0 || dp > MAX_DP) {
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+ throwErr('!Big.DP!');
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+ }
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+
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+ // Either 0?
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+ if (!dvd[0] || !dvs[0]) {
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+
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+ // If both are 0, throw NaN
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+ if (dvd[0] == dvs[0]) {
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+ throwErr(NaN);
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+ }
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+
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+ // If dvs is 0, throw +-Infinity.
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+ if (!dvs[0]) {
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+ throwErr(s / 0);
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+ }
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+
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+ // dvd is 0, return +-0.
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+ return new Big(s * 0);
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+ }
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+
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+ var dvsL, dvsT, next, cmp, remI, u,
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+ dvsZ = dvs.slice(),
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+ dvdI = dvsL = dvs.length,
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+ dvdL = dvd.length,
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+ // remainder
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+ rem = dvd.slice(0, dvsL),
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+ remL = rem.length,
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+ // quotient
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+ q = y,
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+ qc = q.c = [],
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+ qi = 0,
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+ digits = dp + (q.e = x.e - y.e) + 1;
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+
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+ q.s = s;
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+ s = digits < 0 ? 0 : digits;
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+
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+ // Create version of divisor with leading zero.
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+ dvsZ.unshift(0);
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+
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+ // Add zeros to make remainder as long as divisor.
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+ for (; remL++ < dvsL; rem.push(0)) {
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+ }
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+
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+ do {
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+
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+ // 'next' is how many times the divisor goes into current remainder.
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|
|
+ for (next = 0; next < 10; next++) {
|
|
|
+
|
|
|
+ // Compare divisor and remainder.
|
|
|
+ if (dvsL != (remL = rem.length)) {
|
|
|
+ cmp = dvsL > remL ? 1 : -1;
|
|
|
+ } else {
|
|
|
+
|
|
|
+ for (remI = -1, cmp = 0; ++remI < dvsL;) {
|
|
|
+
|
|
|
+ if (dvs[remI] != rem[remI]) {
|
|
|
+ cmp = dvs[remI] > rem[remI] ? 1 : -1;
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ // If divisor < remainder, subtract divisor from remainder.
|
|
|
+ if (cmp < 0) {
|
|
|
+
|
|
|
+ // Remainder can't be more than 1 digit longer than divisor.
|
|
|
+ // Equalise lengths using divisor with extra leading zero?
|
|
|
+ for (dvsT = remL == dvsL ? dvs : dvsZ; remL;) {
|
|
|
+
|
|
|
+ if (rem[--remL] < dvsT[remL]) {
|
|
|
+ remI = remL;
|
|
|
+
|
|
|
+ for (; remI && !rem[--remI]; rem[remI] = 9) {
|
|
|
+ }
|
|
|
+ --rem[remI];
|
|
|
+ rem[remL] += 10;
|
|
|
+ }
|
|
|
+ rem[remL] -= dvsT[remL];
|
|
|
+ }
|
|
|
+ for (; !rem[0]; rem.shift()) {
|
|
|
+ }
|
|
|
+ } else {
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ // Add the 'next' digit to the result array.
|
|
|
+ qc[qi++] = cmp ? next : ++next;
|
|
|
+
|
|
|
+ // Update the remainder.
|
|
|
+ if (rem[0] && cmp) {
|
|
|
+ rem[remL] = dvd[dvdI] || 0;
|
|
|
+ } else {
|
|
|
+ rem = [ dvd[dvdI] ];
|
|
|
+ }
|
|
|
+
|
|
|
+ } while ((dvdI++ < dvdL || rem[0] !== u) && s--);
|
|
|
+
|
|
|
+ // Leading zero? Do not remove if result is simply zero (qi == 1).
|
|
|
+ if (!qc[0] && qi != 1) {
|
|
|
+
|
|
|
+ // There can't be more than one zero.
|
|
|
+ qc.shift();
|
|
|
+ q.e--;
|
|
|
+ }
|
|
|
+
|
|
|
+ // Round?
|
|
|
+ if (qi > digits) {
|
|
|
+ rnd(q, dp, Big.RM, rem[0] !== u);
|
|
|
+ }
|
|
|
+
|
|
|
+ return q;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return true if the value of this Big is equal to the value of Big y,
|
|
|
+ * otherwise returns false.
|
|
|
+ */
|
|
|
+ P.eq = function (y) {
|
|
|
+ return !this.cmp(y);
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return true if the value of this Big is greater than the value of Big y,
|
|
|
+ * otherwise returns false.
|
|
|
+ */
|
|
|
+ P.gt = function (y) {
|
|
|
+ return this.cmp(y) > 0;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return true if the value of this Big is greater than or equal to the
|
|
|
+ * value of Big y, otherwise returns false.
|
|
|
+ */
|
|
|
+ P.gte = function (y) {
|
|
|
+ return this.cmp(y) > -1;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return true if the value of this Big is less than the value of Big y,
|
|
|
+ * otherwise returns false.
|
|
|
+ */
|
|
|
+ P.lt = function (y) {
|
|
|
+ return this.cmp(y) < 0;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return true if the value of this Big is less than or equal to the value
|
|
|
+ * of Big y, otherwise returns false.
|
|
|
+ */
|
|
|
+ P.lte = function (y) {
|
|
|
+ return this.cmp(y) < 1;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a new Big whose value is the value of this Big minus the value
|
|
|
+ * of Big y.
|
|
|
+ */
|
|
|
+ P.sub = P.minus = function (y) {
|
|
|
+ var i, j, t, xLTy,
|
|
|
+ x = this,
|
|
|
+ Big = x.constructor,
|
|
|
+ a = x.s,
|
|
|
+ b = (y = new Big(y)).s;
|
|
|
+
|
|
|
+ // Signs differ?
|
|
|
+ if (a != b) {
|
|
|
+ y.s = -b;
|
|
|
+ return x.plus(y);
|
|
|
+ }
|
|
|
+
|
|
|
+ var xc = x.c.slice(),
|
|
|
+ xe = x.e,
|
|
|
+ yc = y.c,
|
|
|
+ ye = y.e;
|
|
|
+
|
|
|
+ // Either zero?
|
|
|
+ if (!xc[0] || !yc[0]) {
|
|
|
+
|
|
|
+ // y is non-zero? x is non-zero? Or both are zero.
|
|
|
+ return yc[0] ? (y.s = -b, y) : new Big(xc[0] ? x : 0);
|
|
|
+ }
|
|
|
+
|
|
|
+ // Determine which is the bigger number.
|
|
|
+ // Prepend zeros to equalise exponents.
|
|
|
+ if (a = xe - ye) {
|
|
|
+
|
|
|
+ if (xLTy = a < 0) {
|
|
|
+ a = -a;
|
|
|
+ t = xc;
|
|
|
+ } else {
|
|
|
+ ye = xe;
|
|
|
+ t = yc;
|
|
|
+ }
|
|
|
+
|
|
|
+ t.reverse();
|
|
|
+ for (b = a; b--; t.push(0)) {
|
|
|
+ }
|
|
|
+ t.reverse();
|
|
|
+ } else {
|
|
|
+
|
|
|
+ // Exponents equal. Check digit by digit.
|
|
|
+ j = ((xLTy = xc.length < yc.length) ? xc : yc).length;
|
|
|
+
|
|
|
+ for (a = b = 0; b < j; b++) {
|
|
|
+
|
|
|
+ if (xc[b] != yc[b]) {
|
|
|
+ xLTy = xc[b] < yc[b];
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ // x < y? Point xc to the array of the bigger number.
|
|
|
+ if (xLTy) {
|
|
|
+ t = xc;
|
|
|
+ xc = yc;
|
|
|
+ yc = t;
|
|
|
+ y.s = -y.s;
|
|
|
+ }
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Append zeros to xc if shorter. No need to add zeros to yc if shorter
|
|
|
+ * as subtraction only needs to start at yc.length.
|
|
|
+ */
|
|
|
+ if (( b = (j = yc.length) - (i = xc.length) ) > 0) {
|
|
|
+
|
|
|
+ for (; b--; xc[i++] = 0) {
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ // Subtract yc from xc.
|
|
|
+ for (b = i; j > a;){
|
|
|
+
|
|
|
+ if (xc[--j] < yc[j]) {
|
|
|
+
|
|
|
+ for (i = j; i && !xc[--i]; xc[i] = 9) {
|
|
|
+ }
|
|
|
+ --xc[i];
|
|
|
+ xc[j] += 10;
|
|
|
+ }
|
|
|
+ xc[j] -= yc[j];
|
|
|
+ }
|
|
|
+
|
|
|
+ // Remove trailing zeros.
|
|
|
+ for (; xc[--b] === 0; xc.pop()) {
|
|
|
+ }
|
|
|
+
|
|
|
+ // Remove leading zeros and adjust exponent accordingly.
|
|
|
+ for (; xc[0] === 0;) {
|
|
|
+ xc.shift();
|
|
|
+ --ye;
|
|
|
+ }
|
|
|
+
|
|
|
+ if (!xc[0]) {
|
|
|
+
|
|
|
+ // n - n = +0
|
|
|
+ y.s = 1;
|
|
|
+
|
|
|
+ // Result must be zero.
|
|
|
+ xc = [ye = 0];
|
|
|
+ }
|
|
|
+
|
|
|
+ y.c = xc;
|
|
|
+ y.e = ye;
|
|
|
+
|
|
|
+ return y;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a new Big whose value is the value of this Big modulo the
|
|
|
+ * value of Big y.
|
|
|
+ */
|
|
|
+ P.mod = function (y) {
|
|
|
+ var yGTx,
|
|
|
+ x = this,
|
|
|
+ Big = x.constructor,
|
|
|
+ a = x.s,
|
|
|
+ b = (y = new Big(y)).s;
|
|
|
+
|
|
|
+ if (!y.c[0]) {
|
|
|
+ throwErr(NaN);
|
|
|
+ }
|
|
|
+
|
|
|
+ x.s = y.s = 1;
|
|
|
+ yGTx = y.cmp(x) == 1;
|
|
|
+ x.s = a;
|
|
|
+ y.s = b;
|
|
|
+
|
|
|
+ if (yGTx) {
|
|
|
+ return new Big(x);
|
|
|
+ }
|
|
|
+
|
|
|
+ a = Big.DP;
|
|
|
+ b = Big.RM;
|
|
|
+ Big.DP = Big.RM = 0;
|
|
|
+ x = x.div(y);
|
|
|
+ Big.DP = a;
|
|
|
+ Big.RM = b;
|
|
|
+
|
|
|
+ return this.minus( x.times(y) );
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a new Big whose value is the value of this Big plus the value
|
|
|
+ * of Big y.
|
|
|
+ */
|
|
|
+ P.add = P.plus = function (y) {
|
|
|
+ var t,
|
|
|
+ x = this,
|
|
|
+ Big = x.constructor,
|
|
|
+ a = x.s,
|
|
|
+ b = (y = new Big(y)).s;
|
|
|
+
|
|
|
+ // Signs differ?
|
|
|
+ if (a != b) {
|
|
|
+ y.s = -b;
|
|
|
+ return x.minus(y);
|
|
|
+ }
|
|
|
+
|
|
|
+ var xe = x.e,
|
|
|
+ xc = x.c,
|
|
|
+ ye = y.e,
|
|
|
+ yc = y.c;
|
|
|
+
|
|
|
+ // Either zero?
|
|
|
+ if (!xc[0] || !yc[0]) {
|
|
|
+
|
|
|
+ // y is non-zero? x is non-zero? Or both are zero.
|
|
|
+ return yc[0] ? y : new Big(xc[0] ? x : a * 0);
|
|
|
+ }
|
|
|
+ xc = xc.slice();
|
|
|
+
|
|
|
+ // Prepend zeros to equalise exponents.
|
|
|
+ // Note: Faster to use reverse then do unshifts.
|
|
|
+ if (a = xe - ye) {
|
|
|
+
|
|
|
+ if (a > 0) {
|
|
|
+ ye = xe;
|
|
|
+ t = yc;
|
|
|
+ } else {
|
|
|
+ a = -a;
|
|
|
+ t = xc;
|
|
|
+ }
|
|
|
+
|
|
|
+ t.reverse();
|
|
|
+ for (; a--; t.push(0)) {
|
|
|
+ }
|
|
|
+ t.reverse();
|
|
|
+ }
|
|
|
+
|
|
|
+ // Point xc to the longer array.
|
|
|
+ if (xc.length - yc.length < 0) {
|
|
|
+ t = yc;
|
|
|
+ yc = xc;
|
|
|
+ xc = t;
|
|
|
+ }
|
|
|
+ a = yc.length;
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Only start adding at yc.length - 1 as the further digits of xc can be
|
|
|
+ * left as they are.
|
|
|
+ */
|
|
|
+ for (b = 0; a;) {
|
|
|
+ b = (xc[--a] = xc[a] + yc[a] + b) / 10 | 0;
|
|
|
+ xc[a] %= 10;
|
|
|
+ }
|
|
|
+
|
|
|
+ // No need to check for zero, as +x + +y != 0 && -x + -y != 0
|
|
|
+
|
|
|
+ if (b) {
|
|
|
+ xc.unshift(b);
|
|
|
+ ++ye;
|
|
|
+ }
|
|
|
+
|
|
|
+ // Remove trailing zeros.
|
|
|
+ for (a = xc.length; xc[--a] === 0; xc.pop()) {
|
|
|
+ }
|
|
|
+
|
|
|
+ y.c = xc;
|
|
|
+ y.e = ye;
|
|
|
+
|
|
|
+ return y;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a Big whose value is the value of this Big raised to the power n.
|
|
|
+ * If n is negative, round, if necessary, to a maximum of Big.DP decimal
|
|
|
+ * places using rounding mode Big.RM.
|
|
|
+ *
|
|
|
+ * n {number} Integer, -MAX_POWER to MAX_POWER inclusive.
|
|
|
+ */
|
|
|
+ P.pow = function (n) {
|
|
|
+ var x = this,
|
|
|
+ one = new x.constructor(1),
|
|
|
+ y = one,
|
|
|
+ isNeg = n < 0;
|
|
|
+
|
|
|
+ if (n !== ~~n || n < -MAX_POWER || n > MAX_POWER) {
|
|
|
+ throwErr('!pow!');
|
|
|
+ }
|
|
|
+
|
|
|
+ n = isNeg ? -n : n;
|
|
|
+
|
|
|
+ for (;;) {
|
|
|
+
|
|
|
+ if (n & 1) {
|
|
|
+ y = y.times(x);
|
|
|
+ }
|
|
|
+ n >>= 1;
|
|
|
+
|
|
|
+ if (!n) {
|
|
|
+ break;
|
|
|
+ }
|
|
|
+ x = x.times(x);
|
|
|
+ }
|
|
|
+
|
|
|
+ return isNeg ? one.div(y) : y;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a new Big whose value is the value of this Big rounded to a
|
|
|
+ * maximum of dp decimal places using rounding mode rm.
|
|
|
+ * If dp is not specified, round to 0 decimal places.
|
|
|
+ * If rm is not specified, use Big.RM.
|
|
|
+ *
|
|
|
+ * [dp] {number} Integer, 0 to MAX_DP inclusive.
|
|
|
+ * [rm] 0, 1, 2 or 3 (ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_UP)
|
|
|
+ */
|
|
|
+ P.round = function (dp, rm) {
|
|
|
+ var x = this,
|
|
|
+ Big = x.constructor;
|
|
|
+
|
|
|
+ if (dp == null) {
|
|
|
+ dp = 0;
|
|
|
+ } else if (dp !== ~~dp || dp < 0 || dp > MAX_DP) {
|
|
|
+ throwErr('!round!');
|
|
|
+ }
|
|
|
+ rnd(x = new Big(x), dp, rm == null ? Big.RM : rm);
|
|
|
+
|
|
|
+ return x;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a new Big whose value is the square root of the value of this Big,
|
|
|
+ * rounded, if necessary, to a maximum of Big.DP decimal places using
|
|
|
+ * rounding mode Big.RM.
|
|
|
+ */
|
|
|
+ P.sqrt = function () {
|
|
|
+ var estimate, r, approx,
|
|
|
+ x = this,
|
|
|
+ Big = x.constructor,
|
|
|
+ xc = x.c,
|
|
|
+ i = x.s,
|
|
|
+ e = x.e,
|
|
|
+ half = new Big('0.5');
|
|
|
+
|
|
|
+ // Zero?
|
|
|
+ if (!xc[0]) {
|
|
|
+ return new Big(x);
|
|
|
+ }
|
|
|
+
|
|
|
+ // If negative, throw NaN.
|
|
|
+ if (i < 0) {
|
|
|
+ throwErr(NaN);
|
|
|
+ }
|
|
|
+
|
|
|
+ // Estimate.
|
|
|
+ i = Math.sqrt(x.toString());
|
|
|
+
|
|
|
+ // Math.sqrt underflow/overflow?
|
|
|
+ // Pass x to Math.sqrt as integer, then adjust the result exponent.
|
|
|
+ if (i === 0 || i === 1 / 0) {
|
|
|
+ estimate = xc.join('');
|
|
|
+
|
|
|
+ if (!(estimate.length + e & 1)) {
|
|
|
+ estimate += '0';
|
|
|
+ }
|
|
|
+
|
|
|
+ r = new Big( Math.sqrt(estimate).toString() );
|
|
|
+ r.e = ((e + 1) / 2 | 0) - (e < 0 || e & 1);
|
|
|
+ } else {
|
|
|
+ r = new Big(i.toString());
|
|
|
+ }
|
|
|
+
|
|
|
+ i = r.e + (Big.DP += 4);
|
|
|
+
|
|
|
+ // Newton-Raphson iteration.
|
|
|
+ do {
|
|
|
+ approx = r;
|
|
|
+ r = half.times( approx.plus( x.div(approx) ) );
|
|
|
+ } while ( approx.c.slice(0, i).join('') !==
|
|
|
+ r.c.slice(0, i).join('') );
|
|
|
+
|
|
|
+ rnd(r, Big.DP -= 4, Big.RM);
|
|
|
+
|
|
|
+ return r;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a new Big whose value is the value of this Big times the value of
|
|
|
+ * Big y.
|
|
|
+ */
|
|
|
+ P.mul = P.times = function (y) {
|
|
|
+ var c,
|
|
|
+ x = this,
|
|
|
+ Big = x.constructor,
|
|
|
+ xc = x.c,
|
|
|
+ yc = (y = new Big(y)).c,
|
|
|
+ a = xc.length,
|
|
|
+ b = yc.length,
|
|
|
+ i = x.e,
|
|
|
+ j = y.e;
|
|
|
+
|
|
|
+ // Determine sign of result.
|
|
|
+ y.s = x.s == y.s ? 1 : -1;
|
|
|
+
|
|
|
+ // Return signed 0 if either 0.
|
|
|
+ if (!xc[0] || !yc[0]) {
|
|
|
+ return new Big(y.s * 0);
|
|
|
+ }
|
|
|
+
|
|
|
+ // Initialise exponent of result as x.e + y.e.
|
|
|
+ y.e = i + j;
|
|
|
+
|
|
|
+ // If array xc has fewer digits than yc, swap xc and yc, and lengths.
|
|
|
+ if (a < b) {
|
|
|
+ c = xc;
|
|
|
+ xc = yc;
|
|
|
+ yc = c;
|
|
|
+ j = a;
|
|
|
+ a = b;
|
|
|
+ b = j;
|
|
|
+ }
|
|
|
+
|
|
|
+ // Initialise coefficient array of result with zeros.
|
|
|
+ for (c = new Array(j = a + b); j--; c[j] = 0) {
|
|
|
+ }
|
|
|
+
|
|
|
+ // Multiply.
|
|
|
+
|
|
|
+ // i is initially xc.length.
|
|
|
+ for (i = b; i--;) {
|
|
|
+ b = 0;
|
|
|
+
|
|
|
+ // a is yc.length.
|
|
|
+ for (j = a + i; j > i;) {
|
|
|
+
|
|
|
+ // Current sum of products at this digit position, plus carry.
|
|
|
+ b = c[j] + yc[i] * xc[j - i - 1] + b;
|
|
|
+ c[j--] = b % 10;
|
|
|
+
|
|
|
+ // carry
|
|
|
+ b = b / 10 | 0;
|
|
|
+ }
|
|
|
+ c[j] = (c[j] + b) % 10;
|
|
|
+ }
|
|
|
+
|
|
|
+ // Increment result exponent if there is a final carry.
|
|
|
+ if (b) {
|
|
|
+ ++y.e;
|
|
|
+ }
|
|
|
+
|
|
|
+ // Remove any leading zero.
|
|
|
+ if (!c[0]) {
|
|
|
+ c.shift();
|
|
|
+ }
|
|
|
+
|
|
|
+ // Remove trailing zeros.
|
|
|
+ for (i = c.length; !c[--i]; c.pop()) {
|
|
|
+ }
|
|
|
+ y.c = c;
|
|
|
+
|
|
|
+ return y;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a string representing the value of this Big.
|
|
|
+ * Return exponential notation if this Big has a positive exponent equal to
|
|
|
+ * or greater than Big.E_POS, or a negative exponent equal to or less than
|
|
|
+ * Big.E_NEG.
|
|
|
+ */
|
|
|
+ P.toString = P.valueOf = P.toJSON = function () {
|
|
|
+ var x = this,
|
|
|
+ Big = x.constructor,
|
|
|
+ e = x.e,
|
|
|
+ str = x.c.join(''),
|
|
|
+ strL = str.length;
|
|
|
+
|
|
|
+ // Exponential notation?
|
|
|
+ if (e <= Big.E_NEG || e >= Big.E_POS) {
|
|
|
+ str = str.charAt(0) + (strL > 1 ? '.' + str.slice(1) : '') +
|
|
|
+ (e < 0 ? 'e' : 'e+') + e;
|
|
|
+
|
|
|
+ // Negative exponent?
|
|
|
+ } else if (e < 0) {
|
|
|
+
|
|
|
+ // Prepend zeros.
|
|
|
+ for (; ++e; str = '0' + str) {
|
|
|
+ }
|
|
|
+ str = '0.' + str;
|
|
|
+
|
|
|
+ // Positive exponent?
|
|
|
+ } else if (e > 0) {
|
|
|
+
|
|
|
+ if (++e > strL) {
|
|
|
+
|
|
|
+ // Append zeros.
|
|
|
+ for (e -= strL; e-- ; str += '0') {
|
|
|
+ }
|
|
|
+ } else if (e < strL) {
|
|
|
+ str = str.slice(0, e) + '.' + str.slice(e);
|
|
|
+ }
|
|
|
+
|
|
|
+ // Exponent zero.
|
|
|
+ } else if (strL > 1) {
|
|
|
+ str = str.charAt(0) + '.' + str.slice(1);
|
|
|
+ }
|
|
|
+
|
|
|
+ // Avoid '-0'
|
|
|
+ return x.s < 0 && x.c[0] ? '-' + str : str;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ ***************************************************************************
|
|
|
+ * If toExponential, toFixed, toPrecision and format are not required they
|
|
|
+ * can safely be commented-out or deleted. No redundant code will be left.
|
|
|
+ * format is used only by toExponential, toFixed and toPrecision.
|
|
|
+ ***************************************************************************
|
|
|
+ */
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a string representing the value of this Big in exponential
|
|
|
+ * notation to dp fixed decimal places and rounded, if necessary, using
|
|
|
+ * Big.RM.
|
|
|
+ *
|
|
|
+ * [dp] {number} Integer, 0 to MAX_DP inclusive.
|
|
|
+ */
|
|
|
+ P.toExponential = function (dp) {
|
|
|
+
|
|
|
+ if (dp == null) {
|
|
|
+ dp = this.c.length - 1;
|
|
|
+ } else if (dp !== ~~dp || dp < 0 || dp > MAX_DP) {
|
|
|
+ throwErr('!toExp!');
|
|
|
+ }
|
|
|
+
|
|
|
+ return format(this, dp, 1);
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a string representing the value of this Big in normal notation
|
|
|
+ * to dp fixed decimal places and rounded, if necessary, using Big.RM.
|
|
|
+ *
|
|
|
+ * [dp] {number} Integer, 0 to MAX_DP inclusive.
|
|
|
+ */
|
|
|
+ P.toFixed = function (dp) {
|
|
|
+ var str,
|
|
|
+ x = this,
|
|
|
+ Big = x.constructor,
|
|
|
+ neg = Big.E_NEG,
|
|
|
+ pos = Big.E_POS;
|
|
|
+
|
|
|
+ // Prevent the possibility of exponential notation.
|
|
|
+ Big.E_NEG = -(Big.E_POS = 1 / 0);
|
|
|
+
|
|
|
+ if (dp == null) {
|
|
|
+ str = x.toString();
|
|
|
+ } else if (dp === ~~dp && dp >= 0 && dp <= MAX_DP) {
|
|
|
+ str = format(x, x.e + dp);
|
|
|
+
|
|
|
+ // (-0).toFixed() is '0', but (-0.1).toFixed() is '-0'.
|
|
|
+ // (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
|
|
|
+ if (x.s < 0 && x.c[0] && str.indexOf('-') < 0) {
|
|
|
+ //E.g. -0.5 if rounded to -0 will cause toString to omit the minus sign.
|
|
|
+ str = '-' + str;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ Big.E_NEG = neg;
|
|
|
+ Big.E_POS = pos;
|
|
|
+
|
|
|
+ if (!str) {
|
|
|
+ throwErr('!toFix!');
|
|
|
+ }
|
|
|
+
|
|
|
+ return str;
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ /*
|
|
|
+ * Return a string representing the value of this Big rounded to sd
|
|
|
+ * significant digits using Big.RM. Use exponential notation if sd is less
|
|
|
+ * than the number of digits necessary to represent the integer part of the
|
|
|
+ * value in normal notation.
|
|
|
+ *
|
|
|
+ * sd {number} Integer, 1 to MAX_DP inclusive.
|
|
|
+ */
|
|
|
+ P.toPrecision = function (sd) {
|
|
|
+
|
|
|
+ if (sd == null) {
|
|
|
+ return this.toString();
|
|
|
+ } else if (sd !== ~~sd || sd < 1 || sd > MAX_DP) {
|
|
|
+ throwErr('!toPre!');
|
|
|
+ }
|
|
|
+
|
|
|
+ return format(this, sd - 1, 2);
|
|
|
+ };
|
|
|
+
|
|
|
+
|
|
|
+ // Export
|
|
|
+
|
|
|
+
|
|
|
+ Big = bigFactory();
|
|
|
+
|
|
|
+ //AMD.
|
|
|
+ if (typeof define === 'function' && define.amd) {
|
|
|
+ define(function () {
|
|
|
+ return Big;
|
|
|
+ });
|
|
|
+
|
|
|
+ // Node and other CommonJS-like environments that support module.exports.
|
|
|
+ } else if (typeof module !== 'undefined' && module.exports) {
|
|
|
+ module.exports = Big;
|
|
|
+
|
|
|
+ //Browser.
|
|
|
+ } else {
|
|
|
+ global.Big = Big;
|
|
|
+ }
|
|
|
+})(this);
|
hejq