/* big.js v3.1.3 https://github.com/MikeMcl/big.js/LICENCE */ ;(function (global) { 'use strict'; /* big.js v3.1.3 A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic. https://github.com/MikeMcl/big.js/ Copyright (c) 2014 Michael Mclaughlin MIT Expat Licence */ /***************************** EDITABLE DEFAULTS ******************************/ // The default values below must be integers within the stated ranges. /* * The maximum number of decimal places of the results of operations * involving division: div and sqrt, and pow with negative exponents. */ var DP = 20, // 0 to MAX_DP /* * The rounding mode used when rounding to the above decimal places. * * 0 Towards zero (i.e. truncate, no rounding). (ROUND_DOWN) * 1 To nearest neighbour. If equidistant, round up. (ROUND_HALF_UP) * 2 To nearest neighbour. If equidistant, to even. (ROUND_HALF_EVEN) * 3 Away from zero. (ROUND_UP) */ RM = 1, // 0, 1, 2 or 3 // The maximum value of DP and Big.DP. MAX_DP = 1E6, // 0 to 1000000 // The maximum magnitude of the exponent argument to the pow method. MAX_POWER = 1E6, // 1 to 1000000 /* * The exponent value at and beneath which toString returns exponential * notation. * JavaScript's Number type: -7 * -1000000 is the minimum recommended exponent value of a Big. */ E_NEG = -7, // 0 to -1000000 /* * The exponent value at and above which toString returns exponential * notation. * JavaScript's Number type: 21 * 1000000 is the maximum recommended exponent value of a Big. * (This limit is not enforced or checked.) */ E_POS = 21, // 0 to 1000000 /******************************************************************************/ // The shared prototype object. P = {}, isValid = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i, Big; /* * Create and return a Big constructor. * */ function bigFactory() { /* * The Big constructor and exported function. * Create and return a new instance of a Big number object. * * n {number|string|Big} A numeric value. */ function Big(n) { var x = this; // Enable constructor usage without new. if (!(x instanceof Big)) { return n === void 0 ? bigFactory() : new Big(n); } // Duplicate. if (n instanceof Big) { x.s = n.s; x.e = n.e; x.c = n.c.slice(); } else { parse(x, n); } /* * Retain a reference to this Big constructor, and shadow * Big.prototype.constructor which points to Object. */ x.constructor = Big; } Big.prototype = P; Big.DP = DP; Big.RM = RM; Big.E_NEG = E_NEG; Big.E_POS = E_POS; return Big; } // Private functions /* * Return a string representing the value of Big x in normal or exponential * notation to dp fixed decimal places or significant digits. * * x {Big} The Big to format. * dp {number} Integer, 0 to MAX_DP inclusive. * toE {number} 1 (toExponential), 2 (toPrecision) or undefined (toFixed). */ function format(x, dp, toE) { var Big = x.constructor, // The index (normal notation) of the digit that may be rounded up. i = dp - (x = new Big(x)).e, c = x.c; // Round? if (c.length > ++dp) { rnd(x, i, Big.RM); } if (!c[0]) { ++i; } else if (toE) { i = dp; // toFixed } else { c = x.c; // Recalculate i as x.e may have changed if value rounded up. i = x.e + i + 1; } // Append zeros? for (; c.length < i; c.push(0)) { } i = x.e; /* * toPrecision returns exponential notation if the number of * significant digits specified is less than the number of digits * necessary to represent the integer part of the value in normal * notation. */ return toE === 1 || toE && (dp <= i || i <= Big.E_NEG) ? // Exponential notation. (x.s < 0 && c[0] ? '-' : '') + (c.length > 1 ? c[0] + '.' + c.join('').slice(1) : c[0]) + (i < 0 ? 'e' : 'e+') + i // Normal notation. : x.toString(); } /* * Parse the number or string value passed to a Big constructor. * * x {Big} A Big number instance. * n {number|string} A numeric value. */ function parse(x, n) { var e, i, nL; // Minus zero? if (n === 0 && 1 / n < 0) { n = '-0'; // Ensure n is string and check validity. } else if (!isValid.test(n += '')) { throwErr(NaN); } // Determine sign. x.s = n.charAt(0) == '-' ? (n = n.slice(1), -1) : 1; // Decimal point? if ((e = n.indexOf('.')) > -1) { n = n.replace('.', ''); } // Exponential form? if ((i = n.search(/e/i)) > 0) { // Determine exponent. if (e < 0) { e = i; } e += +n.slice(i + 1); n = n.substring(0, i); } else if (e < 0) { // Integer. e = n.length; } // Determine leading zeros. for (i = 0; n.charAt(i) == '0'; i++) { } if (i == (nL = n.length)) { // Zero. x.c = [ x.e = 0 ]; } else { // Determine trailing zeros. for (; n.charAt(--nL) == '0';) { } x.e = e - i - 1; x.c = []; // Convert string to array of digits without leading/trailing zeros. for (e = 0; i <= nL; x.c[e++] = +n.charAt(i++)) { } } return x; } /* * Round Big x to a maximum of dp decimal places using rounding mode rm. * Called by div, sqrt and round. * * x {Big} The Big to round. * dp {number} Integer, 0 to MAX_DP inclusive. * rm {number} 0, 1, 2 or 3 (DOWN, HALF_UP, HALF_EVEN, UP) * [more] {boolean} Whether the result of division was truncated. */ function rnd(x, dp, rm, more) { var u, xc = x.c, i = x.e + dp + 1; if (rm === 1) { // xc[i] is the digit after the digit that may be rounded up. more = xc[i] >= 5; } else if (rm === 2) { more = xc[i] > 5 || xc[i] == 5 && (more || i < 0 || xc[i + 1] !== u || xc[i - 1] & 1); } else if (rm === 3) { more = more || xc[i] !== u || i < 0; } else { more = false; if (rm !== 0) { throwErr('!Big.RM!'); } } if (i < 1 || !xc[0]) { if (more) { // 1, 0.1, 0.01, 0.001, 0.0001 etc. x.e = -dp; x.c = [1]; } else { // Zero. x.c = [x.e = 0]; } } else { // Remove any digits after the required decimal places. xc.length = i--; // Round up? if (more) { // Rounding up may mean the previous digit has to be rounded up. for (; ++xc[i] > 9;) { xc[i] = 0; if (!i--) { ++x.e; xc.unshift(1); } } } // Remove trailing zeros. for (i = xc.length; !xc[--i]; xc.pop()) { } } return x; } /* * Throw a BigError. * * message {string} The error message. */ function throwErr(message) { var err = new Error(message); err.name = 'BigError'; throw err; } // Prototype/instance methods /* * Return a new Big whose value is the absolute value of this Big. */ P.abs = function () { var x = new this.constructor(this); x.s = 1; return x; }; /* * Return * 1 if the value of this Big is greater than the value of Big y, * -1 if the value of this Big is less than the value of Big y, or * 0 if they have the same value. */ P.cmp = function (y) { var xNeg, x = this, xc = x.c, yc = (y = new x.constructor(y)).c, i = x.s, j = y.s, k = x.e, l = y.e; // Either zero? if (!xc[0] || !yc[0]) { return !xc[0] ? !yc[0] ? 0 : -j : i; } // Signs differ? if (i != j) { return i; } xNeg = i < 0; // Compare exponents. if (k != l) { return k > l ^ xNeg ? 1 : -1; } i = -1; j = (k = xc.length) < (l = yc.length) ? k : l; // Compare digit by digit. for (; ++i < j;) { if (xc[i] != yc[i]) { return xc[i] > yc[i] ^ xNeg ? 1 : -1; } } // Compare lengths. return k == l ? 0 : k > l ^ xNeg ? 1 : -1; }; /* * Return a new Big whose value is the value of this Big divided by the * value of Big y, rounded, if necessary, to a maximum of Big.DP decimal * places using rounding mode Big.RM. */ P.div = function (y) { var x = this, Big = x.constructor, // dividend dvd = x.c, //divisor dvs = (y = new Big(y)).c, s = x.s == y.s ? 1 : -1, dp = Big.DP; if (dp !== ~~dp || dp < 0 || dp > MAX_DP) { throwErr('!Big.DP!'); } // Either 0? if (!dvd[0] || !dvs[0]) { // If both are 0, throw NaN if (dvd[0] == dvs[0]) { throwErr(NaN); } // If dvs is 0, throw +-Infinity. if (!dvs[0]) { throwErr(s / 0); } // dvd is 0, return +-0. return new Big(s * 0); } var dvsL, dvsT, next, cmp, remI, u, dvsZ = dvs.slice(), dvdI = dvsL = dvs.length, dvdL = dvd.length, // remainder rem = dvd.slice(0, dvsL), remL = rem.length, // quotient q = y, qc = q.c = [], qi = 0, digits = dp + (q.e = x.e - y.e) + 1; q.s = s; s = digits < 0 ? 0 : digits; // Create version of divisor with leading zero. dvsZ.unshift(0); // Add zeros to make remainder as long as divisor. for (; remL++ < dvsL; rem.push(0)) { } do { // 'next' is how many times the divisor goes into current remainder. 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);