85bf1341f3
Frontend Enhancements: - Complete React TypeScript frontend with modern UI components - Distributed workflows management interface with real-time updates - Socket.IO integration for live agent status monitoring - Agent management dashboard with cluster visualization - Project management interface with metrics and task tracking - Responsive design with proper error handling and loading states Backend Infrastructure: - Distributed coordinator for multi-agent workflow orchestration - Cluster management API with comprehensive agent operations - Enhanced database models for agents and projects - Project service for filesystem-based project discovery - Performance monitoring and metrics collection - Comprehensive API documentation and error handling Documentation: - Complete distributed development guide (README_DISTRIBUTED.md) - Comprehensive development report with architecture insights - System configuration templates and deployment guides The platform now provides a complete web interface for managing the distributed AI cluster with real-time monitoring, workflow orchestration, and agent coordination capabilities. 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <noreply@anthropic.com>
1986 lines
48 KiB
JavaScript
1986 lines
48 KiB
JavaScript
/*
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* decimal.js-light v2.5.1
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* An arbitrary-precision Decimal type for JavaScript.
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* https://github.com/MikeMcl/decimal.js-light
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* Copyright (c) 2020 Michael Mclaughlin <M8ch88l@gmail.com>
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* MIT Expat Licence
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*/
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// ------------------------------------ EDITABLE DEFAULTS ------------------------------------- //
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// The limit on the value of `precision`, and on the value of the first argument to
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// `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`.
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var MAX_DIGITS = 1e9, // 0 to 1e9
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// The initial configuration properties of the Decimal constructor.
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defaults = {
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// These values must be integers within the stated ranges (inclusive).
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// Most of these values can be changed during run-time using `Decimal.config`.
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// The maximum number of significant digits of the result of a calculation or base conversion.
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// E.g. `Decimal.config({ precision: 20 });`
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precision: 20, // 1 to MAX_DIGITS
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// The rounding mode used by default by `toInteger`, `toDecimalPlaces`, `toExponential`,
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// `toFixed`, `toPrecision` and `toSignificantDigits`.
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//
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// ROUND_UP 0 Away from zero.
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// ROUND_DOWN 1 Towards zero.
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// ROUND_CEIL 2 Towards +Infinity.
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// ROUND_FLOOR 3 Towards -Infinity.
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// ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up.
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// ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.
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// ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.
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// ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.
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// ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
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//
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// E.g.
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// `Decimal.rounding = 4;`
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// `Decimal.rounding = Decimal.ROUND_HALF_UP;`
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rounding: 4, // 0 to 8
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// The exponent value at and beneath which `toString` returns exponential notation.
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// JavaScript numbers: -7
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toExpNeg: -7, // 0 to -MAX_E
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// The exponent value at and above which `toString` returns exponential notation.
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// JavaScript numbers: 21
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toExpPos: 21, // 0 to MAX_E
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// The natural logarithm of 10.
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// 115 digits
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LN10: '2.302585092994045684017991454684364207601101488628772976033327900967572609677352480235997205089598298341967784042286'
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},
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// ------------------------------------ END OF EDITABLE DEFAULTS -------------------------------- //
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Decimal,
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external = true,
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decimalError = '[DecimalError] ',
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invalidArgument = decimalError + 'Invalid argument: ',
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exponentOutOfRange = decimalError + 'Exponent out of range: ',
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mathfloor = Math.floor,
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mathpow = Math.pow,
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isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
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ONE,
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BASE = 1e7,
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LOG_BASE = 7,
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MAX_SAFE_INTEGER = 9007199254740991,
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MAX_E = mathfloor(MAX_SAFE_INTEGER / LOG_BASE), // 1286742750677284
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// Decimal.prototype object
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P = {};
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// Decimal prototype methods
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/*
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* absoluteValue abs
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* comparedTo cmp
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* decimalPlaces dp
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* dividedBy div
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* dividedToIntegerBy idiv
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* equals eq
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* exponent
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* greaterThan gt
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* greaterThanOrEqualTo gte
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* isInteger isint
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* isNegative isneg
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* isPositive ispos
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* isZero
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* lessThan lt
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* lessThanOrEqualTo lte
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* logarithm log
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* minus sub
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* modulo mod
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* naturalExponential exp
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* naturalLogarithm ln
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* negated neg
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* plus add
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* precision sd
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* squareRoot sqrt
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* times mul
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* toDecimalPlaces todp
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* toExponential
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* toFixed
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* toInteger toint
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* toNumber
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* toPower pow
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* toPrecision
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* toSignificantDigits tosd
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* toString
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* valueOf val
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*/
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/*
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* Return a new Decimal whose value is the absolute value of this Decimal.
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*
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*/
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P.absoluteValue = P.abs = function () {
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var x = new this.constructor(this);
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if (x.s) x.s = 1;
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return x;
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};
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/*
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* Return
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* 1 if the value of this Decimal is greater than the value of `y`,
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* -1 if the value of this Decimal is less than the value of `y`,
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* 0 if they have the same value
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*
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*/
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P.comparedTo = P.cmp = function (y) {
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var i, j, xdL, ydL,
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x = this;
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y = new x.constructor(y);
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// Signs differ?
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if (x.s !== y.s) return x.s || -y.s;
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// Compare exponents.
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if (x.e !== y.e) return x.e > y.e ^ x.s < 0 ? 1 : -1;
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xdL = x.d.length;
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ydL = y.d.length;
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// Compare digit by digit.
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for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) {
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if (x.d[i] !== y.d[i]) return x.d[i] > y.d[i] ^ x.s < 0 ? 1 : -1;
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}
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// Compare lengths.
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return xdL === ydL ? 0 : xdL > ydL ^ x.s < 0 ? 1 : -1;
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};
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/*
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* Return the number of decimal places of the value of this Decimal.
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*
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*/
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P.decimalPlaces = P.dp = function () {
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var x = this,
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w = x.d.length - 1,
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dp = (w - x.e) * LOG_BASE;
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// Subtract the number of trailing zeros of the last word.
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w = x.d[w];
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if (w) for (; w % 10 == 0; w /= 10) dp--;
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return dp < 0 ? 0 : dp;
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};
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/*
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* Return a new Decimal whose value is the value of this Decimal divided by `y`, truncated to
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* `precision` significant digits.
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*
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*/
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P.dividedBy = P.div = function (y) {
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return divide(this, new this.constructor(y));
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};
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/*
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* Return a new Decimal whose value is the integer part of dividing the value of this Decimal
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* by the value of `y`, truncated to `precision` significant digits.
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*
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*/
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P.dividedToIntegerBy = P.idiv = function (y) {
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var x = this,
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Ctor = x.constructor;
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return round(divide(x, new Ctor(y), 0, 1), Ctor.precision);
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};
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/*
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* Return true if the value of this Decimal is equal to the value of `y`, otherwise return false.
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*
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*/
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P.equals = P.eq = function (y) {
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return !this.cmp(y);
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};
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/*
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* Return the (base 10) exponent value of this Decimal (this.e is the base 10000000 exponent).
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*
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*/
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P.exponent = function () {
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return getBase10Exponent(this);
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};
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/*
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* Return true if the value of this Decimal is greater than the value of `y`, otherwise return
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* false.
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*
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*/
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P.greaterThan = P.gt = function (y) {
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return this.cmp(y) > 0;
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};
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/*
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* Return true if the value of this Decimal is greater than or equal to the value of `y`,
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* otherwise return false.
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*
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*/
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P.greaterThanOrEqualTo = P.gte = function (y) {
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return this.cmp(y) >= 0;
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};
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/*
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* Return true if the value of this Decimal is an integer, otherwise return false.
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*
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*/
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P.isInteger = P.isint = function () {
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return this.e > this.d.length - 2;
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};
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/*
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* Return true if the value of this Decimal is negative, otherwise return false.
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*
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*/
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P.isNegative = P.isneg = function () {
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return this.s < 0;
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};
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/*
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* Return true if the value of this Decimal is positive, otherwise return false.
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*
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*/
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P.isPositive = P.ispos = function () {
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return this.s > 0;
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};
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/*
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* Return true if the value of this Decimal is 0, otherwise return false.
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*
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*/
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P.isZero = function () {
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return this.s === 0;
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};
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/*
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* Return true if the value of this Decimal is less than `y`, otherwise return false.
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*
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*/
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P.lessThan = P.lt = function (y) {
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return this.cmp(y) < 0;
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};
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/*
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* Return true if the value of this Decimal is less than or equal to `y`, otherwise return false.
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*
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*/
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P.lessThanOrEqualTo = P.lte = function (y) {
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return this.cmp(y) < 1;
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};
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/*
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* Return the logarithm of the value of this Decimal to the specified base, truncated to
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* `precision` significant digits.
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*
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* If no base is specified, return log[10](x).
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*
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* log[base](x) = ln(x) / ln(base)
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*
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* The maximum error of the result is 1 ulp (unit in the last place).
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*
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* [base] {number|string|Decimal} The base of the logarithm.
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*
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*/
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P.logarithm = P.log = function (base) {
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var r,
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x = this,
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Ctor = x.constructor,
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pr = Ctor.precision,
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wpr = pr + 5;
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// Default base is 10.
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if (base === void 0) {
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base = new Ctor(10);
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} else {
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base = new Ctor(base);
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// log[-b](x) = NaN
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// log[0](x) = NaN
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// log[1](x) = NaN
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if (base.s < 1 || base.eq(ONE)) throw Error(decimalError + 'NaN');
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}
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// log[b](-x) = NaN
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// log[b](0) = -Infinity
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if (x.s < 1) throw Error(decimalError + (x.s ? 'NaN' : '-Infinity'));
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// log[b](1) = 0
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if (x.eq(ONE)) return new Ctor(0);
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external = false;
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r = divide(ln(x, wpr), ln(base, wpr), wpr);
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external = true;
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return round(r, pr);
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};
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/*
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* Return a new Decimal whose value is the value of this Decimal minus `y`, truncated to
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* `precision` significant digits.
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*
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*/
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P.minus = P.sub = function (y) {
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var x = this;
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y = new x.constructor(y);
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return x.s == y.s ? subtract(x, y) : add(x, (y.s = -y.s, y));
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};
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/*
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* Return a new Decimal whose value is the value of this Decimal modulo `y`, truncated to
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* `precision` significant digits.
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*
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*/
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P.modulo = P.mod = function (y) {
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var q,
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x = this,
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Ctor = x.constructor,
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pr = Ctor.precision;
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y = new Ctor(y);
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// x % 0 = NaN
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if (!y.s) throw Error(decimalError + 'NaN');
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// Return x if x is 0.
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if (!x.s) return round(new Ctor(x), pr);
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// Prevent rounding of intermediate calculations.
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external = false;
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q = divide(x, y, 0, 1).times(y);
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external = true;
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return x.minus(q);
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};
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/*
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* Return a new Decimal whose value is the natural exponential of the value of this Decimal,
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* i.e. the base e raised to the power the value of this Decimal, truncated to `precision`
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* significant digits.
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*
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*/
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P.naturalExponential = P.exp = function () {
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return exp(this);
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};
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/*
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* Return a new Decimal whose value is the natural logarithm of the value of this Decimal,
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* truncated to `precision` significant digits.
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*
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*/
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P.naturalLogarithm = P.ln = function () {
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return ln(this);
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};
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/*
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* Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by
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* -1.
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*
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*/
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P.negated = P.neg = function () {
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var x = new this.constructor(this);
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x.s = -x.s || 0;
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return x;
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};
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/*
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* Return a new Decimal whose value is the value of this Decimal plus `y`, truncated to
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* `precision` significant digits.
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*
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*/
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P.plus = P.add = function (y) {
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var x = this;
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y = new x.constructor(y);
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return x.s == y.s ? add(x, y) : subtract(x, (y.s = -y.s, y));
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};
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/*
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* Return the number of significant digits of the value of this Decimal.
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*
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* [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
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*
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*/
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P.precision = P.sd = function (z) {
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var e, sd, w,
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x = this;
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if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z);
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e = getBase10Exponent(x) + 1;
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w = x.d.length - 1;
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sd = w * LOG_BASE + 1;
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w = x.d[w];
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// If non-zero...
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if (w) {
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// Subtract the number of trailing zeros of the last word.
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for (; w % 10 == 0; w /= 10) sd--;
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// Add the number of digits of the first word.
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for (w = x.d[0]; w >= 10; w /= 10) sd++;
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}
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return z && e > sd ? e : sd;
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};
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/*
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* Return a new Decimal whose value is the square root of this Decimal, truncated to `precision`
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* significant digits.
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*
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*/
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P.squareRoot = P.sqrt = function () {
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var e, n, pr, r, s, t, wpr,
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x = this,
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Ctor = x.constructor;
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// Negative or zero?
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if (x.s < 1) {
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if (!x.s) return new Ctor(0);
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// sqrt(-x) = NaN
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throw Error(decimalError + 'NaN');
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}
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e = getBase10Exponent(x);
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external = false;
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// Initial estimate.
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s = Math.sqrt(+x);
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// Math.sqrt underflow/overflow?
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// Pass x to Math.sqrt as integer, then adjust the exponent of the result.
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if (s == 0 || s == 1 / 0) {
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n = digitsToString(x.d);
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if ((n.length + e) % 2 == 0) n += '0';
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s = Math.sqrt(n);
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e = mathfloor((e + 1) / 2) - (e < 0 || e % 2);
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if (s == 1 / 0) {
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n = '5e' + e;
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} else {
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n = s.toExponential();
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n = n.slice(0, n.indexOf('e') + 1) + e;
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}
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r = new Ctor(n);
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} else {
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r = new Ctor(s.toString());
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}
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pr = Ctor.precision;
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s = wpr = pr + 3;
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// Newton-Raphson iteration.
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for (;;) {
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t = r;
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r = t.plus(divide(x, t, wpr + 2)).times(0.5);
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if (digitsToString(t.d).slice(0, wpr) === (n = digitsToString(r.d)).slice(0, wpr)) {
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n = n.slice(wpr - 3, wpr + 1);
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// The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or
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// 4999, i.e. approaching a rounding boundary, continue the iteration.
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if (s == wpr && n == '4999') {
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// On the first iteration only, check to see if rounding up gives the exact result as the
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// nines may infinitely repeat.
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round(t, pr + 1, 0);
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if (t.times(t).eq(x)) {
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r = t;
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break;
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}
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} else if (n != '9999') {
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break;
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}
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wpr += 4;
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}
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}
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external = true;
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return round(r, pr);
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};
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/*
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* Return a new Decimal whose value is the value of this Decimal times `y`, truncated to
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* `precision` significant digits.
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*
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*/
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P.times = P.mul = function (y) {
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var carry, e, i, k, r, rL, t, xdL, ydL,
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x = this,
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Ctor = x.constructor,
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|
xd = x.d,
|
|
yd = (y = new Ctor(y)).d;
|
|
|
|
// Return 0 if either is 0.
|
|
if (!x.s || !y.s) return new Ctor(0);
|
|
|
|
y.s *= x.s;
|
|
e = x.e + y.e;
|
|
xdL = xd.length;
|
|
ydL = yd.length;
|
|
|
|
// Ensure xd points to the longer array.
|
|
if (xdL < ydL) {
|
|
r = xd;
|
|
xd = yd;
|
|
yd = r;
|
|
rL = xdL;
|
|
xdL = ydL;
|
|
ydL = rL;
|
|
}
|
|
|
|
// Initialise the result array with zeros.
|
|
r = [];
|
|
rL = xdL + ydL;
|
|
for (i = rL; i--;) r.push(0);
|
|
|
|
// Multiply!
|
|
for (i = ydL; --i >= 0;) {
|
|
carry = 0;
|
|
for (k = xdL + i; k > i;) {
|
|
t = r[k] + yd[i] * xd[k - i - 1] + carry;
|
|
r[k--] = t % BASE | 0;
|
|
carry = t / BASE | 0;
|
|
}
|
|
|
|
r[k] = (r[k] + carry) % BASE | 0;
|
|
}
|
|
|
|
// Remove trailing zeros.
|
|
for (; !r[--rL];) r.pop();
|
|
|
|
if (carry) ++e;
|
|
else r.shift();
|
|
|
|
y.d = r;
|
|
y.e = e;
|
|
|
|
return external ? round(y, Ctor.precision) : y;
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp`
|
|
* decimal places using rounding mode `rm` or `rounding` if `rm` is omitted.
|
|
*
|
|
* If `dp` is omitted, return a new Decimal whose value is the value of this Decimal.
|
|
*
|
|
* [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
|
|
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
|
|
*
|
|
*/
|
|
P.toDecimalPlaces = P.todp = function (dp, rm) {
|
|
var x = this,
|
|
Ctor = x.constructor;
|
|
|
|
x = new Ctor(x);
|
|
if (dp === void 0) return x;
|
|
|
|
checkInt32(dp, 0, MAX_DIGITS);
|
|
|
|
if (rm === void 0) rm = Ctor.rounding;
|
|
else checkInt32(rm, 0, 8);
|
|
|
|
return round(x, dp + getBase10Exponent(x) + 1, rm);
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a string representing the value of this Decimal in exponential notation rounded to
|
|
* `dp` fixed decimal places using rounding mode `rounding`.
|
|
*
|
|
* [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
|
|
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
|
|
*
|
|
*/
|
|
P.toExponential = function (dp, rm) {
|
|
var str,
|
|
x = this,
|
|
Ctor = x.constructor;
|
|
|
|
if (dp === void 0) {
|
|
str = toString(x, true);
|
|
} else {
|
|
checkInt32(dp, 0, MAX_DIGITS);
|
|
|
|
if (rm === void 0) rm = Ctor.rounding;
|
|
else checkInt32(rm, 0, 8);
|
|
|
|
x = round(new Ctor(x), dp + 1, rm);
|
|
str = toString(x, true, dp + 1);
|
|
}
|
|
|
|
return str;
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a string representing the value of this Decimal in normal (fixed-point) notation to
|
|
* `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is
|
|
* omitted.
|
|
*
|
|
* As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'.
|
|
*
|
|
* [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive.
|
|
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
|
|
*
|
|
* (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'.
|
|
* (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
|
|
* (-0).toFixed(3) is '0.000'.
|
|
* (-0.5).toFixed(0) is '-0'.
|
|
*
|
|
*/
|
|
P.toFixed = function (dp, rm) {
|
|
var str, y,
|
|
x = this,
|
|
Ctor = x.constructor;
|
|
|
|
if (dp === void 0) return toString(x);
|
|
|
|
checkInt32(dp, 0, MAX_DIGITS);
|
|
|
|
if (rm === void 0) rm = Ctor.rounding;
|
|
else checkInt32(rm, 0, 8);
|
|
|
|
y = round(new Ctor(x), dp + getBase10Exponent(x) + 1, rm);
|
|
str = toString(y.abs(), false, dp + getBase10Exponent(y) + 1);
|
|
|
|
// To determine whether to add the minus sign look at the value before it was rounded,
|
|
// i.e. look at `x` rather than `y`.
|
|
return x.isneg() && !x.isZero() ? '-' + str : str;
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a new Decimal whose value is the value of this Decimal rounded to a whole number using
|
|
* rounding mode `rounding`.
|
|
*
|
|
*/
|
|
P.toInteger = P.toint = function () {
|
|
var x = this,
|
|
Ctor = x.constructor;
|
|
return round(new Ctor(x), getBase10Exponent(x) + 1, Ctor.rounding);
|
|
};
|
|
|
|
|
|
/*
|
|
* Return the value of this Decimal converted to a number primitive.
|
|
*
|
|
*/
|
|
P.toNumber = function () {
|
|
return +this;
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a new Decimal whose value is the value of this Decimal raised to the power `y`,
|
|
* truncated to `precision` significant digits.
|
|
*
|
|
* For non-integer or very large exponents pow(x, y) is calculated using
|
|
*
|
|
* x^y = exp(y*ln(x))
|
|
*
|
|
* The maximum error is 1 ulp (unit in last place).
|
|
*
|
|
* y {number|string|Decimal} The power to which to raise this Decimal.
|
|
*
|
|
*/
|
|
P.toPower = P.pow = function (y) {
|
|
var e, k, pr, r, sign, yIsInt,
|
|
x = this,
|
|
Ctor = x.constructor,
|
|
guard = 12,
|
|
yn = +(y = new Ctor(y));
|
|
|
|
// pow(x, 0) = 1
|
|
if (!y.s) return new Ctor(ONE);
|
|
|
|
x = new Ctor(x);
|
|
|
|
// pow(0, y > 0) = 0
|
|
// pow(0, y < 0) = Infinity
|
|
if (!x.s) {
|
|
if (y.s < 1) throw Error(decimalError + 'Infinity');
|
|
return x;
|
|
}
|
|
|
|
// pow(1, y) = 1
|
|
if (x.eq(ONE)) return x;
|
|
|
|
pr = Ctor.precision;
|
|
|
|
// pow(x, 1) = x
|
|
if (y.eq(ONE)) return round(x, pr);
|
|
|
|
e = y.e;
|
|
k = y.d.length - 1;
|
|
yIsInt = e >= k;
|
|
sign = x.s;
|
|
|
|
if (!yIsInt) {
|
|
|
|
// pow(x < 0, y non-integer) = NaN
|
|
if (sign < 0) throw Error(decimalError + 'NaN');
|
|
|
|
// If y is a small integer use the 'exponentiation by squaring' algorithm.
|
|
} else if ((k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) {
|
|
r = new Ctor(ONE);
|
|
|
|
// Max k of 9007199254740991 takes 53 loop iterations.
|
|
// Maximum digits array length; leaves [28, 34] guard digits.
|
|
e = Math.ceil(pr / LOG_BASE + 4);
|
|
|
|
external = false;
|
|
|
|
for (;;) {
|
|
if (k % 2) {
|
|
r = r.times(x);
|
|
truncate(r.d, e);
|
|
}
|
|
|
|
k = mathfloor(k / 2);
|
|
if (k === 0) break;
|
|
|
|
x = x.times(x);
|
|
truncate(x.d, e);
|
|
}
|
|
|
|
external = true;
|
|
|
|
return y.s < 0 ? new Ctor(ONE).div(r) : round(r, pr);
|
|
}
|
|
|
|
// Result is negative if x is negative and the last digit of integer y is odd.
|
|
sign = sign < 0 && y.d[Math.max(e, k)] & 1 ? -1 : 1;
|
|
|
|
x.s = 1;
|
|
external = false;
|
|
r = y.times(ln(x, pr + guard));
|
|
external = true;
|
|
r = exp(r);
|
|
r.s = sign;
|
|
|
|
return r;
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a string representing the value of this Decimal rounded to `sd` significant digits
|
|
* using rounding mode `rounding`.
|
|
*
|
|
* Return 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} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
|
|
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
|
|
*
|
|
*/
|
|
P.toPrecision = function (sd, rm) {
|
|
var e, str,
|
|
x = this,
|
|
Ctor = x.constructor;
|
|
|
|
if (sd === void 0) {
|
|
e = getBase10Exponent(x);
|
|
str = toString(x, e <= Ctor.toExpNeg || e >= Ctor.toExpPos);
|
|
} else {
|
|
checkInt32(sd, 1, MAX_DIGITS);
|
|
|
|
if (rm === void 0) rm = Ctor.rounding;
|
|
else checkInt32(rm, 0, 8);
|
|
|
|
x = round(new Ctor(x), sd, rm);
|
|
e = getBase10Exponent(x);
|
|
str = toString(x, sd <= e || e <= Ctor.toExpNeg, sd);
|
|
}
|
|
|
|
return str;
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd`
|
|
* significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if
|
|
* omitted.
|
|
*
|
|
* [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive.
|
|
* [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
|
|
*
|
|
*/
|
|
P.toSignificantDigits = P.tosd = function (sd, rm) {
|
|
var x = this,
|
|
Ctor = x.constructor;
|
|
|
|
if (sd === void 0) {
|
|
sd = Ctor.precision;
|
|
rm = Ctor.rounding;
|
|
} else {
|
|
checkInt32(sd, 1, MAX_DIGITS);
|
|
|
|
if (rm === void 0) rm = Ctor.rounding;
|
|
else checkInt32(rm, 0, 8);
|
|
}
|
|
|
|
return round(new Ctor(x), sd, rm);
|
|
};
|
|
|
|
|
|
/*
|
|
* Return a string representing the value of this Decimal.
|
|
*
|
|
* Return exponential notation if this Decimal has a positive exponent equal to or greater than
|
|
* `toExpPos`, or a negative exponent equal to or less than `toExpNeg`.
|
|
*
|
|
*/
|
|
P.toString = P.valueOf = P.val = P.toJSON = P[Symbol.for('nodejs.util.inspect.custom')] = function () {
|
|
var x = this,
|
|
e = getBase10Exponent(x),
|
|
Ctor = x.constructor;
|
|
|
|
return toString(x, e <= Ctor.toExpNeg || e >= Ctor.toExpPos);
|
|
};
|
|
|
|
|
|
// Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers.
|
|
|
|
|
|
/*
|
|
* add P.minus, P.plus
|
|
* checkInt32 P.todp, P.toExponential, P.toFixed, P.toPrecision, P.tosd
|
|
* digitsToString P.log, P.sqrt, P.pow, toString, exp, ln
|
|
* divide P.div, P.idiv, P.log, P.mod, P.sqrt, exp, ln
|
|
* exp P.exp, P.pow
|
|
* getBase10Exponent P.exponent, P.sd, P.toint, P.sqrt, P.todp, P.toFixed, P.toPrecision,
|
|
* P.toString, divide, round, toString, exp, ln
|
|
* getLn10 P.log, ln
|
|
* getZeroString digitsToString, toString
|
|
* ln P.log, P.ln, P.pow, exp
|
|
* parseDecimal Decimal
|
|
* round P.abs, P.idiv, P.log, P.minus, P.mod, P.neg, P.plus, P.toint, P.sqrt,
|
|
* P.times, P.todp, P.toExponential, P.toFixed, P.pow, P.toPrecision, P.tosd,
|
|
* divide, getLn10, exp, ln
|
|
* subtract P.minus, P.plus
|
|
* toString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf
|
|
* truncate P.pow
|
|
*
|
|
* Throws: P.log, P.mod, P.sd, P.sqrt, P.pow, checkInt32, divide, round,
|
|
* getLn10, exp, ln, parseDecimal, Decimal, config
|
|
*/
|
|
|
|
|
|
function add(x, y) {
|
|
var carry, d, e, i, k, len, xd, yd,
|
|
Ctor = x.constructor,
|
|
pr = Ctor.precision;
|
|
|
|
// If either is zero...
|
|
if (!x.s || !y.s) {
|
|
|
|
// Return x if y is zero.
|
|
// Return y if y is non-zero.
|
|
if (!y.s) y = new Ctor(x);
|
|
return external ? round(y, pr) : y;
|
|
}
|
|
|
|
xd = x.d;
|
|
yd = y.d;
|
|
|
|
// x and y are finite, non-zero numbers with the same sign.
|
|
|
|
k = x.e;
|
|
e = y.e;
|
|
xd = xd.slice();
|
|
i = k - e;
|
|
|
|
// If base 1e7 exponents differ...
|
|
if (i) {
|
|
if (i < 0) {
|
|
d = xd;
|
|
i = -i;
|
|
len = yd.length;
|
|
} else {
|
|
d = yd;
|
|
e = k;
|
|
len = xd.length;
|
|
}
|
|
|
|
// Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1.
|
|
k = Math.ceil(pr / LOG_BASE);
|
|
len = k > len ? k + 1 : len + 1;
|
|
|
|
if (i > len) {
|
|
i = len;
|
|
d.length = 1;
|
|
}
|
|
|
|
// Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts.
|
|
d.reverse();
|
|
for (; i--;) d.push(0);
|
|
d.reverse();
|
|
}
|
|
|
|
len = xd.length;
|
|
i = yd.length;
|
|
|
|
// If yd is longer than xd, swap xd and yd so xd points to the longer array.
|
|
if (len - i < 0) {
|
|
i = len;
|
|
d = yd;
|
|
yd = xd;
|
|
xd = d;
|
|
}
|
|
|
|
// Only start adding at yd.length - 1 as the further digits of xd can be left as they are.
|
|
for (carry = 0; i;) {
|
|
carry = (xd[--i] = xd[i] + yd[i] + carry) / BASE | 0;
|
|
xd[i] %= BASE;
|
|
}
|
|
|
|
if (carry) {
|
|
xd.unshift(carry);
|
|
++e;
|
|
}
|
|
|
|
// Remove trailing zeros.
|
|
// No need to check for zero, as +x + +y != 0 && -x + -y != 0
|
|
for (len = xd.length; xd[--len] == 0;) xd.pop();
|
|
|
|
y.d = xd;
|
|
y.e = e;
|
|
|
|
return external ? round(y, pr) : y;
|
|
}
|
|
|
|
|
|
function checkInt32(i, min, max) {
|
|
if (i !== ~~i || i < min || i > max) {
|
|
throw Error(invalidArgument + i);
|
|
}
|
|
}
|
|
|
|
|
|
function digitsToString(d) {
|
|
var i, k, ws,
|
|
indexOfLastWord = d.length - 1,
|
|
str = '',
|
|
w = d[0];
|
|
|
|
if (indexOfLastWord > 0) {
|
|
str += w;
|
|
for (i = 1; i < indexOfLastWord; i++) {
|
|
ws = d[i] + '';
|
|
k = LOG_BASE - ws.length;
|
|
if (k) str += getZeroString(k);
|
|
str += ws;
|
|
}
|
|
|
|
w = d[i];
|
|
ws = w + '';
|
|
k = LOG_BASE - ws.length;
|
|
if (k) str += getZeroString(k);
|
|
} else if (w === 0) {
|
|
return '0';
|
|
}
|
|
|
|
// Remove trailing zeros of last w.
|
|
for (; w % 10 === 0;) w /= 10;
|
|
|
|
return str + w;
|
|
}
|
|
|
|
|
|
var divide = (function () {
|
|
|
|
// Assumes non-zero x and k, and hence non-zero result.
|
|
function multiplyInteger(x, k) {
|
|
var temp,
|
|
carry = 0,
|
|
i = x.length;
|
|
|
|
for (x = x.slice(); i--;) {
|
|
temp = x[i] * k + carry;
|
|
x[i] = temp % BASE | 0;
|
|
carry = temp / BASE | 0;
|
|
}
|
|
|
|
if (carry) x.unshift(carry);
|
|
|
|
return x;
|
|
}
|
|
|
|
function compare(a, b, aL, bL) {
|
|
var i, r;
|
|
|
|
if (aL != bL) {
|
|
r = aL > bL ? 1 : -1;
|
|
} else {
|
|
for (i = r = 0; i < aL; i++) {
|
|
if (a[i] != b[i]) {
|
|
r = a[i] > b[i] ? 1 : -1;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
return r;
|
|
}
|
|
|
|
function subtract(a, b, aL) {
|
|
var i = 0;
|
|
|
|
// Subtract b from a.
|
|
for (; aL--;) {
|
|
a[aL] -= i;
|
|
i = a[aL] < b[aL] ? 1 : 0;
|
|
a[aL] = i * BASE + a[aL] - b[aL];
|
|
}
|
|
|
|
// Remove leading zeros.
|
|
for (; !a[0] && a.length > 1;) a.shift();
|
|
}
|
|
|
|
return function (x, y, pr, dp) {
|
|
var cmp, e, i, k, prod, prodL, q, qd, rem, remL, rem0, sd, t, xi, xL, yd0, yL, yz,
|
|
Ctor = x.constructor,
|
|
sign = x.s == y.s ? 1 : -1,
|
|
xd = x.d,
|
|
yd = y.d;
|
|
|
|
// Either 0?
|
|
if (!x.s) return new Ctor(x);
|
|
if (!y.s) throw Error(decimalError + 'Division by zero');
|
|
|
|
e = x.e - y.e;
|
|
yL = yd.length;
|
|
xL = xd.length;
|
|
q = new Ctor(sign);
|
|
qd = q.d = [];
|
|
|
|
// Result exponent may be one less than e.
|
|
for (i = 0; yd[i] == (xd[i] || 0); ) ++i;
|
|
if (yd[i] > (xd[i] || 0)) --e;
|
|
|
|
if (pr == null) {
|
|
sd = pr = Ctor.precision;
|
|
} else if (dp) {
|
|
sd = pr + (getBase10Exponent(x) - getBase10Exponent(y)) + 1;
|
|
} else {
|
|
sd = pr;
|
|
}
|
|
|
|
if (sd < 0) return new Ctor(0);
|
|
|
|
// Convert precision in number of base 10 digits to base 1e7 digits.
|
|
sd = sd / LOG_BASE + 2 | 0;
|
|
i = 0;
|
|
|
|
// divisor < 1e7
|
|
if (yL == 1) {
|
|
k = 0;
|
|
yd = yd[0];
|
|
sd++;
|
|
|
|
// k is the carry.
|
|
for (; (i < xL || k) && sd--; i++) {
|
|
t = k * BASE + (xd[i] || 0);
|
|
qd[i] = t / yd | 0;
|
|
k = t % yd | 0;
|
|
}
|
|
|
|
// divisor >= 1e7
|
|
} else {
|
|
|
|
// Normalise xd and yd so highest order digit of yd is >= BASE/2
|
|
k = BASE / (yd[0] + 1) | 0;
|
|
|
|
if (k > 1) {
|
|
yd = multiplyInteger(yd, k);
|
|
xd = multiplyInteger(xd, k);
|
|
yL = yd.length;
|
|
xL = xd.length;
|
|
}
|
|
|
|
xi = yL;
|
|
rem = xd.slice(0, yL);
|
|
remL = rem.length;
|
|
|
|
// Add zeros to make remainder as long as divisor.
|
|
for (; remL < yL;) rem[remL++] = 0;
|
|
|
|
yz = yd.slice();
|
|
yz.unshift(0);
|
|
yd0 = yd[0];
|
|
|
|
if (yd[1] >= BASE / 2) ++yd0;
|
|
|
|
do {
|
|
k = 0;
|
|
|
|
// Compare divisor and remainder.
|
|
cmp = compare(yd, rem, yL, remL);
|
|
|
|
// If divisor < remainder.
|
|
if (cmp < 0) {
|
|
|
|
// Calculate trial digit, k.
|
|
rem0 = rem[0];
|
|
if (yL != remL) rem0 = rem0 * BASE + (rem[1] || 0);
|
|
|
|
// k will be how many times the divisor goes into the current remainder.
|
|
k = rem0 / yd0 | 0;
|
|
|
|
// Algorithm:
|
|
// 1. product = divisor * trial digit (k)
|
|
// 2. if product > remainder: product -= divisor, k--
|
|
// 3. remainder -= product
|
|
// 4. if product was < remainder at 2:
|
|
// 5. compare new remainder and divisor
|
|
// 6. If remainder > divisor: remainder -= divisor, k++
|
|
|
|
if (k > 1) {
|
|
if (k >= BASE) k = BASE - 1;
|
|
|
|
// product = divisor * trial digit.
|
|
prod = multiplyInteger(yd, k);
|
|
prodL = prod.length;
|
|
remL = rem.length;
|
|
|
|
// Compare product and remainder.
|
|
cmp = compare(prod, rem, prodL, remL);
|
|
|
|
// product > remainder.
|
|
if (cmp == 1) {
|
|
k--;
|
|
|
|
// Subtract divisor from product.
|
|
subtract(prod, yL < prodL ? yz : yd, prodL);
|
|
}
|
|
} else {
|
|
|
|
// cmp is -1.
|
|
// If k is 0, there is no need to compare yd and rem again below, so change cmp to 1
|
|
// to avoid it. If k is 1 there is a need to compare yd and rem again below.
|
|
if (k == 0) cmp = k = 1;
|
|
prod = yd.slice();
|
|
}
|
|
|
|
prodL = prod.length;
|
|
if (prodL < remL) prod.unshift(0);
|
|
|
|
// Subtract product from remainder.
|
|
subtract(rem, prod, remL);
|
|
|
|
// If product was < previous remainder.
|
|
if (cmp == -1) {
|
|
remL = rem.length;
|
|
|
|
// Compare divisor and new remainder.
|
|
cmp = compare(yd, rem, yL, remL);
|
|
|
|
// If divisor < new remainder, subtract divisor from remainder.
|
|
if (cmp < 1) {
|
|
k++;
|
|
|
|
// Subtract divisor from remainder.
|
|
subtract(rem, yL < remL ? yz : yd, remL);
|
|
}
|
|
}
|
|
|
|
remL = rem.length;
|
|
} else if (cmp === 0) {
|
|
k++;
|
|
rem = [0];
|
|
} // if cmp === 1, k will be 0
|
|
|
|
// Add the next digit, k, to the result array.
|
|
qd[i++] = k;
|
|
|
|
// Update the remainder.
|
|
if (cmp && rem[0]) {
|
|
rem[remL++] = xd[xi] || 0;
|
|
} else {
|
|
rem = [xd[xi]];
|
|
remL = 1;
|
|
}
|
|
|
|
} while ((xi++ < xL || rem[0] !== void 0) && sd--);
|
|
}
|
|
|
|
// Leading zero?
|
|
if (!qd[0]) qd.shift();
|
|
|
|
q.e = e;
|
|
|
|
return round(q, dp ? pr + getBase10Exponent(q) + 1 : pr);
|
|
};
|
|
})();
|
|
|
|
|
|
/*
|
|
* Return a new Decimal whose value is the natural exponential of `x` truncated to `sd`
|
|
* significant digits.
|
|
*
|
|
* Taylor/Maclaurin series.
|
|
*
|
|
* exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ...
|
|
*
|
|
* Argument reduction:
|
|
* Repeat x = x / 32, k += 5, until |x| < 0.1
|
|
* exp(x) = exp(x / 2^k)^(2^k)
|
|
*
|
|
* Previously, the argument was initially reduced by
|
|
* exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10)
|
|
* to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was
|
|
* found to be slower than just dividing repeatedly by 32 as above.
|
|
*
|
|
* (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324)
|
|
*
|
|
* exp(x) is non-terminating for any finite, non-zero x.
|
|
*
|
|
*/
|
|
function exp(x, sd) {
|
|
var denominator, guard, pow, sum, t, wpr,
|
|
i = 0,
|
|
k = 0,
|
|
Ctor = x.constructor,
|
|
pr = Ctor.precision;
|
|
|
|
if (getBase10Exponent(x) > 16) throw Error(exponentOutOfRange + getBase10Exponent(x));
|
|
|
|
// exp(0) = 1
|
|
if (!x.s) return new Ctor(ONE);
|
|
|
|
if (sd == null) {
|
|
external = false;
|
|
wpr = pr;
|
|
} else {
|
|
wpr = sd;
|
|
}
|
|
|
|
t = new Ctor(0.03125);
|
|
|
|
while (x.abs().gte(0.1)) {
|
|
x = x.times(t); // x = x / 2^5
|
|
k += 5;
|
|
}
|
|
|
|
// Estimate the precision increase necessary to ensure the first 4 rounding digits are correct.
|
|
guard = Math.log(mathpow(2, k)) / Math.LN10 * 2 + 5 | 0;
|
|
wpr += guard;
|
|
denominator = pow = sum = new Ctor(ONE);
|
|
Ctor.precision = wpr;
|
|
|
|
for (;;) {
|
|
pow = round(pow.times(x), wpr);
|
|
denominator = denominator.times(++i);
|
|
t = sum.plus(divide(pow, denominator, wpr));
|
|
|
|
if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
|
|
while (k--) sum = round(sum.times(sum), wpr);
|
|
Ctor.precision = pr;
|
|
return sd == null ? (external = true, round(sum, pr)) : sum;
|
|
}
|
|
|
|
sum = t;
|
|
}
|
|
}
|
|
|
|
|
|
// Calculate the base 10 exponent from the base 1e7 exponent.
|
|
function getBase10Exponent(x) {
|
|
var e = x.e * LOG_BASE,
|
|
w = x.d[0];
|
|
|
|
// Add the number of digits of the first word of the digits array.
|
|
for (; w >= 10; w /= 10) e++;
|
|
return e;
|
|
}
|
|
|
|
|
|
function getLn10(Ctor, sd, pr) {
|
|
|
|
if (sd > Ctor.LN10.sd()) {
|
|
|
|
|
|
// Reset global state in case the exception is caught.
|
|
external = true;
|
|
if (pr) Ctor.precision = pr;
|
|
throw Error(decimalError + 'LN10 precision limit exceeded');
|
|
}
|
|
|
|
return round(new Ctor(Ctor.LN10), sd);
|
|
}
|
|
|
|
|
|
function getZeroString(k) {
|
|
var zs = '';
|
|
for (; k--;) zs += '0';
|
|
return zs;
|
|
}
|
|
|
|
|
|
/*
|
|
* Return a new Decimal whose value is the natural logarithm of `x` truncated to `sd` significant
|
|
* digits.
|
|
*
|
|
* ln(n) is non-terminating (n != 1)
|
|
*
|
|
*/
|
|
function ln(y, sd) {
|
|
var c, c0, denominator, e, numerator, sum, t, wpr, x2,
|
|
n = 1,
|
|
guard = 10,
|
|
x = y,
|
|
xd = x.d,
|
|
Ctor = x.constructor,
|
|
pr = Ctor.precision;
|
|
|
|
// ln(-x) = NaN
|
|
// ln(0) = -Infinity
|
|
if (x.s < 1) throw Error(decimalError + (x.s ? 'NaN' : '-Infinity'));
|
|
|
|
// ln(1) = 0
|
|
if (x.eq(ONE)) return new Ctor(0);
|
|
|
|
if (sd == null) {
|
|
external = false;
|
|
wpr = pr;
|
|
} else {
|
|
wpr = sd;
|
|
}
|
|
|
|
if (x.eq(10)) {
|
|
if (sd == null) external = true;
|
|
return getLn10(Ctor, wpr);
|
|
}
|
|
|
|
wpr += guard;
|
|
Ctor.precision = wpr;
|
|
c = digitsToString(xd);
|
|
c0 = c.charAt(0);
|
|
e = getBase10Exponent(x);
|
|
|
|
if (Math.abs(e) < 1.5e15) {
|
|
|
|
// Argument reduction.
|
|
// The series converges faster the closer the argument is to 1, so using
|
|
// ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b
|
|
// multiply the argument by itself until the leading digits of the significand are 7, 8, 9,
|
|
// 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can
|
|
// later be divided by this number, then separate out the power of 10 using
|
|
// ln(a*10^b) = ln(a) + b*ln(10).
|
|
|
|
// max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14).
|
|
//while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) {
|
|
// max n is 6 (gives 0.7 - 1.3)
|
|
while (c0 < 7 && c0 != 1 || c0 == 1 && c.charAt(1) > 3) {
|
|
x = x.times(y);
|
|
c = digitsToString(x.d);
|
|
c0 = c.charAt(0);
|
|
n++;
|
|
}
|
|
|
|
e = getBase10Exponent(x);
|
|
|
|
if (c0 > 1) {
|
|
x = new Ctor('0.' + c);
|
|
e++;
|
|
} else {
|
|
x = new Ctor(c0 + '.' + c.slice(1));
|
|
}
|
|
} else {
|
|
|
|
// The argument reduction method above may result in overflow if the argument y is a massive
|
|
// number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this
|
|
// function using ln(x*10^e) = ln(x) + e*ln(10).
|
|
t = getLn10(Ctor, wpr + 2, pr).times(e + '');
|
|
x = ln(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t);
|
|
|
|
Ctor.precision = pr;
|
|
return sd == null ? (external = true, round(x, pr)) : x;
|
|
}
|
|
|
|
// x is reduced to a value near 1.
|
|
|
|
// Taylor series.
|
|
// ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...)
|
|
// where x = (y - 1)/(y + 1) (|x| < 1)
|
|
sum = numerator = x = divide(x.minus(ONE), x.plus(ONE), wpr);
|
|
x2 = round(x.times(x), wpr);
|
|
denominator = 3;
|
|
|
|
for (;;) {
|
|
numerator = round(numerator.times(x2), wpr);
|
|
t = sum.plus(divide(numerator, new Ctor(denominator), wpr));
|
|
|
|
if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) {
|
|
sum = sum.times(2);
|
|
|
|
// Reverse the argument reduction.
|
|
if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + ''));
|
|
sum = divide(sum, new Ctor(n), wpr);
|
|
|
|
Ctor.precision = pr;
|
|
return sd == null ? (external = true, round(sum, pr)) : sum;
|
|
}
|
|
|
|
sum = t;
|
|
denominator += 2;
|
|
}
|
|
}
|
|
|
|
|
|
/*
|
|
* Parse the value of a new Decimal `x` from string `str`.
|
|
*/
|
|
function parseDecimal(x, str) {
|
|
var e, i, len;
|
|
|
|
// Decimal point?
|
|
if ((e = str.indexOf('.')) > -1) str = str.replace('.', '');
|
|
|
|
// Exponential form?
|
|
if ((i = str.search(/e/i)) > 0) {
|
|
|
|
// Determine exponent.
|
|
if (e < 0) e = i;
|
|
e += +str.slice(i + 1);
|
|
str = str.substring(0, i);
|
|
} else if (e < 0) {
|
|
|
|
// Integer.
|
|
e = str.length;
|
|
}
|
|
|
|
// Determine leading zeros.
|
|
for (i = 0; str.charCodeAt(i) === 48;) ++i;
|
|
|
|
// Determine trailing zeros.
|
|
for (len = str.length; str.charCodeAt(len - 1) === 48;) --len;
|
|
str = str.slice(i, len);
|
|
|
|
if (str) {
|
|
len -= i;
|
|
e = e - i - 1;
|
|
x.e = mathfloor(e / LOG_BASE);
|
|
x.d = [];
|
|
|
|
// Transform base
|
|
|
|
// e is the base 10 exponent.
|
|
// i is where to slice str to get the first word of the digits array.
|
|
i = (e + 1) % LOG_BASE;
|
|
if (e < 0) i += LOG_BASE;
|
|
|
|
if (i < len) {
|
|
if (i) x.d.push(+str.slice(0, i));
|
|
for (len -= LOG_BASE; i < len;) x.d.push(+str.slice(i, i += LOG_BASE));
|
|
str = str.slice(i);
|
|
i = LOG_BASE - str.length;
|
|
} else {
|
|
i -= len;
|
|
}
|
|
|
|
for (; i--;) str += '0';
|
|
x.d.push(+str);
|
|
|
|
if (external && (x.e > MAX_E || x.e < -MAX_E)) throw Error(exponentOutOfRange + e);
|
|
} else {
|
|
|
|
// Zero.
|
|
x.s = 0;
|
|
x.e = 0;
|
|
x.d = [0];
|
|
}
|
|
|
|
return x;
|
|
}
|
|
|
|
|
|
/*
|
|
* Round `x` to `sd` significant digits, using rounding mode `rm` if present (truncate otherwise).
|
|
*/
|
|
function round(x, sd, rm) {
|
|
var i, j, k, n, rd, doRound, w, xdi,
|
|
xd = x.d;
|
|
|
|
// rd: the rounding digit, i.e. the digit after the digit that may be rounded up.
|
|
// w: the word of xd which contains the rounding digit, a base 1e7 number.
|
|
// xdi: the index of w within xd.
|
|
// n: the number of digits of w.
|
|
// i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if
|
|
// they had leading zeros)
|
|
// j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero).
|
|
|
|
// Get the length of the first word of the digits array xd.
|
|
for (n = 1, k = xd[0]; k >= 10; k /= 10) n++;
|
|
i = sd - n;
|
|
|
|
// Is the rounding digit in the first word of xd?
|
|
if (i < 0) {
|
|
i += LOG_BASE;
|
|
j = sd;
|
|
w = xd[xdi = 0];
|
|
} else {
|
|
xdi = Math.ceil((i + 1) / LOG_BASE);
|
|
k = xd.length;
|
|
if (xdi >= k) return x;
|
|
w = k = xd[xdi];
|
|
|
|
// Get the number of digits of w.
|
|
for (n = 1; k >= 10; k /= 10) n++;
|
|
|
|
// Get the index of rd within w.
|
|
i %= LOG_BASE;
|
|
|
|
// Get the index of rd within w, adjusted for leading zeros.
|
|
// The number of leading zeros of w is given by LOG_BASE - n.
|
|
j = i - LOG_BASE + n;
|
|
}
|
|
|
|
if (rm !== void 0) {
|
|
k = mathpow(10, n - j - 1);
|
|
|
|
// Get the rounding digit at index j of w.
|
|
rd = w / k % 10 | 0;
|
|
|
|
// Are there any non-zero digits after the rounding digit?
|
|
doRound = sd < 0 || xd[xdi + 1] !== void 0 || w % k;
|
|
|
|
// The expression `w % mathpow(10, n - j - 1)` returns all the digits of w to the right of the
|
|
// digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression will give
|
|
// 714.
|
|
|
|
doRound = rm < 4
|
|
? (rd || doRound) && (rm == 0 || rm == (x.s < 0 ? 3 : 2))
|
|
: rd > 5 || rd == 5 && (rm == 4 || doRound || rm == 6 &&
|
|
|
|
// Check whether the digit to the left of the rounding digit is odd.
|
|
((i > 0 ? j > 0 ? w / mathpow(10, n - j) : 0 : xd[xdi - 1]) % 10) & 1 ||
|
|
rm == (x.s < 0 ? 8 : 7));
|
|
}
|
|
|
|
if (sd < 1 || !xd[0]) {
|
|
if (doRound) {
|
|
k = getBase10Exponent(x);
|
|
xd.length = 1;
|
|
|
|
// Convert sd to decimal places.
|
|
sd = sd - k - 1;
|
|
|
|
// 1, 0.1, 0.01, 0.001, 0.0001 etc.
|
|
xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE);
|
|
x.e = mathfloor(-sd / LOG_BASE) || 0;
|
|
} else {
|
|
xd.length = 1;
|
|
|
|
// Zero.
|
|
xd[0] = x.e = x.s = 0;
|
|
}
|
|
|
|
return x;
|
|
}
|
|
|
|
// Remove excess digits.
|
|
if (i == 0) {
|
|
xd.length = xdi;
|
|
k = 1;
|
|
xdi--;
|
|
} else {
|
|
xd.length = xdi + 1;
|
|
k = mathpow(10, LOG_BASE - i);
|
|
|
|
// E.g. 56700 becomes 56000 if 7 is the rounding digit.
|
|
// j > 0 means i > number of leading zeros of w.
|
|
xd[xdi] = j > 0 ? (w / mathpow(10, n - j) % mathpow(10, j) | 0) * k : 0;
|
|
}
|
|
|
|
if (doRound) {
|
|
for (;;) {
|
|
|
|
// Is the digit to be rounded up in the first word of xd?
|
|
if (xdi == 0) {
|
|
if ((xd[0] += k) == BASE) {
|
|
xd[0] = 1;
|
|
++x.e;
|
|
}
|
|
|
|
break;
|
|
} else {
|
|
xd[xdi] += k;
|
|
if (xd[xdi] != BASE) break;
|
|
xd[xdi--] = 0;
|
|
k = 1;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Remove trailing zeros.
|
|
for (i = xd.length; xd[--i] === 0;) xd.pop();
|
|
|
|
if (external && (x.e > MAX_E || x.e < -MAX_E)) {
|
|
throw Error(exponentOutOfRange + getBase10Exponent(x));
|
|
}
|
|
|
|
return x;
|
|
}
|
|
|
|
|
|
function subtract(x, y) {
|
|
var d, e, i, j, k, len, xd, xe, xLTy, yd,
|
|
Ctor = x.constructor,
|
|
pr = Ctor.precision;
|
|
|
|
// Return y negated if x is zero.
|
|
// Return x if y is zero and x is non-zero.
|
|
if (!x.s || !y.s) {
|
|
if (y.s) y.s = -y.s;
|
|
else y = new Ctor(x);
|
|
return external ? round(y, pr) : y;
|
|
}
|
|
|
|
xd = x.d;
|
|
yd = y.d;
|
|
|
|
// x and y are non-zero numbers with the same sign.
|
|
|
|
e = y.e;
|
|
xe = x.e;
|
|
xd = xd.slice();
|
|
k = xe - e;
|
|
|
|
// If exponents differ...
|
|
if (k) {
|
|
xLTy = k < 0;
|
|
|
|
if (xLTy) {
|
|
d = xd;
|
|
k = -k;
|
|
len = yd.length;
|
|
} else {
|
|
d = yd;
|
|
e = xe;
|
|
len = xd.length;
|
|
}
|
|
|
|
// Numbers with massively different exponents would result in a very high number of zeros
|
|
// needing to be prepended, but this can be avoided while still ensuring correct rounding by
|
|
// limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`.
|
|
i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2;
|
|
|
|
if (k > i) {
|
|
k = i;
|
|
d.length = 1;
|
|
}
|
|
|
|
// Prepend zeros to equalise exponents.
|
|
d.reverse();
|
|
for (i = k; i--;) d.push(0);
|
|
d.reverse();
|
|
|
|
// Base 1e7 exponents equal.
|
|
} else {
|
|
|
|
// Check digits to determine which is the bigger number.
|
|
|
|
i = xd.length;
|
|
len = yd.length;
|
|
xLTy = i < len;
|
|
if (xLTy) len = i;
|
|
|
|
for (i = 0; i < len; i++) {
|
|
if (xd[i] != yd[i]) {
|
|
xLTy = xd[i] < yd[i];
|
|
break;
|
|
}
|
|
}
|
|
|
|
k = 0;
|
|
}
|
|
|
|
if (xLTy) {
|
|
d = xd;
|
|
xd = yd;
|
|
yd = d;
|
|
y.s = -y.s;
|
|
}
|
|
|
|
len = xd.length;
|
|
|
|
// Append zeros to xd if shorter.
|
|
// Don't add zeros to yd if shorter as subtraction only needs to start at yd length.
|
|
for (i = yd.length - len; i > 0; --i) xd[len++] = 0;
|
|
|
|
// Subtract yd from xd.
|
|
for (i = yd.length; i > k;) {
|
|
if (xd[--i] < yd[i]) {
|
|
for (j = i; j && xd[--j] === 0;) xd[j] = BASE - 1;
|
|
--xd[j];
|
|
xd[i] += BASE;
|
|
}
|
|
|
|
xd[i] -= yd[i];
|
|
}
|
|
|
|
// Remove trailing zeros.
|
|
for (; xd[--len] === 0;) xd.pop();
|
|
|
|
// Remove leading zeros and adjust exponent accordingly.
|
|
for (; xd[0] === 0; xd.shift()) --e;
|
|
|
|
// Zero?
|
|
if (!xd[0]) return new Ctor(0);
|
|
|
|
y.d = xd;
|
|
y.e = e;
|
|
|
|
//return external && xd.length >= pr / LOG_BASE ? round(y, pr) : y;
|
|
return external ? round(y, pr) : y;
|
|
}
|
|
|
|
|
|
function toString(x, isExp, sd) {
|
|
var k,
|
|
e = getBase10Exponent(x),
|
|
str = digitsToString(x.d),
|
|
len = str.length;
|
|
|
|
if (isExp) {
|
|
if (sd && (k = sd - len) > 0) {
|
|
str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k);
|
|
} else if (len > 1) {
|
|
str = str.charAt(0) + '.' + str.slice(1);
|
|
}
|
|
|
|
str = str + (e < 0 ? 'e' : 'e+') + e;
|
|
} else if (e < 0) {
|
|
str = '0.' + getZeroString(-e - 1) + str;
|
|
if (sd && (k = sd - len) > 0) str += getZeroString(k);
|
|
} else if (e >= len) {
|
|
str += getZeroString(e + 1 - len);
|
|
if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k);
|
|
} else {
|
|
if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k);
|
|
if (sd && (k = sd - len) > 0) {
|
|
if (e + 1 === len) str += '.';
|
|
str += getZeroString(k);
|
|
}
|
|
}
|
|
|
|
return x.s < 0 ? '-' + str : str;
|
|
}
|
|
|
|
|
|
// Does not strip trailing zeros.
|
|
function truncate(arr, len) {
|
|
if (arr.length > len) {
|
|
arr.length = len;
|
|
return true;
|
|
}
|
|
}
|
|
|
|
|
|
// Decimal methods
|
|
|
|
|
|
/*
|
|
* clone
|
|
* config/set
|
|
*/
|
|
|
|
|
|
/*
|
|
* Create and return a Decimal constructor with the same configuration properties as this Decimal
|
|
* constructor.
|
|
*
|
|
*/
|
|
function clone(obj) {
|
|
var i, p, ps;
|
|
|
|
/*
|
|
* The Decimal constructor and exported function.
|
|
* Return a new Decimal instance.
|
|
*
|
|
* value {number|string|Decimal} A numeric value.
|
|
*
|
|
*/
|
|
function Decimal(value) {
|
|
var x = this;
|
|
|
|
// Decimal called without new.
|
|
if (!(x instanceof Decimal)) return new Decimal(value);
|
|
|
|
// Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor
|
|
// which points to Object.
|
|
x.constructor = Decimal;
|
|
|
|
// Duplicate.
|
|
if (value instanceof Decimal) {
|
|
x.s = value.s;
|
|
x.e = value.e;
|
|
x.d = (value = value.d) ? value.slice() : value;
|
|
return;
|
|
}
|
|
|
|
if (typeof value === 'number') {
|
|
|
|
// Reject Infinity/NaN.
|
|
if (value * 0 !== 0) {
|
|
throw Error(invalidArgument + value);
|
|
}
|
|
|
|
if (value > 0) {
|
|
x.s = 1;
|
|
} else if (value < 0) {
|
|
value = -value;
|
|
x.s = -1;
|
|
} else {
|
|
x.s = 0;
|
|
x.e = 0;
|
|
x.d = [0];
|
|
return;
|
|
}
|
|
|
|
// Fast path for small integers.
|
|
if (value === ~~value && value < 1e7) {
|
|
x.e = 0;
|
|
x.d = [value];
|
|
return;
|
|
}
|
|
|
|
return parseDecimal(x, value.toString());
|
|
} else if (typeof value !== 'string') {
|
|
throw Error(invalidArgument + value);
|
|
}
|
|
|
|
// Minus sign?
|
|
if (value.charCodeAt(0) === 45) {
|
|
value = value.slice(1);
|
|
x.s = -1;
|
|
} else {
|
|
x.s = 1;
|
|
}
|
|
|
|
if (isDecimal.test(value)) parseDecimal(x, value);
|
|
else throw Error(invalidArgument + value);
|
|
}
|
|
|
|
Decimal.prototype = P;
|
|
|
|
Decimal.ROUND_UP = 0;
|
|
Decimal.ROUND_DOWN = 1;
|
|
Decimal.ROUND_CEIL = 2;
|
|
Decimal.ROUND_FLOOR = 3;
|
|
Decimal.ROUND_HALF_UP = 4;
|
|
Decimal.ROUND_HALF_DOWN = 5;
|
|
Decimal.ROUND_HALF_EVEN = 6;
|
|
Decimal.ROUND_HALF_CEIL = 7;
|
|
Decimal.ROUND_HALF_FLOOR = 8;
|
|
|
|
Decimal.clone = clone;
|
|
Decimal.config = Decimal.set = config;
|
|
|
|
if (obj === void 0) obj = {};
|
|
if (obj) {
|
|
ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'LN10'];
|
|
for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p];
|
|
}
|
|
|
|
Decimal.config(obj);
|
|
|
|
return Decimal;
|
|
}
|
|
|
|
|
|
/*
|
|
* Configure global settings for a Decimal constructor.
|
|
*
|
|
* `obj` is an object with one or more of the following properties,
|
|
*
|
|
* precision {number}
|
|
* rounding {number}
|
|
* toExpNeg {number}
|
|
* toExpPos {number}
|
|
*
|
|
* E.g. Decimal.config({ precision: 20, rounding: 4 })
|
|
*
|
|
*/
|
|
function config(obj) {
|
|
if (!obj || typeof obj !== 'object') {
|
|
throw Error(decimalError + 'Object expected');
|
|
}
|
|
var i, p, v,
|
|
ps = [
|
|
'precision', 1, MAX_DIGITS,
|
|
'rounding', 0, 8,
|
|
'toExpNeg', -1 / 0, 0,
|
|
'toExpPos', 0, 1 / 0
|
|
];
|
|
|
|
for (i = 0; i < ps.length; i += 3) {
|
|
if ((v = obj[p = ps[i]]) !== void 0) {
|
|
if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v;
|
|
else throw Error(invalidArgument + p + ': ' + v);
|
|
}
|
|
}
|
|
|
|
if ((v = obj[p = 'LN10']) !== void 0) {
|
|
if (v == Math.LN10) this[p] = new this(v);
|
|
else throw Error(invalidArgument + p + ': ' + v);
|
|
}
|
|
|
|
return this;
|
|
}
|
|
|
|
|
|
// Create and configure initial Decimal constructor.
|
|
export var Decimal = clone(defaults);
|
|
|
|
// Internal constant.
|
|
ONE = new Decimal(1);
|
|
|
|
export default Decimal;
|