From 23563c7188e089929b60f9e10721c6fc43a220ff Mon Sep 17 00:00:00 2001 From: RaindropsSys Date: Thu, 22 Jun 2023 23:06:12 +0200 Subject: Updated 15 files, added includes/maintenance/deleteUnusedAssets.php and deleted 4944 files (automated) --- .../school/node_modules/decimal.js/decimal.mjs | 4898 -------------------- 1 file changed, 4898 deletions(-) delete mode 100644 includes/external/school/node_modules/decimal.js/decimal.mjs (limited to 'includes/external/school/node_modules/decimal.js/decimal.mjs') diff --git a/includes/external/school/node_modules/decimal.js/decimal.mjs b/includes/external/school/node_modules/decimal.js/decimal.mjs deleted file mode 100644 index 5d9101b..0000000 --- a/includes/external/school/node_modules/decimal.js/decimal.mjs +++ /dev/null @@ -1,4898 +0,0 @@ -/*! - * decimal.js v10.4.1 - * An arbitrary-precision Decimal type for JavaScript. - * https://github.com/MikeMcl/decimal.js - * Copyright (c) 2022 Michael Mclaughlin - * MIT Licence - */ - - -// ----------------------------------- EDITABLE DEFAULTS ------------------------------------ // - - - // The maximum exponent magnitude. - // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`. -var EXP_LIMIT = 9e15, // 0 to 9e15 - - // The limit on the value of `precision`, and on the value of the first argument to - // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`. - MAX_DIGITS = 1e9, // 0 to 1e9 - - // Base conversion alphabet. - NUMERALS = '0123456789abcdef', - - // The natural logarithm of 10 (1025 digits). - LN10 = '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058', - - // Pi (1025 digits). - PI = '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789', - - - // The initial configuration properties of the Decimal constructor. - DEFAULTS = { - - // These values must be integers within the stated ranges (inclusive). - // Most of these values can be changed at run-time using the `Decimal.config` method. - - // The maximum number of significant digits of the result of a calculation or base conversion. - // E.g. `Decimal.config({ precision: 20 });` - precision: 20, // 1 to MAX_DIGITS - - // The rounding mode used when rounding to `precision`. - // - // ROUND_UP 0 Away from zero. - // ROUND_DOWN 1 Towards zero. - // ROUND_CEIL 2 Towards +Infinity. - // ROUND_FLOOR 3 Towards -Infinity. - // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up. - // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. - // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. - // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. - // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. - // - // E.g. - // `Decimal.rounding = 4;` - // `Decimal.rounding = Decimal.ROUND_HALF_UP;` - rounding: 4, // 0 to 8 - - // The modulo mode used when calculating the modulus: a mod n. - // The quotient (q = a / n) is calculated according to the corresponding rounding mode. - // The remainder (r) is calculated as: r = a - n * q. - // - // UP 0 The remainder is positive if the dividend is negative, else is negative. - // DOWN 1 The remainder has the same sign as the dividend (JavaScript %). - // FLOOR 3 The remainder has the same sign as the divisor (Python %). - // HALF_EVEN 6 The IEEE 754 remainder function. - // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive. - // - // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian - // division (9) are commonly used for the modulus operation. The other rounding modes can also - // be used, but they may not give useful results. - modulo: 1, // 0 to 9 - - // The exponent value at and beneath which `toString` returns exponential notation. - // JavaScript numbers: -7 - toExpNeg: -7, // 0 to -EXP_LIMIT - - // The exponent value at and above which `toString` returns exponential notation. - // JavaScript numbers: 21 - toExpPos: 21, // 0 to EXP_LIMIT - - // The minimum exponent value, beneath which underflow to zero occurs. - // JavaScript numbers: -324 (5e-324) - minE: -EXP_LIMIT, // -1 to -EXP_LIMIT - - // The maximum exponent value, above which overflow to Infinity occurs. - // JavaScript numbers: 308 (1.7976931348623157e+308) - maxE: EXP_LIMIT, // 1 to EXP_LIMIT - - // Whether to use cryptographically-secure random number generation, if available. - crypto: false // true/false - }, - - -// ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- // - - - inexact, quadrant, - external = true, - - decimalError = '[DecimalError] ', - invalidArgument = decimalError + 'Invalid argument: ', - precisionLimitExceeded = decimalError + 'Precision limit exceeded', - cryptoUnavailable = decimalError + 'crypto unavailable', - tag = '[object Decimal]', - - mathfloor = Math.floor, - mathpow = Math.pow, - - isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i, - isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i, - isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i, - isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i, - - BASE = 1e7, - LOG_BASE = 7, - MAX_SAFE_INTEGER = 9007199254740991, - - LN10_PRECISION = LN10.length - 1, - PI_PRECISION = PI.length - 1, - - // Decimal.prototype object - P = { toStringTag: tag }; - - -// Decimal prototype methods - - -/* - * absoluteValue abs - * ceil - * clampedTo clamp - * comparedTo cmp - * cosine cos - * cubeRoot cbrt - * decimalPlaces dp - * dividedBy div - * dividedToIntegerBy divToInt - * equals eq - * floor - * greaterThan gt - * greaterThanOrEqualTo gte - * hyperbolicCosine cosh - * hyperbolicSine sinh - * hyperbolicTangent tanh - * inverseCosine acos - * inverseHyperbolicCosine acosh - * inverseHyperbolicSine asinh - * inverseHyperbolicTangent atanh - * inverseSine asin - * inverseTangent atan - * isFinite - * isInteger isInt - * isNaN - * isNegative isNeg - * isPositive isPos - * isZero - * lessThan lt - * lessThanOrEqualTo lte - * logarithm log - * [maximum] [max] - * [minimum] [min] - * minus sub - * modulo mod - * naturalExponential exp - * naturalLogarithm ln - * negated neg - * plus add - * precision sd - * round - * sine sin - * squareRoot sqrt - * tangent tan - * times mul - * toBinary - * toDecimalPlaces toDP - * toExponential - * toFixed - * toFraction - * toHexadecimal toHex - * toNearest - * toNumber - * toOctal - * toPower pow - * toPrecision - * toSignificantDigits toSD - * toString - * truncated trunc - * valueOf toJSON - */ - - -/* - * Return a new Decimal whose value is the absolute value of this Decimal. - * - */ -P.absoluteValue = P.abs = function () { - var x = new this.constructor(this); - if (x.s < 0) x.s = 1; - return finalise(x); -}; - - -/* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of positive Infinity. - * - */ -P.ceil = function () { - return finalise(new this.constructor(this), this.e + 1, 2); -}; - - -/* - * Return a new Decimal whose value is the value of this Decimal clamped to the range - * delineated by `min` and `max`. - * - * min {number|string|Decimal} - * max {number|string|Decimal} - * - */ -P.clampedTo = P.clamp = function (min, max) { - var k, - x = this, - Ctor = x.constructor; - min = new Ctor(min); - max = new Ctor(max); - if (!min.s || !max.s) return new Ctor(NaN); - if (min.gt(max)) throw Error(invalidArgument + max); - k = x.cmp(min); - return k < 0 ? min : x.cmp(max) > 0 ? max : new Ctor(x); -}; - - -/* - * Return - * 1 if the value of this Decimal is greater than the value of `y`, - * -1 if the value of this Decimal is less than the value of `y`, - * 0 if they have the same value, - * NaN if the value of either Decimal is NaN. - * - */ -P.comparedTo = P.cmp = function (y) { - var i, j, xdL, ydL, - x = this, - xd = x.d, - yd = (y = new x.constructor(y)).d, - xs = x.s, - ys = y.s; - - // Either NaN or ±Infinity? - if (!xd || !yd) { - return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ xs < 0 ? 1 : -1; - } - - // Either zero? - if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0; - - // Signs differ? - if (xs !== ys) return xs; - - // Compare exponents. - if (x.e !== y.e) return x.e > y.e ^ xs < 0 ? 1 : -1; - - xdL = xd.length; - ydL = yd.length; - - // Compare digit by digit. - for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) { - if (xd[i] !== yd[i]) return xd[i] > yd[i] ^ xs < 0 ? 1 : -1; - } - - // Compare lengths. - return xdL === ydL ? 0 : xdL > ydL ^ xs < 0 ? 1 : -1; -}; - - -/* - * Return a new Decimal whose value is the cosine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * cos(0) = 1 - * cos(-0) = 1 - * cos(Infinity) = NaN - * cos(-Infinity) = NaN - * cos(NaN) = NaN - * - */ -P.cosine = P.cos = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.d) return new Ctor(NaN); - - // cos(0) = cos(-0) = 1 - if (!x.d[0]) return new Ctor(1); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; - Ctor.rounding = 1; - - x = cosine(Ctor, toLessThanHalfPi(Ctor, x)); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true); -}; - - -/* - * - * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * cbrt(0) = 0 - * cbrt(-0) = -0 - * cbrt(1) = 1 - * cbrt(-1) = -1 - * cbrt(N) = N - * cbrt(-I) = -I - * cbrt(I) = I - * - * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3)) - * - */ -P.cubeRoot = P.cbrt = function () { - var e, m, n, r, rep, s, sd, t, t3, t3plusx, - x = this, - Ctor = x.constructor; - - if (!x.isFinite() || x.isZero()) return new Ctor(x); - external = false; - - // Initial estimate. - s = x.s * mathpow(x.s * x, 1 / 3); - - // Math.cbrt underflow/overflow? - // Pass x to Math.pow as integer, then adjust the exponent of the result. - if (!s || Math.abs(s) == 1 / 0) { - n = digitsToString(x.d); - e = x.e; - - // Adjust n exponent so it is a multiple of 3 away from x exponent. - if (s = (e - n.length + 1) % 3) n += (s == 1 || s == -2 ? '0' : '00'); - s = mathpow(n, 1 / 3); - - // Rarely, e may be one less than the result exponent value. - e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2)); - - if (s == 1 / 0) { - n = '5e' + e; - } else { - n = s.toExponential(); - n = n.slice(0, n.indexOf('e') + 1) + e; - } - - r = new Ctor(n); - r.s = x.s; - } else { - r = new Ctor(s.toString()); - } - - sd = (e = Ctor.precision) + 3; - - // Halley's method. - // TODO? Compare Newton's method. - for (;;) { - t = r; - t3 = t.times(t).times(t); - t3plusx = t3.plus(x); - r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1); - - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1); - - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999 - // , i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || !rep && n == '4999') { - - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0); - - if (t.times(t).times(t).eq(x)) { - r = t; - break; - } - } - - sd += 4; - rep = 1; - } else { - - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || !+n.slice(1) && n.charAt(0) == '5') { - - // Truncate to the first rounding digit. - finalise(r, e + 1, 1); - m = !r.times(r).times(r).eq(x); - } - - break; - } - } - } - - external = true; - - return finalise(r, e, Ctor.rounding, m); -}; - - -/* - * Return the number of decimal places of the value of this Decimal. - * - */ -P.decimalPlaces = P.dp = function () { - var w, - d = this.d, - n = NaN; - - if (d) { - w = d.length - 1; - n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE; - - // Subtract the number of trailing zeros of the last word. - w = d[w]; - if (w) for (; w % 10 == 0; w /= 10) n--; - if (n < 0) n = 0; - } - - return n; -}; - - -/* - * n / 0 = I - * n / N = N - * n / I = 0 - * 0 / n = 0 - * 0 / 0 = N - * 0 / N = N - * 0 / I = 0 - * N / n = N - * N / 0 = N - * N / N = N - * N / I = N - * I / n = I - * I / 0 = I - * I / N = N - * I / I = N - * - * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - */ -P.dividedBy = P.div = function (y) { - return divide(this, new this.constructor(y)); -}; - - -/* - * Return a new Decimal whose value is the integer part of dividing the value of this Decimal - * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`. - * - */ -P.dividedToIntegerBy = P.divToInt = function (y) { - var x = this, - Ctor = x.constructor; - return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding); -}; - - -/* - * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false. - * - */ -P.equals = P.eq = function (y) { - return this.cmp(y) === 0; -}; - - -/* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of negative Infinity. - * - */ -P.floor = function () { - return finalise(new this.constructor(this), this.e + 1, 3); -}; - - -/* - * Return true if the value of this Decimal is greater than the value of `y`, otherwise return - * false. - * - */ -P.greaterThan = P.gt = function (y) { - return this.cmp(y) > 0; -}; - - -/* - * Return true if the value of this Decimal is greater than or equal to the value of `y`, - * otherwise return false. - * - */ -P.greaterThanOrEqualTo = P.gte = function (y) { - var k = this.cmp(y); - return k == 1 || k === 0; -}; - - -/* - * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [1, Infinity] - * - * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ... - * - * cosh(0) = 1 - * cosh(-0) = 1 - * cosh(Infinity) = Infinity - * cosh(-Infinity) = Infinity - * cosh(NaN) = NaN - * - * x time taken (ms) result - * 1000 9 9.8503555700852349694e+433 - * 10000 25 4.4034091128314607936e+4342 - * 100000 171 1.4033316802130615897e+43429 - * 1000000 3817 1.5166076984010437725e+434294 - * 10000000 abandoned after 2 minute wait - * - * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x)) - * - */ -P.hyperbolicCosine = P.cosh = function () { - var k, n, pr, rm, len, - x = this, - Ctor = x.constructor, - one = new Ctor(1); - - if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN); - if (x.isZero()) return one; - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; - Ctor.rounding = 1; - len = x.d.length; - - // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1 - // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4)) - - // Estimate the optimum number of times to use the argument reduction. - // TODO? Estimation reused from cosine() and may not be optimal here. - if (len < 32) { - k = Math.ceil(len / 3); - n = (1 / tinyPow(4, k)).toString(); - } else { - k = 16; - n = '2.3283064365386962890625e-10'; - } - - x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true); - - // Reverse argument reduction - var cosh2_x, - i = k, - d8 = new Ctor(8); - for (; i--;) { - cosh2_x = x.times(x); - x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8)))); - } - - return finalise(x, Ctor.precision = pr, Ctor.rounding = rm, true); -}; - - -/* - * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ... - * - * sinh(0) = 0 - * sinh(-0) = -0 - * sinh(Infinity) = Infinity - * sinh(-Infinity) = -Infinity - * sinh(NaN) = NaN - * - * x time taken (ms) - * 10 2 ms - * 100 5 ms - * 1000 14 ms - * 10000 82 ms - * 100000 886 ms 1.4033316802130615897e+43429 - * 200000 2613 ms - * 300000 5407 ms - * 400000 8824 ms - * 500000 13026 ms 8.7080643612718084129e+217146 - * 1000000 48543 ms - * - * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x)) - * - */ -P.hyperbolicSine = P.sinh = function () { - var k, pr, rm, len, - x = this, - Ctor = x.constructor; - - if (!x.isFinite() || x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4; - Ctor.rounding = 1; - len = x.d.length; - - if (len < 3) { - x = taylorSeries(Ctor, 2, x, x, true); - } else { - - // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x)) - // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3)) - // 3 multiplications and 1 addition - - // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x))) - // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5))) - // 4 multiplications and 2 additions - - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len); - k = k > 16 ? 16 : k | 0; - - x = x.times(1 / tinyPow(5, k)); - x = taylorSeries(Ctor, 2, x, x, true); - - // Reverse argument reduction - var sinh2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20); - for (; k--;) { - sinh2_x = x.times(x); - x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20)))); - } - } - - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(x, pr, rm, true); -}; - - -/* - * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * tanh(x) = sinh(x) / cosh(x) - * - * tanh(0) = 0 - * tanh(-0) = -0 - * tanh(Infinity) = 1 - * tanh(-Infinity) = -1 - * tanh(NaN) = NaN - * - */ -P.hyperbolicTangent = P.tanh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(x.s); - if (x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 7; - Ctor.rounding = 1; - - return divide(x.sinh(), x.cosh(), Ctor.precision = pr, Ctor.rounding = rm); -}; - - -/* - * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of - * this Decimal. - * - * Domain: [-1, 1] - * Range: [0, pi] - * - * acos(x) = pi/2 - asin(x) - * - * acos(0) = pi/2 - * acos(-0) = pi/2 - * acos(1) = 0 - * acos(-1) = pi - * acos(1/2) = pi/3 - * acos(-1/2) = 2*pi/3 - * acos(|x| > 1) = NaN - * acos(NaN) = NaN - * - */ -P.inverseCosine = P.acos = function () { - var halfPi, - x = this, - Ctor = x.constructor, - k = x.abs().cmp(1), - pr = Ctor.precision, - rm = Ctor.rounding; - - if (k !== -1) { - return k === 0 - // |x| is 1 - ? x.isNeg() ? getPi(Ctor, pr, rm) : new Ctor(0) - // |x| > 1 or x is NaN - : new Ctor(NaN); - } - - if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5); - - // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3 - - Ctor.precision = pr + 6; - Ctor.rounding = 1; - - x = x.asin(); - halfPi = getPi(Ctor, pr + 4, rm).times(0.5); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return halfPi.minus(x); -}; - - -/* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the - * value of this Decimal. - * - * Domain: [1, Infinity] - * Range: [0, Infinity] - * - * acosh(x) = ln(x + sqrt(x^2 - 1)) - * - * acosh(x < 1) = NaN - * acosh(NaN) = NaN - * acosh(Infinity) = Infinity - * acosh(-Infinity) = NaN - * acosh(0) = NaN - * acosh(-0) = NaN - * acosh(1) = 0 - * acosh(-1) = NaN - * - */ -P.inverseHyperbolicCosine = P.acosh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN); - if (!x.isFinite()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4; - Ctor.rounding = 1; - external = false; - - x = x.times(x).minus(1).sqrt().plus(x); - - external = true; - Ctor.precision = pr; - Ctor.rounding = rm; - - return x.ln(); -}; - - -/* - * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * asinh(x) = ln(x + sqrt(x^2 + 1)) - * - * asinh(NaN) = NaN - * asinh(Infinity) = Infinity - * asinh(-Infinity) = -Infinity - * asinh(0) = 0 - * asinh(-0) = -0 - * - */ -P.inverseHyperbolicSine = P.asinh = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite() || x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6; - Ctor.rounding = 1; - external = false; - - x = x.times(x).plus(1).sqrt().plus(x); - - external = true; - Ctor.precision = pr; - Ctor.rounding = rm; - - return x.ln(); -}; - - -/* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the - * value of this Decimal. - * - * Domain: [-1, 1] - * Range: [-Infinity, Infinity] - * - * atanh(x) = 0.5 * ln((1 + x) / (1 - x)) - * - * atanh(|x| > 1) = NaN - * atanh(NaN) = NaN - * atanh(Infinity) = NaN - * atanh(-Infinity) = NaN - * atanh(0) = 0 - * atanh(-0) = -0 - * atanh(1) = Infinity - * atanh(-1) = -Infinity - * - */ -P.inverseHyperbolicTangent = P.atanh = function () { - var pr, rm, wpr, xsd, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(NaN); - if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN); - - pr = Ctor.precision; - rm = Ctor.rounding; - xsd = x.sd(); - - if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true); - - Ctor.precision = wpr = xsd - x.e; - - x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1); - - Ctor.precision = pr + 4; - Ctor.rounding = 1; - - x = x.ln(); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return x.times(0.5); -}; - - -/* - * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2))) - * - * asin(0) = 0 - * asin(-0) = -0 - * asin(1/2) = pi/6 - * asin(-1/2) = -pi/6 - * asin(1) = pi/2 - * asin(-1) = -pi/2 - * asin(|x| > 1) = NaN - * asin(NaN) = NaN - * - * TODO? Compare performance of Taylor series. - * - */ -P.inverseSine = P.asin = function () { - var halfPi, k, - pr, rm, - x = this, - Ctor = x.constructor; - - if (x.isZero()) return new Ctor(x); - - k = x.abs().cmp(1); - pr = Ctor.precision; - rm = Ctor.rounding; - - if (k !== -1) { - - // |x| is 1 - if (k === 0) { - halfPi = getPi(Ctor, pr + 4, rm).times(0.5); - halfPi.s = x.s; - return halfPi; - } - - // |x| > 1 or x is NaN - return new Ctor(NaN); - } - - // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6 - - Ctor.precision = pr + 6; - Ctor.rounding = 1; - - x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan(); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return x.times(2); -}; - - -/* - * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - * - * atan(0) = 0 - * atan(-0) = -0 - * atan(1) = pi/4 - * atan(-1) = -pi/4 - * atan(Infinity) = pi/2 - * atan(-Infinity) = -pi/2 - * atan(NaN) = NaN - * - */ -P.inverseTangent = P.atan = function () { - var i, j, k, n, px, t, r, wpr, x2, - x = this, - Ctor = x.constructor, - pr = Ctor.precision, - rm = Ctor.rounding; - - if (!x.isFinite()) { - if (!x.s) return new Ctor(NaN); - if (pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.5); - r.s = x.s; - return r; - } - } else if (x.isZero()) { - return new Ctor(x); - } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.25); - r.s = x.s; - return r; - } - - Ctor.precision = wpr = pr + 10; - Ctor.rounding = 1; - - // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x); - - // Argument reduction - // Ensure |x| < 0.42 - // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2))) - - k = Math.min(28, wpr / LOG_BASE + 2 | 0); - - for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1)); - - external = false; - - j = Math.ceil(wpr / LOG_BASE); - n = 1; - x2 = x.times(x); - r = new Ctor(x); - px = x; - - // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - for (; i !== -1;) { - px = px.times(x2); - t = r.minus(px.div(n += 2)); - - px = px.times(x2); - r = t.plus(px.div(n += 2)); - - if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--;); - } - - if (k) r = r.times(2 << (k - 1)); - - external = true; - - return finalise(r, Ctor.precision = pr, Ctor.rounding = rm, true); -}; - - -/* - * Return true if the value of this Decimal is a finite number, otherwise return false. - * - */ -P.isFinite = function () { - return !!this.d; -}; - - -/* - * Return true if the value of this Decimal is an integer, otherwise return false. - * - */ -P.isInteger = P.isInt = function () { - return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2; -}; - - -/* - * Return true if the value of this Decimal is NaN, otherwise return false. - * - */ -P.isNaN = function () { - return !this.s; -}; - - -/* - * Return true if the value of this Decimal is negative, otherwise return false. - * - */ -P.isNegative = P.isNeg = function () { - return this.s < 0; -}; - - -/* - * Return true if the value of this Decimal is positive, otherwise return false. - * - */ -P.isPositive = P.isPos = function () { - return this.s > 0; -}; - - -/* - * Return true if the value of this Decimal is 0 or -0, otherwise return false. - * - */ -P.isZero = function () { - return !!this.d && this.d[0] === 0; -}; - - -/* - * Return true if the value of this Decimal is less than `y`, otherwise return false. - * - */ -P.lessThan = P.lt = function (y) { - return this.cmp(y) < 0; -}; - - -/* - * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false. - * - */ -P.lessThanOrEqualTo = P.lte = function (y) { - return this.cmp(y) < 1; -}; - - -/* - * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * If no base is specified, return log[10](arg). - * - * log[base](arg) = ln(arg) / ln(base) - * - * The result will always be correctly rounded if the base of the log is 10, and 'almost always' - * otherwise: - * - * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen - * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error - * between the result and the correctly rounded result will be one ulp (unit in the last place). - * - * log[-b](a) = NaN - * log[0](a) = NaN - * log[1](a) = NaN - * log[NaN](a) = NaN - * log[Infinity](a) = NaN - * log[b](0) = -Infinity - * log[b](-0) = -Infinity - * log[b](-a) = NaN - * log[b](1) = 0 - * log[b](Infinity) = Infinity - * log[b](NaN) = NaN - * - * [base] {number|string|Decimal} The base of the logarithm. - * - */ -P.logarithm = P.log = function (base) { - var isBase10, d, denominator, k, inf, num, sd, r, - arg = this, - Ctor = arg.constructor, - pr = Ctor.precision, - rm = Ctor.rounding, - guard = 5; - - // Default base is 10. - if (base == null) { - base = new Ctor(10); - isBase10 = true; - } else { - base = new Ctor(base); - d = base.d; - - // Return NaN if base is negative, or non-finite, or is 0 or 1. - if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN); - - isBase10 = base.eq(10); - } - - d = arg.d; - - // Is arg negative, non-finite, 0 or 1? - if (arg.s < 0 || !d || !d[0] || arg.eq(1)) { - return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0); - } - - // The result will have a non-terminating decimal expansion if base is 10 and arg is not an - // integer power of 10. - if (isBase10) { - if (d.length > 1) { - inf = true; - } else { - for (k = d[0]; k % 10 === 0;) k /= 10; - inf = k !== 1; - } - } - - external = false; - sd = pr + guard; - num = naturalLogarithm(arg, sd); - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - - // The result will have 5 rounding digits. - r = divide(num, denominator, sd, 1); - - // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000, - // calculate 10 further digits. - // - // If the result is known to have an infinite decimal expansion, repeat this until it is clear - // that the result is above or below the boundary. Otherwise, if after calculating the 10 - // further digits, the last 14 are nines, round up and assume the result is exact. - // Also assume the result is exact if the last 14 are zero. - // - // Example of a result that will be incorrectly rounded: - // log[1048576](4503599627370502) = 2.60000000000000009610279511444746... - // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it - // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so - // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal - // place is still 2.6. - if (checkRoundingDigits(r.d, k = pr, rm)) { - - do { - sd += 10; - num = naturalLogarithm(arg, sd); - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd); - r = divide(num, denominator, sd, 1); - - if (!inf) { - - // Check for 14 nines from the 2nd rounding digit, as the first may be 4. - if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0); - } - - break; - } - } while (checkRoundingDigits(r.d, k += 10, rm)); - } - - external = true; - - return finalise(r, pr, rm); -}; - - -/* - * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * -P.max = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'lt'); -}; - */ - - -/* - * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * -P.min = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'gt'); -}; - */ - - -/* - * n - 0 = n - * n - N = N - * n - I = -I - * 0 - n = -n - * 0 - 0 = 0 - * 0 - N = N - * 0 - I = -I - * N - n = N - * N - 0 = N - * N - N = N - * N - I = N - * I - n = I - * I - 0 = I - * I - N = N - * I - I = N - * - * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ -P.minus = P.sub = function (y) { - var d, e, i, j, k, len, pr, rm, xd, xe, xLTy, yd, - x = this, - Ctor = x.constructor; - - y = new Ctor(y); - - // If either is not finite... - if (!x.d || !y.d) { - - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN); - - // Return y negated if x is finite and y is ±Infinity. - else if (x.d) y.s = -y.s; - - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with different signs. - // Return NaN if both are ±Infinity with the same sign. - else y = new Ctor(y.d || x.s !== y.s ? x : NaN); - - return y; - } - - // If signs differ... - if (x.s != y.s) { - y.s = -y.s; - return x.plus(y); - } - - xd = x.d; - yd = y.d; - pr = Ctor.precision; - rm = Ctor.rounding; - - // If either is zero... - if (!xd[0] || !yd[0]) { - - // Return y negated if x is zero and y is non-zero. - if (yd[0]) y.s = -y.s; - - // Return x if y is zero and x is non-zero. - else if (xd[0]) y = new Ctor(x); - - // Return zero if both are zero. - // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity. - else return new Ctor(rm === 3 ? -0 : 0); - - return external ? finalise(y, pr, rm) : y; - } - - // x and y are finite, non-zero numbers with the same sign. - - // Calculate base 1e7 exponents. - e = mathfloor(y.e / LOG_BASE); - xe = mathfloor(x.e / LOG_BASE); - - xd = xd.slice(); - k = xe - e; - - // If base 1e7 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(rm === 3 ? -0 : 0); - - y.d = xd; - y.e = getBase10Exponent(xd, e); - - return external ? finalise(y, pr, rm) : y; -}; - - -/* - * n % 0 = N - * n % N = N - * n % I = n - * 0 % n = 0 - * -0 % n = -0 - * 0 % 0 = N - * 0 % N = N - * 0 % I = 0 - * N % n = N - * N % 0 = N - * N % N = N - * N % I = N - * I % n = N - * I % 0 = N - * I % N = N - * I % I = N - * - * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * The result depends on the modulo mode. - * - */ -P.modulo = P.mod = function (y) { - var q, - x = this, - Ctor = x.constructor; - - y = new Ctor(y); - - // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0. - if (!x.d || !y.s || y.d && !y.d[0]) return new Ctor(NaN); - - // Return x if y is ±Infinity or x is ±0. - if (!y.d || x.d && !x.d[0]) { - return finalise(new Ctor(x), Ctor.precision, Ctor.rounding); - } - - // Prevent rounding of intermediate calculations. - external = false; - - if (Ctor.modulo == 9) { - - // Euclidian division: q = sign(y) * floor(x / abs(y)) - // result = x - q * y where 0 <= result < abs(y) - q = divide(x, y.abs(), 0, 3, 1); - q.s *= y.s; - } else { - q = divide(x, y, 0, Ctor.modulo, 1); - } - - q = q.times(y); - - external = true; - - return x.minus(q); -}; - - -/* - * Return a new Decimal whose value is the natural exponential of the value of this Decimal, - * i.e. the base e raised to the power the value of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ -P.naturalExponential = P.exp = function () { - return naturalExponential(this); -}; - - -/* - * Return a new Decimal whose value is the natural logarithm of the value of this Decimal, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - */ -P.naturalLogarithm = P.ln = function () { - return naturalLogarithm(this); -}; - - -/* - * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by - * -1. - * - */ -P.negated = P.neg = function () { - var x = new this.constructor(this); - x.s = -x.s; - return finalise(x); -}; - - -/* - * n + 0 = n - * n + N = N - * n + I = I - * 0 + n = n - * 0 + 0 = 0 - * 0 + N = N - * 0 + I = I - * N + n = N - * N + 0 = N - * N + N = N - * N + I = N - * I + n = I - * I + 0 = I - * I + N = N - * I + I = I - * - * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ -P.plus = P.add = function (y) { - var carry, d, e, i, k, len, pr, rm, xd, yd, - x = this, - Ctor = x.constructor; - - y = new Ctor(y); - - // If either is not finite... - if (!x.d || !y.d) { - - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN); - - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with the same sign. - // Return NaN if both are ±Infinity with different signs. - // Return y if x is finite and y is ±Infinity. - else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN); - - return y; - } - - // If signs differ... - if (x.s != y.s) { - y.s = -y.s; - return x.minus(y); - } - - xd = x.d; - yd = y.d; - pr = Ctor.precision; - rm = Ctor.rounding; - - // If either is zero... - if (!xd[0] || !yd[0]) { - - // Return x if y is zero. - // Return y if y is non-zero. - if (!yd[0]) y = new Ctor(x); - - return external ? finalise(y, pr, rm) : y; - } - - // x and y are finite, non-zero numbers with the same sign. - - // Calculate base 1e7 exponents. - k = mathfloor(x.e / LOG_BASE); - e = mathfloor(y.e / LOG_BASE); - - 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 = getBase10Exponent(xd, e); - - return external ? finalise(y, pr, rm) : y; -}; - - -/* - * Return the number of significant digits of the value of this Decimal. - * - * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0. - * - */ -P.precision = P.sd = function (z) { - var k, - x = this; - - if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z); - - if (x.d) { - k = getPrecision(x.d); - if (z && x.e + 1 > k) k = x.e + 1; - } else { - k = NaN; - } - - return k; -}; - - -/* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using - * rounding mode `rounding`. - * - */ -P.round = function () { - var x = this, - Ctor = x.constructor; - - return finalise(new Ctor(x), x.e + 1, Ctor.rounding); -}; - - -/* - * Return a new Decimal whose value is the sine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * sin(x) = x - x^3/3! + x^5/5! - ... - * - * sin(0) = 0 - * sin(-0) = -0 - * sin(Infinity) = NaN - * sin(-Infinity) = NaN - * sin(NaN) = NaN - * - */ -P.sine = P.sin = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(NaN); - if (x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE; - Ctor.rounding = 1; - - x = sine(Ctor, toLessThanHalfPi(Ctor, x)); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true); -}; - - -/* - * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * sqrt(-n) = N - * sqrt(N) = N - * sqrt(-I) = N - * sqrt(I) = I - * sqrt(0) = 0 - * sqrt(-0) = -0 - * - */ -P.squareRoot = P.sqrt = function () { - var m, n, sd, r, rep, t, - x = this, - d = x.d, - e = x.e, - s = x.s, - Ctor = x.constructor; - - // Negative/NaN/Infinity/zero? - if (s !== 1 || !d || !d[0]) { - return new Ctor(!s || s < 0 && (!d || d[0]) ? NaN : d ? x : 1 / 0); - } - - external = false; - - // Initial estimate. - s = Math.sqrt(+x); - - // Math.sqrt underflow/overflow? - // Pass x to Math.sqrt as integer, then adjust the exponent of the result. - if (s == 0 || s == 1 / 0) { - n = digitsToString(d); - - if ((n.length + e) % 2 == 0) n += '0'; - s = Math.sqrt(n); - e = mathfloor((e + 1) / 2) - (e < 0 || e % 2); - - if (s == 1 / 0) { - n = '5e' + e; - } else { - n = s.toExponential(); - n = n.slice(0, n.indexOf('e') + 1) + e; - } - - r = new Ctor(n); - } else { - r = new Ctor(s.toString()); - } - - sd = (e = Ctor.precision) + 3; - - // Newton-Raphson iteration. - for (;;) { - t = r; - r = t.plus(divide(x, t, sd + 2, 1)).times(0.5); - - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1); - - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or - // 4999, i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || !rep && n == '4999') { - - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0); - - if (t.times(t).eq(x)) { - r = t; - break; - } - } - - sd += 4; - rep = 1; - } else { - - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || !+n.slice(1) && n.charAt(0) == '5') { - - // Truncate to the first rounding digit. - finalise(r, e + 1, 1); - m = !r.times(r).eq(x); - } - - break; - } - } - } - - external = true; - - return finalise(r, e, Ctor.rounding, m); -}; - - -/* - * Return a new Decimal whose value is the tangent of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * tan(0) = 0 - * tan(-0) = -0 - * tan(Infinity) = NaN - * tan(-Infinity) = NaN - * tan(NaN) = NaN - * - */ -P.tangent = P.tan = function () { - var pr, rm, - x = this, - Ctor = x.constructor; - - if (!x.isFinite()) return new Ctor(NaN); - if (x.isZero()) return new Ctor(x); - - pr = Ctor.precision; - rm = Ctor.rounding; - Ctor.precision = pr + 10; - Ctor.rounding = 1; - - x = x.sin(); - x.s = 1; - x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0); - - Ctor.precision = pr; - Ctor.rounding = rm; - - return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true); -}; - - -/* - * n * 0 = 0 - * n * N = N - * n * I = I - * 0 * n = 0 - * 0 * 0 = 0 - * 0 * N = N - * 0 * I = N - * N * n = N - * N * 0 = N - * N * N = N - * N * I = N - * I * n = I - * I * 0 = N - * I * N = N - * I * I = I - * - * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - */ -P.times = P.mul = function (y) { - var carry, e, i, k, r, rL, t, xdL, ydL, - x = this, - Ctor = x.constructor, - xd = x.d, - yd = (y = new Ctor(y)).d; - - y.s *= x.s; - - // If either is NaN, ±Infinity or ±0... - if (!xd || !xd[0] || !yd || !yd[0]) { - - return new Ctor(!y.s || xd && !xd[0] && !yd || yd && !yd[0] && !xd - - // Return NaN if either is NaN. - // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity. - ? NaN - - // Return ±Infinity if either is ±Infinity. - // Return ±0 if either is ±0. - : !xd || !yd ? y.s / 0 : y.s * 0); - } - - e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE); - 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 = getBase10Exponent(r, e); - - return external ? finalise(y, Ctor.precision, Ctor.rounding) : y; -}; - - -/* - * Return a string representing the value of this Decimal in base 2, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ -P.toBinary = function (sd, rm) { - return toStringBinary(this, 2, sd, rm); -}; - - -/* - * 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 finalise(x, dp + x.e + 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 = finiteToString(x, true); - } else { - checkInt32(dp, 0, MAX_DIGITS); - - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - - x = finalise(new Ctor(x), dp + 1, rm); - str = finiteToString(x, true, dp + 1); - } - - return x.isNeg() && !x.isZero() ? '-' + str : 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) { - str = finiteToString(x); - } else { - checkInt32(dp, 0, MAX_DIGITS); - - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - - y = finalise(new Ctor(x), dp + x.e + 1, rm); - str = finiteToString(y, false, dp + y.e + 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 an array representing the value of this Decimal as a simple fraction with an integer - * numerator and an integer denominator. - * - * The denominator will be a positive non-zero value less than or equal to the specified maximum - * denominator. If a maximum denominator is not specified, the denominator will be the lowest - * value necessary to represent the number exactly. - * - * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity. - * - */ -P.toFraction = function (maxD) { - var d, d0, d1, d2, e, k, n, n0, n1, pr, q, r, - x = this, - xd = x.d, - Ctor = x.constructor; - - if (!xd) return new Ctor(x); - - n1 = d0 = new Ctor(1); - d1 = n0 = new Ctor(0); - - d = new Ctor(d1); - e = d.e = getPrecision(xd) - x.e - 1; - k = e % LOG_BASE; - d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k); - - if (maxD == null) { - - // d is 10**e, the minimum max-denominator needed. - maxD = e > 0 ? d : n1; - } else { - n = new Ctor(maxD); - if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n); - maxD = n.gt(d) ? (e > 0 ? d : n1) : n; - } - - external = false; - n = new Ctor(digitsToString(xd)); - pr = Ctor.precision; - Ctor.precision = e = xd.length * LOG_BASE * 2; - - for (;;) { - q = divide(n, d, 0, 1, 1); - d2 = d0.plus(q.times(d1)); - if (d2.cmp(maxD) == 1) break; - d0 = d1; - d1 = d2; - d2 = n1; - n1 = n0.plus(q.times(d2)); - n0 = d2; - d2 = d; - d = n.minus(q.times(d2)); - n = d2; - } - - d2 = divide(maxD.minus(d0), d1, 0, 1, 1); - n0 = n0.plus(d2.times(n1)); - d0 = d0.plus(d2.times(d1)); - n0.s = n1.s = x.s; - - // Determine which fraction is closer to x, n0/d0 or n1/d1? - r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1 - ? [n1, d1] : [n0, d0]; - - Ctor.precision = pr; - external = true; - - return r; -}; - - -/* - * Return a string representing the value of this Decimal in base 16, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ -P.toHexadecimal = P.toHex = function (sd, rm) { - return toStringBinary(this, 16, sd, rm); -}; - - -/* - * Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding - * mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal. - * - * The return value will always have the same sign as this Decimal, unless either this Decimal - * or `y` is NaN, in which case the return value will be also be NaN. - * - * The return value is not affected by the value of `precision`. - * - * y {number|string|Decimal} The magnitude to round to a multiple of. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toNearest() rounding mode not an integer: {rm}' - * 'toNearest() rounding mode out of range: {rm}' - * - */ -P.toNearest = function (y, rm) { - var x = this, - Ctor = x.constructor; - - x = new Ctor(x); - - if (y == null) { - - // If x is not finite, return x. - if (!x.d) return x; - - y = new Ctor(1); - rm = Ctor.rounding; - } else { - y = new Ctor(y); - if (rm === void 0) { - rm = Ctor.rounding; - } else { - checkInt32(rm, 0, 8); - } - - // If x is not finite, return x if y is not NaN, else NaN. - if (!x.d) return y.s ? x : y; - - // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN. - if (!y.d) { - if (y.s) y.s = x.s; - return y; - } - } - - // If y is not zero, calculate the nearest multiple of y to x. - if (y.d[0]) { - external = false; - x = divide(x, y, 0, rm, 1).times(y); - external = true; - finalise(x); - - // If y is zero, return zero with the sign of x. - } else { - y.s = x.s; - x = y; - } - - return x; -}; - - -/* - * Return the value of this Decimal converted to a number primitive. - * Zero keeps its sign. - * - */ -P.toNumber = function () { - return +this; -}; - - -/* - * Return a string representing the value of this Decimal in base 8, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ -P.toOctal = function (sd, rm) { - return toStringBinary(this, 8, sd, rm); -}; - - -/* - * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded - * to `precision` significant digits using rounding mode `rounding`. - * - * ECMAScript compliant. - * - * pow(x, NaN) = NaN - * pow(x, ±0) = 1 - - * pow(NaN, non-zero) = NaN - * pow(abs(x) > 1, +Infinity) = +Infinity - * pow(abs(x) > 1, -Infinity) = +0 - * pow(abs(x) == 1, ±Infinity) = NaN - * pow(abs(x) < 1, +Infinity) = +0 - * pow(abs(x) < 1, -Infinity) = +Infinity - * pow(+Infinity, y > 0) = +Infinity - * pow(+Infinity, y < 0) = +0 - * pow(-Infinity, odd integer > 0) = -Infinity - * pow(-Infinity, even integer > 0) = +Infinity - * pow(-Infinity, odd integer < 0) = -0 - * pow(-Infinity, even integer < 0) = +0 - * pow(+0, y > 0) = +0 - * pow(+0, y < 0) = +Infinity - * pow(-0, odd integer > 0) = -0 - * pow(-0, even integer > 0) = +0 - * pow(-0, odd integer < 0) = -Infinity - * pow(-0, even integer < 0) = +Infinity - * pow(finite x < 0, finite non-integer) = NaN - * - * For non-integer or very large exponents pow(x, y) is calculated using - * - * x^y = exp(y*ln(x)) - * - * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the - * probability of an incorrectly rounded result - * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14 - * i.e. 1 in 250,000,000,000,000 - * - * If a result is incorrectly rounded the maximum error will be 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, rm, s, - x = this, - Ctor = x.constructor, - yn = +(y = new Ctor(y)); - - // Either ±Infinity, NaN or ±0? - if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn)); - - x = new Ctor(x); - - if (x.eq(1)) return x; - - pr = Ctor.precision; - rm = Ctor.rounding; - - if (y.eq(1)) return finalise(x, pr, rm); - - // y exponent - e = mathfloor(y.e / LOG_BASE); - - // If y is a small integer use the 'exponentiation by squaring' algorithm. - if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) { - r = intPow(Ctor, x, k, pr); - return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm); - } - - s = x.s; - - // if x is negative - if (s < 0) { - - // if y is not an integer - if (e < y.d.length - 1) return new Ctor(NaN); - - // Result is positive if x is negative and the last digit of integer y is even. - if ((y.d[e] & 1) == 0) s = 1; - - // if x.eq(-1) - if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) { - x.s = s; - return x; - } - } - - // Estimate result exponent. - // x^y = 10^e, where e = y * log10(x) - // log10(x) = log10(x_significand) + x_exponent - // log10(x_significand) = ln(x_significand) / ln(10) - k = mathpow(+x, yn); - e = k == 0 || !isFinite(k) - ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1)) - : new Ctor(k + '').e; - - // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1. - - // Overflow/underflow? - if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0); - - external = false; - Ctor.rounding = x.s = 1; - - // Estimate the extra guard digits needed to ensure five correct rounding digits from - // naturalLogarithm(x). Example of failure without these extra digits (precision: 10): - // new Decimal(2.32456).pow('2087987436534566.46411') - // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815 - k = Math.min(12, (e + '').length); - - // r = x^y = exp(y*ln(x)) - r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr); - - // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40) - if (r.d) { - - // Truncate to the required precision plus five rounding digits. - r = finalise(r, pr + 5, 1); - - // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate - // the result. - if (checkRoundingDigits(r.d, pr, rm)) { - e = pr + 10; - - // Truncate to the increased precision plus five rounding digits. - r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1); - - // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9). - if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0); - } - } - } - - r.s = s; - external = true; - Ctor.rounding = rm; - - return finalise(r, pr, rm); -}; - - -/* - * 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 str, - x = this, - Ctor = x.constructor; - - if (sd === void 0) { - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - } else { - checkInt32(sd, 1, MAX_DIGITS); - - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - - x = finalise(new Ctor(x), sd, rm); - str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd); - } - - return x.isNeg() && !x.isZero() ? '-' + str : 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. - * - * 'toSD() digits out of range: {sd}' - * 'toSD() digits not an integer: {sd}' - * 'toSD() rounding mode not an integer: {rm}' - * 'toSD() rounding mode out of range: {rm}' - * - */ -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 finalise(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 = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - - return x.isNeg() && !x.isZero() ? '-' + str : str; -}; - - -/* - * Return a new Decimal whose value is the value of this Decimal truncated to a whole number. - * - */ -P.truncated = P.trunc = function () { - return finalise(new this.constructor(this), this.e + 1, 1); -}; - - -/* - * Return a string representing the value of this Decimal. - * Unlike `toString`, negative zero will include the minus sign. - * - */ -P.valueOf = P.toJSON = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos); - - return x.isNeg() ? '-' + str : str; -}; - - -// Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers. - - -/* - * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower, - * finiteToString, naturalExponential, naturalLogarithm - * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest, - * P.toPrecision, P.toSignificantDigits, toStringBinary, random - * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm - * convertBase toStringBinary, parseOther - * cos P.cos - * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy, - * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction, - * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm, - * taylorSeries, atan2, parseOther - * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh, - * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus, - * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot, - * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed, - * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits, - * P.truncated, divide, getLn10, getPi, naturalExponential, - * naturalLogarithm, ceil, floor, round, trunc - * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf, - * toStringBinary - * getBase10Exponent P.minus, P.plus, P.times, parseOther - * getLn10 P.logarithm, naturalLogarithm - * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2 - * getPrecision P.precision, P.toFraction - * getZeroString digitsToString, finiteToString - * intPow P.toPower, parseOther - * isOdd toLessThanHalfPi - * maxOrMin max, min - * naturalExponential P.naturalExponential, P.toPower - * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm, - * P.toPower, naturalExponential - * nonFiniteToString finiteToString, toStringBinary - * parseDecimal Decimal - * parseOther Decimal - * sin P.sin - * taylorSeries P.cosh, P.sinh, cos, sin - * toLessThanHalfPi P.cos, P.sin - * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal - * truncate intPow - * - * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi, - * naturalLogarithm, config, parseOther, random, Decimal - */ - - -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; -} - - -function checkInt32(i, min, max) { - if (i !== ~~i || i < min || i > max) { - throw Error(invalidArgument + i); - } -} - - -/* - * Check 5 rounding digits if `repeating` is null, 4 otherwise. - * `repeating == null` if caller is `log` or `pow`, - * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`. - */ -function checkRoundingDigits(d, i, rm, repeating) { - var di, k, r, rd; - - // Get the length of the first word of the array d. - for (k = d[0]; k >= 10; k /= 10) --i; - - // Is the rounding digit in the first word of d? - if (--i < 0) { - i += LOG_BASE; - di = 0; - } else { - di = Math.ceil((i + 1) / LOG_BASE); - i %= LOG_BASE; - } - - // i is the index (0 - 6) of the rounding digit. - // E.g. if within the word 3487563 the first rounding digit is 5, - // then i = 4, k = 1000, rd = 3487563 % 1000 = 563 - k = mathpow(10, LOG_BASE - i); - rd = d[di] % k | 0; - - if (repeating == null) { - if (i < 3) { - if (i == 0) rd = rd / 100 | 0; - else if (i == 1) rd = rd / 10 | 0; - r = rm < 4 && rd == 99999 || rm > 3 && rd == 49999 || rd == 50000 || rd == 0; - } else { - r = (rm < 4 && rd + 1 == k || rm > 3 && rd + 1 == k / 2) && - (d[di + 1] / k / 100 | 0) == mathpow(10, i - 2) - 1 || - (rd == k / 2 || rd == 0) && (d[di + 1] / k / 100 | 0) == 0; - } - } else { - if (i < 4) { - if (i == 0) rd = rd / 1000 | 0; - else if (i == 1) rd = rd / 100 | 0; - else if (i == 2) rd = rd / 10 | 0; - r = (repeating || rm < 4) && rd == 9999 || !repeating && rm > 3 && rd == 4999; - } else { - r = ((repeating || rm < 4) && rd + 1 == k || - (!repeating && rm > 3) && rd + 1 == k / 2) && - (d[di + 1] / k / 1000 | 0) == mathpow(10, i - 3) - 1; - } - } - - return r; -} - - -// Convert string of `baseIn` to an array of numbers of `baseOut`. -// Eg. convertBase('255', 10, 16) returns [15, 15]. -// Eg. convertBase('ff', 16, 10) returns [2, 5, 5]. -function convertBase(str, baseIn, baseOut) { - var j, - arr = [0], - arrL, - i = 0, - strL = str.length; - - for (; i < strL;) { - for (arrL = arr.length; arrL--;) arr[arrL] *= baseIn; - arr[0] += NUMERALS.indexOf(str.charAt(i++)); - for (j = 0; j < arr.length; j++) { - if (arr[j] > baseOut - 1) { - if (arr[j + 1] === void 0) arr[j + 1] = 0; - arr[j + 1] += arr[j] / baseOut | 0; - arr[j] %= baseOut; - } - } - } - - return arr.reverse(); -} - - -/* - * cos(x) = 1 - x^2/2! + x^4/4! - ... - * |x| < pi/2 - * - */ -function cosine(Ctor, x) { - var k, len, y; - - if (x.isZero()) return x; - - // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1 - // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1 - - // Estimate the optimum number of times to use the argument reduction. - len = x.d.length; - if (len < 32) { - k = Math.ceil(len / 3); - y = (1 / tinyPow(4, k)).toString(); - } else { - k = 16; - y = '2.3283064365386962890625e-10'; - } - - Ctor.precision += k; - - x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1)); - - // Reverse argument reduction - for (var i = k; i--;) { - var cos2x = x.times(x); - x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1); - } - - Ctor.precision -= k; - - return x; -} - - -/* - * Perform division in the specified base. - */ -var divide = (function () { - - // Assumes non-zero x and k, and hence non-zero result. - function multiplyInteger(x, k, base) { - 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, base) { - 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, rm, dp, base) { - var cmp, e, i, k, logBase, more, 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 NaN, Infinity or 0? - if (!xd || !xd[0] || !yd || !yd[0]) { - - return new Ctor(// Return NaN if either NaN, or both Infinity or 0. - !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) ? NaN : - - // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0. - xd && xd[0] == 0 || !yd ? sign * 0 : sign / 0); - } - - if (base) { - logBase = 1; - e = x.e - y.e; - } else { - base = BASE; - logBase = LOG_BASE; - e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase); - } - - yL = yd.length; - xL = xd.length; - q = new Ctor(sign); - qd = q.d = []; - - // Result exponent may be one less than e. - // The digit array of a Decimal from toStringBinary may have trailing zeros. - for (i = 0; yd[i] == (xd[i] || 0); i++); - - if (yd[i] > (xd[i] || 0)) e--; - - if (pr == null) { - sd = pr = Ctor.precision; - rm = Ctor.rounding; - } else if (dp) { - sd = pr + (x.e - y.e) + 1; - } else { - sd = pr; - } - - if (sd < 0) { - qd.push(1); - more = true; - } else { - - // Convert precision in number of base 10 digits to base 1e7 digits. - sd = sd / logBase + 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; - } - - more = k || i < xL; - - // 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, base); - xd = multiplyInteger(xd, k, base); - 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, base); - 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, base); - } - } 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, base); - - // 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, base); - } - } - - 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--); - - more = rem[0] !== void 0; - } - - // Leading zero? - if (!qd[0]) qd.shift(); - } - - // logBase is 1 when divide is being used for base conversion. - if (logBase == 1) { - q.e = e; - inexact = more; - } else { - - // To calculate q.e, first get the number of digits of qd[0]. - for (i = 1, k = qd[0]; k >= 10; k /= 10) i++; - q.e = i + e * logBase - 1; - - finalise(q, dp ? pr + q.e + 1 : pr, rm, more); - } - - return q; - }; -})(); - - -/* - * Round `x` to `sd` significant digits using rounding mode `rm`. - * Check for over/under-flow. - */ - function finalise(x, sd, rm, isTruncated) { - var digits, i, j, k, rd, roundUp, w, xd, xdi, - Ctor = x.constructor; - - // Don't round if sd is null or undefined. - out: if (sd != null) { - xd = x.d; - - // Infinity/NaN. - if (!xd) return x; - - // rd: the rounding digit, i.e. the digit after the digit that may be rounded up. - // w: the word of xd containing rd, a base 1e7 number. - // xdi: the index of w within xd. - // digits: 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 (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++; - i = sd - digits; - - // Is the rounding digit in the first word of xd? - if (i < 0) { - i += LOG_BASE; - j = sd; - w = xd[xdi = 0]; - - // Get the rounding digit at index j of w. - rd = w / mathpow(10, digits - j - 1) % 10 | 0; - } else { - xdi = Math.ceil((i + 1) / LOG_BASE); - k = xd.length; - if (xdi >= k) { - if (isTruncated) { - - // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`. - for (; k++ <= xdi;) xd.push(0); - w = rd = 0; - digits = 1; - i %= LOG_BASE; - j = i - LOG_BASE + 1; - } else { - break out; - } - } else { - w = k = xd[xdi]; - - // Get the number of digits of w. - for (digits = 1; k >= 10; k /= 10) digits++; - - // 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 - digits. - j = i - LOG_BASE + digits; - - // Get the rounding digit at index j of w. - rd = j < 0 ? 0 : w / mathpow(10, digits - j - 1) % 10 | 0; - } - } - - // Are there any non-zero digits after the rounding digit? - isTruncated = isTruncated || sd < 0 || - xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1)); - - // The expression `w % mathpow(10, digits - 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. - - roundUp = rm < 4 - ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) - : rd > 5 || rd == 5 && (rm == 4 || isTruncated || rm == 6 && - - // Check whether the digit to the left of the rounding digit is odd. - ((i > 0 ? j > 0 ? w / mathpow(10, digits - j) : 0 : xd[xdi - 1]) % 10) & 1 || - rm == (x.s < 0 ? 8 : 7)); - - if (sd < 1 || !xd[0]) { - xd.length = 0; - if (roundUp) { - - // Convert sd to decimal places. - sd -= x.e + 1; - - // 1, 0.1, 0.01, 0.001, 0.0001 etc. - xd[0] = mathpow(10, (LOG_BASE - sd % LOG_BASE) % LOG_BASE); - x.e = -sd || 0; - } else { - - // Zero. - xd[0] = x.e = 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, digits - j) % mathpow(10, j) | 0) * k : 0; - } - - if (roundUp) { - for (;;) { - - // Is the digit to be rounded up in the first word of xd? - if (xdi == 0) { - - // i will be the length of xd[0] before k is added. - for (i = 1, j = xd[0]; j >= 10; j /= 10) i++; - j = xd[0] += k; - for (k = 1; j >= 10; j /= 10) k++; - - // if i != k the length has increased. - if (i != k) { - x.e++; - if (xd[0] == BASE) xd[0] = 1; - } - - 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) { - - // Overflow? - if (x.e > Ctor.maxE) { - - // Infinity. - x.d = null; - x.e = NaN; - - // Underflow? - } else if (x.e < Ctor.minE) { - - // Zero. - x.e = 0; - x.d = [0]; - // Ctor.underflow = true; - } // else Ctor.underflow = false; - } - - return x; -} - - -function finiteToString(x, isExp, sd) { - if (!x.isFinite()) return nonFiniteToString(x); - var k, - e = x.e, - 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 + (x.e < 0 ? 'e' : 'e+') + x.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 str; -} - - -// Calculate the base 10 exponent from the base 1e7 exponent. -function getBase10Exponent(digits, e) { - var w = digits[0]; - - // Add the number of digits of the first word of the digits array. - for ( e *= LOG_BASE; w >= 10; w /= 10) e++; - return e; -} - - -function getLn10(Ctor, sd, pr) { - if (sd > LN10_PRECISION) { - - // Reset global state in case the exception is caught. - external = true; - if (pr) Ctor.precision = pr; - throw Error(precisionLimitExceeded); - } - return finalise(new Ctor(LN10), sd, 1, true); -} - - -function getPi(Ctor, sd, rm) { - if (sd > PI_PRECISION) throw Error(precisionLimitExceeded); - return finalise(new Ctor(PI), sd, rm, true); -} - - -function getPrecision(digits) { - var w = digits.length - 1, - len = w * LOG_BASE + 1; - - w = digits[w]; - - // If non-zero... - if (w) { - - // Subtract the number of trailing zeros of the last word. - for (; w % 10 == 0; w /= 10) len--; - - // Add the number of digits of the first word. - for (w = digits[0]; w >= 10; w /= 10) len++; - } - - return len; -} - - -function getZeroString(k) { - var zs = ''; - for (; k--;) zs += '0'; - return zs; -} - - -/* - * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an - * integer of type number. - * - * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`. - * - */ -function intPow(Ctor, x, n, pr) { - var isTruncated, - r = new Ctor(1), - - // Max n of 9007199254740991 takes 53 loop iterations. - // Maximum digits array length; leaves [28, 34] guard digits. - k = Math.ceil(pr / LOG_BASE + 4); - - external = false; - - for (;;) { - if (n % 2) { - r = r.times(x); - if (truncate(r.d, k)) isTruncated = true; - } - - n = mathfloor(n / 2); - if (n === 0) { - - // To ensure correct rounding when r.d is truncated, increment the last word if it is zero. - n = r.d.length - 1; - if (isTruncated && r.d[n] === 0) ++r.d[n]; - break; - } - - x = x.times(x); - truncate(x.d, k); - } - - external = true; - - return r; -} - - -function isOdd(n) { - return n.d[n.d.length - 1] & 1; -} - - -/* - * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'. - */ -function maxOrMin(Ctor, args, ltgt) { - var y, - x = new Ctor(args[0]), - i = 0; - - for (; ++i < args.length;) { - y = new Ctor(args[i]); - if (!y.s) { - x = y; - break; - } else if (x[ltgt](y)) { - x = y; - } - } - - return x; -} - - -/* - * Return a new Decimal whose value is the natural exponential of `x` rounded 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. - * - * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000 - * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000 - * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324) - * - * exp(Infinity) = Infinity - * exp(-Infinity) = 0 - * exp(NaN) = NaN - * exp(±0) = 1 - * - * exp(x) is non-terminating for any finite, non-zero x. - * - * The result will always be correctly rounded. - * - */ -function naturalExponential(x, sd) { - var denominator, guard, j, pow, sum, t, wpr, - rep = 0, - i = 0, - k = 0, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision; - - // 0/NaN/Infinity? - if (!x.d || !x.d[0] || x.e > 17) { - - return new Ctor(x.d - ? !x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0 - : x.s ? x.s < 0 ? 0 : x : 0 / 0); - } - - if (sd == null) { - external = false; - wpr = pr; - } else { - wpr = sd; - } - - t = new Ctor(0.03125); - - // while abs(x) >= 0.1 - while (x.e > -2) { - - // x = x / 2^5 - x = x.times(t); - k += 5; - } - - // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision - // 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(1); - Ctor.precision = wpr; - - for (;;) { - pow = finalise(pow.times(x), wpr, 1); - denominator = denominator.times(++i); - t = sum.plus(divide(pow, denominator, wpr, 1)); - - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - j = k; - while (j--) sum = finalise(sum.times(sum), wpr, 1); - - // Check to see if the first 4 rounding digits are [49]999. - // If so, repeat the summation with a higher precision, otherwise - // e.g. with precision: 18, rounding: 1 - // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123) - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { - - if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += 10; - denominator = pow = t = new Ctor(1); - i = 0; - rep++; - } else { - return finalise(sum, Ctor.precision = pr, rm, external = true); - } - } else { - Ctor.precision = pr; - return sum; - } - } - - sum = t; - } -} - - -/* - * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant - * digits. - * - * ln(-n) = NaN - * ln(0) = -Infinity - * ln(-0) = -Infinity - * ln(1) = 0 - * ln(Infinity) = Infinity - * ln(-Infinity) = NaN - * ln(NaN) = NaN - * - * ln(n) (n != 1) is non-terminating. - * - */ -function naturalLogarithm(y, sd) { - var c, c0, denominator, e, numerator, rep, sum, t, wpr, x1, x2, - n = 1, - guard = 10, - x = y, - xd = x.d, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision; - - // Is x negative or Infinity, NaN, 0 or 1? - if (x.s < 0 || !xd || !xd[0] || !x.e && xd[0] == 1 && xd.length == 1) { - return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x); - } - - if (sd == null) { - external = false; - wpr = pr; - } else { - wpr = sd; - } - - Ctor.precision = wpr += guard; - c = digitsToString(xd); - c0 = c.charAt(0); - - if (Math.abs(e = x.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 = x.e; - - 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 = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t); - Ctor.precision = pr; - - return sd == null ? finalise(x, pr, rm, external = true) : x; - } - - // x1 is x reduced to a value near 1. - x1 = x; - - // 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(1), x.plus(1), wpr, 1); - x2 = finalise(x.times(x), wpr, 1); - denominator = 3; - - for (;;) { - numerator = finalise(numerator.times(x2), wpr, 1); - t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1)); - - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - sum = sum.times(2); - - // Reverse the argument reduction. Check that e is not 0 because, besides preventing an - // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0. - if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + '')); - sum = divide(sum, new Ctor(n), wpr, 1); - - // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has - // been repeated previously) and the first 4 rounding digits 9999? - // If so, restart the summation with a higher precision, otherwise - // e.g. with precision: 12, rounding: 1 - // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463. - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { - if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += guard; - t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1); - x2 = finalise(x.times(x), wpr, 1); - denominator = rep = 1; - } else { - return finalise(sum, Ctor.precision = pr, rm, external = true); - } - } else { - Ctor.precision = pr; - return sum; - } - } - - sum = t; - denominator += 2; - } -} - - -// ±Infinity, NaN. -function nonFiniteToString(x) { - // Unsigned. - return String(x.s * x.s / 0); -} - - -/* - * 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; - x.e = e = e - i - 1; - 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) { - - // Overflow? - if (x.e > x.constructor.maxE) { - - // Infinity. - x.d = null; - x.e = NaN; - - // Underflow? - } else if (x.e < x.constructor.minE) { - - // Zero. - x.e = 0; - x.d = [0]; - // x.constructor.underflow = true; - } // else x.constructor.underflow = false; - } - } else { - - // Zero. - x.e = 0; - x.d = [0]; - } - - return x; -} - - -/* - * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value. - */ -function parseOther(x, str) { - var base, Ctor, divisor, i, isFloat, len, p, xd, xe; - - if (str.indexOf('_') > -1) { - str = str.replace(/(\d)_(?=\d)/g, '$1'); - if (isDecimal.test(str)) return parseDecimal(x, str); - } else if (str === 'Infinity' || str === 'NaN') { - if (!+str) x.s = NaN; - x.e = NaN; - x.d = null; - return x; - } - - if (isHex.test(str)) { - base = 16; - str = str.toLowerCase(); - } else if (isBinary.test(str)) { - base = 2; - } else if (isOctal.test(str)) { - base = 8; - } else { - throw Error(invalidArgument + str); - } - - // Is there a binary exponent part? - i = str.search(/p/i); - - if (i > 0) { - p = +str.slice(i + 1); - str = str.substring(2, i); - } else { - str = str.slice(2); - } - - // Convert `str` as an integer then divide the result by `base` raised to a power such that the - // fraction part will be restored. - i = str.indexOf('.'); - isFloat = i >= 0; - Ctor = x.constructor; - - if (isFloat) { - str = str.replace('.', ''); - len = str.length; - i = len - i; - - // log[10](16) = 1.2041... , log[10](88) = 1.9444.... - divisor = intPow(Ctor, new Ctor(base), i, i * 2); - } - - xd = convertBase(str, base, BASE); - xe = xd.length - 1; - - // Remove trailing zeros. - for (i = xe; xd[i] === 0; --i) xd.pop(); - if (i < 0) return new Ctor(x.s * 0); - x.e = getBase10Exponent(xd, xe); - x.d = xd; - external = false; - - // At what precision to perform the division to ensure exact conversion? - // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount) - // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412 - // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits. - // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount - // Therefore using 4 * the number of digits of str will always be enough. - if (isFloat) x = divide(x, divisor, len * 4); - - // Multiply by the binary exponent part if present. - if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p)); - external = true; - - return x; -} - - -/* - * sin(x) = x - x^3/3! + x^5/5! - ... - * |x| < pi/2 - * - */ -function sine(Ctor, x) { - var k, - len = x.d.length; - - if (len < 3) { - return x.isZero() ? x : taylorSeries(Ctor, 2, x, x); - } - - // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x) - // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5) - // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20)) - - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len); - k = k > 16 ? 16 : k | 0; - - x = x.times(1 / tinyPow(5, k)); - x = taylorSeries(Ctor, 2, x, x); - - // Reverse argument reduction - var sin2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20); - for (; k--;) { - sin2_x = x.times(x); - x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20)))); - } - - return x; -} - - -// Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`. -function taylorSeries(Ctor, n, x, y, isHyperbolic) { - var j, t, u, x2, - i = 1, - pr = Ctor.precision, - k = Math.ceil(pr / LOG_BASE); - - external = false; - x2 = x.times(x); - u = new Ctor(y); - - for (;;) { - t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1); - u = isHyperbolic ? y.plus(t) : y.minus(t); - y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1); - t = u.plus(y); - - if (t.d[k] !== void 0) { - for (j = k; t.d[j] === u.d[j] && j--;); - if (j == -1) break; - } - - j = u; - u = y; - y = t; - t = j; - i++; - } - - external = true; - t.d.length = k + 1; - - return t; -} - - -// Exponent e must be positive and non-zero. -function tinyPow(b, e) { - var n = b; - while (--e) n *= b; - return n; -} - - -// Return the absolute value of `x` reduced to less than or equal to half pi. -function toLessThanHalfPi(Ctor, x) { - var t, - isNeg = x.s < 0, - pi = getPi(Ctor, Ctor.precision, 1), - halfPi = pi.times(0.5); - - x = x.abs(); - - if (x.lte(halfPi)) { - quadrant = isNeg ? 4 : 1; - return x; - } - - t = x.divToInt(pi); - - if (t.isZero()) { - quadrant = isNeg ? 3 : 2; - } else { - x = x.minus(t.times(pi)); - - // 0 <= x < pi - if (x.lte(halfPi)) { - quadrant = isOdd(t) ? (isNeg ? 2 : 3) : (isNeg ? 4 : 1); - return x; - } - - quadrant = isOdd(t) ? (isNeg ? 1 : 4) : (isNeg ? 3 : 2); - } - - return x.minus(pi).abs(); -} - - -/* - * Return the value of Decimal `x` as a string in base `baseOut`. - * - * If the optional `sd` argument is present include a binary exponent suffix. - */ -function toStringBinary(x, baseOut, sd, rm) { - var base, e, i, k, len, roundUp, str, xd, y, - Ctor = x.constructor, - isExp = sd !== void 0; - - if (isExp) { - checkInt32(sd, 1, MAX_DIGITS); - if (rm === void 0) rm = Ctor.rounding; - else checkInt32(rm, 0, 8); - } else { - sd = Ctor.precision; - rm = Ctor.rounding; - } - - if (!x.isFinite()) { - str = nonFiniteToString(x); - } else { - str = finiteToString(x); - i = str.indexOf('.'); - - // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required: - // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10)) - // minBinaryExponent = floor(decimalExponent * log[2](10)) - // log[2](10) = 3.321928094887362347870319429489390175864 - - if (isExp) { - base = 2; - if (baseOut == 16) { - sd = sd * 4 - 3; - } else if (baseOut == 8) { - sd = sd * 3 - 2; - } - } else { - base = baseOut; - } - - // Convert the number as an integer then divide the result by its base raised to a power such - // that the fraction part will be restored. - - // Non-integer. - if (i >= 0) { - str = str.replace('.', ''); - y = new Ctor(1); - y.e = str.length - i; - y.d = convertBase(finiteToString(y), 10, base); - y.e = y.d.length; - } - - xd = convertBase(str, 10, base); - e = len = xd.length; - - // Remove trailing zeros. - for (; xd[--len] == 0;) xd.pop(); - - if (!xd[0]) { - str = isExp ? '0p+0' : '0'; - } else { - if (i < 0) { - e--; - } else { - x = new Ctor(x); - x.d = xd; - x.e = e; - x = divide(x, y, sd, rm, 0, base); - xd = x.d; - e = x.e; - roundUp = inexact; - } - - // The rounding digit, i.e. the digit after the digit that may be rounded up. - i = xd[sd]; - k = base / 2; - roundUp = roundUp || xd[sd + 1] !== void 0; - - roundUp = rm < 4 - ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2)) - : i > k || i === k && (rm === 4 || roundUp || rm === 6 && xd[sd - 1] & 1 || - rm === (x.s < 0 ? 8 : 7)); - - xd.length = sd; - - if (roundUp) { - - // Rounding up may mean the previous digit has to be rounded up and so on. - for (; ++xd[--sd] > base - 1;) { - xd[sd] = 0; - if (!sd) { - ++e; - xd.unshift(1); - } - } - } - - // Determine trailing zeros. - for (len = xd.length; !xd[len - 1]; --len); - - // E.g. [4, 11, 15] becomes 4bf. - for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]); - - // Add binary exponent suffix? - if (isExp) { - if (len > 1) { - if (baseOut == 16 || baseOut == 8) { - i = baseOut == 16 ? 4 : 3; - for (--len; len % i; len++) str += '0'; - xd = convertBase(str, base, baseOut); - for (len = xd.length; !xd[len - 1]; --len); - - // xd[0] will always be be 1 - for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]); - } else { - str = str.charAt(0) + '.' + str.slice(1); - } - } - - str = str + (e < 0 ? 'p' : 'p+') + e; - } else if (e < 0) { - for (; ++e;) str = '0' + str; - str = '0.' + str; - } else { - if (++e > len) for (e -= len; e-- ;) str += '0'; - else if (e < len) str = str.slice(0, e) + '.' + str.slice(e); - } - } - - str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str; - } - - 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 - - -/* - * abs - * acos - * acosh - * add - * asin - * asinh - * atan - * atanh - * atan2 - * cbrt - * ceil - * clamp - * clone - * config - * cos - * cosh - * div - * exp - * floor - * hypot - * ln - * log - * log2 - * log10 - * max - * min - * mod - * mul - * pow - * random - * round - * set - * sign - * sin - * sinh - * sqrt - * sub - * sum - * tan - * tanh - * trunc - */ - - -/* - * Return a new Decimal whose value is the absolute value of `x`. - * - * x {number|string|Decimal} - * - */ -function abs(x) { - return new this(x).abs(); -} - - -/* - * Return a new Decimal whose value is the arccosine in radians of `x`. - * - * x {number|string|Decimal} - * - */ -function acos(x) { - return new this(x).acos(); -} - - -/* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function acosh(x) { - return new this(x).acosh(); -} - - -/* - * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ -function add(x, y) { - return new this(x).plus(y); -} - - -/* - * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ -function asin(x) { - return new this(x).asin(); -} - - -/* - * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function asinh(x) { - return new this(x).asinh(); -} - - -/* - * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ -function atan(x) { - return new this(x).atan(); -} - - -/* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function atanh(x) { - return new this(x).atanh(); -} - - -/* - * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi - * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi, pi] - * - * y {number|string|Decimal} The y-coordinate. - * x {number|string|Decimal} The x-coordinate. - * - * atan2(±0, -0) = ±pi - * atan2(±0, +0) = ±0 - * atan2(±0, -x) = ±pi for x > 0 - * atan2(±0, x) = ±0 for x > 0 - * atan2(-y, ±0) = -pi/2 for y > 0 - * atan2(y, ±0) = pi/2 for y > 0 - * atan2(±y, -Infinity) = ±pi for finite y > 0 - * atan2(±y, +Infinity) = ±0 for finite y > 0 - * atan2(±Infinity, x) = ±pi/2 for finite x - * atan2(±Infinity, -Infinity) = ±3*pi/4 - * atan2(±Infinity, +Infinity) = ±pi/4 - * atan2(NaN, x) = NaN - * atan2(y, NaN) = NaN - * - */ -function atan2(y, x) { - y = new this(y); - x = new this(x); - var r, - pr = this.precision, - rm = this.rounding, - wpr = pr + 4; - - // Either NaN - if (!y.s || !x.s) { - r = new this(NaN); - - // Both ±Infinity - } else if (!y.d && !x.d) { - r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75); - r.s = y.s; - - // x is ±Infinity or y is ±0 - } else if (!x.d || y.isZero()) { - r = x.s < 0 ? getPi(this, pr, rm) : new this(0); - r.s = y.s; - - // y is ±Infinity or x is ±0 - } else if (!y.d || x.isZero()) { - r = getPi(this, wpr, 1).times(0.5); - r.s = y.s; - - // Both non-zero and finite - } else if (x.s < 0) { - this.precision = wpr; - this.rounding = 1; - r = this.atan(divide(y, x, wpr, 1)); - x = getPi(this, wpr, 1); - this.precision = pr; - this.rounding = rm; - r = y.s < 0 ? r.minus(x) : r.plus(x); - } else { - r = this.atan(divide(y, x, wpr, 1)); - } - - return r; -} - - -/* - * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ -function cbrt(x) { - return new this(x).cbrt(); -} - - -/* - * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`. - * - * x {number|string|Decimal} - * - */ -function ceil(x) { - return finalise(x = new this(x), x.e + 1, 2); -} - - -/* - * Return a new Decimal whose value is `x` clamped to the range delineated by `min` and `max`. - * - * x {number|string|Decimal} - * min {number|string|Decimal} - * max {number|string|Decimal} - * - */ -function clamp(x, min, max) { - return new this(x).clamp(min, max); -} - - -/* - * 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} - * maxE {number} - * minE {number} - * modulo {number} - * crypto {boolean|number} - * defaults {true} - * - * 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, - useDefaults = obj.defaults === true, - ps = [ - 'precision', 1, MAX_DIGITS, - 'rounding', 0, 8, - 'toExpNeg', -EXP_LIMIT, 0, - 'toExpPos', 0, EXP_LIMIT, - 'maxE', 0, EXP_LIMIT, - 'minE', -EXP_LIMIT, 0, - 'modulo', 0, 9 - ]; - - for (i = 0; i < ps.length; i += 3) { - if (p = ps[i], useDefaults) this[p] = DEFAULTS[p]; - if ((v = obj[p]) !== void 0) { - if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v; - else throw Error(invalidArgument + p + ': ' + v); - } - } - - if (p = 'crypto', useDefaults) this[p] = DEFAULTS[p]; - if ((v = obj[p]) !== void 0) { - if (v === true || v === false || v === 0 || v === 1) { - if (v) { - if (typeof crypto != 'undefined' && crypto && - (crypto.getRandomValues || crypto.randomBytes)) { - this[p] = true; - } else { - throw Error(cryptoUnavailable); - } - } else { - this[p] = false; - } - } else { - throw Error(invalidArgument + p + ': ' + v); - } - } - - return this; -} - - -/* - * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function cos(x) { - return new this(x).cos(); -} - - -/* - * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function cosh(x) { - return new this(x).cosh(); -} - - -/* - * 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. - * - * v {number|string|Decimal} A numeric value. - * - */ - function Decimal(v) { - var e, i, t, - x = this; - - // Decimal called without new. - if (!(x instanceof Decimal)) return new Decimal(v); - - // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor - // which points to Object. - x.constructor = Decimal; - - // Duplicate. - if (isDecimalInstance(v)) { - x.s = v.s; - - if (external) { - if (!v.d || v.e > Decimal.maxE) { - - // Infinity. - x.e = NaN; - x.d = null; - } else if (v.e < Decimal.minE) { - - // Zero. - x.e = 0; - x.d = [0]; - } else { - x.e = v.e; - x.d = v.d.slice(); - } - } else { - x.e = v.e; - x.d = v.d ? v.d.slice() : v.d; - } - - return; - } - - t = typeof v; - - if (t === 'number') { - if (v === 0) { - x.s = 1 / v < 0 ? -1 : 1; - x.e = 0; - x.d = [0]; - return; - } - - if (v < 0) { - v = -v; - x.s = -1; - } else { - x.s = 1; - } - - // Fast path for small integers. - if (v === ~~v && v < 1e7) { - for (e = 0, i = v; i >= 10; i /= 10) e++; - - if (external) { - if (e > Decimal.maxE) { - x.e = NaN; - x.d = null; - } else if (e < Decimal.minE) { - x.e = 0; - x.d = [0]; - } else { - x.e = e; - x.d = [v]; - } - } else { - x.e = e; - x.d = [v]; - } - - return; - - // Infinity, NaN. - } else if (v * 0 !== 0) { - if (!v) x.s = NaN; - x.e = NaN; - x.d = null; - return; - } - - return parseDecimal(x, v.toString()); - - } else if (t !== 'string') { - throw Error(invalidArgument + v); - } - - // Minus sign? - if ((i = v.charCodeAt(0)) === 45) { - v = v.slice(1); - x.s = -1; - } else { - // Plus sign? - if (i === 43) v = v.slice(1); - x.s = 1; - } - - return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v); - } - - 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.EUCLID = 9; - - Decimal.config = Decimal.set = config; - Decimal.clone = clone; - Decimal.isDecimal = isDecimalInstance; - - Decimal.abs = abs; - Decimal.acos = acos; - Decimal.acosh = acosh; // ES6 - Decimal.add = add; - Decimal.asin = asin; - Decimal.asinh = asinh; // ES6 - Decimal.atan = atan; - Decimal.atanh = atanh; // ES6 - Decimal.atan2 = atan2; - Decimal.cbrt = cbrt; // ES6 - Decimal.ceil = ceil; - Decimal.clamp = clamp; - Decimal.cos = cos; - Decimal.cosh = cosh; // ES6 - Decimal.div = div; - Decimal.exp = exp; - Decimal.floor = floor; - Decimal.hypot = hypot; // ES6 - Decimal.ln = ln; - Decimal.log = log; - Decimal.log10 = log10; // ES6 - Decimal.log2 = log2; // ES6 - Decimal.max = max; - Decimal.min = min; - Decimal.mod = mod; - Decimal.mul = mul; - Decimal.pow = pow; - Decimal.random = random; - Decimal.round = round; - Decimal.sign = sign; // ES6 - Decimal.sin = sin; - Decimal.sinh = sinh; // ES6 - Decimal.sqrt = sqrt; - Decimal.sub = sub; - Decimal.sum = sum; - Decimal.tan = tan; - Decimal.tanh = tanh; // ES6 - Decimal.trunc = trunc; // ES6 - - if (obj === void 0) obj = {}; - if (obj) { - if (obj.defaults !== true) { - ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto']; - for (i = 0; i < ps.length;) if (!obj.hasOwnProperty(p = ps[i++])) obj[p] = this[p]; - } - } - - Decimal.config(obj); - - return Decimal; -} - - -/* - * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ -function div(x, y) { - return new this(x).div(y); -} - - -/* - * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The power to which to raise the base of the natural log. - * - */ -function exp(x) { - return new this(x).exp(); -} - - -/* - * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`. - * - * x {number|string|Decimal} - * - */ -function floor(x) { - return finalise(x = new this(x), x.e + 1, 3); -} - - -/* - * Return a new Decimal whose value is the square root of the sum of the squares of the arguments, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...) - * - * arguments {number|string|Decimal} - * - */ -function hypot() { - var i, n, - t = new this(0); - - external = false; - - for (i = 0; i < arguments.length;) { - n = new this(arguments[i++]); - if (!n.d) { - if (n.s) { - external = true; - return new this(1 / 0); - } - t = n; - } else if (t.d) { - t = t.plus(n.times(n)); - } - } - - external = true; - - return t.sqrt(); -} - - -/* - * Return true if object is a Decimal instance (where Decimal is any Decimal constructor), - * otherwise return false. - * - */ -function isDecimalInstance(obj) { - return obj instanceof Decimal || obj && obj.toStringTag === tag || false; -} - - -/* - * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ -function ln(x) { - return new this(x).ln(); -} - - -/* - * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base - * is specified, rounded to `precision` significant digits using rounding mode `rounding`. - * - * log[y](x) - * - * x {number|string|Decimal} The argument of the logarithm. - * y {number|string|Decimal} The base of the logarithm. - * - */ -function log(x, y) { - return new this(x).log(y); -} - - -/* - * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ -function log2(x) { - return new this(x).log(2); -} - - -/* - * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ -function log10(x) { - return new this(x).log(10); -} - - -/* - * Return a new Decimal whose value is the maximum of the arguments. - * - * arguments {number|string|Decimal} - * - */ -function max() { - return maxOrMin(this, arguments, 'lt'); -} - - -/* - * Return a new Decimal whose value is the minimum of the arguments. - * - * arguments {number|string|Decimal} - * - */ -function min() { - return maxOrMin(this, arguments, 'gt'); -} - - -/* - * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ -function mod(x, y) { - return new this(x).mod(y); -} - - -/* - * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ -function mul(x, y) { - return new this(x).mul(y); -} - - -/* - * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The base. - * y {number|string|Decimal} The exponent. - * - */ -function pow(x, y) { - return new this(x).pow(y); -} - - -/* - * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with - * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros - * are produced). - * - * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive. - * - */ -function random(sd) { - var d, e, k, n, - i = 0, - r = new this(1), - rd = []; - - if (sd === void 0) sd = this.precision; - else checkInt32(sd, 1, MAX_DIGITS); - - k = Math.ceil(sd / LOG_BASE); - - if (!this.crypto) { - for (; i < k;) rd[i++] = Math.random() * 1e7 | 0; - - // Browsers supporting crypto.getRandomValues. - } else if (crypto.getRandomValues) { - d = crypto.getRandomValues(new Uint32Array(k)); - - for (; i < k;) { - n = d[i]; - - // 0 <= n < 4294967296 - // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865). - if (n >= 4.29e9) { - d[i] = crypto.getRandomValues(new Uint32Array(1))[0]; - } else { - - // 0 <= n <= 4289999999 - // 0 <= (n % 1e7) <= 9999999 - rd[i++] = n % 1e7; - } - } - - // Node.js supporting crypto.randomBytes. - } else if (crypto.randomBytes) { - - // buffer - d = crypto.randomBytes(k *= 4); - - for (; i < k;) { - - // 0 <= n < 2147483648 - n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24); - - // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286). - if (n >= 2.14e9) { - crypto.randomBytes(4).copy(d, i); - } else { - - // 0 <= n <= 2139999999 - // 0 <= (n % 1e7) <= 9999999 - rd.push(n % 1e7); - i += 4; - } - } - - i = k / 4; - } else { - throw Error(cryptoUnavailable); - } - - k = rd[--i]; - sd %= LOG_BASE; - - // Convert trailing digits to zeros according to sd. - if (k && sd) { - n = mathpow(10, LOG_BASE - sd); - rd[i] = (k / n | 0) * n; - } - - // Remove trailing words which are zero. - for (; rd[i] === 0; i--) rd.pop(); - - // Zero? - if (i < 0) { - e = 0; - rd = [0]; - } else { - e = -1; - - // Remove leading words which are zero and adjust exponent accordingly. - for (; rd[0] === 0; e -= LOG_BASE) rd.shift(); - - // Count the digits of the first word of rd to determine leading zeros. - for (k = 1, n = rd[0]; n >= 10; n /= 10) k++; - - // Adjust the exponent for leading zeros of the first word of rd. - if (k < LOG_BASE) e -= LOG_BASE - k; - } - - r.e = e; - r.d = rd; - - return r; -} - - -/* - * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`. - * - * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL). - * - * x {number|string|Decimal} - * - */ -function round(x) { - return finalise(x = new this(x), x.e + 1, this.rounding); -} - - -/* - * Return - * 1 if x > 0, - * -1 if x < 0, - * 0 if x is 0, - * -0 if x is -0, - * NaN otherwise - * - * x {number|string|Decimal} - * - */ -function sign(x) { - x = new this(x); - return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN; -} - - -/* - * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function sin(x) { - return new this(x).sin(); -} - - -/* - * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function sinh(x) { - return new this(x).sinh(); -} - - -/* - * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ -function sqrt(x) { - return new this(x).sqrt(); -} - - -/* - * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ -function sub(x, y) { - return new this(x).sub(y); -} - - -/* - * Return a new Decimal whose value is the sum of the arguments, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * Only the result is rounded, not the intermediate calculations. - * - * arguments {number|string|Decimal} - * - */ -function sum() { - var i = 0, - args = arguments, - x = new this(args[i]); - - external = false; - for (; x.s && ++i < args.length;) x = x.plus(args[i]); - external = true; - - return finalise(x, this.precision, this.rounding); -} - - -/* - * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function tan(x) { - return new this(x).tan(); -} - - -/* - * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ -function tanh(x) { - return new this(x).tanh(); -} - - -/* - * Return a new Decimal whose value is `x` truncated to an integer. - * - * x {number|string|Decimal} - * - */ -function trunc(x) { - return finalise(x = new this(x), x.e + 1, 1); -} - - -P[Symbol.for('nodejs.util.inspect.custom')] = P.toString; -P[Symbol.toStringTag] = 'Decimal'; - -// Create and configure initial Decimal constructor. -export var Decimal = P.constructor = clone(DEFAULTS); - -// Create the internal constants from their string values. -LN10 = new Decimal(LN10); -PI = new Decimal(PI); - -export default Decimal; -- cgit