{"version":3,"file":"complex.js-Cp1BX5IE.js","sources":["../../node_modules/complex.js/dist/complex.js"],"sourcesContent":["'use strict';\n\n/**\n *\n * This class allows the manipulation of complex numbers.\n * You can pass a complex number in different formats. Either as object, double, string or two integer parameters.\n *\n * Object form\n * { re: , im: }\n * { arg: , abs: }\n * { phi: , r: }\n *\n * Array / Vector form\n * [ real, imaginary ]\n *\n * Double form\n * 99.3 - Single double value\n *\n * String form\n * '23.1337' - Simple real number\n * '15+3i' - a simple complex number\n * '3-i' - a simple complex number\n *\n * Example:\n *\n * const c = new Complex('99.3+8i');\n * c.mul({r: 3, i: 9}).div(4.9).sub(3, 2);\n *\n */\n\n\nconst cosh = Math.cosh || function (x) {\n return Math.abs(x) < 1e-9 ? 1 - x : (Math.exp(x) + Math.exp(-x)) * 0.5;\n};\n\nconst sinh = Math.sinh || function (x) {\n return Math.abs(x) < 1e-9 ? x : (Math.exp(x) - Math.exp(-x)) * 0.5;\n};\n\n/**\n * Calculates cos(x) - 1 using Taylor series if x is small (-¼π ≤ x ≤ ¼π).\n *\n * @param {number} x\n * @returns {number} cos(x) - 1\n */\nconst cosm1 = function (x) {\n\n const b = Math.PI / 4;\n if (-b > x || x > b) {\n return Math.cos(x) - 1.0;\n }\n\n /* Calculate horner form of polynomial of taylor series in Q\n let fac = 1, alt = 1, pol = {};\n for (let i = 0; i <= 16; i++) {\n fac*= i || 1;\n if (i % 2 == 0) {\n pol[i] = new Fraction(1, alt * fac);\n alt = -alt;\n }\n }\n console.log(new Polynomial(pol).toHorner()); // (((((((1/20922789888000x^2-1/87178291200)x^2+1/479001600)x^2-1/3628800)x^2+1/40320)x^2-1/720)x^2+1/24)x^2-1/2)x^2+1\n */\n\n const xx = x * x;\n return xx * (\n xx * (\n xx * (\n xx * (\n xx * (\n xx * (\n xx * (\n xx / 20922789888000\n - 1 / 87178291200)\n + 1 / 479001600)\n - 1 / 3628800)\n + 1 / 40320)\n - 1 / 720)\n + 1 / 24)\n - 1 / 2);\n};\n\nconst hypot = function (x, y) {\n\n x = Math.abs(x);\n y = Math.abs(y);\n\n // Ensure `x` is the larger value\n if (x < y) [x, y] = [y, x];\n\n // If both are below the threshold, use straightforward Pythagoras\n if (x < 1e8) return Math.sqrt(x * x + y * y);\n\n // For larger values, scale to avoid overflow\n y /= x;\n return x * Math.sqrt(1 + y * y);\n};\n\nconst parser_exit = function () {\n throw SyntaxError('Invalid Param');\n};\n\n/**\n * Calculates log(sqrt(a^2+b^2)) in a way to avoid overflows\n *\n * @param {number} a\n * @param {number} b\n * @returns {number}\n */\nfunction logHypot(a, b) {\n\n const _a = Math.abs(a);\n const _b = Math.abs(b);\n\n if (a === 0) {\n return Math.log(_b);\n }\n\n if (b === 0) {\n return Math.log(_a);\n }\n\n if (_a < 3000 && _b < 3000) {\n return Math.log(a * a + b * b) * 0.5;\n }\n\n /* I got 4 ideas to compute this property without overflow:\n *\n * Testing 1000000 times with random samples for a,b ∈ [1, 1000000000] against a big decimal library to get an error estimate\n *\n * 1. Only eliminate the square root: (OVERALL ERROR: 3.9122483030951116e-11)\n\n Math.log(a * a + b * b) / 2\n\n *\n *\n * 2. Try to use the non-overflowing pythagoras: (OVERALL ERROR: 8.889760039210159e-10)\n\n const fn = function(a, b) {\n a = Math.abs(a);\n b = Math.abs(b);\n let t = Math.min(a, b);\n a = Math.max(a, b);\n t = t / a;\n\n return Math.log(a) + Math.log(1 + t * t) / 2;\n };\n\n * 3. Abuse the identity cos(atan(y/x) = x / sqrt(x^2+y^2): (OVERALL ERROR: 3.4780178737037204e-10)\n\n Math.log(a / Math.cos(Math.atan2(b, a)))\n\n * 4. Use 3. and apply log rules: (OVERALL ERROR: 1.2014087502620896e-9)\n\n Math.log(a) - Math.log(Math.cos(Math.atan2(b, a)))\n\n */\n\n a = a * 0.5;\n b = b * 0.5;\n\n return 0.5 * Math.log(a * a + b * b) + Math.LN2;\n}\n\nconst P = { 're': 0, 'im': 0 };\nconst parse = function (a, b) {\n\n const z = P;\n\n if (a === undefined || a === null) {\n z['re'] =\n z['im'] = 0;\n } else if (b !== undefined) {\n z['re'] = a;\n z['im'] = b;\n } else\n switch (typeof a) {\n\n case 'object':\n\n if ('im' in a && 're' in a) {\n z['re'] = a['re'];\n z['im'] = a['im'];\n } else if ('abs' in a && 'arg' in a) {\n if (!isFinite(a['abs']) && isFinite(a['arg'])) {\n return Complex['INFINITY'];\n }\n z['re'] = a['abs'] * Math.cos(a['arg']);\n z['im'] = a['abs'] * Math.sin(a['arg']);\n } else if ('r' in a && 'phi' in a) {\n if (!isFinite(a['r']) && isFinite(a['phi'])) {\n return Complex['INFINITY'];\n }\n z['re'] = a['r'] * Math.cos(a['phi']);\n z['im'] = a['r'] * Math.sin(a['phi']);\n } else if (a.length === 2) { // Quick array check\n z['re'] = a[0];\n z['im'] = a[1];\n } else {\n parser_exit();\n }\n break;\n\n case 'string':\n\n z['im'] = /* void */\n z['re'] = 0;\n\n const tokens = a.replace(/_/g, '')\n .match(/\\d+\\.?\\d*e[+-]?\\d+|\\d+\\.?\\d*|\\.\\d+|./g);\n let plus = 1;\n let minus = 0;\n\n if (tokens === null) {\n parser_exit();\n }\n\n for (let i = 0; i < tokens.length; i++) {\n\n const c = tokens[i];\n\n if (c === ' ' || c === '\\t' || c === '\\n') {\n /* void */\n } else if (c === '+') {\n plus++;\n } else if (c === '-') {\n minus++;\n } else if (c === 'i' || c === 'I') {\n\n if (plus + minus === 0) {\n parser_exit();\n }\n\n if (tokens[i + 1] !== ' ' && !isNaN(tokens[i + 1])) {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + tokens[i + 1]);\n i++;\n } else {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + '1');\n }\n plus = minus = 0;\n\n } else {\n\n if (plus + minus === 0 || isNaN(c)) {\n parser_exit();\n }\n\n if (tokens[i + 1] === 'i' || tokens[i + 1] === 'I') {\n z['im'] += parseFloat((minus % 2 ? '-' : '') + c);\n i++;\n } else {\n z['re'] += parseFloat((minus % 2 ? '-' : '') + c);\n }\n plus = minus = 0;\n }\n }\n\n // Still something on the stack\n if (plus + minus > 0) {\n parser_exit();\n }\n break;\n\n case 'number':\n z['im'] = 0;\n z['re'] = a;\n break;\n\n default:\n parser_exit();\n }\n\n if (isNaN(z['re']) || isNaN(z['im'])) {\n // If a calculation is NaN, we treat it as NaN and don't throw\n //parser_exit();\n }\n\n return z;\n};\n\n/**\n * @constructor\n * @returns {Complex}\n */\nfunction Complex(a, b) {\n\n if (!(this instanceof Complex)) {\n return new Complex(a, b);\n }\n\n const z = parse(a, b);\n\n this['re'] = z['re'];\n this['im'] = z['im'];\n}\n\nComplex.prototype = {\n\n 're': 0,\n 'im': 0,\n\n /**\n * Calculates the sign of a complex number, which is a normalized complex\n *\n * @returns {Complex}\n */\n 'sign': function () {\n\n const abs = hypot(this['re'], this['im']);\n\n return new Complex(\n this['re'] / abs,\n this['im'] / abs);\n },\n\n /**\n * Adds two complex numbers\n *\n * @returns {Complex}\n */\n 'add': function (a, b) {\n\n const z = parse(a, b);\n\n const tInfin = this['isInfinite']();\n const zInfin = !(isFinite(z['re']) && isFinite(z['im']));\n\n if (tInfin || zInfin) {\n\n if (tInfin && zInfin) {\n // Infinity + Infinity = NaN\n return Complex['NAN'];\n }\n // Infinity + z = Infinity { where z != Infinity }\n return Complex['INFINITY'];\n }\n\n return new Complex(\n this['re'] + z['re'],\n this['im'] + z['im']);\n },\n\n /**\n * Subtracts two complex numbers\n *\n * @returns {Complex}\n */\n 'sub': function (a, b) {\n\n const z = parse(a, b);\n\n const tInfin = this['isInfinite']();\n const zInfin = !(isFinite(z['re']) && isFinite(z['im']));\n\n if (tInfin || zInfin) {\n\n if (tInfin && zInfin) {\n // Infinity - Infinity = NaN\n return Complex['NAN'];\n }\n // Infinity - z = Infinity { where z != Infinity }\n return Complex['INFINITY'];\n }\n\n return new Complex(\n this['re'] - z['re'],\n this['im'] - z['im']);\n },\n\n /**\n * Multiplies two complex numbers\n *\n * @returns {Complex}\n */\n 'mul': function (a, b) {\n\n const z = parse(a, b);\n\n const tInfin = this['isInfinite']();\n const zInfin = !(isFinite(z['re']) && isFinite(z['im']));\n const tIsZero = this['re'] === 0 && this['im'] === 0;\n const zIsZero = z['re'] === 0 && z['im'] === 0;\n\n // Infinity * 0 = NaN\n if (tInfin && zIsZero || zInfin && tIsZero) {\n return Complex['NAN'];\n }\n\n // Infinity * z = Infinity { where z != 0 }\n if (tInfin || zInfin) {\n return Complex['INFINITY'];\n }\n\n // Shortcut for real values\n if (z['im'] === 0 && this['im'] === 0) {\n return new Complex(this['re'] * z['re'], 0);\n }\n\n return new Complex(\n this['re'] * z['re'] - this['im'] * z['im'],\n this['re'] * z['im'] + this['im'] * z['re']);\n },\n\n /**\n * Divides two complex numbers\n *\n * @returns {Complex}\n */\n 'div': function (a, b) {\n\n const z = parse(a, b);\n\n const tInfin = this['isInfinite']();\n const zInfin = !(isFinite(z['re']) && isFinite(z['im']));\n const tIsZero = this['re'] === 0 && this['im'] === 0;\n const zIsZero = z['re'] === 0 && z['im'] === 0;\n\n // 0 / 0 = NaN and Infinity / Infinity = NaN\n if (tIsZero && zIsZero || tInfin && zInfin) {\n return Complex['NAN'];\n }\n\n // Infinity / 0 = Infinity\n if (zIsZero || tInfin) {\n return Complex['INFINITY'];\n }\n\n // 0 / Infinity = 0\n if (tIsZero || zInfin) {\n return Complex['ZERO'];\n }\n\n if (0 === z['im']) {\n // Divisor is real\n return new Complex(this['re'] / z['re'], this['im'] / z['re']);\n }\n\n if (Math.abs(z['re']) < Math.abs(z['im'])) {\n\n const x = z['re'] / z['im'];\n const t = z['re'] * x + z['im'];\n\n return new Complex(\n (this['re'] * x + this['im']) / t,\n (this['im'] * x - this['re']) / t);\n\n } else {\n\n const x = z['im'] / z['re'];\n const t = z['im'] * x + z['re'];\n\n return new Complex(\n (this['re'] + this['im'] * x) / t,\n (this['im'] - this['re'] * x) / t);\n }\n },\n\n /**\n * Calculate the power of two complex numbers\n *\n * @returns {Complex}\n */\n 'pow': function (a, b) {\n\n const z = parse(a, b);\n\n const tIsZero = this['re'] === 0 && this['im'] === 0;\n const zIsZero = z['re'] === 0 && z['im'] === 0;\n\n if (zIsZero) {\n return Complex['ONE'];\n }\n\n // If the exponent is real\n if (z['im'] === 0) {\n\n if (this['im'] === 0 && this['re'] > 0) {\n\n return new Complex(Math.pow(this['re'], z['re']), 0);\n\n } else if (this['re'] === 0) { // If base is fully imaginary\n\n switch ((z['re'] % 4 + 4) % 4) {\n case 0:\n return new Complex(Math.pow(this['im'], z['re']), 0);\n case 1:\n return new Complex(0, Math.pow(this['im'], z['re']));\n case 2:\n return new Complex(-Math.pow(this['im'], z['re']), 0);\n case 3:\n return new Complex(0, -Math.pow(this['im'], z['re']));\n }\n }\n }\n\n /* I couldn't find a good formula, so here is a derivation and optimization\n *\n * z_1^z_2 = (a + bi)^(c + di)\n * = exp((c + di) * log(a + bi)\n * = pow(a^2 + b^2, (c + di) / 2) * exp(i(c + di)atan2(b, a))\n * =>...\n * Re = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * cos(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n * Im = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * sin(d * log(a^2 + b^2) / 2 + c * atan2(b, a))\n *\n * =>...\n * Re = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * cos(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n * Im = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * sin(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))\n *\n * =>\n * Re = exp(c * logsq2 - d * arg(z_1)) * cos(d * logsq2 + c * arg(z_1))\n * Im = exp(c * logsq2 - d * arg(z_1)) * sin(d * logsq2 + c * arg(z_1))\n *\n */\n\n if (tIsZero && z['re'] > 0) { // Same behavior as Wolframalpha, Zero if real part is zero\n return Complex['ZERO'];\n }\n\n const arg = Math.atan2(this['im'], this['re']);\n const loh = logHypot(this['re'], this['im']);\n\n let re = Math.exp(z['re'] * loh - z['im'] * arg);\n let im = z['im'] * loh + z['re'] * arg;\n return new Complex(\n re * Math.cos(im),\n re * Math.sin(im));\n },\n\n /**\n * Calculate the complex square root\n *\n * @returns {Complex}\n */\n 'sqrt': function () {\n\n const a = this['re'];\n const b = this['im'];\n\n if (b === 0) {\n // Real number case\n if (a >= 0) {\n return new Complex(Math.sqrt(a), 0);\n } else {\n return new Complex(0, Math.sqrt(-a));\n }\n }\n\n const r = hypot(a, b);\n\n let re = Math.sqrt(0.5 * (r + Math.abs(a))); // sqrt(2x) / 2 = sqrt(x / 2)\n let im = Math.abs(b) / (2 * re);\n\n if (a >= 0) {\n return new Complex(re, b < 0 ? -im : im);\n } else {\n return new Complex(im, b < 0 ? -re : re);\n }\n },\n\n /**\n * Calculate the complex exponent\n *\n * @returns {Complex}\n */\n 'exp': function () {\n\n const er = Math.exp(this['re']);\n\n if (this['im'] === 0) {\n return new Complex(er, 0);\n }\n return new Complex(\n er * Math.cos(this['im']),\n er * Math.sin(this['im']));\n },\n\n /**\n * Calculate the complex exponent and subtracts one.\n *\n * This may be more accurate than `Complex(x).exp().sub(1)` if\n * `x` is small.\n *\n * @returns {Complex}\n */\n 'expm1': function () {\n\n /**\n * exp(a + i*b) - 1\n = exp(a) * (cos(b) + j*sin(b)) - 1\n = expm1(a)*cos(b) + cosm1(b) + j*exp(a)*sin(b)\n */\n\n const a = this['re'];\n const b = this['im'];\n\n return new Complex(\n Math.expm1(a) * Math.cos(b) + cosm1(b),\n Math.exp(a) * Math.sin(b));\n },\n\n /**\n * Calculate the natural log\n *\n * @returns {Complex}\n */\n 'log': function () {\n\n const a = this['re'];\n const b = this['im'];\n\n if (b === 0 && a > 0) {\n return new Complex(Math.log(a), 0);\n }\n\n return new Complex(\n logHypot(a, b),\n Math.atan2(b, a));\n },\n\n /**\n * Calculate the magnitude of the complex number\n *\n * @returns {number}\n */\n 'abs': function () {\n\n return hypot(this['re'], this['im']);\n },\n\n /**\n * Calculate the angle of the complex number\n *\n * @returns {number}\n */\n 'arg': function () {\n\n return Math.atan2(this['im'], this['re']);\n },\n\n /**\n * Calculate the sine of the complex number\n *\n * @returns {Complex}\n */\n 'sin': function () {\n\n // sin(z) = ( e^iz - e^-iz ) / 2i \n // = sin(a)cosh(b) + i cos(a)sinh(b)\n\n const a = this['re'];\n const b = this['im'];\n\n return new Complex(\n Math.sin(a) * cosh(b),\n Math.cos(a) * sinh(b));\n },\n\n /**\n * Calculate the cosine\n *\n * @returns {Complex}\n */\n 'cos': function () {\n\n // cos(z) = ( e^iz + e^-iz ) / 2 \n // = cos(a)cosh(b) - i sin(a)sinh(b)\n\n const a = this['re'];\n const b = this['im'];\n\n return new Complex(\n Math.cos(a) * cosh(b),\n -Math.sin(a) * sinh(b));\n },\n\n /**\n * Calculate the tangent\n *\n * @returns {Complex}\n */\n 'tan': function () {\n\n // tan(z) = sin(z) / cos(z) \n // = ( e^iz - e^-iz ) / ( i( e^iz + e^-iz ) )\n // = ( e^2iz - 1 ) / i( e^2iz + 1 )\n // = ( sin(2a) + i sinh(2b) ) / ( cos(2a) + cosh(2b) )\n\n const a = 2 * this['re'];\n const b = 2 * this['im'];\n const d = Math.cos(a) + cosh(b);\n\n return new Complex(\n Math.sin(a) / d,\n sinh(b) / d);\n },\n\n /**\n * Calculate the cotangent\n *\n * @returns {Complex}\n */\n 'cot': function () {\n\n // cot(c) = i(e^(ci) + e^(-ci)) / (e^(ci) - e^(-ci))\n\n const a = 2 * this['re'];\n const b = 2 * this['im'];\n const d = Math.cos(a) - cosh(b);\n\n return new Complex(\n -Math.sin(a) / d,\n sinh(b) / d);\n },\n\n /**\n * Calculate the secant\n *\n * @returns {Complex}\n */\n 'sec': function () {\n\n // sec(c) = 2 / (e^(ci) + e^(-ci))\n\n const a = this['re'];\n const b = this['im'];\n const d = 0.5 * cosh(2 * b) + 0.5 * Math.cos(2 * a);\n\n return new Complex(\n Math.cos(a) * cosh(b) / d,\n Math.sin(a) * sinh(b) / d);\n },\n\n /**\n * Calculate the cosecans\n *\n * @returns {Complex}\n */\n 'csc': function () {\n\n // csc(c) = 2i / (e^(ci) - e^(-ci))\n\n const a = this['re'];\n const b = this['im'];\n const d = 0.5 * cosh(2 * b) - 0.5 * Math.cos(2 * a);\n\n return new Complex(\n Math.sin(a) * cosh(b) / d,\n -Math.cos(a) * sinh(b) / d);\n },\n\n /**\n * Calculate the complex arcus sinus\n *\n * @returns {Complex}\n */\n 'asin': function () {\n\n // asin(c) = -i * log(ci + sqrt(1 - c^2))\n\n const a = this['re'];\n const b = this['im'];\n\n const t1 = new Complex(\n b * b - a * a + 1,\n -2 * a * b)['sqrt']();\n\n const t2 = new Complex(\n t1['re'] - b,\n t1['im'] + a)['log']();\n\n return new Complex(t2['im'], -t2['re']);\n },\n\n /**\n * Calculate the complex arcus cosinus\n *\n * @returns {Complex}\n */\n 'acos': function () {\n\n // acos(c) = i * log(c - i * sqrt(1 - c^2))\n\n const a = this['re'];\n const b = this['im'];\n\n const t1 = new Complex(\n b * b - a * a + 1,\n -2 * a * b)['sqrt']();\n\n const t2 = new Complex(\n t1['re'] - b,\n t1['im'] + a)['log']();\n\n return new Complex(Math.PI / 2 - t2['im'], t2['re']);\n },\n\n /**\n * Calculate the complex arcus tangent\n *\n * @returns {Complex}\n */\n 'atan': function () {\n\n // atan(c) = i / 2 log((i + x) / (i - x))\n\n const a = this['re'];\n const b = this['im'];\n\n if (a === 0) {\n\n if (b === 1) {\n return new Complex(0, Infinity);\n }\n\n if (b === -1) {\n return new Complex(0, -Infinity);\n }\n }\n\n const d = a * a + (1.0 - b) * (1.0 - b);\n\n const t1 = new Complex(\n (1 - b * b - a * a) / d,\n -2 * a / d).log();\n\n return new Complex(-0.5 * t1['im'], 0.5 * t1['re']);\n },\n\n /**\n * Calculate the complex arcus cotangent\n *\n * @returns {Complex}\n */\n 'acot': function () {\n\n // acot(c) = i / 2 log((c - i) / (c + i))\n\n const a = this['re'];\n const b = this['im'];\n\n if (b === 0) {\n return new Complex(Math.atan2(1, a), 0);\n }\n\n const d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).atan()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).atan();\n },\n\n /**\n * Calculate the complex arcus secant\n *\n * @returns {Complex}\n */\n 'asec': function () {\n\n // asec(c) = -i * log(1 / c + sqrt(1 - i / c^2))\n\n const a = this['re'];\n const b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(0, Infinity);\n }\n\n const d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).acos()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).acos();\n },\n\n /**\n * Calculate the complex arcus cosecans\n *\n * @returns {Complex}\n */\n 'acsc': function () {\n\n // acsc(c) = -i * log(i / c + sqrt(1 - 1 / c^2))\n\n const a = this['re'];\n const b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(Math.PI / 2, Infinity);\n }\n\n const d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).asin()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).asin();\n },\n\n /**\n * Calculate the complex sinh\n *\n * @returns {Complex}\n */\n 'sinh': function () {\n\n // sinh(c) = (e^c - e^-c) / 2\n\n const a = this['re'];\n const b = this['im'];\n\n return new Complex(\n sinh(a) * Math.cos(b),\n cosh(a) * Math.sin(b));\n },\n\n /**\n * Calculate the complex cosh\n *\n * @returns {Complex}\n */\n 'cosh': function () {\n\n // cosh(c) = (e^c + e^-c) / 2\n\n const a = this['re'];\n const b = this['im'];\n\n return new Complex(\n cosh(a) * Math.cos(b),\n sinh(a) * Math.sin(b));\n },\n\n /**\n * Calculate the complex tanh\n *\n * @returns {Complex}\n */\n 'tanh': function () {\n\n // tanh(c) = (e^c - e^-c) / (e^c + e^-c)\n\n const a = 2 * this['re'];\n const b = 2 * this['im'];\n const d = cosh(a) + Math.cos(b);\n\n return new Complex(\n sinh(a) / d,\n Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'coth': function () {\n\n // coth(c) = (e^c + e^-c) / (e^c - e^-c)\n\n const a = 2 * this['re'];\n const b = 2 * this['im'];\n const d = cosh(a) - Math.cos(b);\n\n return new Complex(\n sinh(a) / d,\n -Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex coth\n *\n * @returns {Complex}\n */\n 'csch': function () {\n\n // csch(c) = 2 / (e^c - e^-c)\n\n const a = this['re'];\n const b = this['im'];\n const d = Math.cos(2 * b) - cosh(2 * a);\n\n return new Complex(\n -2 * sinh(a) * Math.cos(b) / d,\n 2 * cosh(a) * Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex sech\n *\n * @returns {Complex}\n */\n 'sech': function () {\n\n // sech(c) = 2 / (e^c + e^-c)\n\n const a = this['re'];\n const b = this['im'];\n const d = Math.cos(2 * b) + cosh(2 * a);\n\n return new Complex(\n 2 * cosh(a) * Math.cos(b) / d,\n -2 * sinh(a) * Math.sin(b) / d);\n },\n\n /**\n * Calculate the complex asinh\n *\n * @returns {Complex}\n */\n 'asinh': function () {\n\n // asinh(c) = log(c + sqrt(c^2 + 1))\n\n let tmp = this['im'];\n this['im'] = -this['re'];\n this['re'] = tmp;\n const res = this['asin']();\n\n this['re'] = -this['im'];\n this['im'] = tmp;\n tmp = res['re'];\n\n res['re'] = -res['im'];\n res['im'] = tmp;\n return res;\n },\n\n /**\n * Calculate the complex acosh\n *\n * @returns {Complex}\n */\n 'acosh': function () {\n\n // acosh(c) = log(c + sqrt(c^2 - 1))\n\n const res = this['acos']();\n if (res['im'] <= 0) {\n const tmp = res['re'];\n res['re'] = -res['im'];\n res['im'] = tmp;\n } else {\n const tmp = res['im'];\n res['im'] = -res['re'];\n res['re'] = tmp;\n }\n return res;\n },\n\n /**\n * Calculate the complex atanh\n *\n * @returns {Complex}\n */\n 'atanh': function () {\n\n // atanh(c) = log((1+c) / (1-c)) / 2\n\n const a = this['re'];\n const b = this['im'];\n\n const noIM = a > 1 && b === 0;\n const oneMinus = 1 - a;\n const onePlus = 1 + a;\n const d = oneMinus * oneMinus + b * b;\n\n const x = (d !== 0)\n ? new Complex(\n (onePlus * oneMinus - b * b) / d,\n (b * oneMinus + onePlus * b) / d)\n : new Complex(\n (a !== -1) ? (a / 0) : 0,\n (b !== 0) ? (b / 0) : 0);\n\n const temp = x['re'];\n x['re'] = logHypot(x['re'], x['im']) / 2;\n x['im'] = Math.atan2(x['im'], temp) / 2;\n if (noIM) {\n x['im'] = -x['im'];\n }\n return x;\n },\n\n /**\n * Calculate the complex acoth\n *\n * @returns {Complex}\n */\n 'acoth': function () {\n\n // acoth(c) = log((c+1) / (c-1)) / 2\n\n const a = this['re'];\n const b = this['im'];\n\n if (a === 0 && b === 0) {\n return new Complex(0, Math.PI / 2);\n }\n\n const d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).atanh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).atanh();\n },\n\n /**\n * Calculate the complex acsch\n *\n * @returns {Complex}\n */\n 'acsch': function () {\n\n // acsch(c) = log((1+sqrt(1+c^2))/c)\n\n const a = this['re'];\n const b = this['im'];\n\n if (b === 0) {\n\n return new Complex(\n (a !== 0)\n ? Math.log(a + Math.sqrt(a * a + 1))\n : Infinity, 0);\n }\n\n const d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).asinh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).asinh();\n },\n\n /**\n * Calculate the complex asech\n *\n * @returns {Complex}\n */\n 'asech': function () {\n\n // asech(c) = log((1+sqrt(1-c^2))/c)\n\n const a = this['re'];\n const b = this['im'];\n\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n\n const d = a * a + b * b;\n return (d !== 0)\n ? new Complex(\n a / d,\n -b / d).acosh()\n : new Complex(\n (a !== 0) ? a / 0 : 0,\n (b !== 0) ? -b / 0 : 0).acosh();\n },\n\n /**\n * Calculate the complex inverse 1/z\n *\n * @returns {Complex}\n */\n 'inverse': function () {\n\n // 1 / 0 = Infinity and 1 / Infinity = 0\n if (this['isZero']()) {\n return Complex['INFINITY'];\n }\n\n if (this['isInfinite']()) {\n return Complex['ZERO'];\n }\n\n const a = this['re'];\n const b = this['im'];\n\n const d = a * a + b * b;\n\n return new Complex(a / d, -b / d);\n },\n\n /**\n * Returns the complex conjugate\n *\n * @returns {Complex}\n */\n 'conjugate': function () {\n\n return new Complex(this['re'], -this['im']);\n },\n\n /**\n * Gets the negated complex number\n *\n * @returns {Complex}\n */\n 'neg': function () {\n\n return new Complex(-this['re'], -this['im']);\n },\n\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'ceil': function (places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.ceil(this['re'] * places) / places,\n Math.ceil(this['im'] * places) / places);\n },\n\n /**\n * Floors the actual complex number\n *\n * @returns {Complex}\n */\n 'floor': function (places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.floor(this['re'] * places) / places,\n Math.floor(this['im'] * places) / places);\n },\n\n /**\n * Ceils the actual complex number\n *\n * @returns {Complex}\n */\n 'round': function (places) {\n\n places = Math.pow(10, places || 0);\n\n return new Complex(\n Math.round(this['re'] * places) / places,\n Math.round(this['im'] * places) / places);\n },\n\n /**\n * Compares two complex numbers\n *\n * **Note:** new Complex(Infinity).equals(Infinity) === false\n *\n * @returns {boolean}\n */\n 'equals': function (a, b) {\n\n const z = parse(a, b);\n\n return Math.abs(z['re'] - this['re']) <= Complex['EPSILON'] &&\n Math.abs(z['im'] - this['im']) <= Complex['EPSILON'];\n },\n\n /**\n * Clones the actual object\n *\n * @returns {Complex}\n */\n 'clone': function () {\n\n return new Complex(this['re'], this['im']);\n },\n\n /**\n * Gets a string of the actual complex number\n *\n * @returns {string}\n */\n 'toString': function () {\n\n let a = this['re'];\n let b = this['im'];\n let ret = \"\";\n\n if (this['isNaN']()) {\n return 'NaN';\n }\n\n if (this['isInfinite']()) {\n return 'Infinity';\n }\n\n if (Math.abs(a) < Complex['EPSILON']) {\n a = 0;\n }\n\n if (Math.abs(b) < Complex['EPSILON']) {\n b = 0;\n }\n\n // If is real number\n if (b === 0) {\n return ret + a;\n }\n\n if (a !== 0) {\n ret += a;\n ret += \" \";\n if (b < 0) {\n b = -b;\n ret += \"-\";\n } else {\n ret += \"+\";\n }\n ret += \" \";\n } else if (b < 0) {\n b = -b;\n ret += \"-\";\n }\n\n if (1 !== b) { // b is the absolute imaginary part\n ret += b;\n }\n return ret + \"i\";\n },\n\n /**\n * Returns the actual number as a vector\n *\n * @returns {Array}\n */\n 'toVector': function () {\n\n return [this['re'], this['im']];\n },\n\n /**\n * Returns the actual real value of the current object\n *\n * @returns {number|null}\n */\n 'valueOf': function () {\n\n if (this['im'] === 0) {\n return this['re'];\n }\n return null;\n },\n\n /**\n * Determines whether a complex number is not on the Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isNaN': function () {\n return isNaN(this['re']) || isNaN(this['im']);\n },\n\n /**\n * Determines whether or not a complex number is at the zero pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isZero': function () {\n return this['im'] === 0 && this['re'] === 0;\n },\n\n /**\n * Determines whether a complex number is not at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isFinite': function () {\n return isFinite(this['re']) && isFinite(this['im']);\n },\n\n /**\n * Determines whether or not a complex number is at the infinity pole of the\n * Riemann sphere.\n *\n * @returns {boolean}\n */\n 'isInfinite': function () {\n return !this['isFinite']();\n }\n};\n\nComplex['ZERO'] = new Complex(0, 0);\nComplex['ONE'] = new Complex(1, 0);\nComplex['I'] = new Complex(0, 1);\nComplex['PI'] = new Complex(Math.PI, 0);\nComplex['E'] = new Complex(Math.E, 0);\nComplex['INFINITY'] = new Complex(Infinity, Infinity);\nComplex['NAN'] = new Complex(NaN, NaN);\nComplex['EPSILON'] = 1e-15;\n\nObject.defineProperty(Complex, \"__esModule\", { 'value': true });\nComplex['default'] = Complex;\nComplex['Complex'] = Complex;\nmodule['exports'] = 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