389 lines
No EOL
21 KiB
JavaScript
389 lines
No EOL
21 KiB
JavaScript
/**
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* LogarithmPlotter - 2D plotter software to make BODE plots, sequences and distribution functions.
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* Copyright (C) 2021-2024 Ad5001
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <https://www.gnu.org/licenses/>.
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*/
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// Load prior tests
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import "./base.mjs"
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import { describe, it } from "mocha"
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import { expect } from "chai"
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import ExprEval from "../../src/module/expreval.mjs"
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describe("Module/ExprEval", function() {
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describe("#parse.evaluate", function() {
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const evaluate = (expr, vals = {}) => ExprEval.parse(expr).evaluate(vals)
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it("parses simple mathematical expressions", function() {
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expect(evaluate(`"\\'\\"\\\\\\/\\b\\f\\n\\r\\t\\u3509"`)).to.equal(`'"\\/\b\f\n\r\t\u3509`)
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expect(evaluate("1")).to.equal(1)
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expect(evaluate(" 1 ")).to.equal(1)
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expect(evaluate("0xFF")).to.equal(255)
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expect(evaluate("0b11")).to.equal(3)
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expect(evaluate("-1")).to.equal(-1)
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expect(evaluate("-(-1)")).to.equal(1)
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expect(evaluate("+(-1)")).to.equal(-1)
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expect(evaluate("3!")).to.equal(6)
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expect(evaluate("1+1")).to.equal(2)
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expect(evaluate("4*3")).to.equal(12)
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expect(evaluate("4•3")).to.equal(12)
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expect(evaluate("64/4")).to.equal(16)
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expect(evaluate("2^10")).to.equal(1024)
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expect(evaluate("10%3")).to.equal(1)
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expect(evaluate("10%3")).to.equal(1)
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// Test priorities
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expect(evaluate("10*10+10*10")).to.equal(200)
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expect(evaluate("10/10+10/10")).to.equal(2)
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expect(evaluate("10/10+10/10")).to.equal(2)
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expect(evaluate("2^2-2^2")).to.equal(0)
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expect(evaluate("(2^2-2)^2")).to.equal(4)
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})
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it("parses equality and test statements", function() {
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expect(evaluate("10%3 == 1 ? 2 : 1")).to.equal(2)
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expect(evaluate("not(10%3 == 1) ? 2 : 1")).to.equal(1)
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expect(evaluate("10%3 != 1 ? 2 : 1")).to.equal(1)
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expect(evaluate("10 < 3 ? 2 : 1")).to.equal(1)
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expect(evaluate("10 > 3 ? (2+1) : 1")).to.equal(3)
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expect(evaluate("10 <= 3 ? 4 : 1")).to.equal(1)
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expect(evaluate("10 >= 3 ? 4 : 1")).to.equal(4)
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// Check equality
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expect(evaluate("10 < 10 ? 2 : 1")).to.equal(1)
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expect(evaluate("10 > 10 ? 2 : 1")).to.equal(1)
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expect(evaluate("10 <= 10 ? 4 : 1")).to.equal(4)
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expect(evaluate("10 >= 10 ? 4 : 1")).to.equal(4)
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// Check 'and' and 'or'
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expect(evaluate("10 <= 3 and 10 < 10 ? 4 : 1")).to.equal(1)
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expect(evaluate("10 <= 10 and 10 < 10 ? 4 : 1")).to.equal(1)
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expect(evaluate("10 <= 10 and 10 < 20 ? 4 : 1")).to.equal(4)
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expect(evaluate("10 <= 3 or 10 < 10 ? 4 : 1")).to.equal(1)
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expect(evaluate("10 <= 10 or 10 < 10 ? 4 : 1")).to.equal(4)
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expect(evaluate("10 <= 10 or 10 < 20 ? 4 : 1")).to.equal(4)
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})
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it("parses singular function operators (functions with one arguments and no parenthesis)", function() {
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// Trigonometric functions
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expect(evaluate("sin 0")).to.be.approximately(0, Number.EPSILON)
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expect(evaluate("cos 0")).to.be.approximately(1, Number.EPSILON)
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expect(evaluate("tan 0")).to.be.approximately(0, Number.EPSILON)
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expect(evaluate("asin 1")).to.be.approximately(Math.PI / 2, Number.EPSILON)
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expect(evaluate("acos 1")).to.be.approximately(0, Number.EPSILON)
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expect(evaluate("atan 1")).to.be.approximately(Math.PI / 4, Number.EPSILON)
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expect(evaluate("sinh 1")).to.be.approximately(Math.sinh(1), Number.EPSILON)
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expect(evaluate("cosh 1")).to.be.approximately(Math.cosh(1), Number.EPSILON)
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expect(evaluate("tanh 1")).to.be.approximately(Math.tanh(1), Number.EPSILON)
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expect(evaluate("asinh 1")).to.be.approximately(Math.asinh(1), Number.EPSILON)
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expect(evaluate("acosh 1")).to.be.approximately(Math.acosh(1), Number.EPSILON)
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expect(evaluate("atanh 0.5")).to.be.approximately(Math.atanh(0.5), Number.EPSILON)
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// Reverse trigonometric
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expect(evaluate("asin sin 1")).to.be.approximately(1, Number.EPSILON)
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expect(evaluate("acos cos 1")).to.be.approximately(1, Number.EPSILON)
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expect(evaluate("atan tan 1")).to.be.approximately(1, Number.EPSILON)
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expect(evaluate("asinh sinh 1")).to.be.approximately(1, Number.EPSILON)
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expect(evaluate("acosh cosh 1")).to.be.approximately(1, Number.EPSILON)
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expect(evaluate("atanh tanh 1")).to.be.approximately(1, Number.EPSILON)
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// Other functions
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expect(evaluate("sqrt 4")).to.be.approximately(2, Number.EPSILON)
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expect(evaluate("sqrt 2")).to.be.approximately(Math.sqrt(2), Number.EPSILON)
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expect(evaluate("cbrt 27")).to.be.approximately(3, Number.EPSILON)
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expect(evaluate("cbrt 14")).to.be.approximately(Math.cbrt(14), Number.EPSILON)
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expect(evaluate("log 1")).to.be.approximately(Math.log(1), Number.EPSILON)
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expect(evaluate("ln 1")).to.be.approximately(Math.log(1), Number.EPSILON)
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expect(evaluate("log2 8")).to.be.approximately(3, Number.EPSILON)
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expect(evaluate("log10 100")).to.be.approximately(2, Number.EPSILON)
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expect(evaluate("lg 100")).to.be.approximately(2, Number.EPSILON)
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expect(evaluate("expm1 0")).to.be.approximately(0, Number.EPSILON)
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expect(evaluate("expm1 10")).to.be.approximately(Math.expm1(10), Number.EPSILON)
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expect(evaluate("log1p 0")).to.be.approximately(0, Number.EPSILON)
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expect(evaluate("log1p 10")).to.be.approximately(Math.log1p(10), Number.EPSILON)
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// Roundings/Sign transformations
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expect(evaluate("abs -12.34")).to.equal(12.34)
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expect(evaluate("abs 12.45")).to.equal(12.45)
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expect(evaluate("ceil 12.45")).to.equal(13)
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expect(evaluate("ceil 12.75")).to.equal(13)
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expect(evaluate("ceil 12.0")).to.equal(12)
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expect(evaluate("ceil -12.6")).to.equal(-12)
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expect(evaluate("floor 12.45")).to.equal(12)
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expect(evaluate("floor 12.75")).to.equal(12)
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expect(evaluate("floor 12.0")).to.equal(12)
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expect(evaluate("floor -12.2")).to.equal(-13)
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expect(evaluate("round 12.45")).to.equal(12)
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expect(evaluate("round 12.75")).to.equal(13)
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expect(evaluate("round 12.0")).to.equal(12)
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expect(evaluate("round -12.2")).to.equal(-12)
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expect(evaluate("round -12.6")).to.equal(-13)
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expect(evaluate("trunc 12.45")).to.equal(12)
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expect(evaluate("trunc 12.75")).to.equal(12)
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expect(evaluate("trunc 12.0")).to.equal(12)
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expect(evaluate("trunc -12.2")).to.equal(-12)
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expect(evaluate("exp 1")).to.be.approximately(Math.E, Number.EPSILON)
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expect(evaluate("exp 10")).to.be.approximately(Math.pow(Math.E, 10), 1e-8)
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expect(evaluate("length \"string\"")).to.equal(6)
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expect(evaluate("sign 0")).to.equal(0)
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expect(evaluate("sign -0")).to.equal(0)
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expect(evaluate("sign -10")).to.equal(-1)
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expect(evaluate("sign 80")).to.equal(1)
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})
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it("parses regular functions", function() {
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for(let i = 0; i < 1000; i++) {
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expect(evaluate("random()")).to.be.within(0, 1)
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expect(evaluate("random(100)")).to.be.within(0, 100)
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}
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expect(evaluate("fac(3)")).to.equal(6)
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expect(evaluate("fac(10)")).to.equal(3628800)
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expect(evaluate("min(10, 20)")).to.equal(10)
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expect(evaluate("min(-10, -20)")).to.equal(-20)
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expect(evaluate("max(10, 20)")).to.equal(20)
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expect(evaluate("max(-10, -20)")).to.equal(-10)
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expect(evaluate("hypot(3, 4)")).to.equal(5)
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expect(evaluate("pyt(30, 40)")).to.equal(50)
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expect(evaluate("atan2(1, 1)")).to.be.approximately(Math.PI / 4, Number.EPSILON)
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expect(evaluate("atan2(1, 0)")).to.be.approximately(Math.PI / 2, Number.EPSILON)
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expect(evaluate("atan2(0, 1)")).to.be.approximately(0, Number.EPSILON)
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expect(evaluate("if(10 == 10, 1, 0)")).to.be.approximately(1, Number.EPSILON)
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expect(evaluate("if(10 != 10, 1, 0)")).to.be.approximately(0, Number.EPSILON)
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expect(evaluate("gamma(10) == 9!")).to.be.true
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expect(evaluate("Γ(30) == 29!")).to.be.true
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expect(evaluate("Γ(25) == 23!")).to.be.false
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expect(evaluate("roundTo(26.04)")).to.equal(26)
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expect(evaluate("roundTo(26.04, 2)")).to.equal(26.04)
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expect(evaluate("roundTo(26.04836432123, 5)")).to.equal(26.04836)
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expect(evaluate("roundTo(26.04836432123, 5)")).to.equal(26.04836)
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})
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it("parses arrays and access their members", function() {
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expect(evaluate("[6, 7, 9]")).to.have.lengthOf(3)
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expect(evaluate("[6, 7, 9]")).to.deep.equal([6, 7, 9])
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expect(evaluate("[6, \"8\", 9]")).to.have.lengthOf(3)
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expect(evaluate("[6, 7%2]")).to.deep.equal([6, 1])
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// Access array indices
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expect(evaluate("[6, 7][1]")).to.equal(7)
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expect(evaluate("[6, 7, 8, 9, 10][2*2-1]")).to.equal(9)
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})
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it("can apply functions to arrays", function() {
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expect(evaluate("length [6, 7, 9]")).to.equal(3)
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expect(evaluate("length [6, 7, 8, 9]")).to.equal(4)
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expect(evaluate("[6, 7, 9]||[10,11,12]")).to.deep.equal([6, 7, 9, 10, 11, 12])
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expect(evaluate("6 in [6, 7, 9]")).to.be.true
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expect(evaluate("2 in [6, 7, 9]")).to.be.false
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expect(evaluate("min([10, 6, 7, 8, 9])")).to.equal(6)
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expect(evaluate("max([6, 7, 8, 9, 2])")).to.equal(9)
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})
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it("throws errors when invalid function parameters are provided", function() {
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expect(() => evaluate("max()")).to.throw()
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expect(() => evaluate("min()")).to.throw()
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})
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it("parses constants", function() {
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expect(evaluate("pi")).to.equal(Math.PI)
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expect(evaluate("PI")).to.equal(Math.PI)
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expect(evaluate("π")).to.equal(Math.PI)
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expect(evaluate("e")).to.equal(Math.E)
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expect(evaluate("E")).to.equal(Math.E)
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expect(evaluate("true")).to.be.true
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expect(evaluate("false")).to.be.false
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// expect(evaluate("∞")).to.equal(Math.Infinity)
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// expect(evaluate("infinity")).to.equal(Math.Infinity)
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// expect(evaluate("Infinity")).to.equal(Math.Infinity)
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})
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it("can be provided variables", function() {
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const u = [1, 2, 3, 4]
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const x = 10
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const s_ = "string"
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const f = (x) => x * 2
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expect(evaluate("u", { u })).to.deep.equal([...u])
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expect(evaluate("x", { x })).to.equal(x)
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expect(evaluate("s_", { s_ })).to.equal(s_)
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expect(evaluate("f", { f })).to.equal(f)
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expect(evaluate("b", { b: true })).to.equal(true)
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expect(evaluate("u[1]", { u })).to.equal(u[1])
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expect(evaluate("x/2", { x })).to.equal(x / 2)
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expect(evaluate("f(2)", { f })).to.equal(f(2))
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expect(evaluate("if(x == f(2), u[0], s_)", { x, u, s_, f })).to.equal(s_)
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})
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it("can be provided objects", function() {
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const obj = { execute: (x) => x * 3, x: 10, y: { cached: true, execute: () => 20 } }
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expect(evaluate("O(3)+O(2)", { O: obj })).to.equal(9 + 6)
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expect(evaluate("O.x+O.y", { O: obj })).to.equal(30)
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})
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it("throws errors when trying to use variables wrongly", function() {
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const obj = { execute: (x) => x * 3 }
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expect(() => evaluate("O()", { O: obj })).to.throw()
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expect(() => evaluate("O.x", { O: obj })).to.throw()
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expect(() => evaluate("x()", { x: 10 })).to.throw()
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expect(() => evaluate("x")).to.throw()
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expect(() => evaluate("n")).to.throw()
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})
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it("can do it all at once", function() {
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const obj = { execute: (x) => x * 3, x: 20 }
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const u = [1, 2, 3, 4]
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const x = 10
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const s = "string"
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const expr = "random(e) <= e ? fac(x)+u[2]+O(pi) : O.x+length s"
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expect(evaluate(expr, { x, u, s, O: obj })).to.equal(3628803 + obj.execute(Math.PI))
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})
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it("cannot parse invalid expressions", function() {
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expect(() => evaluate("1+")).to.throw()
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expect(() => evaluate("@")).to.throw()
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expect(() => evaluate("]")).to.throw()
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expect(() => evaluate("")).to.throw()
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expect(() => evaluate(`"\\u35P2"`)).to.throw()
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expect(() => evaluate(`"\\x"`)).to.throw()
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})
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})
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describe("#parse.toString", function() {
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it("can be converted back into a string without changes", function() {
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const expressions = ["pi+2*(e+2)^4", "sin(1+2!+pi+cos -3)^2", "[2,3,4][(2-1)*2]", "true ? false : true"]
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for(const ogString of expressions) {
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const expr = ExprEval.parse(ogString)
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const convertedString = expr.toString()
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expect(ExprEval.parse(convertedString)).to.deep.equal(expr) // Can be reparsed just the same
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}
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})
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})
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describe("#parse.substitute", function() {
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const parsed = ExprEval.parse("if(x == 0, 1, 2+x)")
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it("can substitute a variable for a number", function() {
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expect(parsed.substitute("x", 10).evaluate({})).to.equal(12)
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expect(parsed.substitute("x", 0).evaluate({})).to.equal(1)
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})
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it("can substitute a variable for another", function() {
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expect(parsed.substitute("x", "b").evaluate({ b: 10 })).to.equal(12)
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expect(parsed.substitute("x", "b").evaluate({ b: 0 })).to.equal(1)
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})
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it("can substitute a variable for an expression", function() {
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expect(parsed.substitute("x", "sin α").evaluate({ "α": Math.PI / 2 })).to.be.approximately(3, Number.EPSILON)
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expect(parsed.substitute("x", "sin α").evaluate({ "α": 0 })).to.equal(1)
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expect(parsed.substitute("x", "α == 1 ? 0 : 1").evaluate({ "α": 1 })).to.equal(1)
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})
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})
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describe("#parse.variables", function() {
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it("can list all parsed undefined variables", function() {
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expect(ExprEval.parse("a+b+x+pi+sin(b)").variables()).to.deep.equal(["a", "b", "x"])
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})
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})
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describe("#parse.toJSFunction", function() {
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const func = ExprEval.parse("not(false) ? a+b+x+1/x : x!+random()+A.x+[][0]").toJSFunction("x", { a: "10", b: "0" })
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expect(func(10)).to.equal(20.1)
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expect(func(20)).to.equal(30.05)
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})
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describe("#integral", function() {
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it("returns the integral value between two integers", function() {
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expect(ExprEval.integral(0, 1, "1", "t")).to.be.approximately(1, Number.EPSILON)
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expect(ExprEval.integral(0, 1, "t", "t")).to.be.approximately(1 / 2, Number.EPSILON)
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expect(ExprEval.integral(0, 1, "t^2", "t")).to.be.approximately(1 / 3, Number.EPSILON)
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expect(ExprEval.integral(0, 1, "t^3", "t")).to.be.approximately(1 / 4, 0.01)
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expect(ExprEval.integral(0, 1, "t^4", "t")).to.be.approximately(1 / 5, 0.01)
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expect(ExprEval.integral(10, 40, "1", "t")).to.equal(30)
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expect(ExprEval.integral(20, 40, "1", "t")).to.equal(20)
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expect(ExprEval.integral(0, 10, { execute: (x) => 1 })).to.equal(10)
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expect(ExprEval.integral(0, 10, { execute: (x) => x })).to.equal(50)
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expect(ExprEval.integral(0, 1, { execute: (x) => Math.pow(x, 2) })).to.equal(1 / 3)
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})
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it("throws error when provided with invalid arguments", function() {
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const noArg1 = () => ExprEval.integral()
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const noArg2 = () => ExprEval.integral(0)
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const noFunction = () => ExprEval.integral(0, 1)
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const invalidObjectProvided = () => ExprEval.integral(0, 1, { a: 2 })
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const notAnObjectProvided = () => ExprEval.integral(0, 1, "string")
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const invalidFromProvided = () => ExprEval.integral("ze", 1, "t^2", "t")
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const invalidToProvided = () => ExprEval.integral(0, "ze", "t^2", "t")
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const notStringProvided1 = () => ExprEval.integral(0, 1, { a: 2 }, { b: 1 })
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const notStringProvided2 = () => ExprEval.integral(0, 1, { a: 2 }, "t")
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const notStringProvided3 = () => ExprEval.integral(0, 1, "t^2", { b: 1 })
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const invalidVariableProvided = () => ExprEval.integral(0, 1, "t^2", "93IO74")
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const invalidExpressionProvided = () => ExprEval.integral(0, 1, "t^2t", "t")
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const invalidVariableInExpression = () => ExprEval.integral(0, 1, "t^2+x", "t")
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expect(noArg1).to.throw()
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expect(noArg2).to.throw()
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expect(noFunction).to.throw()
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expect(invalidObjectProvided).to.throw()
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expect(invalidFromProvided).to.throw()
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expect(invalidToProvided).to.throw()
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expect(notAnObjectProvided).to.throw()
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expect(notStringProvided1).to.throw()
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expect(notStringProvided2).to.throw()
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expect(notStringProvided3).to.throw()
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expect(invalidVariableProvided).to.throw()
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expect(invalidExpressionProvided).to.throw()
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expect(invalidVariableInExpression).to.throw()
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})
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})
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describe("#derivative", function() {
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const DELTA = 1e-5
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it("returns the derivative value of a function at a given number", function() {
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expect(ExprEval.derivative("1", "t", 2)).to.be.approximately(0, DELTA)
|
||
expect(ExprEval.derivative("t", "t", 2)).to.be.approximately(1, DELTA)
|
||
expect(ExprEval.derivative("t^2", "t", 2)).to.be.approximately(4, DELTA)
|
||
expect(ExprEval.derivative("t^3", "t", 2)).to.be.approximately(12, DELTA)
|
||
expect(ExprEval.derivative("t^4", "t", 2)).to.be.approximately(32, DELTA)
|
||
|
||
expect(ExprEval.derivative({ execute: (x) => 1 }, 10)).to.equal(0)
|
||
expect(ExprEval.derivative({ execute: (x) => x }, 10)).to.be.approximately(1, DELTA)
|
||
expect(ExprEval.derivative({ execute: (x) => Math.pow(x, 2) }, 10)).to.be.approximately(20, DELTA)
|
||
})
|
||
|
||
it("throws error when provided with invalid arguments", function() {
|
||
const noArg1 = () => ExprEval.derivative()
|
||
const noArg2 = () => ExprEval.derivative("1")
|
||
const noValue1 = () => ExprEval.derivative("0", "1")
|
||
const noValue2 = () => ExprEval.derivative({ execute: (x) => 1 })
|
||
const invalidObjectProvided = () => ExprEval.derivative({ a: 2 }, 1)
|
||
const notAnObjectProvided = () => ExprEval.derivative("string", 1)
|
||
const invalidXProvided = () => ExprEval.derivative("t^2+x", "t", "ze")
|
||
const notStringProvided1 = () => ExprEval.derivative({ a: 2 }, { b: 1 }, 1)
|
||
const notStringProvided2 = () => ExprEval.derivative({ a: 2 }, "t", 1)
|
||
const notStringProvided3 = () => ExprEval.derivative("t^2", { b: 1 }, 1)
|
||
const invalidVariableProvided = () => ExprEval.derivative("t^2", "93IO74", 1)
|
||
const invalidExpressionProvided = () => ExprEval.derivative("t^2t", "t", 1)
|
||
const invalidVariableInExpression = () => ExprEval.derivative("t^2+x", "t", 1)
|
||
expect(noArg1).to.throw()
|
||
expect(noArg2).to.throw()
|
||
expect(noValue1).to.throw()
|
||
expect(noValue2).to.throw()
|
||
expect(invalidObjectProvided).to.throw()
|
||
expect(invalidXProvided).to.throw()
|
||
expect(notAnObjectProvided).to.throw()
|
||
expect(notStringProvided1).to.throw()
|
||
expect(notStringProvided2).to.throw()
|
||
expect(notStringProvided3).to.throw()
|
||
expect(invalidVariableProvided).to.throw()
|
||
expect(invalidExpressionProvided).to.throw()
|
||
expect(invalidVariableInExpression).to.throw()
|
||
})
|
||
})
|
||
}) |