Finished expr-eval testing

common/src/lib/expr-eval/expression.mjs

@@ -111,7 +111,7 @@ function simplify(tokens, unaryOps, binaryOps, ternaryOps, values) {
  * In the given instructions, replaces variable by expr.
  * @param {Instruction[]} tokens
  * @param {string} variable
- * @param {number} expr
+ * @param {ExprEvalExpression} expr
  * @return {Instruction[]}
  */
 function substitute(tokens, variable, expr) {
@@ -171,9 +171,6 @@ function evaluate(tokens, expr, values) {
                 nstack.push(n1 ? !!evaluate(n2, expr, values) : false)
             } else if(item.value === "or") {
                 nstack.push(n1 ? true : !!evaluate(n2, expr, values))
-            } else if(item.value === "=") {
-                f = expr.binaryOps[item.value]
-                nstack.push(f(n1, evaluate(n2, expr, values), values))
             } else {
                 f = expr.binaryOps[item.value]
                 nstack.push(f(resolveExpression(n1, values), resolveExpression(n2, values)))
@@ -490,18 +487,6 @@ export class ExprEvalExpression {
         return evaluate(this.tokens, this, values)
     }
 
-    /**
-     * Returns a list of symbols (string of characters) in the expressions.
-     * Can be functions, constants, or variables.
-     * @returns {string[]}
-     */
-    symbols(options) {
-        options = options || {}
-        const vars = []
-        getSymbols(this.tokens, vars, options)
-        return vars
-    }
-
     toString() {
         return expressionToString(this.tokens, false)
     }

common/src/lib/expr-eval/parser.mjs

@@ -47,9 +47,7 @@ const optionNameMap = {
     "not": "logical",
     "?": "conditional",
     ":": "conditional",
-    //'=': 'assignment', // Disable assignment
     "[": "array"
-    //'()=': 'fndef' // Diable function definition
 }
 
 export class Parser {
@@ -109,7 +107,6 @@ export class Parser {
             and: Polyfill.andOperator,
             or: Polyfill.orOperator,
             "in": Polyfill.inOperator,
-            "=": Polyfill.setVar,
             "[": Polyfill.arrayIndex
         }
 
@@ -123,18 +120,13 @@ export class Parser {
             min: Polyfill.min,
             max: Polyfill.max,
             hypot: Math.hypot || Polyfill.hypot,
-            pyt: Math.hypot || Polyfill.hypot, // backward compat
+            pyt: Math.hypot || Polyfill.hypot,
             pow: Math.pow,
             atan2: Math.atan2,
             "if": Polyfill.condition,
             gamma: Polyfill.gamma,
             "Γ": Polyfill.gamma,
             roundTo: Polyfill.roundTo,
-            map: Polyfill.arrayMap,
-            fold: Polyfill.arrayFold,
-            filter: Polyfill.arrayFilter,
-            indexOf: Polyfill.stringOrArrayIndexOf,
-            join: Polyfill.arrayJoin
         }
 
         // These constants will automatically be replaced the MOMENT they are parsed.
@@ -159,10 +151,6 @@ export class Parser {
         return new ExprEvalExpression(instr, this)
     }
 
-    evaluate(expr, variables) {
-        return this.parse(expr).evaluate(variables)
-    }
-
     isOperatorEnabled(op) {
         const optionName = optionNameMap.hasOwnProperty(op) ? optionNameMap[op] : op
         const operators = this.options.operators || {}

common/src/lib/expr-eval/polyfill.mjs

@@ -210,9 +210,8 @@ export function gamma(n) {
 }
 
 export function stringOrArrayLength(s) {
-    if(Array.isArray(s)) {
+    if(Array.isArray(s))
         return s.length
-    }
     return String(s).length
 }
 
@@ -296,58 +295,6 @@ export function min(array) {
     }
 }
 
-export function arrayMap(f, a) {
-    if(typeof f !== "function") {
-        throw new EvalError(qsTranslate("error", "First argument to map is not a function."))
-    }
-    if(!Array.isArray(a)) {
-        throw new EvalError(qsTranslate("error", "Second argument to map is not an array."))
-    }
-    return a.map(function(x, i) {
-        return f(x, i)
-    })
-}
-
-export function arrayFold(f, init, a) {
-    if(typeof f !== "function") {
-        throw new EvalError(qsTranslate("error", "First argument to fold is not a function."))
-    }
-    if(!Array.isArray(a)) {
-        throw new EvalError(qsTranslate("error", "Second argument to fold is not an array."))
-    }
-    return a.reduce(function(acc, x, i) {
-        return f(acc, x, i)
-    }, init)
-}
-
-export function arrayFilter(f, a) {
-    if(typeof f !== "function") {
-        throw new EvalError(qsTranslate("error", "First argument to filter is not a function."))
-    }
-    if(!Array.isArray(a)) {
-        throw new EvalError(qsTranslate("error", "Second argument to filter is not an array."))
-    }
-    return a.filter(function(x, i) {
-        return f(x, i)
-    })
-}
-
-export function stringOrArrayIndexOf(target, s) {
-    if(!(Array.isArray(s) || typeof s === "string")) {
-        throw new Error(qsTranslate("error", "Second argument to indexOf is not a string or array."))
-    }
-
-    return s.indexOf(target)
-}
-
-export function arrayJoin(sep, a) {
-    if(!Array.isArray(a)) {
-        throw new Error(qsTranslate("error", "Second argument to join is not an array."))
-    }
-
-    return a.join(sep)
-}
-
 export function sign(x) {
     return ((x > 0) - (x < 0)) || +x
 }

common/src/lib/expr-eval/tokens.mjs

@@ -472,7 +472,7 @@ export class TokenStream {
                 this.current = this.newToken(TOP, "==")
                 this.pos++
             } else {
-                this.current = this.newToken(TOP, c)
+                return false
             }
         } else if(c === "!") {
             if(this.expression.charAt(this.pos + 1) === "=") {

common/src/module/expreval.mjs

@@ -19,7 +19,7 @@
 import { Module } from "./common.mjs"
 import { Parser } from "../lib/expr-eval/parser.mjs"
 
-const evalVariables = {
+const EVAL_VARIABLES = {
     // Variables not provided by expr-eval.js, needs to be provided manually
     "pi": Math.PI,
     "PI": Math.PI,
@@ -42,7 +42,7 @@ class ExprParserAPI extends Module {
         this.currentVars = {}
         this.#parser = new Parser()
 
-        this.#parser.consts = Object.assign({}, this.#parser.consts, evalVariables)
+        this.#parser.consts = Object.assign({}, this.#parser.consts, EVAL_VARIABLES)
 
         this.#parser.functions.integral = this.integral.bind(this)
         this.#parser.functions.derivative = this.derivative.bind(this)
@@ -84,11 +84,11 @@ class ExprParserAPI extends Module {
         return this.#parser.parse(expression)
     }
 
-    integral(a, b, ...args) {
+    integral(a = null, b = null, ...args) {
         let usage1 = qsTranslate("usage", "integral(<from: number>, <to: number>, <f: ExecutableObject>)")
         let usage2 = qsTranslate("usage", "integral(<from: number>, <to: number>, <f: string>, <variable: string>)")
         let f = this.parseArgumentsForFunction(args, usage1, usage2)
-        if(a == null || b == null)
+        if(typeof a !== "number" || typeof b !== "number")
             throw EvalError(qsTranslate("usage", "Usage:\n%1\n%2").arg(usage1).arg(usage2))
 
         // https://en.wikipedia.org/wiki/Simpson%27s_rule
@@ -101,10 +101,10 @@ class ExprParserAPI extends Module {
         let usage2 = qsTranslate("usage", "derivative(<f: string>, <variable: string>, <x: number>)")
         let x = args.pop()
         let f = this.parseArgumentsForFunction(args, usage1, usage2)
-        if(x == null)
+        if(typeof x !== "number")
             throw EvalError(qsTranslate("usage", "Usage:\n%1\n%2").arg(usage1).arg(usage2))
 
-        let derivative_precision = x / 10
+        let derivative_precision = 1e-8
         return (f(x + derivative_precision / 2) - f(x - derivative_precision / 2)) / derivative_precision
     }
 }

common/test/module/base.mjs

@@ -17,8 +17,8 @@
  */
 
 // Load prior tests
-import "./events.mjs"
+import "../basics/events.mjs"
-import "./interface.mjs"
+import "../basics/interface.mjs"
 
 import { describe, it } from "mocha"
 import { expect } from "chai"

common/test/module/expreval.mjs

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

common/test/module/objects.mjs

@@ -17,14 +17,14 @@
  */
 
 // Load prior tests
-import "./module-base.mjs"
+import "./base.mjs"
-import "./utils.mjs"
+import "../basics/utils.mjs"
 
 import { describe, it } from "mocha"
 import { expect } from "chai"
 
-import Objects from "../../src/module/objects.mjs"
+// import Objects from "../../src/module/objects.mjs"
-
+//
-describe("Module/Objects", function() {
+// describe("Module/Objects", function() {
-
+//
-})
+// })

common/test/module/settings.mjs

@@ -17,8 +17,8 @@
  */
 
 // Load prior tests
-import "./module-base.mjs"
+import "./base.mjs"
-import "./utils.mjs"
+import "../basics/utils.mjs"
 
 import { describe, it } from "mocha"
 import { expect } from "chai"