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Poppe","url":"https://mauriciopoppe.com"},"license":"MIT","homepage":"https://github.com/mauriciopoppe/interval-arithmetic-eval#readme","keywords":["interval-arithmetic-eval","interval","interval-arithmetic","math","arithmetic","interpreter","eval"],"repository":{"type":"git","url":"git+https://github.com/mauriciopoppe/interval-arithmetic-eval.git"},"description":"Interprets/evaluates mathematical expressions using interval arithmetic","maintainers":[{"name":"maurizzzio","email":"mauricio.poppe@gmail.com"},{"name":"mauriciopoppe","email":"5gl9sqyff@mozmail.com"}],"readme":"# interval-arithmetic-eval\n\n[![NPM][npm-image]][npm-url]\n![ci](https://github.com/mauriciopoppe/interval-arithmetic-eval/workflows/ci/badge.svg)\n\n[![js-standard-style](https://cdn.rawgit.com/feross/standard/master/badge.svg)](https://github.com/feross/standard)\n\n> Interprets/evaluates mathematical expressions using interval arithmetic\n\n<!-- START doctoc generated TOC please keep comment here to allow auto update -->\n<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->\n**Table of Contents**  *generated with [DocToc](https://github.com/thlorenz/doctoc)*\n\n- [Description](#description)\n- [Installation](#installation)\n- [API](#api)\n  - [`code = compile(expression)`](#code--compileexpression)\n    - [`code.eval([scope])`](#codeevalscope)\n  - [`compile.policies`](#compilepolicies)\n    - [`compile.policies.identifierAllowed`](#compilepoliciesidentifierallowed)\n    - [`compile.policies.disableRounding`](#compilepoliciesdisablerounding)\n    - [`compile.policies.enableRounding`](#compilepoliciesenablerounding)\n- [Examples](#examples)\n  - [Basic operations](#basic-operations)\n  - [Function calls](#function-calls)\n  - [Scope substitution](#scope-substitution)\n\n<!-- END doctoc generated TOC please keep comment here to allow auto update -->\n\n## Description\n\nThis module evaluates the generated code from [math-codegen](https://github.com/mauriciopoppe/math-codegen)\nfor the namespace [interval-arithmetic](https://github.com/mauriciopoppe/interval-arithmetic) providing\nthe necessary adapter methods\n\n## Installation\n\n```sh\n$ npm install --save interval-arithmetic-eval\n```\n\n## API\n\n```javascript\nvar compile = require('interval-arithmetic-eval');\n```\n\n### `code = compile(expression)`\n\n**params**\n* `expression` {string} the expression to be parsed\n\n`expression` syntax:\n- literals\n  - numbers are turned into [singleton intervals](https://github.com/mauriciopoppe/interval-arithmetic#instancesingletonv)\n- identifiers\n  - All the methods/utilities/constants available in [interval-arithmetic](https://github.com/mauriciopoppe/interval-arithmetic)\n  - The properties declared in a scope object (top level only)\n- binary expressions\n  - `+` addition\n  - `-` subtraction\n  - `*` multiplication\n  - `/` division\n  - `^` power (with the condition that the exponent is a signed integer)\n- unary expressions\n  - `+` identity\n  - `-` negative\n- array expressions\n  - numbers are turned into [intervals](https://github.com/mauriciopoppe/interval-arithmetic#instanceassignlo-hi)\n- call expressions\n  - All the methods/utilities/constants available in [interval-arithmetic](https://github.com/mauriciopoppe/interval-arithmetic)\n  except `pow` (which is a special operator)\n  - The functions declared in a scope object (top level only)\n\n**returns** {Object}\n* `return.eval` {function} The compiled function to be called with some scope variables\n\n#### `code.eval([scope])`\n\n**params**\n* `scope` {Object}\n\nAn optional object which holds some variables used in the original expression\nto be substituted, the following transformations are done with the values when evaluated\n  * a single `number` is converted to a [singleton interval](https://github.com/mauriciopoppe/interval-arithmetic#instancesingletonv)\n  * an `array` is converted to an unbounded [interval](https://github.com/mauriciopoppe/interval-arithmetic#instanceassignlo-hi),\n   NOTE: this method checks empty intervals\n  * an `object` which has the `lo` and `hi` properties is converted into an [interval](https://github.com/mauriciopoppe/interval-arithmetic#instanceassignlo-hi)\n   NOTE: this method checks empty intervals\n\n**returns** {Interval} Returns an instance of the [interval-arithmetic module](https://github.com/mauriciopoppe/interval-arithmetic)\n\n### `compile.policies`\n\nPolicies used during the evaluation of an expression\n\n#### `compile.policies.identifierAllowed`\n\nAssign a function which determines if the given name to be resolved from the scope is valid\n\n**default value**\n```javascript\ncompile.policies.identifierAllowed = function (name) {\n  // any name from the scope is valid\n  return true;\n}\n```\n\n#### `compile.policies.disableRounding`\n\nCall this function to disable rounding interval bounds to the next/previous floating point number\n(rounding is enabled by default)\n\n#### `compile.policies.enableRounding`\n\nCall this function to enable rounding interval bounds to the next/previous floating point number\n(rounding is enabled by default)\n\n## Examples\n\nBoilerplate code for the examples:\n\n```javascript\ncompile(expression).eval(scope)\n\n// e.g.\ncompile('1').eval({});        // { lo: 1, hi: 1 }\ncompile('x').eval({x: 1})     // { lo: 1, hi: 1 }\n```\n\n### Basic operations\n```javascript\n1\n>  { lo: 1, hi: 1 }\n\n// unary minus\n-1\n>  { lo: -1, hi: -1 }\n\n// floating point error is carried over in the operations\n-1 + 3\n>  { lo: 1.9999999999999998, hi: 2.0000000000000004 }\n\n// [1, 1] / [3, 3]\n1 / 3\n>  { lo: 0.33333333333333326, hi: 0.33333333333333337 }\n\n-1 / 3\n>  { lo: -0.33333333333333337, hi: -0.33333333333333326 }\n\n-(1 / 3)\n>  { lo: -0.33333333333333337, hi: -0.33333333333333326 }\n\n-1 / -3\n>  { lo: 0.33333333333333326, hi: 0.33333333333333337 }\n\n2 * 3\n>  { lo: 5.999999999999999, hi: 6.000000000000001 }\n\n[1, 2]\n>  { lo: 1, hi: 2 }\n\n-[1, 2]\n>  { lo: -2, hi: -1 }\n\n[1, 2] + [-1, 2]\n>  { lo: -5e-324, hi: 4.000000000000001 }\n\n// means [1, 2] + [-2, 1]\n[1, 2] - [-1, 2]\n>  { lo: -1.0000000000000002, hi: 3.0000000000000004 }\n\n[1, 2] * [-1, 2]\n>  { lo: -2.0000000000000004, hi: 4.000000000000001 }\n\n[1, 2] / [2, 3]\n>  { lo: 0.33333333333333326, hi: 1.0000000000000002 }\n\n// if the upper interval has zero the result will also contain a zero\n[-1, 1] / [2, 3]\n>  { lo: -0.5000000000000001, hi: 0.5000000000000001 }\n\n// division by an interval that has zero results in a whole interval\n[1, 2] / [-1, 1]\n>  { lo: -Infinity, hi: Infinity }\n\n// integer power\n[-3, 2]^2\n>  { lo: 0, hi: 9.000000000000004 }\n\n// integer negative power, 1 / [-3, 2]^2 = 1 / [0, 9]\n[-3, 2]^-2\n>  { lo: 0.11111111111111105, hi: Infinity }\n\n// integer power (odd power)\n[-3, 2]^3\n>  { lo: -26.99999999999999, hi: 8.000000000000004 }\n\n```\n### Function calls\n```javascript\n// constants available in interval-arithmetic\nZERO + ONE\n>  { lo: 0.9999999999999999, hi: 1.0000000000000002 }\n\n// constant available in interval-arithmetic\nPI\n>  { lo: 3.141592653589793, hi: 3.1415926535897936 }\n\n// same as -1\nnegative(1)\n>  { lo: -1, hi: -1 }\n\n// same as -1 + 3\nadd(-1, 3)\n>  { lo: 1.9999999999999998, hi: 2.0000000000000004 }\n\n// same as [1, 2] + [-1, 2]\nadd([1, 2], [-1, 2])\n>  { lo: -5e-324, hi: 4.000000000000001 }\n\n// cosine of the interval [0, 0]\ncos(0)\n>  { lo: 0.9999999999999999, hi: 1.0000000000000002 }\n\n// cosine of the interval [PI_low, PI_high]\ncos(PI)\n>  { lo: -1, hi: -0.9999999999999999 }\n\n// cosine of the interval [PI_low / 2, PI_high / 2] which contains zero\ncos(PI_HALF)\n>  { lo: -3.82856869892695e-16, hi: 2.8327694488239903e-16 }\n\n// all the available values for cosine\ncos([0, 3.15])\n>  { lo: -1, hi: 1.0000000000000002 }\n\nsin(PI_HALF)\n>  { lo: 0.9999999999999999, hi: 1 }\n\n// absolute value of the interval [-1, 1]\nabs(-1)\n>  { lo: 1, hi: 1 }\n\n// absolute value of the interval [-3, -2]\nabs([-3, -2])\n>  { lo: 2, hi: 3 }\n\n// absolute value of the interval [-2, 3]\nabs([-2, 3])\n>  { lo: 0, hi: 3 }\n\n// 1 / 2\nmultiplicativeInverse(2)\n>  { lo: 0.49999999999999994, hi: 0.5000000000000001 }\n\n```\n### Scope substitution\n```javascript\n// using the number 4 stored in scope.x\n// scope:  { x: 4 }\nx\n>  { lo: 4, hi: 4 }\n\n// using the interval [2, 3] stored in scope.x\n// scope:  { x: [ 2, 3 ] }\nx\n>  { lo: 2, hi: 3 }\n\n// using the interval Instance stored in scope.x\n// scope:  { x: { lo: 2, hi: 3 } }\nx\n>  { lo: 2, hi: 3 }\n\n// adding a constant and a scope variable\n// scope:  { x: [ 1, 1 ] }\nONE + x\n>  { lo: 1.9999999999999998, hi: 2.0000000000000004 }\n\n// division between two variables stored in the scope\n// scope:  { x: [ 2, 3 ], y: [ 1, 2 ] }\nx / y\n>  { lo: 0.9999999999999999, hi: 3.0000000000000004 }\n\n// complex expression\n// scope:  { x: [ 0, 1 ] }\nsin(exp(x)) + tan(x) - 1/cos(PI) * ([1, 3]^2)\n>  { lo: 1.410781290502905, hi: 11.557407724654913 }\n\n```\n\n2015 © Mauricio Poppe\n\n[npm-image]: https://img.shields.io/npm/v/interval-arithmetic-eval.svg?style=flat\n[npm-url]: https://npmjs.org/package/interval-arithmetic-eval\n","readmeFilename":"README.md"}