mathjs
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Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif
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JavaScript
var typedFunction = require('typed-function');
var digits = require('./../utils/number').digits;
var isBigNumber = require('./../utils/bignumber/isBigNumber');
var isMatrix = require('./../utils/collection/isMatrix');
// returns a new instance of typed-function
var createTyped = function () {
// initially, return the original instance of typed-function
// consecutively, return a new instance from typed.create.
createTyped = typedFunction.create;
return typedFunction;
};
/**
* Factory function for creating a new typed instance
* @param {Object} type Object with data types like Complex and BigNumber
* @returns {Function}
*/
exports.create = function create(type) {
// TODO: typed-function must be able to silently ignore signatures with unknown data types
// type checks for all known types
//
// note that:
//
// - check by duck-typing on a property like `isUnit`, instead of checking instanceof.
// instanceof cannot be used because that would not allow to pass data from
// one instance of math.js to another since each has it's own instance of Unit.
// - check the `isUnit` property via the constructor, so there will be no
// matches for "fake" instances like plain objects with a property `isUnit`.
// That is important for security reasons.
// - It must not be possible to override the type checks used internally,
// for security reasons, so these functions are not exposed in the expression
// parser.
type.isNumber = function (x) { return typeof x === 'number' };
type.isComplex = function (x) { return type.Complex && x instanceof type.Complex || false };
type.isBigNumber = isBigNumber;
type.isFraction = function (x) { return type.Fraction && x instanceof type.Fraction || false };
type.isUnit = function (x) { return x && x.constructor.prototype.isUnit || false };
type.isString = function (x) { return typeof x === 'string' };
type.isArray = Array.isArray;
type.isMatrix = isMatrix;
type.isDenseMatrix = function (x) { return x && x.isDenseMatrix && x.constructor.prototype.isMatrix || false };
type.isSparseMatrix = function (x) { return x && x.isSparseMatrix && x.constructor.prototype.isMatrix || false };
type.isRange = function (x) { return x && x.constructor.prototype.isRange || false };
type.isIndex = function (x) { return x && x.constructor.prototype.isIndex || false };
type.isBoolean = function (x) { return typeof x === 'boolean' };
type.isResultSet = function (x) { return x && x.constructor.prototype.isResultSet || false };
type.isHelp = function (x) { return x && x.constructor.prototype.isHelp || false };
type.isFunction = function (x) { return typeof x === 'function'};
type.isDate = function (x) { return x instanceof Date };
type.isRegExp = function (x) { return x instanceof RegExp };
type.isObject = function (x) {
return typeof x === 'object' &&
x.constructor === Object &&
!type.isComplex(x) &&
!type.isFraction(x)
};
type.isNull = function (x) { return x === null };
type.isUndefined = function (x) { return x === undefined };
type.isAccessorNode = function (x) { return x && x.isAccessorNode && x.constructor.prototype.isNode || false };
type.isArrayNode = function (x) { return x && x.isArrayNode && x.constructor.prototype.isNode || false };
type.isAssignmentNode = function (x) { return x && x.isAssignmentNode && x.constructor.prototype.isNode || false };
type.isBlockNode = function (x) { return x && x.isBlockNode && x.constructor.prototype.isNode || false };
type.isConditionalNode = function (x) { return x && x.isConditionalNode && x.constructor.prototype.isNode || false };
type.isConstantNode = function (x) { return x && x.isConstantNode && x.constructor.prototype.isNode || false };
type.isFunctionAssignmentNode = function (x) { return x && x.isFunctionAssignmentNode && x.constructor.prototype.isNode || false };
type.isFunctionNode = function (x) { return x && x.isFunctionNode && x.constructor.prototype.isNode || false };
type.isIndexNode = function (x) { return x && x.isIndexNode && x.constructor.prototype.isNode || false };
type.isNode = function (x) { return x && x.isNode && x.constructor.prototype.isNode || false };
type.isObjectNode = function (x) { return x && x.isObjectNode && x.constructor.prototype.isNode || false };
type.isOperatorNode = function (x) { return x && x.isOperatorNode && x.constructor.prototype.isNode || false };
type.isParenthesisNode = function (x) { return x && x.isParenthesisNode && x.constructor.prototype.isNode || false };
type.isRangeNode = function (x) { return x && x.isRangeNode && x.constructor.prototype.isNode || false };
type.isSymbolNode = function (x) { return x && x.isSymbolNode && x.constructor.prototype.isNode || false };
type.isChain = function (x) { return x && x.constructor.prototype.isChain || false };
// get a new instance of typed-function
var typed = createTyped();
// define all types. The order of the types determines in which order function
// arguments are type-checked (so for performance it's important to put the
// most used types first).
typed.types = [
{ name: 'number', test: type.isNumber },
{ name: 'Complex', test: type.isComplex },
{ name: 'BigNumber', test: type.isBigNumber },
{ name: 'Fraction', test: type.isFraction },
{ name: 'Unit', test: type.isUnit },
{ name: 'string', test: type.isString },
{ name: 'Array', test: type.isArray },
{ name: 'Matrix', test: type.isMatrix },
{ name: 'DenseMatrix', test: type.isDenseMatrix },
{ name: 'SparseMatrix', test: type.isSparseMatrix },
{ name: 'Range', test: type.isRange },
{ name: 'Index', test: type.isIndex },
{ name: 'boolean', test: type.isBoolean },
{ name: 'ResultSet', test: type.isResultSet },
{ name: 'Help', test: type.isHelp },
{ name: 'function', test: type.isFunction },
{ name: 'Date', test: type.isDate },
{ name: 'RegExp', test: type.isRegExp },
{ name: 'null', test: type.isNull },
{ name: 'undefined', test: type.isUndefined },
{ name: 'OperatorNode', test: type.isOperatorNode },
{ name: 'ConstantNode', test: type.isConstantNode },
{ name: 'SymbolNode', test: type.isSymbolNode },
{ name: 'ParenthesisNode', test: type.isParenthesisNode },
{ name: 'FunctionNode', test: type.isFunctionNode },
{ name: 'FunctionAssignmentNode', test: type.isFunctionAssignmentNode },
{ name: 'ArrayNode', test: type.isArrayNode },
{ name: 'AssignmentNode', test: type.isAssignmentNode },
{ name: 'BlockNode', test: type.isBlockNode },
{ name: 'ConditionalNode', test: type.isConditionalNode },
{ name: 'IndexNode', test: type.isIndexNode },
{ name: 'RangeNode', test: type.isRangeNode },
{ name: 'Node', test: type.isNode },
{ name: 'Object', test: type.isObject } // order 'Object' last, it's a tricky one
];
// TODO: add conversion from BigNumber to number?
typed.conversions = [
{
from: 'number',
to: 'BigNumber',
convert: function (x) {
// note: conversion from number to BigNumber can fail if x has >15 digits
if (digits(x) > 15) {
throw new TypeError('Cannot implicitly convert a number with >15 significant digits to BigNumber ' +
'(value: ' + x + '). ' +
'Use function bignumber(x) to convert to BigNumber.');
}
return new type.BigNumber(x);
}
}, {
from: 'number',
to: 'Complex',
convert: function (x) {
return new type.Complex(x, 0);
}
}, {
from: 'number',
to: 'string',
convert: function (x) {
return x + '';
}
}, {
from: 'BigNumber',
to: 'Complex',
convert: function (x) {
return new type.Complex(x.toNumber(), 0);
}
}, {
from: 'Fraction',
to: 'BigNumber',
convert: function (x) {
throw new TypeError('Cannot implicitly convert a Fraction to BigNumber or vice versa. ' +
'Use function bignumber(x) to convert to BigNumber or fraction(x) to convert to Fraction.');
}
}, {
from: 'Fraction',
to: 'Complex',
convert: function (x) {
return new type.Complex(x.valueOf(), 0);
}
}, {
from: 'number',
to: 'Fraction',
convert: function (x) {
var f = new type.Fraction(x);
if (f.valueOf() !== x) {
throw new TypeError('Cannot implicitly convert a number to a Fraction when there will be a loss of precision ' +
'(value: ' + x + '). ' +
'Use function fraction(x) to convert to Fraction.');
}
return new type.Fraction(x);
}
}, {
// FIXME: add conversion from Fraction to number, for example for `sqrt(fraction(1,3))`
// from: 'Fraction',
// to: 'number',
// convert: function (x) {
// return x.valueOf();
// }
//}, {
from: 'string',
to: 'number',
convert: function (x) {
var n = Number(x);
if (isNaN(n)) {
throw new Error('Cannot convert "' + x + '" to a number');
}
return n;
}
}, {
from: 'string',
to: 'BigNumber',
convert: function (x) {
try {
return new type.BigNumber(x);
}
catch (err) {
throw new Error('Cannot convert "' + x + '" to BigNumber');
}
}
}, {
from: 'string',
to: 'Fraction',
convert: function (x) {
try {
return new type.Fraction(x);
}
catch (err) {
throw new Error('Cannot convert "' + x + '" to Fraction');
}
}
}, {
from: 'string',
to: 'Complex',
convert: function (x) {
try {
return new type.Complex(x);
}
catch (err) {
throw new Error('Cannot convert "' + x + '" to Complex');
}
}
}, {
from: 'boolean',
to: 'number',
convert: function (x) {
return +x;
}
}, {
from: 'boolean',
to: 'BigNumber',
convert: function (x) {
return new type.BigNumber(+x);
}
}, {
from: 'boolean',
to: 'Fraction',
convert: function (x) {
return new type.Fraction(+x);
}
}, {
from: 'boolean',
to: 'string',
convert: function (x) {
return +x;
}
}, {
from: 'Array',
to: 'Matrix',
convert: function (array) {
return new type.DenseMatrix(array);
}
}, {
from: 'Matrix',
to: 'Array',
convert: function (matrix) {
return matrix.valueOf();
}
}
];
return typed;
};