Released version 1.3.0

HISTORY.md

@@ -1,8 +1,10 @@
 # History
 
 
-## not yet released, version 1.2.1-SNAPSHOT
+## 2015-02-09, version 1.3.0
 
+- Implemented BigNumber implementations of most trigonometric functions: `sin`,
+  `cos`, `tan`, `asin`, `acos`, `atan`, `cosh`, `sinh`, `tanh`. Thanks @BigFav.
 - Implemented function `trace`. Thanks @pcorey.
 - Faster loading of BigNumber configuration with a high precision by lazy
   loading constants like `pi` and `e`.

NOTICE

@@ -1,7 +1,7 @@
 math.js
 https://github.com/josdejong/mathjs
 
-Copyright (C) 2013 Jos de Jong <wjosdejong@gmail.com>
+Copyright (C) 2013-2015 Jos de Jong <wjosdejong@gmail.com>
 
 Licensed under the Apache License, Version 2.0 (the "License");
 you may not use this file except in compliance with the License.

bin/cli.js

@@ -24,7 +24,7 @@
  *     cat script.txt | mathjs > results.txt  Run input stream, output to file
  *
  * @license
- * Copyright (C) 2013-2014 Jos de Jong <wjosdejong@gmail.com>
+ * Copyright (C) 2013-2015 Jos de Jong <wjosdejong@gmail.com>
  *
  * Licensed under the Apache License, Version 2.0 (the "License"); you may not
  * use this file except in compliance with the License. You may obtain a copy

bower.json

@@ -1,6 +1,6 @@
 {
   "name": "mathjs",
-  "version": "1.2.1-SNAPSHOT",
+  "version": "1.3.0",
   "main": "./dist/math.min.js",
   "ignore": [
     "coverage",

component.json

@@ -2,7 +2,7 @@
   "name": "mathjs",
   "repo": "josdejong/mathjs",
   "description": "Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.",
-  "version": "1.2.1-SNAPSHOT",
+  "version": "1.3.0",
   "main": "dist/math.min.js",
   "keywords": [
     "math",

docs/datatypes/bignumbers.md

@@ -4,6 +4,8 @@ For calculations with an arbitrary precision, math.js supports a `BigNumber`
 data type. BigNumber support is powered by
 [decimal.js](https://github.com/MikeMcl/decimal.js/).
 
+## Usage
+
 A BigNumber can be created using the function `bignumber`:
 
 ```js
@@ -35,10 +37,13 @@ BigNumber is not supported by the following functions:
 gcd, lcm, xgcd,
 arg,
 random,
-acos, asin, atan, atan2, cos, cot, csc, sec, sin, tan,
-cosh, coth, csch, sech, sinh, tanh.
+atan2, cot, csc, sec,
+coth, csch, sech.
 These functions will downgrade BigNumber to Number, and return a Number.*
 
+
+## Round-off errors
+
 Calculations with BigNumber are much slower than calculations with Number,
 but they can be executed with an arbitrary precision. By using a higher
 precision, it is less likely that round-off errors occur:
@@ -53,6 +58,31 @@ math.add(math.bignumber(0.1), math.bignumber(0.2));     // BigNumber, 0.3
 math.divide(math.bignumber(0.3), math.bignumber(0.2));  // BigNumber, 1.5
 ```
 
+
+## Limitations
+
+It's important to realize that BigNumbers do not solve *all* problems related
+to precision and round-off errors. Numbers with an infinite number of digits
+cannot be represented with a regular number nor a BigNumber. Though a BigNumber
+can store a much larger number of digits, the amount of digits remains limited,
+if only to keep calculations fast enough to remain practical.
+
+```js
+var one = math.bignumber(1);
+var three = math.bignumber(3);
+var third = math.divide(one, three);
+console.log(third.toString());
+// outputs 0.3333333333333333333333333333333333333333333333333333333333333333
+
+var ans = math.multiply(third, three);
+console.log(ans.toString());
+// outputs 0.9999999999999999999999999999999999999999999999999999999999999999
+// this should be 1 again, but `third` is rounded to a limited number of digits 3
+```
+
+
+## Conversion
+
 BigNumbers can be converted to numbers and vice versa using the functions
 `number` and `bignumber`. When converting a BigNumber to a Number, the high
 precision of the BigNumber will be lost. When a BigNumber is too large to be represented

docs/reference/functions/acos.md

@@ -15,13 +15,13 @@ math.acos(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Array | Matrix | null | Function input
+`x` | Number | BigNumber Boolean | Complex | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | The arc cosine of x
+Number | BigNumber | Complex | Array | Matrix | The arc cosine of x
 
 
 ## Examples

docs/reference/functions/alphabetical.md

@@ -113,6 +113,7 @@
 - [tan(x)](tan.md)
 - [tanh(x)](tanh.md)
 - [to(x, unit)](to.md)
+- [trace(x)](trace.md)
 - [transpose(x)](transpose.md)
 - [typeof(x)](typeof.md)
 - [unaryMinus(x)](unaryMinus.md)

docs/reference/functions/asin.md

@@ -15,13 +15,13 @@ math.asin(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Array | Matrix | null | Function input
+`x` | Number | BigNumber | Boolean | Complex | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | The arc sine of x
+Number | BigNumber | Complex | Array | Matrix | The arc sine of x
 
 
 ## Examples

docs/reference/functions/atan.md

@@ -15,13 +15,13 @@ math.atan(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Array | Matrix | null | Function input
+`x` | Number | BigNumber | Boolean | Complex | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | The arc tangent of x
+Number | BigNumber | Complex | Array | Matrix | The arc tangent of x
 
 
 ## Examples

docs/reference/functions/categorical.md

@@ -91,6 +91,7 @@
 - [size(x)](size.md)
 - [squeeze(x)](squeeze.md)
 - [subset(x, index [, replacement])](subset.md)
+- [trace(x)](trace.md)
 - [transpose(x)](transpose.md)
 - [zeros(m, n, p, ...)](zeros.md)
 

docs/reference/functions/cos.md

@@ -15,13 +15,13 @@ math.cos(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Unit | Array | Matrix | null | Function input
+`x` | Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | Cosine of x
+Number | BigNumber | Complex | Array | Matrix | Cosine of x
 
 
 ## Examples

docs/reference/functions/cosh.md

@@ -16,13 +16,13 @@ math.cosh(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Unit | Array | Matrix | null | Function input
+`x` | Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | Hyperbolic cosine of x
+Number | BigNumber | Complex | Array | Matrix | Hyperbolic cosine of x
 
 
 ## Examples

docs/reference/functions/sech.md

@@ -30,7 +30,7 @@ Number | Complex | Array | Matrix | Hyperbolic secant of x
 ```js
 // sech(x) = 1/ cosh(x)
 math.sech(0.5);       // returns 0.886818883970074
-1 / math.cosh(0.5);   // returns 1.9190347513349437
+1 / math.cosh(0.5);   // returns 0.886818883970074
 ```
 
 

docs/reference/functions/sin.md

@@ -15,13 +15,13 @@ math.sin(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Unit | Array | Matrix | null | Function input
+`x` | Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | Sine of x
+Number | BigNumber | Complex | Array | Matrix | Sine of x
 
 
 ## Examples

docs/reference/functions/sinh.md

@@ -16,13 +16,13 @@ math.sinh(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Unit | Array | Matrix | null | Function input
+`x` | Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | Hyperbolic sine of x
+Number | BigNumber | Complex | Array | Matrix | Hyperbolic sine of x
 
 
 ## Examples

docs/reference/functions/tan.md

@@ -15,13 +15,13 @@ math.tan(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Unit | Array | Matrix | null | Function input
+`x` | Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | Tangent of x
+Number | BigNumber | Complex | Array | Matrix | Tangent of x
 
 
 ## Examples

docs/reference/functions/tanh.md

@@ -16,13 +16,13 @@ math.tanh(x)
 
 Parameter | Type | Description
 --------- | ---- | -----------
-`x` | Number | Boolean | Complex | Unit | Array | Matrix | null | Function input
+`x` | Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null | Function input
 
 ### Returns
 
 Type | Description
 ---- | -----------
-Number | Complex | Array | Matrix | Hyperbolic tangent of x
+Number | BigNumber | Complex | Array | Matrix | Hyperbolic tangent of x
 
 
 ## Examples

lib/expression/docs/function/matrix/concat.js

@@ -14,6 +14,6 @@ module.exports = {
     'concat(A, B, 2)'
   ],
   'seealso': [
-    'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'
+    'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/det.js

@@ -10,6 +10,6 @@ module.exports = {
     'det([-2, 2, 3; -1, 1, 3; 2, 0, -1])'
   ],
   'seealso': [
-    'concat', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'
+    'concat', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/diag.js

@@ -13,6 +13,6 @@ module.exports = {
     'diag(a)'
   ],
   'seealso': [
-    'concat', 'det', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'
+    'concat', 'det', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/eye.js

@@ -15,6 +15,6 @@ module.exports = {
     'eye(size(a))'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'
+    'concat', 'det', 'diag', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/inv.js

@@ -11,6 +11,6 @@ module.exports = {
     '1 / 4'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'eye', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'
+    'concat', 'det', 'diag', 'eye', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/ones.js

@@ -19,6 +19,6 @@ module.exports = {
     'ones(size(a))'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'eye', 'inv', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'
+    'concat', 'det', 'diag', 'eye', 'inv', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/range.js

@@ -20,6 +20,6 @@ module.exports = {
     'a[1:2, 1:2]'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'size', 'squeeze', 'subset', 'transpose', 'zeros'
+    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'size', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/size.js

@@ -13,6 +13,6 @@ module.exports = {
     'size(1:6)'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'squeeze', 'subset', 'transpose', 'zeros'
+    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'squeeze', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/squeeze.js

@@ -12,6 +12,6 @@ module.exports = {
     'size(squeeze(b))'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'subset', 'transpose', 'zeros'
+    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'subset', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/subset.js

@@ -20,6 +20,6 @@ module.exports = {
     'f[:, 1]'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'transpose', 'zeros'
+    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'trace', 'transpose', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/trace.js

@@ -0,0 +1,15 @@
+module.exports = {
+  'name': 'trace',
+  'category': 'Matrix',
+  'syntax': [
+    'trace(A)'
+  ],
+  'description': 'Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.',
+  'examples': [
+    'A = [1, 2, 3; -1, 2, 3; 2, 0, 3]',
+    'trace(A)'
+  ],
+  'seealso': [
+    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose', 'zeros'
+  ]
+};

lib/expression/docs/function/matrix/transpose.js

@@ -12,6 +12,6 @@ module.exports = {
     'transpose(a)'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'zeros'
+    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'zeros'
   ]
 };

lib/expression/docs/function/matrix/zeros.js

@@ -18,6 +18,6 @@ module.exports = {
     'zeros(size(a))'
   ],
   'seealso': [
-    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'transpose'
+    'concat', 'det', 'diag', 'eye', 'inv', 'ones', 'range', 'size', 'squeeze', 'subset', 'trace', 'transpose'
   ]
 };

lib/expression/docs/index.js

@@ -99,6 +99,7 @@ exports.resize = require('./function/matrix/resize');
 exports.size = require('./function/matrix/size');
 exports.squeeze = require('./function/matrix/squeeze');
 exports.subset = require('./function/matrix/subset');
+exports.trace = require('./function/matrix/trace');
 exports.transpose = require('./function/matrix/transpose');
 exports.zeros = require('./function/matrix/zeros');
 

lib/function/matrix/trace.js

@@ -9,7 +9,8 @@ module.exports = function (math) {
       string = util.string;
 
   /**
-   * Calculate the trace of a matrix.
+   * Calculate the trace of a matrix: the sum of the elements on the main
+   * diagonal of a square matrix.
    *
    * Syntax:
    *
@@ -26,6 +27,10 @@ module.exports = function (math) {
    *    ]
    *    math.trace(A); // returns 6
    *
+   * See also:
+   *
+   *    diag
+   *
    * @param {Array | Matrix} x  A matrix
    * @return {Number} The trace of `x`
    */

lib/function/trigonometry/acos.js

@@ -34,8 +34,8 @@ module.exports = function (math) {
    *
    *    cos, atan, asin
    *
-   * @param {Number | Boolean | Complex | Array | Matrix | null} x  Function input
-   * @return {Number | Complex | Array | Matrix} The arc cosine of x
+   * @param {Number | BigNumber Boolean | Complex | Array | Matrix | null} x  Function input
+   * @return {Number | BigNumber | Complex | Array | Matrix} The arc cosine of x
    */
   math.acos = function acos(x) {
     if (arguments.length != 1) {

lib/function/trigonometry/asin.js

@@ -34,8 +34,8 @@ module.exports = function (math) {
    *
    *    sin, atan, acos
    *
-   * @param {Number | Boolean | Complex | Array | Matrix | null} x   Function input
-   * @return {Number | Complex | Array | Matrix} The arc sine of x
+   * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x   Function input
+   * @return {Number | BigNumber | Complex | Array | Matrix} The arc sine of x
    */
   math.asin = function asin(x) {
     if (arguments.length != 1) {

lib/function/trigonometry/atan.js

@@ -34,8 +34,8 @@ module.exports = function (math) {
    *
    *    tan, asin, acos
    *
-   * @param {Number | Boolean | Complex | Array | Matrix | null} x   Function input
-   * @return {Number | Complex | Array | Matrix} The arc tangent of x
+   * @param {Number | BigNumber | Boolean | Complex | Array | Matrix | null} x   Function input
+   * @return {Number | BigNumber | Complex | Array | Matrix} The arc tangent of x
    */
   math.atan = function atan(x) {
     if (arguments.length != 1) {

lib/function/trigonometry/cos.js

@@ -39,8 +39,8 @@ module.exports = function (math, config) {
    *
    *    cos, tan
    *
-   * @param {Number | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
-   * @return {Number | Complex | Array | Matrix} Cosine of x
+   * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
+   * @return {Number | BigNumber | Complex | Array | Matrix} Cosine of x
    */
   math.cos = function cos(x) {
     if (arguments.length != 1) {

lib/function/trigonometry/cosh.js

@@ -34,8 +34,8 @@ module.exports = function (math) {
    *
    *    sinh, tanh
    *
-   * @param {Number | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
-   * @return {Number | Complex | Array | Matrix} Hyperbolic cosine of x
+   * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
+   * @return {Number | BigNumber | Complex | Array | Matrix} Hyperbolic cosine of x
    */
   math.cosh = function cosh(x) {
     if (arguments.length != 1) {

lib/function/trigonometry/sinh.js

@@ -34,8 +34,8 @@ module.exports = function (math) {
    *
    *    cosh, tanh
    *
-   * @param {Number | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
-   * @return {Number | Complex | Array | Matrix} Hyperbolic sine of x
+   * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
+   * @return {Number | BigNumber | Complex | Array | Matrix} Hyperbolic sine of x
    */
   math.sinh = function sinh(x) {
     if (arguments.length != 1) {

lib/function/trigonometry/tan.js

@@ -36,8 +36,8 @@ module.exports = function (math, config) {
    *
    *    atan, sin, cos
    *
-   * @param {Number | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
-   * @return {Number | Complex | Array | Matrix} Tangent of x
+   * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
+   * @return {Number | BigNumber | Complex | Array | Matrix} Tangent of x
    */
   math.tan = function tan(x) {
     if (arguments.length != 1) {

lib/function/trigonometry/tanh.js

@@ -37,8 +37,8 @@ module.exports = function (math) {
    *
    *    sinh, cosh, coth
    *
-   * @param {Number | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
-   * @return {Number | Complex | Array | Matrix} Hyperbolic tangent of x
+   * @param {Number | BigNumber | Boolean | Complex | Unit | Array | Matrix | null} x  Function input
+   * @return {Number | BigNumber | Complex | Array | Matrix} Hyperbolic tangent of x
    */
   math.tanh = function tanh(x) {
     if (arguments.length != 1) {

lib/header.js

@@ -10,7 +10,7 @@
  * @date    @@date
  *
  * @license
- * Copyright (C) 2013-2014 Jos de Jong <wjosdejong@gmail.com>
+ * Copyright (C) 2013-2015 Jos de Jong <wjosdejong@gmail.com>
  *
  * Licensed under the Apache License, Version 2.0 (the "License"); you may not
  * use this file except in compliance with the License. You may obtain a copy

lib/version.js

@@ -1,3 +1,3 @@
-module.exports = '1.2.1-SNAPSHOT';
+module.exports = '1.3.0';
 // Note: This file is automatically generated when building math.js.
 // Changes made in this file will be overwritten.

package.json

@@ -1,6 +1,6 @@
 {
   "name": "mathjs",
-  "version": "1.2.1-SNAPSHOT",
+  "version": "1.3.0",
   "description": "Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.",
   "author": "Jos de Jong <wjosdejong@gmail.com> (https://github.com/josdejong)",
   "contributors": [