Prepare release 1.7.0

node_modules/add/.npmignore

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+node_modules
+

node_modules/add/.travis.yml

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+language: node_js
+node_js:
+  - "0.11"
+  - "0.10"
+  - "0.8"
+  - "0.6"
+

node_modules/add/Readme.md

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+# Add
+
+[![Build Status](https://travis-ci.org/ben-ng/add.svg?branch=master)](https://travis-ci.org/ben-ng/add)
+
+[![browser support](https://ci.testling.com/ben-ng/add.png)
+](https://ci.testling.com/ben-ng/add)
+
+A cross-browser, numerically stable way to add floats in Javascript. Produces a faithful rounding of the sum (the result is an immediate floating-point neighbor of the true value).
+
+Algorithm: Rump-Ogita-Oishi
+
+## Usage
+
+```javascript
+var add = require('add')
+  , evil = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7]
+  , dumbsum = function (a,b) { return a+b }
+
+console.log(evil.reduce(dumbsum)) => 15.299999999999999
+
+console.log(add(evil)) => 15.3
+```
+
+## License
+
+The MIT License (MIT)
+
+Copyright (c) 2014 Ben Ng
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+

node_modules/add/bower.json

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+{
+  "name": "add",
+  "main": "index.js",
+  "version": "2.0.5",
+  "homepage": "https://github.com/ben-ng/add",
+  "authors": [
+    "Ben Ng <me@benng.me>"
+  ],
+  "description": "A cross-browser, numerically stable algorithm to add floats accurately",
+  "moduleType": [
+    "amd",
+    "globals",
+    "node"
+  ],
+  "keywords": [
+    "numerical",
+    "stable",
+    "faithful",
+    "rounding",
+    "float",
+    "error",
+    "propagation",
+    "summation",
+    "accumulate",
+    "addition",
+    "numerical",
+    "analysis"
+  ],
+  "license": "MIT",
+  "ignore": [
+    "**/.*",
+    "node_modules",
+    "bower_components",
+    "test.js"
+  ]
+}

node_modules/add/index.js

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+(function (root, factory) {
+  "use strict";
+
+  // AMD
+  if (typeof define === 'function' && define.amd) {
+    define([], factory);
+  }
+  // CommonJS
+  else if (typeof exports === 'object') {
+    module.exports = factory();
+  }
+  // Browser
+  else {
+    root.add = factory();
+  }
+})(this, function () {
+  "use strict";
+
+  // The minimum machine rounding error
+  var Epsilon = Math.pow(2, -53)
+    , EpsilonReciprocal = (1 / Epsilon)
+      /// The smallest positive number that can be represented
+    , Eta = Math.pow(2, -1074)
+      // limitB is a constant used in the transform function
+    , limitB = 0.5 * EpsilonReciprocal * Eta
+
+  /**
+  * S. M. RUMP, T. OGITA AND S. OISHI
+  * http://www.ti3.tu-harburg.de/paper/rump/RuOgOi07I.pdf
+  */
+
+  // Page 8
+  // x is result, y is error
+  // third is so the array is allocated for 4 spaces
+  // it speeds up transform
+  function fastTwoSum(a, b) {
+    var x = a + b
+      , q = x - a
+      , y = b - q
+
+    return [x, y, null]
+  }
+
+  // Page 12
+  // p = q + p'
+  // sigma is a power of 2 greater than or equal to |p|
+  function extractScalar(sigma, p) {
+    var q = (sigma + p) - sigma
+      , pPrime = p - q
+
+    return [q, pPrime]
+  }
+
+  // Page 12
+  function extractVector(sigma, p) {
+    var tau = 0.0
+      , extracted
+      , i = 0
+      , ii = p.length
+      , pPrime = new Array(ii)
+
+    for(; i<ii; ++i) {
+      extracted = extractScalar(sigma, p[i])
+      pPrime[i] = extracted[1]
+      tau += extracted[0]
+    }
+
+    return [tau, pPrime]
+  }
+
+  // Finds the immediate power of 2 that is larger than p
+  //// in a fast way
+  function nextPowerTwo (p) {
+    var q = EpsilonReciprocal * p
+      , L = Math.abs((q + p) - q)
+
+    if(L === 0)
+      return Math.abs(p)
+
+    return L
+  }
+
+  // Helper, gets the maximum of the absolute values of an array
+  function maxAbs(arr) {
+    var i = 0
+      , ii = arr.length
+      , best = -1
+
+    for(; i<ii; ++i) {
+      if(Math.abs(arr[i]) > best) {
+        best = arr[i]
+      }
+    }
+
+    return best
+  }
+
+  function transform (p) {
+    var mu = maxAbs(p)
+      , M
+      , sigmaPrime
+      , tPrime
+      , t
+      , tau
+      , sigma
+      , extracted
+      , res
+
+        // Not part of the original paper, here for optimization
+      , temp
+      , bigPow
+      , limitA
+      , twoToTheM
+
+    if(mu === 0) {
+      return [0, 0, p, 0]
+    }
+
+    M = nextPowerTwo(p.length + 2)
+    twoToTheM = Math.pow(2, M)
+    bigPow = 2 * twoToTheM // equiv to Math.pow(2, 2 * M), faster
+    sigmaPrime = twoToTheM * nextPowerTwo(mu)
+    tPrime = 0
+
+    do {
+      t = tPrime
+      sigma = sigmaPrime
+      extracted = extractVector(sigma, p)
+      tau = extracted[0]
+      tPrime = t + tau
+      p = extracted[1]
+
+      if(tPrime === 0) {
+        return transform(p)
+      }
+
+      temp = Epsilon * sigma
+      sigmaPrime = twoToTheM * temp
+      limitA = bigPow * temp
+    }
+    while( Math.abs(tPrime) < limitA && sigma > limitB )
+
+    // res already allocated for 4
+    res = fastTwoSum(t, tau)
+    res[2] = p
+
+    return res
+  }
+
+  function dumbSum(p) {
+    var i, ii, sum = 0.0
+    for(i=0, ii=p.length; i<ii; ++i) {
+      sum += p[i]
+    }
+    return sum
+  }
+
+  function accSum(p) {
+
+    // Zero length array, or all values are zeros
+    if(p.length === 0 || maxAbs(p) === 0) {
+      return 0
+    }
+
+    var tfmd = transform(p)
+
+    return tfmd[0] + (tfmd[1] +dumbSum(tfmd[2]))
+  }
+
+
+  // exports
+  accSum.dumbSum = dumbSum;
+  accSum.fastTwoSum = fastTwoSum;
+  accSum.nextPowerTwo = nextPowerTwo;
+  return accSum;
+});
+

node_modules/add/package.json

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+{
+  "name": "add",
+  "version": "2.0.6",
+  "description": "A cross-browser, numerically stable algorithm to add floats accurately",
+  "main": "index.js",
+  "scripts": {
+    "test": "node test.js"
+  },
+  "repository": {
+    "type": "git",
+    "url": "https://github.com/ben-ng/add.git"
+  },
+  "keywords": [
+    "numerically",
+    "stable",
+    "faithful",
+    "rounding",
+    "float",
+    "error",
+    "propagation",
+    "summation",
+    "accumulate",
+    "addition",
+    "numerical",
+    "analysis"
+  ],
+  "devDependencies": {
+    "tape": "2.x.x"
+  },
+  "testling": {
+    "files": "test.js",
+    "browsers": [
+      "ie/6..latest",
+      "chrome/22..latest",
+      "firefox/16..latest",
+      "safari/latest",
+      "opera/11.0..latest",
+      "iphone/6",
+      "ipad/6"
+    ]
+  },
+  "author": "Ben Ng <me@benng.me>",
+  "license": "MIT",
+  "bugs": {
+    "url": "https://github.com/ben-ng/add/issues"
+  },
+  "homepage": "https://github.com/ben-ng/add"
+}

node_modules/add/test.js

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+/**
+* Tests for numeric stability
+*/
+var algorithm = require('./')
+  , test = require('tape')
+  , badVector
+
+badVector = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7]
+
+test('fastSum', function (t) {
+    t.plan(1);
+
+    t.deepEqual(algorithm.fastTwoSum(1/3, 1/6)
+                , [0.5, -2.7755575615628914e-17, null]
+                , 'Result and error should have been returned')
+});
+
+test('nextPowerTwo', function (t) {
+  t.plan(1)
+
+  t.equal(algorithm.nextPowerTwo(1534)
+              , 2048
+              , 'Should be Math.pow(2, Math.ceil(algorithm.logBase2(Math.abs(1534))))')
+})
+
+test('accumulate', function (t) {
+  t.plan(5)
+
+
+  t.equal(algorithm([1,2,3,4]), 10, 'Integer sum should work')
+
+
+  t.equal(algorithm.dumbSum(badVector), 15.299999999999999, 'Inaccurate summation using naive method')
+
+  t.equal(algorithm(badVector), 15.3, 'Rump-Ogita-Oishi summation of insidious sum')
+
+  t.equal(algorithm([0, 0, 0]), 0, 'Rump-Ogita-Oishi summation of zero array')
+
+  t.equal(algorithm([]), 0, 'Rump-Ogita-Oishi summation of empty array')
+})
+