random.js

// seedrandom.js version 2.0.
// Author: David Bau 4/2/2011
//
// Defines a method Math.seedrandom() that, when called, substitutes
// an explicitly seeded RC4-based algorithm for Math.random().  Also
// supports automatic seeding from local or network sources of entropy.
//
// Usage:
//
//   <script src=http://davidbau.com/encode/seedrandom-min.js></script>
//
//   Math.seedrandom('yipee'); Sets Math.random to a function that is
//                             initialized using the given explicit seed.
//
//   Math.seedrandom();        Sets Math.random to a function that is
//                             seeded using the current time, dom state,
//                             and other accumulated local entropy.
//                             The generated seed string is returned.
//
//   Math.seedrandom('yowza', true);
//                             Seeds using the given explicit seed mixed
//                             together with accumulated entropy.
//
//   <script src="http://bit.ly/srandom-512"></script>
//                             Seeds using physical random bits downloaded
//                             from random.org.
//
//   <script src="https://jsonlib.appspot.com/urandom?callback=Math.seedrandom">
//   </script>                 Seeds using urandom bits from call.jsonlib.com,
//                             which is faster than random.org.
//
// Examples:
//
//   Math.seedrandom("hello");            // Use "hello" as the seed.
//   document.write(Math.random());       // Always 0.5463663768140734
//   document.write(Math.random());       // Always 0.43973793770592234
//   var rng1 = Math.random;              // Remember the current prng.
//
//   var autoseed = Math.seedrandom();    // New prng with an automatic seed.
//   document.write(Math.random());       // Pretty much unpredictable.
//
//   Math.random = rng1;                  // Continue "hello" prng sequence.
//   document.write(Math.random());       // Always 0.554769432473455
//
//   Math.seedrandom(autoseed);           // Restart at the previous seed.
//   document.write(Math.random());       // Repeat the 'unpredictable' value.
//
// Notes:
//
// Each time seedrandom('arg') is called, entropy from the passed seed
// is accumulated in a pool to help generate future seeds for the
// zero-argument form of Math.seedrandom, so entropy can be injected over
// time by calling seedrandom with explicit data repeatedly.
//
// On speed - This javascript implementation of Math.random() is about
// 3-10x slower than the built-in Math.random() because it is not native
// code, but this is typically fast enough anyway.  Seeding is more expensive,
// especially if you use auto-seeding.  Some details (timings on Chrome 4):
//
// Our Math.random()            - avg less than 0.002 milliseconds per call
// seedrandom('explicit')       - avg less than 0.5 milliseconds per call
// seedrandom('explicit', true) - avg less than 2 milliseconds per call
// seedrandom()                 - avg about 38 milliseconds per call
//
// LICENSE (BSD):
//
// Copyright 2010 David Bau, all rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
// 
//   1. Redistributions of source code must retain the above copyright
//      notice, this list of conditions and the following disclaimer.
//
//   2. Redistributions in binary form must reproduce the above copyright
//      notice, this list of conditions and the following disclaimer in the
//      documentation and/or other materials provided with the distribution.
// 
//   3. Neither the name of this module nor the names of its contributors may
//      be used to endorse or promote products derived from this software
//      without specific prior written permission.
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
/**
 * All code is in an anonymous closure to keep the global namespace clean.
 *
 * @param {number=} overflow 
 * @param {number=} startdenom
 */
(function (pool, math, width, chunks, significance, overflow, startdenom) {


    //
    // seedrandom()
    // This is the seedrandom function described above.
    //
    math.seedrandom = function seedrandom(seed, use_entropy) {
      var key = [];
      var arc4;
    
      // Flatten the seed string or build one from local entropy if needed.
      seed = mixkey(flatten(
        use_entropy ? [seed, pool] :
        arguments.length ? seed :
        [Date.now(), pool, window], 3), key);
    
      // Use the seed to initialize an ARC4 generator.
      arc4 = new ARC4(key);
    
      // Mix the randomness into accumulated entropy.
      mixkey(arc4.S, pool);
    
      // Override Math.random
    
      // This function returns a random double in [0, 1) that contains
      // randomness in every bit of the mantissa of the IEEE 754 value.
    
      math.random = function random() {  // Closure to return a random double:
        var n = arc4.g(chunks);             // Start with a numerator n < 2 ^ 48
        var d = startdenom;                 //   and denominator d = 2 ^ 48.
        var x = 0;                          //   and no 'extra last byte'.
        while (n < significance) {          // Fill up all significant digits by
          n = (n + x) * width;              //   shifting numerator and
          d *= width;                       //   denominator and generating a
          x = arc4.g(1);                    //   new least-significant-byte.
        }
        while (n >= overflow) {             // To avoid rounding up, before adding
          n /= 2;                           //   last byte, shift everything
          d /= 2;                           //   right using integer math until
          x >>>= 1;                         //   we have exactly the desired bits.
        }
        return (n + x) / d;                 // Form the number within [0, 1).
      };
    
      // Return the seed that was used
      return seed;
    };
    
    //
    // ARC4
    //
    // An ARC4 implementation.  The constructor takes a key in the form of
    // an array of at most (width) integers that should be 0 <= x < (width).
    //
    // The g(count) method returns a pseudorandom integer that concatenates
    // the next (count) outputs from ARC4.  Its return value is a number x
    // that is in the range 0 <= x < (width ^ count).
    //
    /** @constructor */
    function ARC4(key) {
      var t, u, me = this, keylen = key.length;
      var i = 0, j = me.i = me.j = me.m = 0;
      me.S = [];
      me.c = [];
    
      // The empty key [] is treated as [0].
      if (!keylen) { key = [keylen++]; }
    
      // Set up S using the standard key scheduling algorithm.
      while (i < width) { me.S[i] = i++; }
      for (i = 0; i < width; i++) {
        t = me.S[i];
        j = lowbits(j + t + key[i % keylen]);
        u = me.S[j];
        me.S[i] = u;
        me.S[j] = t;
      }
    
      // The "g" method returns the next (count) outputs as one number.
      me.g = function getnext(count) {
        var s = me.S;
        var i = lowbits(me.i + 1); var t = s[i];
        var j = lowbits(me.j + t); var u = s[j];
        s[i] = u;
        s[j] = t;
        var r = s[lowbits(t + u)];
        while (--count) {
          i = lowbits(i + 1); t = s[i];
          j = lowbits(j + t); u = s[j];
          s[i] = u;
          s[j] = t;
          r = r * width + s[lowbits(t + u)];
        }
        me.i = i;
        me.j = j;
        return r;
      };
      // For robust unpredictability discard an initial batch of values.
      // See http://www.rsa.com/rsalabs/node.asp?id=2009
      me.g(width);
    }
    
    //
    // flatten()
    // Converts an object tree to nested arrays of strings.
    //
    /** @param {Object=} result 
      * @param {string=} prop
      * @param {string=} typ */
    function flatten(obj, depth, result, prop, typ) {
      result = [];
      typ = typeof(obj);
      if (depth && typ == 'object') {
        for (prop in obj) {
          if (prop.indexOf('S') < 5) {    // Avoid FF3 bug (local/sessionStorage)
            try { result.push(flatten(obj[prop], depth - 1)); } catch (e) {}
          }
        }
      }
      return (result.length ? result : obj + (typ != 'string' ? '\0' : ''));
    }
    
    //
    // mixkey()
    // Mixes a string seed into a key that is an array of integers, and
    // returns a shortened string seed that is equivalent to the result key.
    //
    /** @param {number=} smear 
      * @param {number=} j */
    function mixkey(seed, key, smear, j) {
      seed += '';                         // Ensure the seed is a string
      smear = 0;
      for (j = 0; j < seed.length; j++) {
        key[lowbits(j)] =
          lowbits((smear ^= key[lowbits(j)] * 19) + seed.charCodeAt(j));
      }
      seed = '';
      for (j in key) { seed += String.fromCharCode(key[j]); }
      return seed;
    }
    
    //
    // lowbits()
    // A quick "n mod width" for width a power of 2.
    //
    function lowbits(n) { return n & (width - 1); }
    
    //
    // The following constants are related to IEEE 754 limits.
    //
    startdenom = math.pow(width, chunks);
    significance = math.pow(2, significance);
    overflow = significance * 2;
    
    //
    // When seedrandom.js is loaded, we immediately mix a few bits
    // from the built-in RNG into the entropy pool.  Because we do
    // not want to intefere with determinstic PRNG state later,
    // seedrandom will not call math.random on its own again after
    // initialization.
    //
    mixkey(math.random(), pool);
    
    // End anonymous scope, and pass initial values.
    })(
      [],   // pool: entropy pool starts empty
      Math, // math: package containing random, pow, and seedrandom
      256,  // width: each RC4 output is 0 <= x < 256
      6,    // chunks: at least six RC4 outputs for each double
      52    // significance: there are 52 significant digits in a double
    );