[ https://issues.apache.org/jira/browse/RNG-95?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16886537#comment-16886537 ]

Alex D Herbert commented on RNG-95: ----------------------------------- This method has been documented by Danial Lamire: [Fast Random Integer Generation in an Interval|https://arxiv.org/abs/1805.10941] > DiscreteUniformSampler > ---------------------- > > Key: RNG-95 > URL: https://issues.apache.org/jira/browse/RNG-95 > Project: Commons RNG > Issue Type: Improvement > Components: sampling > Affects Versions: 1.3 > Reporter: Alex D Herbert > Assignee: Alex D Herbert > Priority: Minor > > The {{DiscreteUniformSampler}} delegates the creation of an integer in the > range {{[0, n)}} to the {{UniformRandomProvider}}. > This sampler will be repeatedly used to sample the same range. The default > method in {{BaseProvider}} uses a dynamic algorithm that handles {{n}} > differently when a power of 2. > When the range is a power of 2 the method can use a series of bits from a > random integer to generate a uniform integer in the range. This is fast. > When the range is not a power of 2 the algorithm must reject samples when the > sample would result in an over-representation of a particular value in the > uniform range. This is necessary as {{n}} does not exactly fit into the > number of possible values {{[0, 2^31)}} that can be produced by the generator > (when using 31-bit signed integers). The rejection method uses integer > arithmetic to determine the number of samples that fit into the range: > {{samples = 2^31 / n}}. Extra samples that lead to over-representation are > rejected: {{extra = 2^31 % n}}. > Since {{n}} will not change a pre-computation step is possible to select the > best algorithm. > n is a power of 2: > {code:java} > // Favouring the least significant bits > // Pre-compute > int mask = n - 1; > return nextInt() & mask; > // Or favouring the most significant bits > // Pre-compute > int shift = Integer.numberOfLeadingZeros(n) + 1; > return nextInt() >>> shift; > {code} > n is not a power of 2: > {code:java} > // Sample using modulus > // Pre-compute > final int fence = (int)(0x80000000L - 0x80000000L % n - 1); > int bits; > do { > bits = rng.nextInt() >>> 1; > } while (bits > fence); > return bits % n; > // Or using 32-bit unsigned arithmetic avoiding modulus > // Pre-compute > final long fence = (1L << 32) % n; > long result; > do { > // Compute 64-bit unsigned product of n * [0, 2^32 - 1) > result = n * (rng.nextInt() & 0xffffffffL); > // Test the sample uniformity. > } while ((result & 0xffffffffL) < fence); > // Divide by 2^32 to get the sample > return (int)(result >>> 32); > {code} > The second method uses a range of 2^32 instead of 2^31 so reducing the > rejection probability and avoids the modulus operator; these both increase > speed. > Note algorithm 1 returns sample values in a repeat cycle from all values in > the range {{[0, 2^31)}} due to the use of modulus, e.g. > {noformat} > 0, 1, 2, ..., 0, 1, 2, ... > {noformat} > Algorithm 2 returns sample values in a linear order, e.g. > {noformat} > 0, 0, 1, 1, 2, 2, ... > {noformat} > The suggested change is to implement smart pre-computation in the > {{DiscreteUniformSampler}} based on the range and use the algorithms that > favour the most significant bits from the generator. -- This message was sent by Atlassian JIRA (v7.6.14#76016)