Description
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:
// 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;
n is not a power of 2:
// 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);
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.
0, 1, 2, ..., 0, 1, 2, ...
Algorithm 2 returns sample values in a linear order, e.g.
0, 0, 1, 1, 2, 2, ...
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.
Attachments
Issue Links
- is related to
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RNG-90 Improve nextInt(int) and nextLong(long) for powers of 2
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- Closed
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- links to
