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/**
* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* 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 of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
* ## Notice
*
* The original C++ code and copyright notice are from the [Boost library]{http://www.boost.org/doc/libs/1_65_1/doc/html/boost/random/uniform_int_distribution.html}. The implementation has been modified for JavaScript.
*
* ```text
* (C) Copyright John Maddock 2006.
* (C) Copyright Steven Watanabe 2011.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var MAX_SAFE_INTEGER = require( '@stdlib/constants/float64/max-safe-integer' );
var floor = require( '@stdlib/math/base/special/floor' );
// MAIN //
/**
* Returns a pseudorandom number drawn from a discrete uniform distribution with minimum support `a` and maximum support `b`.
*
* @private
* @param {PRNG} rand - pseudorandom number generator which outputs integer values
* @param {integer} a - minimum support
* @param {integer} b - maximum support
* @returns {integer} pseudorandom number
*/
function discreteUniform( rand, a, b ) {
var result;
var RANGE;
var range;
var limit;
var bsize;
var mult;
var MIN;
var MAX;
var inc;
range = b - a;
if ( range === 0 ) {
return a;
}
MIN = rand.MIN;
MAX = rand.MAX;
RANGE = MAX - MIN;
if ( RANGE === range ) {
return ( rand()-MIN ) + a;
}
if ( RANGE < range ) {
limit = 0;
while ( true ) {
// Avoid overflow...
if ( range === MAX_SAFE_INTEGER ) { // in JavaScript, we only explicitly have doubles
limit = floor( range / (RANGE+1) );
if ( range%(RANGE+1) === RANGE ) { // e.g., 5%(2+1) == 2
limit += 1;
}
} else {
limit = floor( (range+1) / (RANGE+1) );
}
// We consider `result` as expressed base `(RANGE+1)`:
result = 0;
// For every power of `(RANGE+1)`, we determine a random factor:
mult = 1;
// Loop invariants: result < mult && mult <= range
while ( mult <= limit ) {
// Note: see first and second post-conditions.
result += (rand() - MIN) * mult;
// Equivalent to (mult * (RANGE+1)) == range+1, but avoids overflow...
if ( mult*RANGE === range-mult+1 ) {
// The destination range is an integer power of the generator's range...
return result;
}
// Note: see third post-condition.
mult *= RANGE + 1;
}
// range/mult < RANGE+1 (no endless loop)
inc = discreteUniform( rand, 0, floor( range/mult ) );
if ( inc > MAX_SAFE_INTEGER/mult ) {
// The multiplication would overflow, so reject immediately...
continue;
}
inc *= mult;
result += inc;
// NOTE: if we were working with unsigned integers, we would need to check that `result` is NOT less than `inc`, as unsigned integers wrap on overflow. In which case, we would need to reject.
if ( result > range ) {
// Result is too big, so reject...
continue;
}
return result + a;
}
}
// Case: RANGE > range
// When determining the bucket size, avoid overflow...
if ( RANGE === MAX_SAFE_INTEGER ) { // in JavaScript, we only explicitly have doubles
bsize = floor( RANGE / (range+1) );
if ( RANGE%(range+1) === range ) { // e.g., 5%(2+1) == 2
bsize += 1;
}
} else {
bsize = floor( (RANGE+1) / (range+1) );
}
while ( true ) {
result = rand() - MIN;
result = floor( result / bsize );
if ( result <= range ) {
return result + a;
}
}
}
// EXPORTS //
module.exports = discreteUniform;
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