9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi/* $OpenBSD: arc4random_uniform.c,v 1.1 2014/07/12 13:24:54 deraadt Exp $ */
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * Copyright (c) 2008, Damien Miller <djm@openbsd.org>
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * Permission to use, copy, modify, and distribute this software for any
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * purpose with or without fee is hereby granted, provided that the above
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * copyright notice and this permission notice appear in all copies.
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * Calculate a uniformly distributed random number less than upper_bound
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * avoiding "modulo bias".
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * Uniformity is achieved by generating new random numbers until the one
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * returned is outside the range [0, 2**32 % upper_bound). This
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * guarantees the selected random number will be inside
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * [2**32 % upper_bound, 2**32) which maps back to [0, upper_bound)
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * after reduction modulo upper_bound.
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi /* 2**32 % x == (2**32 - x) % x */
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * This could theoretically loop forever but each retry has
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * p > 0.5 (worst case, usually far better) of selecting a
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * number inside the range we need, so it should rarely need
9d12795f87b63c2e39e87bff369182edd34677d3Robert Mustacchi * to re-roll.