C的兰德()使用了哪些常见算法?

xqk2d5yq  于 2023-03-01  发布在  其他
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我知道C规范没有给予rand()具体实现的规范,那么在不同的主流平台上,常用的算法有哪些不同,有何区别?

im9ewurl

im9ewurl1#

参见本文:http://en.wikipedia.org/wiki/List_of_random_number_generators
这是glibc的rand()的源代码:

/* Reentrant random function from POSIX.1c.
   Copyright (C) 1996, 1999, 2009 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

#include <stdlib.h>

/* This algorithm is mentioned in the ISO C standard, here extended
   for 32 bits.  */
int
rand_r (unsigned int *seed)
{
  unsigned int next = *seed;
  int result;

  next *= 1103515245;
  next += 12345;
  result = (unsigned int) (next / 65536) % 2048;

  next *= 1103515245;
  next += 12345;
  result <<= 10;
  result ^= (unsigned int) (next / 65536) % 1024;

  next *= 1103515245;
  next += 12345;
  result <<= 10;
  result ^= (unsigned int) (next / 65536) % 1024;

  *seed = next;

  return result;
}

来源:https://sourceware.org/git/?p=glibc.git;a=blob_plain;f=stdlib/rand_r.c;hb=HEAD
正如你所看到的,它只是一个简单的乘法,一个加法和一个移位。值被仔细地选择,以确保你不会得到重复的输出为RAND_MAX迭代。
请注意,这是一个旧的实现,已被更复杂的算法所取代:https://sourceware.org/git/?p=glibc.git;a=blob_plain;f=stdlib/random_r.c;hb=HEAD
如果链接断开,请搜索"glibc rand_r"

muk1a3rh

muk1a3rh2#

我曾经为一门离散数学课程写过一篇关于CRNG的报告,为此,我在msvcrt.dll中分解了兰德():

msvcrt.dll:77C271D8 mov     ecx, [eax+14h]
msvcrt.dll:77C271DB imul    ecx, 343FDh
msvcrt.dll:77C271E1 add     ecx, 269EC3h
msvcrt.dll:77C271E7 mov     [eax+14h], ecx
msvcrt.dll:77C271EA mov     eax, ecx
msvcrt.dll:77C271EC shr     eax, 10h
msvcrt.dll:77C271EF and     eax, 7FFFh

所以这是一个LCG类似的东西(未经测试)...

int ms_rand(int& seed)
{
  seed = seed*0x343fd+0x269EC3;  // a=214013, b=2531011
  return (seed >> 0x10) & 0x7FFF;
}
bjp0bcyl

bjp0bcyl3#

伪随机数发生器(PRNG)的领域相当广阔。
首先,你必须明白,没有外部输入(通常是物理的),你不能得到一个真实的的随机数源..这就是为什么这些算法被称为 * 伪随机 *:他们通常使用种子来初始化一个很长序列中的一个位置,这个序列看起来是随机的,但实际上不是随机的。
最简单的算法之一是Linear Congruential GeneratorLCG),它有一些约束以保证长序列,并且它根本不安全。
另一个有趣的(至少名字)是Blum Blum Shub Generator(BBS),这是不寻常的正常PRNG,因为它依赖于求幂在模算术提供了一个安全性可比的其他算法,如RSA和El Gamal在打破序列(如果我不知道它的证明)

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