Mersenne Twister到double-precision浮点数的转换
Conversion of Mersenne Twister to double-precision floating-point numbers
摘要：
32位Mersenne Twister发生器MT 19937是一种广泛使用的随机数发生器。为了生成位长度大于32位的数字，特别是当转换成IEEE 754格式的$[0,1)$中的53位双精度浮点数时，典型的实现方式将两个连续的32位整数连接起来，并将它们除以$2$的幂。在这种情况下，在假设主要使用32位输出值的情况下，32位MT 19937在其等分布属性（所谓的具有$v$位精度的等分布维度）方面进行了优化，因此与简单使用32位输出相比，串联有时会降低等分布的维度。在本文中，我们分析了这种现象，通过调查隐藏的$\mathbb{F}_2$ -线性关系之间的比特的高维输出。因此，我们报告说，MT 19937与一个特定的滞后集失败的几个统计测试，如重叠碰撞测试，矩阵秩检验，和汉明独立性测试。
英文摘要：
The 32-bit Mersenne Twister generator MT19937 is a widely used random number generator. To generate numbers with more than 32 bits in bit length, and particularly when converting into 53-bit double-precision floating-point numbers in $[0,1)$ in the IEEE 754 format, the typical implementation concatenates two successive 32-bit integers and divides them by a power of $2$. In this case, the 32-bit MT19937 is optimized in terms of its equidistribution properties (the so-called dimension of equidistribution with $v$-bit accuracy) under the assumption that one will mainly be using 32-bit output values, and hence the concatenation sometimes degrades the dimension of equidistribution compared with the simple use of 32-bit outputs. In this paper, we analyze such phenomena by investigating hidden $\mathbb{F}_2$-linear relations among the bits of high-dimensional outputs. Accordingly, we report that MT19937 with a specific lag set fails several statistical tests, such as the overlapping collision test, matrix rank test, and Hamming independence test.
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