Conversion of Mersenne Twister to double-precision floating-point numbers
Conversion of Mersenne Twister to double-precision floating-point numbers
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Mersenne Twister 到双精度浮点数的转换
DOI：
10.1016/j.matcom.2018.08.006
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发表时间：
2019
影响因子：
4.6
通讯作者：
Shin Harase
中科院分区：
文献类型：
--
作者：
Junpei Komiyama;Akiko Takeda;Junya Honda;Hajime Shimao;清水優祐;清水優祐;清水優祐;Shin Harase;Shin Harase;Shin Harase
32位Mersenne捻线发生器MT19937是一种应用广泛的随机数发生器。为了生成位长超过32位的数字，特别是在转换为IEEE 754格式[0,1]中的53位双精度浮点数时，典型的实现是将两个连续的32位整数连接起来，然后除以2的幂。在这种情况下，32位MT19937在假设主要使用32位输出值的情况下，根据其均匀分布属性（即所谓的具有v位精度的均匀分布维度）进行了优化，因此与简单使用32位输出相比，串联有时会降低均匀分布的维度。在本文中，我们通过研究高维输出的位之间隐藏的f2 -线性关系来分析这种现象。因此，我们报告具有特定滞后集的MT19937无法通过重叠碰撞检验、矩阵秩检验和Hamming独立性检验等统计检验。
Abstract 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 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.