Title: Conversion of Mersenne Twister to double-precision floating-point numbers,
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 $\mathbb{F}_2$-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.