Conversion of Mersenne Twister to double-precision floating-point numbers
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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.
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