Online Appendix to: Implementing 64-bit Maximally Equidistributed F2-Linear Generators with Mersenne Prime Period

In this appendix, we examine the 64-bit integer output sequences of the SFMT19937 generator (or the double-precision floating-point numbers in [0, 1) converted from them). In fact, the SFMT generators are optimized under the assumption that one will mainly be using 32-bit output sequences, so that the dimensions of equidistribution with v-bit accuracy for 64-bit output sequences are worse than those for 32-bit cases. We therefore study the structure of SFMT19937 and point out its weaknesses. We also apply empirical statistical tests to non-successive values of SFMT19937 and find that the generator fails them.