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

  title={Conversion of Mersenne Twister to double-precision floating-point numbers},
  author={Shin Harase},
  journal={Math. Comput. Simul.},
  • S. Harase
  • Published 20 August 2017
  • Computer Science, Mathematics
  • Math. Comput. Simul.
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… 
Improving the statistical quality of random number generators by applying a simple ratio transformation
The ratio of two random number generators is investigated as an alternative approach: the smaller of two input random numbers is divided by the larger, resulting in a rational number from [ 0 , 1 ] .
On testing pseudorandom generators via statistical tests based on the arcsine law
A second level statistical test based on the arcsine law for random walks is proposed, which provides a Berry-Essen type inequality for approximating the arcine distribution, what allows for a detailed error analysis of the proposed test.
Custo anual uniforme equivalente de máquinas de colheita de madeira: uma abordagem estocástica
Determining the economic life of wood harvesting machines, time when the machine performed its functions at the lowest operating cost is associated with the lowest production cost. Thus, the
De–randomized Meta-Differential Evolution for Calculating and Predicting Glucose Levels
An optimization method based on zooming with derandomized sequences as an alternative to the Meta-Differential Evolution exhibited the same accuracy and precision as completely non-deterministic differential evolution.
Comparing the PaGMO Framework to a De-randomized Meta-Differential Evolution on Calculation and Prediction of Glucose Levels
The PaGMO framework is evaluated for calculating and predicting glucose levels for diabetic patients, and its individual algorithms are tested for signal reconstruction and prediction.
An efficient weak Euler-Maruyama type approximation scheme of very high dimensional SDEs by orthogonal random variables
It is concluded that an Euler-Maruyama approximation generated by the Walsh system is efficient in high dimensions.


Implementing 64-bit Maximally Equidistributed Mersenne Twisters
64-bit maximally equidistributed pseudorandom number generators that are optimal in this respect and have speeds equivalent to 64-bit Mersenne Twisters are developed.
On the F2-linear relations of Mersenne Twister pseudorandom number generators
  • S. Harase
  • Mathematics, Computer Science
    Math. Comput. Simul.
  • 2014
Assessment of non-random bit patterns in dimensions that are higher than the dimension of equidistribution with v -bit accuracy, which focuses on the relationship between points in the Couture-L'Ecuyer dual lattices and F 2 -linear relations on the most significant v bits of output sequences.
A PRNG Specialized in Double Precision Floating Point Numbers Using an Affine Transition
We propose a pseudorandom number generator specialized to generate double precision floating point numbers. It generates 52-bit pseudorandom patterns supplemented by a constant most significant 12
SIMD-Oriented Fast Mersenne Twister: a 128-bit Pseudorandom Number Generator
A 128-bit based PRNG, named SIMD-oriented Fast Mersenne Twister (SFMT), which is analogous to MT but making full use of these features, and is roughly twice as fast as optimised MT using SIMD operations.
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
A new algorithm called Mersenne Twister (MT) is proposed for generating uniform pseudorandom numbers, which provides a super astronomical period of 2 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words.
Fast lattice reduction for F2-linear pseudorandom number generators
This paper proposes a similar but faster algorithm, where the state space is used to represent vectors with components in the formal power series, the dual lattice is not necessary, and Lenstra reduction is replaced with a simpler basis reduction.
A Non-empirical Test on the Second to the Sixth Least Significant Bits of Pseudorandom Number Generators
Lagged Fibonacci generators are widely used random number generators. Some implementations discard the least significant bit of their outputs, because their weight distribution has a strong
An efficient lattice reduction method for F2-linear pseudorandom number generators using Mulders and Storjohann algorithm
  • S. Harase
  • Computer Science, Mathematics
    J. Comput. Appl. Math.
  • 2011
A fast lattice reduction algorithm by Mulders and Storjohann is used instead of Schmidt’s algorithm, and the order of computational complexity is lessened, and it is reported that just using a sparsest initial state significantly accelerates the lattice computation, in the case of Mersenne Twister generators.
On the xorshift random number generators
It is found that the vast majority of xorshift generators with only threexorshift operations, including those having good equidistribution, fail several simple statistical tests.
Sparse Serial Tests of Uniformity for Random Number Generators
For the classes of alternatives that correspond to linear generators, the most efficient tests turn out to have $k \gg n$ (in contrast to what is usually done or recommended in simulation books) and to use overlapping vectors.