At the highest possible level=4 its 24 bits of mantissa are completely chaotic, however, already for default level=3 its quality is high enough for most of practical applications.
Upgrade of the Cellular General Purpose Monte Carlo Tool FOAM to version 2.06
In Table 1, assuming no truncation error, the predicted maximum with an effective mantissa of 53 bits is at n = 76, the actual maximum, including truncation error, is at n = 74.
Golden and Alternating, fast simple O(lg n) algorithms for Fibonacci
Schatte, P., On Mantissa Distributions in Computing and Benford’s law, J.
The Uneven Distribution of Numbers in Nature
If any of (A or B)’s mantissa is only of 12 bits then the Checker will check this and will switch of the multiply blocks which are not required using the control signal.
Combined Integer and Floating Point Multiplication Architecture(CIFM) for FPGAs and Its Reversible Logic Implementation
Our code is compliant with the IEEE double-precision standard (so that the mantissas of variables have approximately one bit of precision less than 16 digits, yielding a relative precision of about 2E–16).
Computing the confidence levels for a root-mean-square test of goodness-of-fit
Our code is compliant with the IEEE double-precision standard (so that the mantissas of variables have approximately one bit of precision less than 16 digits, yielding a relative precision of about 2E–16).
Computing the confidence levels for a root-mean-square test of goodness-of-fit, II
It should be represented in ﬂoating-point, with at least n = ⌈log2 Y ⌉ + 1 bits in the mantissa, so that each multiplication by p magniﬁes the relative error by at most 1 + 2−n .
A multimodular algorithm for computing Bernoulli numbers
The computations are done using multiprecision intervals with 200 bits of mantissa.
Rigorous KAM results around arbitrary periodic orbits for Hamiltonian Systems
The values k/252 in the deﬁnition of G and the values (m− 252)/252 in the deﬁnition of F are called mantissas of the considered IEEE-Double-Numbers.
Rigorous Computing of Rectangle Scan Probabilities for Markov Increments
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