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The time saving is minimal, as the most expensive operation (the 64×64-bit multiply) remains, so the normal version is preferred except in extremis. Still, this faster version also passes statistical tests. [4] When executing on a 32-bit processor, the 64×64-bit multiply must be implemented using three 32×32→64-bit multiply operations.
A C version [a] of three xorshift algorithms [1]: 4,5 is given here. The first has one 32-bit word of state, and period 2 32 −1. The second has one 64-bit word of state and period 2 64 −1. The last one has four 32-bit words of state, and period 2 128 −1. The 128-bit algorithm passes the diehard tests.
For Monte Carlo simulations, an LCG must use a modulus greater and preferably much greater than the cube of the number of random samples which are required. This means, for example, that a (good) 32-bit LCG can be used to obtain about a thousand random numbers; a 64-bit LCG is good for about 2 21 random samples (a little over two million), etc ...
The generator computes an odd 128-bit value and returns its upper 64 bits. This generator passes BigCrush from TestU01 , but fails the TMFn test from PractRand . That test has been designed to catch exactly the defect of this type of generator: since the modulus is a power of 2, the period of the lowest bit in the output is only 2 62 , rather ...
The butterfly can also be used to improve the randomness of large arrays of partially random numbers, by bringing every 32 or 64 bit word into causal contact with every other word through a desired hashing algorithm, so that a change in any one bit has the possibility of changing all the bits in the large array. [4]
The F-function splits the 32-bit input into four 8-bit quarters and uses the quarters as input to the S-boxes. The S-boxes accept 8-bit input and produce 32-bit output. The outputs are added modulo 2 32 and XORed to produce the final 32-bit output (see image in the upper right corner). [6]
MurmurHash64A (64-bit, x64)—The original 64-bit version. Optimized for 64-bit arithmetic. MurmurHash64B (64-bit, x86)—A 64-bit version optimized for 32-bit platforms. It is not a true 64-bit hash due to insufficient mixing of the stripes. [10] The person who originally found the flaw [clarification needed] in MurmurHash2 created an ...
However, many microprocessors can compute a full 64-bit product in almost the same time as the low 32 bits. Indeed, many compute the 64-bit product and then ignore the high half. A lag-1 multiply-with-carry generator allows us to make the period nearly 2 63 by using almost the same computer operations, except that the top
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