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Atmospheric Electrostatics by Wahlin

By Wahlin

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Random Numbers Generated by Linear Recurrence Modulo Two. Mathematics of Computation, 19, 1965, pp. 201-209 [20] TEZUKA, S. and L'ECUYER, P. Efficient and Portable Combined Tausworthe Random Number Generators. ACM. Trans. Model. Comput. , 1, 1991, pp. , ALA-NISSILÄ, T. and KANKAALA, K. Physical Tests for Random Numbers in Simulations. Physical Review Letters, 73(19), 1994, pp. , ALA-NISSILÄ, T. and KANKAALA, K. Physical Models as Tests of Randomness. Physical Review, E52, 1995, pp.

Y ^= (y >> 18); LET genrand = y ! long genrand_31(void) ! 1 Usage Linear congruential methods are widely used in software since they combine economy of use of memory with rapid execution. However, they have a relatively short period and are consequently not sufficiently random, particularly for generating random multi-dimensional sequences. 2 Definition Most linear congruential methods generate pseudo-random number sequences X1, X2, ... by using the following recurrence relationship. Xn = mod(aXn – 1 + c; m) n = 1, 2, ....

In this program, the length of type “unsigned long” is presumed to be not less than 32 bits. ************************************************* C code : Mersenne Twister **************************************************/ /* Period parameters */ #define P 624 #define Q 397 #define MATRIX_A 0x9908b0dfUL /* constant vector a */ #define UPPER_MASK 0x80000000UL /* most significant w-r bits */ #define LOWER_MASK 0x7fffffffUL /* least significant r bits */ static unsigned long mt [P] ; /* the array for the state vector */ 32 © ISO 2010 – All rights reserved BS ISO 28640:2010 ISO 28640:2010(E) static int mti=P+1 ; /* mti==P+1 means mt [P] is not initialized */ /* initializes mt [P] with a seed */ void init_genrand (unsigned long s) { mt [0] = s & 0xffffffffUL ; for (mti=1 ; mti

=P) { /* generate P words at one time */ int kk ; if (mti == P+1) /* if init _genrand ( ) has not been called, */ init_genrand (5489UL) ; /* a default initial seed is used */ for (kk=0 ; kk> 1) ^ mag01 [y & 0x1UL] ; } for ( ; kk> 1) ^ mag01 [y & 0x1UL] ; } y = (mt [P-1] &UPPER_MASK) | (mt [0] &LOWER_MASK) ; mt [P-1] = mt [Q-1] ^ (y >> 1) ^ mag01 [y & 0x1UL] ; mti = 0 ; } y = mt [mti++] ; /* Tempering */ y ^= (y >> 11) ; y ^= (y << 7) & 0x9d2c5680UL ; y ^= (y << 15) & 0xefc60000UL ; y ^= (y >> 18) ; return y ; } /* generates a random number on [0, 0x7fffffff] -interval */ long genrand_31 (void) { return (long) (genrand( ) >>1) ; } NOTE The corresponding Full Basic code of the Mersenne Twister method is shown for information as follows.

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