#include "RandMT.h" using namespace std; // // uint32_t must be an unsigned integer type capable of holding at least 32 // bits; exactly 32 should be fastest, but 64 is better on an Alpha with // GCC at -O3 optimization so try your options and see what's best for you // RandMT::RandMT() { seedMT(1U); } RandMT::RandMT(uint32_t seed) { seedMT(seed); } void RandMT::seedMT(uint32_t seed) { // // We initialize state[0..(N-1)] via the generator // // x_new = (69069 * x_old) mod 2^32 // // from Line 15 of Table 1, p. 106, Sec. 3.3.4 of Knuth's // _The Art of Computer Programming_, Volume 2, 3rd ed. // // Notes (SJC): I do not know what the initial state requirements // of the Mersenne Twister are, but it seems this seeding generator // could be better. It achieves the maximum period for its modulus // (2^30) iff x_initial is odd (p. 20-21, Sec. 3.2.1.2, Knuth); if // x_initial can be even, you have sequences like 0, 0, 0, ...; // 2^31, 2^31, 2^31, ...; 2^30, 2^30, 2^30, ...; 2^29, 2^29 + 2^31, // 2^29, 2^29 + 2^31, ..., etc. so I force seed to be odd below. // // Even if x_initial is odd, if x_initial is 1 mod 4 then // // the lowest bit of x is always 1, // the next-to-lowest bit of x is always 0, // the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... , // the 3rd-from-lowest bit of x 4-cycles ... 0 1 1 0 0 1 1 0 ... , // the 4th-from-lowest bit of x has the 8-cycle ... 0 0 0 1 1 1 1 0 ... , // ... // // and if x_initial is 3 mod 4 then // // the lowest bit of x is always 1, // the next-to-lowest bit of x is always 1, // the 2nd-from-lowest bit of x alternates ... 0 1 0 1 0 1 0 1 ... , // the 3rd-from-lowest bit of x 4-cycles ... 0 0 1 1 0 0 1 1 ... , // the 4th-from-lowest bit of x has the 8-cycle ... 0 0 1 1 1 1 0 0 ... , // ... // // The generator's potency (min. s>=0 with (69069-1)^s = 0 mod 2^32) is // 16, which seems to be alright by p. 25, Sec. 3.2.1.3 of Knuth. It // also does well in the dimension 2..5 spectral tests, but it could be // better in dimension 6 (Line 15, Table 1, p. 106, Sec. 3.3.4, Knuth). // // Note that the random number user does not see the values generated // here directly since reloadMT() will always munge them first, so maybe // none of all of this matters. In fact, the seed values made here could // even be extra-special desirable if the Mersenne Twister theory says // so-- that's why the only change I made is to restrict to odd seeds. // initseed = seed; register uint32_t x = (seed | 1U) & 0xFFFFFFFFU, *s = state; register int j; left = 0; for(*s++=x, j=N; --j; *s++ = (x*=69069U) & 0xFFFFFFFFU); } uint32_t RandMT::reloadMT(void) { register uint32_t *p0=state, *p2=state+2, *pM=state+M, s0, s1; register int j; if(left < -1) seedMT(initseed); left=N-1, next=state+1; for(s0=state[0], s1=state[1], j=N-M+1; --j; s0=s1, s1=*p2++) *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); for(pM=state, j=M; --j; s0=s1, s1=*p2++) *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); s1=state[0], *p0 = *pM ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); s1 ^= (s1 >> 11); s1 ^= (s1 << 7) & 0x9D2C5680U; s1 ^= (s1 << 15) & 0xEFC60000U; return(s1 ^ (s1 >> 18)); } uint32_t RandMT::randomMT(void) { uint32_t y; if(--left < 0) return(reloadMT()); y = *next++; y ^= (y >> 11); y ^= (y << 7) & 0x9D2C5680U; y ^= (y << 15) & 0xEFC60000U; return(y ^ (y >> 18)); }