diff options
| -rw-r--r-- | ext/standard/rand.c | 142 |
1 files changed, 72 insertions, 70 deletions
diff --git a/ext/standard/rand.c b/ext/standard/rand.c index 33d6f260e1..8f94577e1c 100644 --- a/ext/standard/rand.c +++ b/ext/standard/rand.c @@ -98,96 +98,98 @@ */ static void seedMT(php_uint32 seed TSRMLS_DC) { - /* - 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 + /* + 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 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 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 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). + 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. - */ - - register php_uint32 x = (seed | 1U) & 0xFFFFFFFFU, *s = BG(state); - register int j; - - for(BG(left)=0, *s++=x, j=N; --j; - *s++ = (x*=69069U) & 0xFFFFFFFFU); + 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. + */ + + register php_uint32 x = (seed | 1U) & 0xFFFFFFFFU, *s = BG(state); + register int j; + + for (BG(left) = 0, *s++ = x, j = N; --j; + *s++ = (x *= 69069U) & 0xFFFFFFFFU); } /* }}} */ static php_uint32 reloadMT(TSRMLS_D) { - register php_uint32 *p0=BG(state), *p2=BG(state)+2, *pM=BG(state)+M, s0, s1; - register int j; + register php_uint32 *p0 = BG(state), *p2 = BG(state) + 2, *pM = BG(state) + M, s0, s1; + register int j; - if(BG(left) < -1) - seedMT(4357U TSRMLS_CC); + if (BG(left) < -1) + seedMT(4357U TSRMLS_CC); - BG(left)=N-1, BG(next)=BG(state)+1; + BG(left) = N - 1, BG(next) = BG(state) + 1; - for(s0=BG(state)[0], s1=BG(state)[1], j=N-M+1; --j; s0=s1, s1=*p2++) - *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); + for (s0 = BG(state)[0], s1 = BG(state)[1], j = N - M + 1; --j; s0 = s1, s1 = *p2++) + *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); - for(pM=BG(state), j=M; --j; s0=s1, s1=*p2++) - *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); + for (pM = BG(state), j = M; --j; s0 = s1, s1 = *p2++) + *p0++ = *pM++ ^ (mixBits(s0, s1) >> 1) ^ (loBit(s1) ? K : 0U); - s1=BG(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)); + s1 = BG(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); } static php_uint32 randomMT(TSRMLS_D) { - php_uint32 y; + php_uint32 y; + + if (--BG(left) < 0) + return reloadMT(TSRMLS_C); - if(--BG(left) < 0) - return(reloadMT(TSRMLS_C)); + y = *BG(next)++; + y ^= (y >> 11); + y ^= (y << 7) & 0x9D2C5680U; + y ^= (y << 15) & 0xEFC60000U; - y = *BG(next)++; - y ^= (y >> 11); - y ^= (y << 7) & 0x9D2C5680U; - y ^= (y << 15) & 0xEFC60000U; - return(y ^ (y >> 18)); + return y ^ (y >> 18); } /* {{{ proto void srand(int seed) |