/** * @file SFMT.c * @brief SIMD oriented Fast Mersenne Twister(SFMT) * * @author Mutsuo Saito (Hiroshima University) * @author Makoto Matsumoto (Hiroshima University) * * Copyright (C) 2006,2007 Mutsuo Saito, Makoto Matsumoto and Hiroshima * University. All rights reserved. * * The new BSD License is applied to this software, see LICENSE.txt */ #include #include #include "SFMTObj.h" #include "SFMT-params.h" #if defined(__BIG_ENDIAN__) && !defined(__amd64) && !defined(BIG_ENDIAN64) #define BIG_ENDIAN64 1 #endif #if defined(HAVE_ALTIVEC) && !defined(BIG_ENDIAN64) #define BIG_ENDIAN64 1 #endif #if defined(ONLY64) && !defined(BIG_ENDIAN64) #if defined(__GNUC__) #error "-DONLY64 must be specified with -DBIG_ENDIAN64" #endif #undef ONLY64 #endif /** a parity check vector which certificate the period of 2^{MEXP} */ static const uint32_t parity[4] = { PARITY1, PARITY2, PARITY3, PARITY4 }; /*---------------- STATIC FUNCTIONS ----------------*/ inline static int idxof(int i); inline static void rshift128(w128_t *out, w128_t const *in, int shift); inline static void lshift128(w128_t *out, w128_t const *in, int shift); inline static uint32_t func1(uint32_t x); inline static uint32_t func2(uint32_t x); #if defined(BIG_ENDIAN64) && !defined(ONLY64) inline static void swap(w128_t *array, int size); #endif // These SIMD versions WILL NOT work as-is. I'm not even sure SSE2 is // safe to provide as a runtime option without significant changes to // how the state is stored, since the VC++ docs warn that: // Using variables of type __m128i will cause the compiler to generate // the SSE2 movdqa instruction. This instruction does not cause a fault // on Pentium III processors but will result in silent failure, with // possible side effects caused by whatever instructions movdqa // translates into on Pentium III processors. #if defined(HAVE_ALTIVEC) #include "SFMT-alti.h" #elif defined(HAVE_SSE2) #include "SFMT-sse2.h" #endif /** * This function simulate a 64-bit index of LITTLE ENDIAN * in BIG ENDIAN machine. */ #ifdef ONLY64 inline static int idxof(int i) { return i ^ 1; } #else inline static int idxof(int i) { return i; } #endif /** * This function simulates SIMD 128-bit right shift by the standard C. * The 128-bit integer given in in is shifted by (shift * 8) bits. * This function simulates the LITTLE ENDIAN SIMD. * @param out the output of this function * @param in the 128-bit data to be shifted * @param shift the shift value */ #ifdef ONLY64 inline static void rshift128(w128_t *out, w128_t const *in, int shift) { uint64_t th, tl, oh, ol; th = ((uint64_t)in->u[2] << 32) | ((uint64_t)in->u[3]); tl = ((uint64_t)in->u[0] << 32) | ((uint64_t)in->u[1]); oh = th >> (shift * 8); ol = tl >> (shift * 8); ol |= th << (64 - shift * 8); out->u[0] = (uint32_t)(ol >> 32); out->u[1] = (uint32_t)ol; out->u[2] = (uint32_t)(oh >> 32); out->u[3] = (uint32_t)oh; } #else inline static void rshift128(w128_t *out, w128_t const *in, int shift) { uint64_t th, tl, oh, ol; th = ((uint64_t)in->u[3] << 32) | ((uint64_t)in->u[2]); tl = ((uint64_t)in->u[1] << 32) | ((uint64_t)in->u[0]); oh = th >> (shift * 8); ol = tl >> (shift * 8); ol |= th << (64 - shift * 8); out->u[1] = (uint32_t)(ol >> 32); out->u[0] = (uint32_t)ol; out->u[3] = (uint32_t)(oh >> 32); out->u[2] = (uint32_t)oh; } #endif /** * This function simulates SIMD 128-bit left shift by the standard C. * The 128-bit integer given in in is shifted by (shift * 8) bits. * This function simulates the LITTLE ENDIAN SIMD. * @param out the output of this function * @param in the 128-bit data to be shifted * @param shift the shift value */ #ifdef ONLY64 inline static void lshift128(w128_t *out, w128_t const *in, int shift) { uint64_t th, tl, oh, ol; th = ((uint64_t)in->u[2] << 32) | ((uint64_t)in->u[3]); tl = ((uint64_t)in->u[0] << 32) | ((uint64_t)in->u[1]); oh = th << (shift * 8); ol = tl << (shift * 8); oh |= tl >> (64 - shift * 8); out->u[0] = (uint32_t)(ol >> 32); out->u[1] = (uint32_t)ol; out->u[2] = (uint32_t)(oh >> 32); out->u[3] = (uint32_t)oh; } #else inline static void lshift128(w128_t *out, w128_t const *in, int shift) { uint64_t th, tl, oh, ol; th = ((uint64_t)in->u[3] << 32) | ((uint64_t)in->u[2]); tl = ((uint64_t)in->u[1] << 32) | ((uint64_t)in->u[0]); oh = th << (shift * 8); ol = tl << (shift * 8); oh |= tl >> (64 - shift * 8); out->u[1] = (uint32_t)(ol >> 32); out->u[0] = (uint32_t)ol; out->u[3] = (uint32_t)(oh >> 32); out->u[2] = (uint32_t)oh; } #endif /** * This function represents the recursion formula. * @param r output * @param a a 128-bit part of the internal state array * @param b a 128-bit part of the internal state array * @param c a 128-bit part of the internal state array * @param d a 128-bit part of the internal state array */ #if (!defined(HAVE_ALTIVEC)) && (!defined(HAVE_SSE2)) #ifdef ONLY64 inline static void do_recursion(w128_t *r, w128_t *a, w128_t *b, w128_t *c, w128_t *d) { w128_t x; w128_t y; lshift128(&x, a, SL2); rshift128(&y, c, SR2); r->u[0] = a->u[0] ^ x.u[0] ^ ((b->u[0] >> SR1) & MSK2) ^ y.u[0] ^ (d->u[0] << SL1); r->u[1] = a->u[1] ^ x.u[1] ^ ((b->u[1] >> SR1) & MSK1) ^ y.u[1] ^ (d->u[1] << SL1); r->u[2] = a->u[2] ^ x.u[2] ^ ((b->u[2] >> SR1) & MSK4) ^ y.u[2] ^ (d->u[2] << SL1); r->u[3] = a->u[3] ^ x.u[3] ^ ((b->u[3] >> SR1) & MSK3) ^ y.u[3] ^ (d->u[3] << SL1); } #else inline static void do_recursion(w128_t *r, w128_t *a, w128_t *b, w128_t *c, w128_t *d) { w128_t x; w128_t y; lshift128(&x, a, SL2); rshift128(&y, c, SR2); r->u[0] = a->u[0] ^ x.u[0] ^ ((b->u[0] >> SR1) & MSK1) ^ y.u[0] ^ (d->u[0] << SL1); r->u[1] = a->u[1] ^ x.u[1] ^ ((b->u[1] >> SR1) & MSK2) ^ y.u[1] ^ (d->u[1] << SL1); r->u[2] = a->u[2] ^ x.u[2] ^ ((b->u[2] >> SR1) & MSK3) ^ y.u[2] ^ (d->u[2] << SL1); r->u[3] = a->u[3] ^ x.u[3] ^ ((b->u[3] >> SR1) & MSK4) ^ y.u[3] ^ (d->u[3] << SL1); } #endif #endif #if (!defined(HAVE_ALTIVEC)) && (!defined(HAVE_SSE2)) /** * This function fills the internal state array with pseudorandom * integers. */ void SFMTObj::GenRandAll() { int i; w128_t *r1, *r2; r1 = &sfmt.w128[SFMT::N - 2]; r2 = &sfmt.w128[SFMT::N - 1]; for (i = 0; i < SFMT::N - POS1; i++) { do_recursion(&sfmt.w128[i], &sfmt.w128[i], &sfmt.w128[i + POS1], r1, r2); r1 = r2; r2 = &sfmt.w128[i]; } for (; i < SFMT::N; i++) { do_recursion(&sfmt.w128[i], &sfmt.w128[i], &sfmt.w128[i + POS1 - SFMT::N], r1, r2); r1 = r2; r2 = &sfmt.w128[i]; } } /** * This function fills the user-specified array with pseudorandom * integers. * * @param array an 128-bit array to be filled by pseudorandom numbers. * @param size number of 128-bit pseudorandom numbers to be generated. */ void SFMTObj::GenRandArray(w128_t *array, int size) { int i, j; w128_t *r1, *r2; r1 = &sfmt.w128[SFMT::N - 2]; r2 = &sfmt.w128[SFMT::N - 1]; for (i = 0; i < SFMT::N - POS1; i++) { do_recursion(&array[i], &sfmt.w128[i], &sfmt.w128[i + POS1], r1, r2); r1 = r2; r2 = &array[i]; } for (; i < SFMT::N; i++) { do_recursion(&array[i], &sfmt.w128[i], &array[i + POS1 - SFMT::N], r1, r2); r1 = r2; r2 = &array[i]; } for (; i < size - SFMT::N; i++) { do_recursion(&array[i], &array[i - SFMT::N], &array[i + POS1 - SFMT::N], r1, r2); r1 = r2; r2 = &array[i]; } for (j = 0; j < 2 * SFMT::N - size; j++) { sfmt.w128[j] = array[j + size - SFMT::N]; } for (; i < size; i++, j++) { do_recursion(&array[i], &array[i - SFMT::N], &array[i + POS1 - SFMT::N], r1, r2); r1 = r2; r2 = &array[i]; sfmt.w128[j] = array[i]; } } #endif #if defined(BIG_ENDIAN64) && !defined(ONLY64) && !defined(HAVE_ALTIVEC) inline static void swap(w128_t *array, int size) { int i; uint32_t x, y; for (i = 0; i < size; i++) { x = array[i].u[0]; y = array[i].u[2]; array[i].u[0] = array[i].u[1]; array[i].u[2] = array[i].u[3]; array[i].u[1] = x; array[i].u[3] = y; } } #endif /** * This function represents a function used in the initialization * by init_by_array * @param x 32-bit integer * @return 32-bit integer */ static uint32_t func1(uint32_t x) { return (x ^ (x >> 27)) * (uint32_t)1664525UL; } /** * This function represents a function used in the initialization * by init_by_array * @param x 32-bit integer * @return 32-bit integer */ static uint32_t func2(uint32_t x) { return (x ^ (x >> 27)) * (uint32_t)1566083941UL; } /** * This function certificate the period of 2^{MEXP} */ void SFMTObj::PeriodCertification() { int inner = 0; int i, j; uint32_t work; for (i = 0; i < 4; i++) inner ^= sfmt.u[idxof(i)] & parity[i]; for (i = 16; i > 0; i >>= 1) inner ^= inner >> i; inner &= 1; /* check OK */ if (inner == 1) { return; } /* check NG, and modification */ for (i = 0; i < 4; i++) { work = 1; for (j = 0; j < 32; j++) { if ((work & parity[i]) != 0) { sfmt.u[idxof(i)] ^= work; return; } work = work << 1; } } } /*---------------- PUBLIC FUNCTIONS ----------------*/ /** * This function returns the minimum size of array used for \b * fill_array32() function. * @return minimum size of array used for FillArray32() function. */ int SFMTObj::GetMinArraySize32() { return SFMT::N32; } /** * This function returns the minimum size of array used for \b * fill_array64() function. * @return minimum size of array used for FillArray64() function. */ int SFMTObj::GetMinArraySize64() { return SFMT::N64; } #ifndef ONLY64 /** * This function generates and returns 32-bit pseudorandom number. * init_gen_rand or init_by_array must be called before this function. * @return 32-bit pseudorandom number */ unsigned int SFMTObj::GenRand32() { uint32_t r; assert(initialized); if (idx >= SFMT::N32) { GenRandAll(); idx = 0; } r = sfmt.u[idx++]; return r; } #endif /** * This function generates and returns 64-bit pseudorandom number. * init_gen_rand or init_by_array must be called before this function. * The function gen_rand64 should not be called after gen_rand32, * unless an initialization is again executed. * @return 64-bit pseudorandom number */ uint64_t SFMTObj::GenRand64() { #if defined(BIG_ENDIAN64) && !defined(ONLY64) uint32_t r1, r2; #else uint64_t r; #endif assert(initialized); assert(idx % 2 == 0); if (idx >= SFMT::N32) { GenRandAll(); idx = 0; } #if defined(BIG_ENDIAN64) && !defined(ONLY64) r1 = sfmt.u[idx]; r2 = sfmt.u[idx + 1]; idx += 2; return ((uint64_t)r2 << 32) | r1; #else r = sfmt.u64[idx / 2]; idx += 2; return r; #endif } #ifndef ONLY64 /** * This function generates pseudorandom 32-bit integers in the * specified array[] by one call. The number of pseudorandom integers * is specified by the argument size, which must be at least 624 and a * multiple of four. The generation by this function is much faster * than the following gen_rand function. * * For initialization, init_gen_rand or init_by_array must be called * before the first call of this function. This function can not be * used after calling gen_rand function, without initialization. * * @param array an array where pseudorandom 32-bit integers are filled * by this function. The pointer to the array must be \b "aligned" * (namely, must be a multiple of 16) in the SIMD version, since it * refers to the address of a 128-bit integer. In the standard C * version, the pointer is arbitrary. * * @param size the number of 32-bit pseudorandom integers to be * generated. size must be a multiple of 4, and greater than or equal * to (MEXP / 128 + 1) * 4. * * @note \b memalign or \b posix_memalign is available to get aligned * memory. Mac OSX doesn't have these functions, but \b malloc of OSX * returns the pointer to the aligned memory block. */ void SFMTObj::FillArray32(uint32_t *array, int size) { assert(initialized); assert(idx == SFMT::N32); assert(size % 4 == 0); assert(size >= SFMT::N32); GenRandArray((w128_t *)array, size / 4); idx = SFMT::N32; } #endif /** * This function generates pseudorandom 64-bit integers in the * specified array[] by one call. The number of pseudorandom integers * is specified by the argument size, which must be at least 312 and a * multiple of two. The generation by this function is much faster * than the following gen_rand function. * * For initialization, init_gen_rand or init_by_array must be called * before the first call of this function. This function can not be * used after calling gen_rand function, without initialization. * * @param array an array where pseudorandom 64-bit integers are filled * by this function. The pointer to the array must be "aligned" * (namely, must be a multiple of 16) in the SIMD version, since it * refers to the address of a 128-bit integer. In the standard C * version, the pointer is arbitrary. * * @param size the number of 64-bit pseudorandom integers to be * generated. size must be a multiple of 2, and greater than or equal * to (MEXP / 128 + 1) * 2 * * @note \b memalign or \b posix_memalign is available to get aligned * memory. Mac OSX doesn't have these functions, but \b malloc of OSX * returns the pointer to the aligned memory block. */ void SFMTObj::FillArray64(uint64_t *array, int size) { assert(initialized); assert(idx == SFMT::N32); assert(size % 2 == 0); assert(size >= SFMT::N64); GenRandArray((w128_t *)array, size / 2); idx = SFMT::N32; #if defined(BIG_ENDIAN64) && !defined(ONLY64) swap((w128_t *)array, size / 2); #endif } /** * This function initializes the internal state array with a 32-bit * integer seed. * * @param seed a 32-bit integer used as the seed. */ void SFMTObj::InitGenRand(uint32_t seed) { int i; sfmt.u[idxof(0)] = seed; for (i = 1; i < SFMT::N32; i++) { sfmt.u[idxof(i)] = 1812433253UL * (sfmt.u[idxof(i - 1)] ^ (sfmt.u[idxof(i - 1)] >> 30)) + i; } idx = SFMT::N32; PeriodCertification(); #ifndef NDEBUG initialized = 1; #endif } /** * This function initializes the internal state array, * with an array of 32-bit integers used as the seeds * @param init_key the array of 32-bit integers, used as a seed. * @param key_length the length of init_key. */ void SFMTObj::InitByArray(uint32_t *init_key, int key_length) { int i, j, count; uint32_t r; int lag; int mid; int size = SFMT::N * 4; if (size >= 623) { lag = 11; } else if (size >= 68) { lag = 7; } else if (size >= 39) { lag = 5; } else { lag = 3; } mid = (size - lag) / 2; memset(&sfmt, 0x8b, sizeof(sfmt)); if (key_length + 1 > SFMT::N32) { count = key_length + 1; } else { count = SFMT::N32; } r = func1(sfmt.u[idxof(0)] ^ sfmt.u[idxof(mid)] ^ sfmt.u[idxof(SFMT::N32 - 1)]); sfmt.u[idxof(mid)] += r; r += key_length; sfmt.u[idxof(mid + lag)] += r; sfmt.u[idxof(0)] = r; count--; for (i = 1, j = 0; (j < count) && (j < key_length); j++) { r = func1(sfmt.u[idxof(i)] ^ sfmt.u[idxof((i + mid) % SFMT::N32)] ^ sfmt.u[idxof((i + SFMT::N32 - 1) % SFMT::N32)]); sfmt.u[idxof((i + mid) % SFMT::N32)] += r; r += init_key[j] + i; sfmt.u[idxof((i + mid + lag) % SFMT::N32)] += r; sfmt.u[idxof(i)] = r; i = (i + 1) % SFMT::N32; } for (; j < count; j++) { r = func1(sfmt.u[idxof(i)] ^ sfmt.u[idxof((i + mid) % SFMT::N32)] ^ sfmt.u[idxof((i + SFMT::N32 - 1) % SFMT::N32)]); sfmt.u[idxof((i + mid) % SFMT::N32)] += r; r += i; sfmt.u[idxof((i + mid + lag) % SFMT::N32)] += r; sfmt.u[idxof(i)] = r; i = (i + 1) % SFMT::N32; } for (j = 0; j < SFMT::N32; j++) { r = func2(sfmt.u[idxof(i)] + sfmt.u[idxof((i + mid) % SFMT::N32)] + sfmt.u[idxof((i + SFMT::N32 - 1) % SFMT::N32)]); sfmt.u[idxof((i + mid) % SFMT::N32)] ^= r; r -= i; sfmt.u[idxof((i + mid + lag) % SFMT::N32)] ^= r; sfmt.u[idxof(i)] = r; i = (i + 1) % SFMT::N32; } idx = SFMT::N32; PeriodCertification(); #ifndef NDEBUG initialized = 1; #endif }