/** * @file dSFMT.c * @brief double precision SIMD-oriented Fast Mersenne Twister (dSFMT) * based on IEEE 754 format. * * @author Mutsuo Saito (Hiroshima University) * @author Makoto Matsumoto (Hiroshima University) * * Copyright (C) 2007,2008 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 #include "dSFMT-params.h" #include "dSFMT-common.h" #if defined(__cplusplus) extern "C" { #endif /** dsfmt internal state vector */ dsfmt_t dsfmt_global_data; /** dsfmt mexp for check */ static const int dsfmt_mexp = DSFMT_MEXP; /*---------------- STATIC FUNCTIONS ----------------*/ inline static uint32_t ini_func1(uint32_t x); inline static uint32_t ini_func2(uint32_t x); inline static void gen_rand_array_c1o2(dsfmt_t *dsfmt, w128_t *array, int size); inline static void gen_rand_array_c0o1(dsfmt_t *dsfmt, w128_t *array, int size); inline static void gen_rand_array_o0c1(dsfmt_t *dsfmt, w128_t *array, int size); inline static void gen_rand_array_o0o1(dsfmt_t *dsfmt, w128_t *array, int size); inline static int idxof(int i); static void initial_mask(dsfmt_t *dsfmt); static void period_certification(dsfmt_t *dsfmt); #if defined(HAVE_SSE2) /** 1 in 64bit for sse2 */ static const union X128I_T sse2_int_one = {{1, 1}}; /** 2.0 double for sse2 */ static const union X128D_T sse2_double_two = {{2.0, 2.0}}; /** -1.0 double for sse2 */ static const union X128D_T sse2_double_m_one = {{-1.0, -1.0}}; #endif /** * This function simulate a 32-bit array index overlapped to 64-bit * array of LITTLE ENDIAN in BIG ENDIAN machine. */ #if defined(DSFMT_BIG_ENDIAN) inline static int idxof(int i) { return i ^ 1; } #else inline static int idxof(int i) { return i; } #endif #if defined(HAVE_SSE2) /** * This function converts the double precision floating point numbers which * distribute uniformly in the range [1, 2) to those which distribute uniformly * in the range [0, 1). * @param w 128bit stracture of double precision floating point numbers (I/O) */ inline static void convert_c0o1(w128_t *w) { w->sd = _mm_add_pd(w->sd, sse2_double_m_one.d128); } /** * This function converts the double precision floating point numbers which * distribute uniformly in the range [1, 2) to those which distribute uniformly * in the range (0, 1]. * @param w 128bit stracture of double precision floating point numbers (I/O) */ inline static void convert_o0c1(w128_t *w) { w->sd = _mm_sub_pd(sse2_double_two.d128, w->sd); } /** * This function converts the double precision floating point numbers which * distribute uniformly in the range [1, 2) to those which distribute uniformly * in the range (0, 1). * @param w 128bit stracture of double precision floating point numbers (I/O) */ inline static void convert_o0o1(w128_t *w) { w->si = _mm_or_si128(w->si, sse2_int_one.i128); w->sd = _mm_add_pd(w->sd, sse2_double_m_one.d128); } #else /* standard C and altivec */ /** * This function converts the double precision floating point numbers which * distribute uniformly in the range [1, 2) to those which distribute uniformly * in the range [0, 1). * @param w 128bit stracture of double precision floating point numbers (I/O) */ inline static void convert_c0o1(w128_t *w) { w->d[0] -= 1.0; w->d[1] -= 1.0; } /** * This function converts the double precision floating point numbers which * distribute uniformly in the range [1, 2) to those which distribute uniformly * in the range (0, 1]. * @param w 128bit stracture of double precision floating point numbers (I/O) */ inline static void convert_o0c1(w128_t *w) { w->d[0] = 2.0 - w->d[0]; w->d[1] = 2.0 - w->d[1]; } /** * This function converts the double precision floating point numbers which * distribute uniformly in the range [1, 2) to those which distribute uniformly * in the range (0, 1). * @param w 128bit stracture of double precision floating point numbers (I/O) */ inline static void convert_o0o1(w128_t *w) { w->u[0] |= 1; w->u[1] |= 1; w->d[0] -= 1.0; w->d[1] -= 1.0; } #endif /** * This function fills the user-specified array with double precision * floating point pseudorandom numbers of the IEEE 754 format. * @param dsfmt dsfmt state vector. * @param array an 128-bit array to be filled by pseudorandom numbers. * @param size number of 128-bit pseudorandom numbers to be generated. */ inline static void gen_rand_array_c1o2(dsfmt_t *dsfmt, w128_t *array, int size) { int i, j; w128_t lung; lung = dsfmt->status[DSFMT_N]; do_recursion(&array[0], &dsfmt->status[0], &dsfmt->status[DSFMT_POS1], &lung); for (i = 1; i < DSFMT_N - DSFMT_POS1; i++) { do_recursion(&array[i], &dsfmt->status[i], &dsfmt->status[i + DSFMT_POS1], &lung); } for (; i < DSFMT_N; i++) { do_recursion(&array[i], &dsfmt->status[i], &array[i + DSFMT_POS1 - DSFMT_N], &lung); } for (; i < size - DSFMT_N; i++) { do_recursion(&array[i], &array[i - DSFMT_N], &array[i + DSFMT_POS1 - DSFMT_N], &lung); } for (j = 0; j < 2 * DSFMT_N - size; j++) { dsfmt->status[j] = array[j + size - DSFMT_N]; } for (; i < size; i++, j++) { do_recursion(&array[i], &array[i - DSFMT_N], &array[i + DSFMT_POS1 - DSFMT_N], &lung); dsfmt->status[j] = array[i]; } dsfmt->status[DSFMT_N] = lung; } /** * This function fills the user-specified array with double precision * floating point pseudorandom numbers of the IEEE 754 format. * @param dsfmt dsfmt state vector. * @param array an 128-bit array to be filled by pseudorandom numbers. * @param size number of 128-bit pseudorandom numbers to be generated. */ inline static void gen_rand_array_c0o1(dsfmt_t *dsfmt, w128_t *array, int size) { int i, j; w128_t lung; lung = dsfmt->status[DSFMT_N]; do_recursion(&array[0], &dsfmt->status[0], &dsfmt->status[DSFMT_POS1], &lung); for (i = 1; i < DSFMT_N - DSFMT_POS1; i++) { do_recursion(&array[i], &dsfmt->status[i], &dsfmt->status[i + DSFMT_POS1], &lung); } for (; i < DSFMT_N; i++) { do_recursion(&array[i], &dsfmt->status[i], &array[i + DSFMT_POS1 - DSFMT_N], &lung); } for (; i < size - DSFMT_N; i++) { do_recursion(&array[i], &array[i - DSFMT_N], &array[i + DSFMT_POS1 - DSFMT_N], &lung); convert_c0o1(&array[i - DSFMT_N]); } for (j = 0; j < 2 * DSFMT_N - size; j++) { dsfmt->status[j] = array[j + size - DSFMT_N]; } for (; i < size; i++, j++) { do_recursion(&array[i], &array[i - DSFMT_N], &array[i + DSFMT_POS1 - DSFMT_N], &lung); dsfmt->status[j] = array[i]; convert_c0o1(&array[i - DSFMT_N]); } for (i = size - DSFMT_N; i < size; i++) { convert_c0o1(&array[i]); } dsfmt->status[DSFMT_N] = lung; } /** * This function fills the user-specified array with double precision * floating point pseudorandom numbers of the IEEE 754 format. * @param dsfmt dsfmt state vector. * @param array an 128-bit array to be filled by pseudorandom numbers. * @param size number of 128-bit pseudorandom numbers to be generated. */ inline static void gen_rand_array_o0o1(dsfmt_t *dsfmt, w128_t *array, int size) { int i, j; w128_t lung; lung = dsfmt->status[DSFMT_N]; do_recursion(&array[0], &dsfmt->status[0], &dsfmt->status[DSFMT_POS1], &lung); for (i = 1; i < DSFMT_N - DSFMT_POS1; i++) { do_recursion(&array[i], &dsfmt->status[i], &dsfmt->status[i + DSFMT_POS1], &lung); } for (; i < DSFMT_N; i++) { do_recursion(&array[i], &dsfmt->status[i], &array[i + DSFMT_POS1 - DSFMT_N], &lung); } for (; i < size - DSFMT_N; i++) { do_recursion(&array[i], &array[i - DSFMT_N], &array[i + DSFMT_POS1 - DSFMT_N], &lung); convert_o0o1(&array[i - DSFMT_N]); } for (j = 0; j < 2 * DSFMT_N - size; j++) { dsfmt->status[j] = array[j + size - DSFMT_N]; } for (; i < size; i++, j++) { do_recursion(&array[i], &array[i - DSFMT_N], &array[i + DSFMT_POS1 - DSFMT_N], &lung); dsfmt->status[j] = array[i]; convert_o0o1(&array[i - DSFMT_N]); } for (i = size - DSFMT_N; i < size; i++) { convert_o0o1(&array[i]); } dsfmt->status[DSFMT_N] = lung; } /** * This function fills the user-specified array with double precision * floating point pseudorandom numbers of the IEEE 754 format. * @param dsfmt dsfmt state vector. * @param array an 128-bit array to be filled by pseudorandom numbers. * @param size number of 128-bit pseudorandom numbers to be generated. */ inline static void gen_rand_array_o0c1(dsfmt_t *dsfmt, w128_t *array, int size) { int i, j; w128_t lung; lung = dsfmt->status[DSFMT_N]; do_recursion(&array[0], &dsfmt->status[0], &dsfmt->status[DSFMT_POS1], &lung); for (i = 1; i < DSFMT_N - DSFMT_POS1; i++) { do_recursion(&array[i], &dsfmt->status[i], &dsfmt->status[i + DSFMT_POS1], &lung); } for (; i < DSFMT_N; i++) { do_recursion(&array[i], &dsfmt->status[i], &array[i + DSFMT_POS1 - DSFMT_N], &lung); } for (; i < size - DSFMT_N; i++) { do_recursion(&array[i], &array[i - DSFMT_N], &array[i + DSFMT_POS1 - DSFMT_N], &lung); convert_o0c1(&array[i - DSFMT_N]); } for (j = 0; j < 2 * DSFMT_N - size; j++) { dsfmt->status[j] = array[j + size - DSFMT_N]; } for (; i < size; i++, j++) { do_recursion(&array[i], &array[i - DSFMT_N], &array[i + DSFMT_POS1 - DSFMT_N], &lung); dsfmt->status[j] = array[i]; convert_o0c1(&array[i - DSFMT_N]); } for (i = size - DSFMT_N; i < size; i++) { convert_o0c1(&array[i]); } dsfmt->status[DSFMT_N] = lung; } /** * 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 ini_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 ini_func2(uint32_t x) { return (x ^ (x >> 27)) * (uint32_t)1566083941UL; } /** * This function initializes the internal state array to fit the IEEE * 754 format. * @param dsfmt dsfmt state vector. */ static void initial_mask(dsfmt_t *dsfmt) { int i; uint64_t *psfmt; psfmt = &dsfmt->status[0].u[0]; for (i = 0; i < DSFMT_N * 2; i++) { psfmt[i] = (psfmt[i] & DSFMT_LOW_MASK) | DSFMT_HIGH_CONST; } } /** * This function certificate the period of 2^{SFMT_MEXP}-1. * @param dsfmt dsfmt state vector. */ static void period_certification(dsfmt_t *dsfmt) { uint64_t pcv[2] = {DSFMT_PCV1, DSFMT_PCV2}; uint64_t tmp[2]; uint64_t inner; int i; #if (DSFMT_PCV2 & 1) != 1 int j; uint64_t work; #endif tmp[0] = (dsfmt->status[DSFMT_N].u[0] ^ DSFMT_FIX1); tmp[1] = (dsfmt->status[DSFMT_N].u[1] ^ DSFMT_FIX2); inner = tmp[0] & pcv[0]; inner ^= tmp[1] & pcv[1]; for (i = 32; i > 0; i >>= 1) { inner ^= inner >> i; } inner &= 1; /* check OK */ if (inner == 1) { return; } /* check NG, and modification */ #if (DSFMT_PCV2 & 1) == 1 dsfmt->status[DSFMT_N].u[1] ^= 1; #else for (i = 1; i >= 0; i--) { work = 1; for (j = 0; j < 64; j++) { if ((work & pcv[i]) != 0) { dsfmt->status[DSFMT_N].u[i] ^= work; return; } work = work << 1; } } #endif return; } /*---------------- PUBLIC FUNCTIONS ----------------*/ /** * This function returns the identification string. The string shows * the Mersenne exponent, and all parameters of this generator. * @return id string. */ const char *dsfmt_get_idstring(void) { return DSFMT_IDSTR; } /** * This function returns the minimum size of array used for \b * fill_array functions. * @return minimum size of array used for fill_array functions. */ int dsfmt_get_min_array_size(void) { return DSFMT_N64; } /** * This function fills the internal state array with double precision * floating point pseudorandom numbers of the IEEE 754 format. * @param dsfmt dsfmt state vector. */ void dsfmt_gen_rand_all(dsfmt_t *dsfmt) { int i; w128_t lung; lung = dsfmt->status[DSFMT_N]; do_recursion(&dsfmt->status[0], &dsfmt->status[0], &dsfmt->status[DSFMT_POS1], &lung); for (i = 1; i < DSFMT_N - DSFMT_POS1; i++) { do_recursion(&dsfmt->status[i], &dsfmt->status[i], &dsfmt->status[i + DSFMT_POS1], &lung); } for (; i < DSFMT_N; i++) { do_recursion(&dsfmt->status[i], &dsfmt->status[i], &dsfmt->status[i + DSFMT_POS1 - DSFMT_N], &lung); } dsfmt->status[DSFMT_N] = lung; } /** * This function generates double precision floating point * pseudorandom numbers which distribute in the range [1, 2) to the * specified array[] by one call. The number of pseudorandom numbers * is specified by the argument \b size, which must be at least (SFMT_MEXP * / 128) * 2 and a multiple of two. The function * get_min_array_size() returns this minimum size. The generation by * this function is much faster than the following fill_array_xxx functions. * * 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 genrand_xxx functions, without initialization. * * @param dsfmt dsfmt state vector. * @param array an array where pseudorandom numbers 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 (SFMT_MEXP / 128) * 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 dsfmt_fill_array_close1_open2(dsfmt_t *dsfmt, double array[], int size) { assert(size % 2 == 0); assert(size >= DSFMT_N64); gen_rand_array_c1o2(dsfmt, (w128_t *)array, size / 2); } /** * This function generates double precision floating point * pseudorandom numbers which distribute in the range (0, 1] to the * specified array[] by one call. This function is the same as * fill_array_close1_open2() except the distribution range. * * @param dsfmt dsfmt state vector. * @param array an array where pseudorandom numbers are filled * by this function. * @param size the number of pseudorandom numbers to be generated. * see also \sa fill_array_close1_open2() */ void dsfmt_fill_array_open_close(dsfmt_t *dsfmt, double array[], int size) { assert(size % 2 == 0); assert(size >= DSFMT_N64); gen_rand_array_o0c1(dsfmt, (w128_t *)array, size / 2); } /** * This function generates double precision floating point * pseudorandom numbers which distribute in the range [0, 1) to the * specified array[] by one call. This function is the same as * fill_array_close1_open2() except the distribution range. * * @param array an array where pseudorandom numbers are filled * by this function. * @param dsfmt dsfmt state vector. * @param size the number of pseudorandom numbers to be generated. * see also \sa fill_array_close1_open2() */ void dsfmt_fill_array_close_open(dsfmt_t *dsfmt, double array[], int size) { assert(size % 2 == 0); assert(size >= DSFMT_N64); gen_rand_array_c0o1(dsfmt, (w128_t *)array, size / 2); } /** * This function generates double precision floating point * pseudorandom numbers which distribute in the range (0, 1) to the * specified array[] by one call. This function is the same as * fill_array_close1_open2() except the distribution range. * * @param dsfmt dsfmt state vector. * @param array an array where pseudorandom numbers are filled * by this function. * @param size the number of pseudorandom numbers to be generated. * see also \sa fill_array_close1_open2() */ void dsfmt_fill_array_open_open(dsfmt_t *dsfmt, double array[], int size) { assert(size % 2 == 0); assert(size >= DSFMT_N64); gen_rand_array_o0o1(dsfmt, (w128_t *)array, size / 2); } #if defined(__INTEL_COMPILER) # pragma warning(disable:981) #endif /** * This function initializes the internal state array with a 32-bit * integer seed. * @param dsfmt dsfmt state vector. * @param seed a 32-bit integer used as the seed. * @param mexp caller's mersenne expornent */ void dsfmt_chk_init_gen_rand(dsfmt_t *dsfmt, uint32_t seed, int mexp) { int i; uint32_t *psfmt; /* make sure caller program is compiled with the same MEXP */ if (mexp != dsfmt_mexp) { fprintf(stderr, "DSFMT_MEXP doesn't match with dSFMT.c\n"); exit(1); } psfmt = &dsfmt->status[0].u32[0]; psfmt[idxof(0)] = seed; for (i = 1; i < (DSFMT_N + 1) * 4; i++) { psfmt[idxof(i)] = 1812433253UL * (psfmt[idxof(i - 1)] ^ (psfmt[idxof(i - 1)] >> 30)) + i; } initial_mask(dsfmt); period_certification(dsfmt); dsfmt->idx = DSFMT_N64; } /** * This function initializes the internal state array, * with an array of 32-bit integers used as the seeds * @param dsfmt dsfmt state vector. * @param init_key the array of 32-bit integers, used as a seed. * @param key_length the length of init_key. * @param mexp caller's mersenne expornent */ void dsfmt_chk_init_by_array(dsfmt_t *dsfmt, uint32_t init_key[], int key_length, int mexp) { int i, j, count; uint32_t r; uint32_t *psfmt32; int lag; int mid; int size = (DSFMT_N + 1) * 4; /* pulmonary */ /* make sure caller program is compiled with the same MEXP */ if (mexp != dsfmt_mexp) { fprintf(stderr, "DSFMT_MEXP doesn't match with dSFMT.c\n"); exit(1); } if (size >= 623) { lag = 11; } else if (size >= 68) { lag = 7; } else if (size >= 39) { lag = 5; } else { lag = 3; } mid = (size - lag) / 2; psfmt32 = &dsfmt->status[0].u32[0]; memset(dsfmt->status, 0x8b, sizeof(dsfmt->status)); if (key_length + 1 > size) { count = key_length + 1; } else { count = size; } r = ini_func1(psfmt32[idxof(0)] ^ psfmt32[idxof(mid % size)] ^ psfmt32[idxof((size - 1) % size)]); psfmt32[idxof(mid % size)] += r; r += key_length; psfmt32[idxof((mid + lag) % size)] += r; psfmt32[idxof(0)] = r; count--; for (i = 1, j = 0; (j < count) && (j < key_length); j++) { r = ini_func1(psfmt32[idxof(i)] ^ psfmt32[idxof((i + mid) % size)] ^ psfmt32[idxof((i + size - 1) % size)]); psfmt32[idxof((i + mid) % size)] += r; r += init_key[j] + i; psfmt32[idxof((i + mid + lag) % size)] += r; psfmt32[idxof(i)] = r; i = (i + 1) % size; } for (; j < count; j++) { r = ini_func1(psfmt32[idxof(i)] ^ psfmt32[idxof((i + mid) % size)] ^ psfmt32[idxof((i + size - 1) % size)]); psfmt32[idxof((i + mid) % size)] += r; r += i; psfmt32[idxof((i + mid + lag) % size)] += r; psfmt32[idxof(i)] = r; i = (i + 1) % size; } for (j = 0; j < size; j++) { r = ini_func2(psfmt32[idxof(i)] + psfmt32[idxof((i + mid) % size)] + psfmt32[idxof((i + size - 1) % size)]); psfmt32[idxof((i + mid) % size)] ^= r; r -= i; psfmt32[idxof((i + mid + lag) % size)] ^= r; psfmt32[idxof(i)] = r; i = (i + 1) % size; } initial_mask(dsfmt); period_certification(dsfmt); dsfmt->idx = DSFMT_N64; } #if defined(__INTEL_COMPILER) # pragma warning(default:981) #endif #if defined(__cplusplus) } #endif