/** 

  * @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 <string.h>

 #include <assert.h>

 #include "SFMT.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

 /*------------------------------------------------------

   128-bit SIMD data type for Altivec, SSE2 or standard C

   ------------------------------------------------------*/

 #if defined(HAVE_ALTIVEC)

   #if !defined(__APPLE__)

     #include <altivec.h>

   #endif

 /** 128-bit data structure */

 union W128_T {

     vector unsigned int s;

     uint32_t u[4];

 };

 /** 128-bit data type */

 typedef union W128_T w128_t;

 

 #elif defined(HAVE_SSE2)

   #include <emmintrin.h>

 

 /** 128-bit data structure */

 union W128_T {

     __m128i si;

     uint32_t u[4];

 };

 /** 128-bit data type */

 typedef union W128_T w128_t;

 

 #else

 

 /** 128-bit data structure */

 struct W128_T {

     uint32_t u[4];

 };

 /** 128-bit data type */

 typedef struct W128_T w128_t;

 

 #endif

 

 /*--------------------------------------

   FILE GLOBAL VARIABLES

   internal state, index counter and flag 

   --------------------------------------*/

 /** the 128-bit internal state array */

 static w128_t sfmt[N];

 /** the 32bit integer pointer to the 128-bit internal state array */

 static uint32_t *psfmt32 = &sfmt[0].u[0];

 #if !defined(BIG_ENDIAN64) || defined(ONLY64)

 /** the 64bit integer pointer to the 128-bit internal state array */

 static uint64_t *psfmt64 = (uint64_t *)&sfmt[0].u[0];

 #endif

 /** index counter to the 32-bit internal state array */

 static int idx;

 /** a flag: it is 0 if and only if the internal state is not yet

  * initialized. */

 static int initialized = 0;

 /** a parity check vector which certificate the period of 2^{MEXP} */

 static 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 void gen_rand_all(void);

 inline static void gen_rand_array(w128_t *array, int size);

 inline static uint32_t func1(uint32_t x);

 inline static uint32_t func2(uint32_t x);

 static void period_certification(void);

 #if defined(BIG_ENDIAN64) && !defined(ONLY64)

 inline static void swap(w128_t *array, int size);

 #endif

 

 #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 & 0xffffffff);

     out->u[2] = (uint32_t)(oh >> 32);

     out->u[3] = (uint32_t)(oh & 0xffffffff);

 }

 #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 & 0xffffffff);

     out->u[3] = (uint32_t)(oh >> 32);

     out->u[2] = (uint32_t)(oh & 0xffffffff);

 }

 #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 & 0xffffffff);

     out->u[2] = (uint32_t)(oh >> 32);

     out->u[3] = (uint32_t)(oh & 0xffffffff);

 }

 #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 & 0xffffffff);

     out->u[3] = (uint32_t)(oh >> 32);

     out->u[2] = (uint32_t)(oh & 0xffffffff);

 }

 #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.

  */

 inline static void gen_rand_all(void) {

     int i;

     w128_t *r1, *r2;

 

     r1 = &sfmt[N - 2];

     r2 = &sfmt[N - 1];

     for (i = 0; i < N - POS1; i++) {

 	do_recursion(&sfmt[i], &sfmt[i], &sfmt[i + POS1], r1, r2);

 	r1 = r2;

 	r2 = &sfmt[i];

     }

     for (; i < N; i++) {

 	do_recursion(&sfmt[i], &sfmt[i], &sfmt[i + POS1 - N], r1, r2);

 	r1 = r2;

 	r2 = &sfmt[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.

  */

 inline static void gen_rand_array(w128_t *array, int size) {

     int i, j;

     w128_t *r1, *r2;

 

     r1 = &sfmt[N - 2];

     r2 = &sfmt[N - 1];

     for (i = 0; i < N - POS1; i++) {

 	do_recursion(&array[i], &sfmt[i], &sfmt[i + POS1], r1, r2);

 	r1 = r2;

 	r2 = &array[i];

     }

     for (; i < N; i++) {

 	do_recursion(&array[i], &sfmt[i], &array[i + POS1 - N], r1, r2);

 	r1 = r2;

 	r2 = &array[i];

     }

     for (; i < size - N; i++) {

 	do_recursion(&array[i], &array[i - N], &array[i + POS1 - N], r1, r2);

 	r1 = r2;

 	r2 = &array[i];

     }

     for (j = 0; j < 2 * N - size; j++) {

 	sfmt[j] = array[j + size - N];

     }

     for (; i < size; i++, j++) {

 	do_recursion(&array[i], &array[i - N], &array[i + POS1 - N], r1, r2);

 	r1 = r2;

 	r2 = &array[i];

 	sfmt[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}

  */

 static void period_certification(void) {

     int inner = 0;

     int i, j;

     uint32_t work;

 

     for (i = 0; i < 4; i++)

 	inner ^= psfmt32[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) {

 		psfmt32[idxof(i)] ^= work;

 		return;

 	    }

 	    work = work << 1;

 	}

     }

 }

 

 /*----------------

   PUBLIC FUNCTIONS

   ----------------*/

 /**

  * This function returns the identification string.

  * The string shows the word size, the Mersenne exponent,

  * and all parameters of this generator.

  */

 const char *get_idstring(void) {

     return IDSTR;

 }

 

 /**

  * This function returns the minimum size of array used for \b

  * fill_array32() function.

  * @return minimum size of array used for fill_array32() function.

  */

 int get_min_array_size32(void) {

     return N32;

 }

 

 /**

  * This function returns the minimum size of array used for \b

  * fill_array64() function.

  * @return minimum size of array used for fill_array64() function.

  */

 int get_min_array_size64(void) {

     return 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

  */

 uint32_t gen_rand32(void) {

     uint32_t r;

 

     assert(initialized);

     if (idx >= N32) {

 	gen_rand_all();

 	idx = 0;

     }

     r = psfmt32[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 gen_rand64(void) {

 #if defined(BIG_ENDIAN64) && !defined(ONLY64)

     uint32_t r1, r2;

 #else

     uint64_t r;

 #endif

 

     assert(initialized);

     assert(idx % 2 == 0);

 

     if (idx >= N32) {

 	gen_rand_all();

 	idx = 0;

     }

 #if defined(BIG_ENDIAN64) && !defined(ONLY64)

     r1 = psfmt32[idx];

     r2 = psfmt32[idx + 1];

     idx += 2;

     return ((uint64_t)r2 << 32) | r1;

 #else

     r = psfmt64[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 fill_array32(uint32_t *array, int size) {

     assert(initialized);

     assert(idx == N32);

     assert(size % 4 == 0);

     assert(size >= N32);

 

     gen_rand_array((w128_t *)array, size / 4);

     idx = 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 fill_array64(uint64_t *array, int size) {

     assert(initialized);

     assert(idx == N32);

     assert(size % 2 == 0);

     assert(size >= N64);

 

     gen_rand_array((w128_t *)array, size / 2);

     idx = 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 init_gen_rand(uint32_t seed) {

     int i;

 

     psfmt32[idxof(0)] = seed;

     for (i = 1; i < N32; i++) {

 	psfmt32[idxof(i)] = 1812433253UL * (psfmt32[idxof(i - 1)] 

 					    ^ (psfmt32[idxof(i - 1)] >> 30))

 	    + i;

     }

     idx = N32;

     period_certification();

     initialized = 1;

 }

 

 /**

  * 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 init_by_array(uint32_t *init_key, int key_length) {

     int i, j, count;

     uint32_t r;

     int lag;

     int mid;

     int size = 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 > N32) {

 	count = key_length + 1;

     } else {

 	count = N32;

     }

     r = func1(psfmt32[idxof(0)] ^ psfmt32[idxof(mid)] 

 	      ^ psfmt32[idxof(N32 - 1)]);

     psfmt32[idxof(mid)] += r;

     r += key_length;

     psfmt32[idxof(mid + lag)] += r;

     psfmt32[idxof(0)] = r;

 

     count--;

     for (i = 1, j = 0; (j < count) && (j < key_length); j++) {

 	r = func1(psfmt32[idxof(i)] ^ psfmt32[idxof((i + mid) % N32)] 

 		  ^ psfmt32[idxof((i + N32 - 1) % N32)]);

 	psfmt32[idxof((i + mid) % N32)] += r;

 	r += init_key[j] + i;

 	psfmt32[idxof((i + mid + lag) % N32)] += r;

 	psfmt32[idxof(i)] = r;

 	i = (i + 1) % N32;

     }

     for (; j < count; j++) {

 	r = func1(psfmt32[idxof(i)] ^ psfmt32[idxof((i + mid) % N32)] 

 		  ^ psfmt32[idxof((i + N32 - 1) % N32)]);

 	psfmt32[idxof((i + mid) % N32)] += r;

 	r += i;

 	psfmt32[idxof((i + mid + lag) % N32)] += r;

 	psfmt32[idxof(i)] = r;

 	i = (i + 1) % N32;

     }

     for (j = 0; j < N32; j++) {

 	r = func2(psfmt32[idxof(i)] + psfmt32[idxof((i + mid) % N32)] 

 		  + psfmt32[idxof((i + N32 - 1) % N32)]);

 	psfmt32[idxof((i + mid) % N32)] ^= r;

 	r -= i;

 	psfmt32[idxof((i + mid + lag) % N32)] ^= r;

 	psfmt32[idxof(i)] = r;

 	i = (i + 1) % N32;

     }

 

     idx = N32;

     period_certification();

     initialized = 1;

 }