// \$Id:\$ // -*- C++ -*- // // ----------------------------------------------------------------------- // MixMax Matrix PseudoRandom Number Generator // --- MixMax --- // class header file // ----------------------------------------------------------------------- // // // Created by Konstantin Savvidy on Sun Feb 22 2004. // The code is released under // GNU Lesser General Public License v3 // // Generator described in // N.Z.Akopov, G.K.Savvidy and N.G.Ter-Arutyunian, Matrix Generator of Pseudorandom Numbers, // J.Comput.Phys. 97, 573 (1991); // Preprint EPI-867(18)-86, Yerevan Jun.1986; // // and // // K.Savvidy // The MIXMAX random number generator // Comp. Phys. Commun. (2015) // http://dx.doi.org/10.1016/j.cpc.2015.06.003 // // ----------------------------------------------------------------------- #ifndef CLHEP_MIXMAX_H_ #define CLHEP_MIXMAX_H_ 1 #include #include #define USE_INLINE_ASM YES namespace CLHEP { #ifdef __cplusplus extern "C" { #endif const int N = 17; /* The currently recommended N are 3150, 1260, 508, 256, 240, 88, 17, 8 Since the algorithm is linear in N, the cost per number is almost independent of N. */ #ifndef __LP64__ typedef uint64_t myuint; //#warning but no problem, 'myuint' is 'uint64_t' #else typedef unsigned long long int myuint; //#warning but no problem, 'myuint' is 'unsigned long long int' #endif struct rng_state_st { myuint V[N]; myuint sumtot; int counter; FILE* fh; }; typedef struct rng_state_st rng_state_t; // C struct alias int rng_get_N(void); // get the N programmatically, useful for checking the value for which the library was compiled rng_state_t *rng_alloc(); /* allocate the state */ int rng_free(rng_state_t* X); /* free memory occupied by the state */ rng_state_t *rng_copy(myuint *Y); /* init from vector, takes the vector Y, returns pointer to the newly allocated and initialized state */ void read_state(rng_state_t* X, const char filename[] ); void print_state(rng_state_t* X); int iterate(rng_state_t* X); myuint iterate_raw_vec(myuint* Y, myuint sumtotOld); // FUNCTIONS FOR SEEDING typedef uint32_t myID_t; void seed_uniquestream(rng_state_t* X, myID_t clusterID, myID_t machineID, myID_t runID, myID_t streamID); /* best choice: will make a state vector from which you can get at least 10^100 numbers guaranteed mathematically to be non-colliding with any other stream prepared from another set of 32bit IDs, so long as it is different by at least one bit in at least one of the four IDs -- useful if you are running a parallel simulation with many clusters, many CPUs each */ void seed_spbox(rng_state_t* X, myuint seed); // non-linear method, makes certified unique vectors, probability for streams to collide is < 1/10^4600 void seed_vielbein(rng_state_t* X, unsigned int i); // seeds with the i-th unit vector, i = 0..N-1, for testing only // FUNCTIONS FOR GETTING RANDOM NUMBERS #ifdef __MIXMAX_C myuint get_next(rng_state_t* X); // returns 64-bit int, which is between 1 and 2^61-1 inclusive double get_next_float(rng_state_t* X); // returns double precision floating point number in (0,1] #endif //__MIXMAX_C void fill_array(rng_state_t* X, unsigned int n, double *array); // fastest method: set n to a multiple of N (e.g. n=256) void iterate_and_fill_array(rng_state_t* X, double *array); // fills the array with N numbers myuint precalc(rng_state_t* X); /* needed if the state has been changed by something other than iterate, but no worries, seeding functions call this for you when necessary */ myuint apply_bigskip(myuint* Vout, myuint* Vin, myID_t clusterID, myID_t machineID, myID_t runID, myID_t streamID ); // applies a skip of some number of steps calculated from the four IDs void branch_inplace( rng_state_t* Xin, myID_t* ID ); // almost the same as apply_bigskip, but in-place and from a vector of IDs #define BITS 61 /* magic with Mersenne Numbers */ #define M61 2305843009213693951ULL myuint modadd(myuint foo, myuint bar); myuint modmulM61(myuint s, myuint a); myuint fmodmulM61(myuint cum, myuint s, myuint a); #define MERSBASE M61 //xSUFF(M61) #define MOD_PAYNE(k) ((((k)) & MERSBASE) + (((k)) >> BITS) ) // slightly faster than my old way, ok for addition #define MOD_REM(k) ((k) % MERSBASE ) // latest Intel CPU is supposed to do this in one CPU cycle, but on my machines it seems to be 20% slower than the best tricks #define MOD_MERSENNE(k) MOD_PAYNE(k) #define INV_MERSBASE (0.43368086899420177360298E-18L) // the charpoly is irreducible for the combinations of N and SPECIAL and has maximal period for N=508, 256, half period for 1260, and 1/12 period for 3150 // #if (N==256) // #define SPECIALMUL 0 // #define SPECIAL 487013230256099064ULL // s=487013230256099064, m=1 -- good old MIXMAX // #define MOD_MULSPEC(k) fmodmulM61( 0, SPECIAL , (k) ); // #elif (N==17) #define SPECIALMUL 36 // m=2^36+1 /* #elif (N==8) #define SPECIALMUL 53 // m=2^53+1 #elif (N==40) #define SPECIALMUL 42 // m=2^42+1 #elif (N==96) #define SPECIALMUL 55 // m=2^55+1 #elif (N==64) #define SPECIALMUL 55 // m=2^55 (!!!) and m=2^37+2 #elif (N==120) #define SPECIALMUL 51 // m=2^51+1 and a SPECIAL=+1 (!!!) #define SPECIAL 1 #define MOD_MULSPEC(k) (k); #else #warning Not a verified N, you are on your own! #define SPECIALMUL 58 #endif // list of interesting N for modulus M61 ends here */ #ifndef __MIXMAX_C // c++ can put code into header files, why cant we? (with the inline declaration, should be safe from duplicate-symbol error) #define get_next(X) GET_BY_MACRO(X) #define get_next_float(X) get_next_float_BY_MACRO(X) #endif // __MIXMAX_C inline myuint GET_BY_MACRO(rng_state_t* X) { int i; i=X->counter; if (i<=(N-1) ){ X->counter++; return X->V[i]; }else{ X->sumtot = iterate_raw_vec(X->V, X->sumtot); X->counter=2; return X->V[1]; } } inline double get_next_float_BY_MACRO(rng_state_t* X){ int64_t Z=(int64_t)get_next(X); #if defined(__x86_64__) && defined(__SSE__) && defined(__AVX__) && defined(USE_INLINE_ASM) double F; __asm__ __volatile__( "pxor %0, %0;" //"cvtsi2sdq %1, %0;" :"=x"(F) //:"r"(Z) ); F=Z; return F*INV_MERSBASE; #else return Z*INV_MERSBASE; #endif } // ERROR CODES - exit() is called with these #define ARRAY_INDEX_OUT_OF_BOUNDS 0xFF01 #define SEED_WAS_ZERO 0xFF02 #define ERROR_READING_STATE_FILE 0xFF03 #define ERROR_READING_STATE_COUNTER 0xFF04 #define ERROR_READING_STATE_CHECKSUM 0xFF05 #ifdef __cplusplus } #endif //#define HOOKUP_GSL 1 #ifdef HOOKUP_GSL // if you need to use mixmax through GSL, pass -DHOOKUP_GSL=1 to the compiler #include unsigned long gsl_get_next(void *vstate); double gsl_get_next_float(void *vstate); void seed_for_gsl(void *vstate, unsigned long seed); static const gsl_rng_type mixmax_type = {"MIXMAX", /* name */ MERSBASE, /* RAND_MAX */ 1, /* RAND_MIN */ sizeof (rng_state_t), &seed_for_gsl, &gsl_get_next, &gsl_get_next_float }; unsigned long gsl_get_next(void *vstate) { rng_state_t* X= (rng_state_t*)vstate; return (unsigned long)get_next(X); } double gsl_get_next_float(void *vstate) { rng_state_t* X= (rng_state_t*)vstate; return ( (double)get_next(X)) * INV_MERSBASE; } void seed_for_gsl(void *vstate, unsigned long seed){ rng_state_t* X= (rng_state_t*)vstate; seed_spbox(X,(myuint)seed); } const gsl_rng_type *gsl_rng_ran3 = &mixmax_type; #endif // HOOKUP_GSL } // namespace CLHEP #endif // closing CLHEP_MIXMAX_H_