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mixmax.h
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1/*
2 * mixmax.c
3 * A Pseudo-Random Number Generator
4 *
5 * Created by Konstantin Savvidy.
6 *
7 * The code is released under GNU Lesser General Public License v3
8 *
9 * G.K.Savvidy and N.G.Ter-Arutyunian,
10 * On the Monte Carlo simulation of physical systems,
11 * J.Comput.Phys. 97, 566 (1991);
12 * Preprint EPI-865-16-86, Yerevan, Jan. 1986
13 *
14 * K.Savvidy
15 * The MIXMAX random number generator
16 * Comp. Phys. Commun. 196 (2015), pp 161–165
17 * http://dx.doi.org/10.1016/j.cpc.2015.06.003
18 *
19 */
20
21#ifndef MIXMAX_H_
22#define MIXMAX_H_
23
24//#define USE_INLINE_ASM
25
26//#ifdef __cplusplus
27//extern "C" {
28//#endif
29
30#ifndef ROOT_MM_N
31#define N 240
32/* The currently recommended generator is the three-parameter MIXMAX with
33N=240, s=487013230256099140, m=2^51+1
34
35 Other newly recommended N are N=8, 17 and 240,
36 as well as the ordinary MIXMAX with N=256 and s=487013230256099064
37
38 Since the algorithm is linear in N, the cost per number is almost independent of N.
39 */
40#else
41#define N ROOT_MM_N
42#endif
43
44#ifndef __LP64__
45typedef uint64_t myuint;
46//#warning but no problem, 'myuint' is 'uint64_t'
47#else
48typedef unsigned long long int myuint;
49//#warning but no problem, 'myuint' is 'unsigned long long int'
50#endif
51
53{
57 FILE* fh;
58};
59
60typedef struct rng_state_st rng_state_t; // C struct alias
61
62int rng_get_N(void); // get the N programmatically, useful for checking the value for which the library was compiled
63
64rng_state_t *rng_alloc(); /* allocate the state */
65int rng_free(rng_state_t* X); /* free memory occupied by the state */
66rng_state_t *rng_copy(myuint *Y); /* init from vector, takes the vector Y,
67 returns pointer to the newly allocated and initialized state */
68void read_state(rng_state_t* X, const char filename[] );
70 int iterate(rng_state_t* X);
71 myuint iterate_raw_vec(myuint* Y, myuint sumtotOld);
72
73
74// FUNCTIONS FOR SEEDING
75
76typedef uint32_t myID_t;
77
78void seed_uniquestream(rng_state_t* X, myID_t clusterID, myID_t machineID, myID_t runID, myID_t streamID );
79/*
80 best choice: will make a state vector from which you can get at least 10^100 numbers
81 guaranteed mathematically to be non-colliding with any other stream prepared from another set of 32bit IDs,
82 so long as it is different by at least one bit in at least one of the four IDs
83 -- useful if you are running a parallel simulation with many clusters, many CPUs each
84 */
85
86void seed_spbox(rng_state_t* X, myuint seed); // non-linear method, makes certified unique vectors, probability for streams to collide is < 1/10^4600
87
88void seed_vielbein(rng_state_t* X, unsigned int i); // seeds with the i-th unit vector, i = 0..N-1, for testing only
89
90
91
92// FUNCTIONS FOR GETTING RANDOM NUMBERS
93
94#ifdef __MIXMAX_C
95 myuint get_next(rng_state_t* X); // returns 64-bit int, which is between 1 and 2^61-1 inclusive
96 double get_next_float(rng_state_t* X); // returns double precision floating point number in (0,1]
97#endif //__MIXMAX_C
98
99void fill_array(rng_state_t* X, unsigned int n, double *array); // fastest method: set n to a multiple of N (e.g. n=256)
100
101void iterate_and_fill_array(rng_state_t* X, double *array); // fills the array with N numbers
102
104/* needed if the state has been changed by something other than iterate, but no worries, seeding functions call this for you when necessary */
105myuint apply_bigskip(myuint* Vout, myuint* Vin, myID_t clusterID, myID_t machineID, myID_t runID, myID_t streamID );
106// applies a skip of some number of steps calculated from the four IDs
107void branch_inplace( rng_state_t* Xin, myID_t* ID ); // almost the same as apply_bigskip, but in-place and from a vector of IDs
108
109
110#define BITS 61
111
112/* magic with Mersenne Numbers */
113
114#define M61 2305843009213693951ULL
115
117//myuint modmulM61(myuint s, myuint a);
119
120#define MERSBASE M61 //xSUFF(M61)
121#define MOD_PAYNE(k) ((((k)) & MERSBASE) + (((k)) >> BITS) ) // slightly faster than my old way, ok for addition
122#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
123#define MOD_MERSENNE(k) MOD_PAYNE(k)
124
125//#define INV_MERSBASE (0x1p-61)
126#define INV_MERSBASE (0.4336808689942017736029811203479766845703E-18)
127//const double INV_MERSBASE=(0.4336808689942017736029811203479766845703E-18); // gives "duplicate symbol" error
128
129// the charpoly is irreducible for the combinations of N and SPECIAL
130
131#if (N==256)
132#define SPECIALMUL 0
133#ifdef USE_MIXMAX_256_NEW
134// for 1.1
135#define SPECIAL 487013230256099064 // s=487013230256099064, m=1 -- good old MIXMAX
136#define MOD_MULSPEC(k) fmodmulM61( 0, SPECIAL , (k) )
137#else
138// for 1.0
139#define SPECIAL -1
140#define MOD_MULSPEC(k) (MERSBASE - (k));
141#endif
142
143#elif (N==8)
144#define SPECIALMUL 53 // m=2^53+1
145#define SPECIAL 0
146
147#elif (N==17)
148#define SPECIALMUL 36 // m=2^36+1, other valid possibilities are m=2^13+1, m=2^19+1, m=2^24+1
149#define SPECIAL 0
150
151#elif (N==40)
152#define SPECIALMUL 42 // m=2^42+1
153#define SPECIAL 0
154
155#elif (N==60)
156#define SPECIALMUL 52 // m=2^52+1
157#define SPECIAL 0
158
159#elif (N==96)
160#define SPECIALMUL 55 // m=2^55+1
161#define SPECIAL 0
162
163#elif (N==120)
164#define SPECIALMUL 51 // m=2^51+1 and a SPECIAL=+1 (!!!)
165#define SPECIAL 1
166#define MOD_MULSPEC(k) (k)
167
168#elif (N==240)
169#define SPECIALMUL 51 // m=2^51+1 and a SPECIAL=487013230256099140
170#define SPECIAL 487013230256099140ULL
171#define MOD_MULSPEC(k) fmodmulM61( 0, SPECIAL , (k) )
172
173#elif (N==44851)
174#define SPECIALMUL 0
175#define SPECIAL -3
176#define MOD_MULSPEC(k) MOD_MERSENNE(3*(MERSBASE-(k)))
177
178
179#else
180#warning Not a verified N, you are on your own!
181#define SPECIALMUL 58
182#define SPECIAL 0
183
184#endif // list of interesting N for modulus M61 ends here
185
186
187#ifndef __MIXMAX_C // c++ can put code into header files, why cant we? (with the inline declaration, should be safe from duplicate-symbol error)
188
189#define get_next(X) GET_BY_MACRO(X)
190#define get_next_float(X) get_next_float_BY_MACRO(X)
191
192#endif // __MIXMAX_C
193
194
196 int i;
197 i=X->counter;
198
199 if (i<=(N-1) ){
200 X->counter++;
201 return X->V[i];
202 }else{
203 X->sumtot = iterate_raw_vec(X->V, X->sumtot);
204 X->counter=2;
205 return X->V[1];
206 }
207}
208
210 /* cast to signed int trick suggested by Andrzej Görlich */
211 int64_t Z=(int64_t)GET_BY_MACRO(X);
212 double F;
213#if defined(__GNUC__) && (__GNUC__ < 5) && (!defined(__ICC)) && defined(__x86_64__) && defined(__SSE2_MATH__) && defined(USE_INLINE_ASM)
214//#warning Using the inline assembler
215/* using SSE inline assemly to zero the xmm register, just before int64 -> double conversion,
216 not really necessary in GCC-5 or better, but huge penalty on earlier compilers
217 */
218 __asm__ __volatile__("pxor %0, %0; "
219 :"=x"(F)
220 );
221#endif
222 F=Z;
223 return F*INV_MERSBASE;
224}
225
226
227// ERROR CODES - exit() is called with these
228#define ARRAY_INDEX_OUT_OF_BOUNDS 0xFF01
229#define SEED_WAS_ZERO 0xFF02
233
234// #ifdef __cplusplus
235// }
236// #endif
237
238//#define HOOKUP_GSL 1
239
240#ifdef HOOKUP_GSL // if you need to use mixmax through GSL, pass -DHOOKUP_GSL=1 to the compiler
241#ifndef __MIXMAX_C
242
243#include <gsl/gsl_rng.h>
244unsigned long gsl_get_next(void *vstate);
245double gsl_get_next_float(void *vstate);
246void seed_for_gsl(void *vstate, unsigned long seed);
247
248static const gsl_rng_type mixmax_type =
249{"MIXMAX", /* name */
250 MERSBASE, /* RAND_MAX */
251 1, /* RAND_MIN */
252 sizeof (rng_state_t),
253 &seed_for_gsl,
254 &gsl_get_next,
255 &gsl_get_next_float
256};
257
258unsigned long gsl_get_next(void *vstate) {
259 rng_state_t* X= (rng_state_t*)vstate;
260 return (unsigned long)get_next(X);
261}
262
263double gsl_get_next_float(void *vstate) {
264 rng_state_t* X= (rng_state_t*)vstate;
265 return ( (double)get_next(X)) * INV_MERSBASE;
266}
267
268void seed_for_gsl(void *vstate, unsigned long seed){
269 rng_state_t* X= (rng_state_t*)vstate;
270 seed_spbox(X,(myuint)seed);
271}
272
273const gsl_rng_type *gsl_rng_mixmax = &mixmax_type;
274
275
276#endif // HOOKUP_GSL
277#endif // not inside __MIXMAX_C
278#endif // closing MIXMAX_H_
const gsl_rng_type * gsl_rng_mixmax
static const gsl_rng_type mixmax_type
const Int_t n
Definition: legend1.C:16
#define F(x, y, z)
#define N
Definition: mixmax.h:31
myuint precalc(rng_state_t *X)
Definition: mixmax.icc:228
void seed_spbox(rng_state_t *X, myuint seed)
Definition: mixmax.icc:205
int rng_get_N(void)
Definition: mixmax.icc:240
myuint fmodmulM61(myuint cum, myuint s, myuint a)
Definition: mixmax.icc:258
myuint iterate_raw_vec(myuint *Y, myuint sumtotOld)
Definition: mixmax.icc:47
int iterate(rng_state_t *X)
Definition: mixmax.icc:34
#define get_next(X)
Definition: mixmax.h:189
struct rng_state_st rng_state_t
Definition: mixmax.h:60
void branch_inplace(rng_state_t *Xin, myID_t *ID)
Definition: mixmax.icc:394
uint32_t myID_t
Definition: mixmax.h:76
void seed_uniquestream(rng_state_t *X, myID_t clusterID, myID_t machineID, myID_t runID, myID_t streamID)
Definition: mixmax.icc:361
void seed_vielbein(rng_state_t *X, unsigned int i)
Definition: mixmax.icc:188
rng_state_t * rng_alloc()
Definition: mixmax.icc:154
void print_state(rng_state_t *X)
Definition: mixmax.icc:273
rng_state_t * rng_copy(myuint *Y)
Definition: mixmax.icc:168
#define get_next_float(X)
Definition: mixmax.h:190
#define INV_MERSBASE
Definition: mixmax.h:126
int rng_free(rng_state_t *X)
Definition: mixmax.icc:162
double get_next_float_BY_MACRO(rng_state_t *X)
Definition: mixmax.h:209
void read_state(rng_state_t *X, const char filename[])
Definition: mixmax.icc:286
Definition: mixmax.icc:137
void fill_array(rng_state_t *X, unsigned int n, double *array)
Definition: mixmax.icc:85
myuint apply_bigskip(myuint *Vout, myuint *Vin, myID_t clusterID, myID_t machineID, myID_t runID, myID_t streamID)
Definition: mixmax.icc:398
#define MERSBASE
Definition: mixmax.h:120
myuint GET_BY_MACRO(rng_state_t *X)
Definition: mixmax.h:195
uint64_t myuint
Definition: mixmax.h:45
void iterate_and_fill_array(rng_state_t *X, double *array)
Definition: mixmax.icc:105
static constexpr double bar
static constexpr double s
myuint V[N]
Definition: mixmax.h:54
int counter
Definition: mixmax.h:56
myuint sumtot
Definition: mixmax.h:55
FILE * fh
Definition: mixmax.h:57
auto * a
Definition: textangle.C:12