diff --git a/math/mathcore/inc/Math/MixMaxEngine.h b/math/mathcore/inc/Math/MixMaxEngine.h
index 2068e41ccf964d98ecdd8fe46180de353c0d26db..75455c003c4d8e3830ecc420374268979c352e42 100644
--- a/math/mathcore/inc/Math/MixMaxEngine.h
+++ b/math/mathcore/inc/Math/MixMaxEngine.h
@@ -8,7 +8,7 @@
* *
**********************************************************************/
-// random engines based on ROOT
+// random engines based on ROOT
#ifndef ROOT_Math_MixMaxEngine
#define ROOT_Math_MixMaxEngine
@@ -24,91 +24,80 @@
// typedef struct rng_state_st rng_state_t;
-// namespace mixmax {
+// namespace mixmax {
// template<int Ndim>
-// class mixmax_engine;
+// class mixmax_engine;
// }
namespace ROOT {
namespace Math {
-
+
template<int N>
class MixMaxEngineImpl;
- /**
- MixMaxEngine is a wrapper class for the MIXMAX Random number generator.
- MIXMAX is a matrix-recursive random number generator introduced by
- G. Savvidy.
-
- The real implementation of the generator, written in C, is in the mixmax.h and mixmax.cxx files.
- This generator code is available also at hepforge: http://mixmax.hepforge.org
- The MIXMAX code has been created and developed by Konstantin Savvidy and it is
- released under GNU Lesser General Public License v3.
-
- This wrapper class provides 3 different variants of MIXMAX according to the template para extra parameter N.
- The extra parameter, `SkipNumber`, is used to perform additional iterations of the generator before returning the random numbers.
- For example, when `SkipNumber = 2`, the generator will have two extra iterations that will be discarder.
-
- * MIXMAX with N = 240. This is a new version of the generator (version 2.0beta) described in the
- <a href="http://dx.doi.org/10.1016/j.chaos.2016.05.003">2016 paper</a> (3rd reference), with
- special number $s=487013230256099140$, $m=2^{51}+1$ and having a period of $10^{4389}$.
-
- * MIXMAX with N = 17, from the 2.0beta version with $s=0$ and $m=2^{36}+1$. The period of the generator is $10^{294}$.
-
- * MIXMAX with N = 256 from the 1.0 version. The period is (for `SkipNumber=0`) $10^{4682}$.
- For this generator we recommend in ROOT using a default value of `SkipNumber=2, while for the previous two generators
- skipping is not needed.
-
- This table describes the properties of the MIXMAX generators. MIXMAX is a genuine 61 bit generator on the Galois field GF[p], where
- $p=2^{61}-1$ is the Mersenne prime number.
- The MIXMAX generators with these parameters pass all of the BigCrush
- tests in the <a href="http://simul.iro.umontreal.ca/testu01/tu01.html">TestU01 suite</a\>.
-
-\latexonly
- \begin{table}[h]
- \centering
- \begin{tabular}{@{} rrlcrr @{}}
-
- \toprule
- Dimension &~ Entropy & Decorrelation Time & Iteration Time & Relaxation Time &Period q\\
- N &~~ $~h(T)$ &~~~ $\tau_0 = {1\over h(T) 2N }$ & t & $\tau ={1\over h(T) \ln {1\over \delta v_0}}$ & $ \log_{10} (q)$ \\ % Crush
- \midrule
- 256 & 194 & ~~~~~0.000012 & 1 & 95.00 & 4682\footnote{full
- period is not confirmed} \\
- \hline
- 8 & 220 & $~~~~~0.00028$ & 1 & 1.54 & 129 \\
- 17 & 374 & ~~~~~0.000079 & 1 & 1.92 & 294 \\
- 240 & 8679 & ~~~~~0.00000024 & 1 & 1.17 & 4389 \\
- \bottomrule
- \end{tabular}
- \caption{The entropy $h(T)$, decorrelation time $\tau_0$
- decorrelation time, relaxation time $\tau $ and period of the MIXMAX generator
- \cite{savvidy2017ex,savvidy2017cl},
- expressed in units of the iteration time $t$, which is
- normalised to 1.
- Clearly $\tau_0~ < t ~< \tau $.
-}
-\end{table}
-\endlatexonly
-
- The References for MIXMAX are
-
- * G.K.Savvidy and N.G.Ter-Arutyunian, *On the Monte Carlo simulation of physical systems,
- J.Comput.Phys. 97, 566 (1991)*;
- Preprint EPI-865-16-86, Yerevan, Jan. 1986
-
- * K.Savvidy, *The MIXMAX random number generator*,
- Comp. Phys. Commun. 196 (2015), pp 161鈥�165
- http://dx.doi.org/10.1016/j.cpc.2015.06.003
-
- * K.Savvidy and G.Savvidy, *Spectrum and Entropy of C-systems MIXMAX Random Number Generator*,
- Chaos, Solitons & Fractals, Volume 91, (2016) pp. 33鈥�38
- http://dx.doi.org/10.1016/j.chaos.2016.05.003
-
-
- @ingroup Random
- */
+/**
+MixMaxEngine is a wrapper class for the MIXMAX Random number generator.
+MIXMAX is a matrix-recursive random number generator introduced by
+G. Savvidy.
+
+The real implementation of the generator, written in C, is in the mixmax.h and mixmax.cxx files.
+This generator code is available also at hepforge: http://mixmax.hepforge.org
+The MIXMAX code has been created and developed by Konstantin Savvidy and it is
+released under GNU Lesser General Public License v3.
+
+This wrapper class provides 3 different variants of MIXMAX according to the template para extra parameter N.
+The extra parameter, `SkipNumber`, is used to perform additional iterations of the generator before returning the random numbers.
+For example, when `SkipNumber = 2`, the generator will have two extra iterations that will be discarder.
+
+ - MIXMAX with N = 240. This is a new version of the generator (version 2.0beta) described in the
+ <a href="http://dx.doi.org/10.1016/j.chaos.2016.05.003">2016 paper</a> (3rd reference), with
+ special number \f$s=487013230256099140\f$, \f$m=2^{51}+1\f$ and having a period of \f$10^{4389}\f$.
+
+ - MIXMAX with N = 17, from the 2.0 beta version with \f$s=0\f$ and \f$m=2^{36}+1\f$. The period of the
+ generator is \f$10^{294}\f$.
+
+ - MIXMAX with N = 256 from the 1.0 version. The period is (for `SkipNumber=0`) \f$10^{4682}\f$.
+ For this generator we recommend in ROOT using a default value of `SkipNumber=2, while for the
+ previous two generators skipping is not needed.
+
+This table describes the properties of the MIXMAX generators. MIXMAX is a genuine 61 bit
+generator on the Galois field GF[p], where \f$p=2^{61}-1\f$ is the Mersenne prime number.
+The MIXMAX generators with these parameters pass all of the BigCrush
+tests in the [TestU01 suite](http://simul.iro.umontreal.ca/testu01/tu01.html)
+
+
+
+| Dimension | Entropy | Decorrelation Time | Iteration Time | Relaxation Time | Period q |
+|-----------|-------------|----------------------------------|-----------------|---------------------------------------------------|-------------------------------------|
+| N | \f$~h(T)\f$ | \f$\tau_0 = {1\over h(T) 2N }\f$ | t | \f$\tau ={1\over h(T) \ln {1\over \delta v_0}}\f$ | \f$\log_{10} (q)\f$ |
+| 256 | 194 | 0.000012 | 1 | 95.00 | 4682 (full period is not confirmed) |
+| 8 | 220 | 0.00028 | 1 | 1.54 | 129 |
+| 17 | 374 | 0.000079 | 1 | 1.92 | 294 |
+| 240 | 8679 | 0.00000024 | 1 | 1.17 | 4389 |
+
+
+The entropy \f$h(T)\f$, decorrelation time \f$\tau_0\f$ decorrelation time, relaxation
+time \f$\tau\f$ and period of the MIXMAX generator, expressed in units of the iteration
+time \f$t\f$, which is normalised to 1. Clearly \f$\tau_0~ < t ~< \tau\f$.
+
+#### The References for MIXMAX are:
+
+ - G.K.Savvidy and N.G.Ter-Arutyunian, *On the Monte Carlo simulation of physical systems,
+ J.Comput.Phys. 97, 566 (1991)*;
+ Preprint EPI-865-16-86, Yerevan, Jan. 1986
+
+ - K.Savvidy, *The MIXMAX random number generator*,
+ Comp. Phys. Commun. 196 (2015), pp 161鈥�165
+ http://dx.doi.org/10.1016/j.cpc.2015.06.003
+
+ - K.Savvidy and G.Savvidy, *Spectrum and Entropy of C-systems MIXMAX Random Number Generator*,
+Chaos, Solitons & Fractals, Volume 91, (2016) pp. 33鈥�38
+http://dx.doi.org/10.1016/j.chaos.2016.05.003
+
+
+@ingroup Random
+*/
template<int N, int SkipNumber>
class MixMaxEngine : public TRandomEngine {
@@ -180,13 +169,13 @@ namespace ROOT {
//rng_state_t * fRngState; // mix-max generator state
//mixmax::mixmax_engine<N> * fRng; // mixmax internal engine class
MixMaxEngineImpl<N> * fRng; // mixmax internal engine class
-
+
};
typedef MixMaxEngine<240,0> MixMaxEngine240;
typedef MixMaxEngine<256,2> MixMaxEngine256;
typedef MixMaxEngine<17,0> MixMaxEngine17;
-
+
extern template class MixMaxEngine<240,0>;
extern template class MixMaxEngine<256,0>;
extern template class MixMaxEngine<256,2>;
@@ -202,4 +191,4 @@ namespace ROOT {
#include "Math/MixMaxEngine.icc"
-#endif /* ROOT_Math_MixMaxEngine */
+#endif /* ROOT_Math_MixMaxEngine */