# class TFormula: public TNamed

```The  F O R M U L A  class*-*-*-*-
*-*                  =========================
-
*-*   This class has been implemented by ```
Nicolas Brun
```(age 18).
*-*   ========================================================

```
/* */
```-
*-*  Example of valid expressions:
*-*     -  sin(x)/x
*-*     -  [0]*sin(x) + [1]*exp(-[2]*x)
*-*     -  x + y**2
*-*     -  x^2 + y^2
*-*     -  [0]*pow([1],4)
*-*     -  2*pi*sqrt(x/y)
*-*     -  gaus(0)*expo(3)  + ypol3(5)*x
*-*     -  gausn(0)*expo(3) + ypol3(5)*x
-
*-*  In the last example above:
*-*     gaus(0) is a substitute for [0]*exp(-0.5*((x-[1])/[2])**2)
*-*        and (0) means start numbering parameters at 0
*-*     gausn(0) is a substitute for [0]*exp(-0.5*((x-[1])/[2])**2)/(sqrt(2*pi)*[2]))
*-*        and (0) means start numbering parameters at 0
*-*     expo(3) is a substitute for exp([3]+[4]*x)
*-*     pol3(5) is a substitute for par[5]+par[6]*x+par[7]*x**2+par[8]*x**3
*-*         (here Pol3 stands for Polynomial of degree 3)
-
*-*   TMath functions can be part of the expression, eg:
*-*     -  TMath::Landau(x)*sin(x)
*-*     -  TMath::Erf(x)
-
*-*   Comparisons operators are also supported (&&, ||, ==, <=, >=, !)
*-*   Examples:
*-*      sin(x*(x<0.5 || x>1))
*-*   If the result of a comparison is TRUE, the result is 1, otherwise 0.
-
*-*   Already predefined names can be given. For example, if the formula
*-*     TFormula old(sin(x*(x<0.5 || x>1))) one can assign a name to the formula. By default
*-*     the name of the object = title = formula itself.
*-*     old.SetName("old").
*-*     then, old can be reused in a new expression.
*-*     TFormula new("x*old") is equivalent to:
*-*     TFormula new("x*sin(x*(x<0.5 || x>1))")
-
*-*   Up to 4 dimensions are supported (indicated by x, y, z, t)
*-*   An expression may have 0 parameters or a list of parameters
*-*   indicated by the sequence [par_number]
-
*-*   A graph showing the logic to compile and analyze a formula
*-*   is shown in TFormula::Compile and TFormula::Analyze.
*-*   Once a formula has been compiled, it can be evaluated for a given
*-*   set of parameters. see graph in TFormula::EvalPar.
-
*-*   This class is the base class for the function classes TF1,TF2 and TF3.
*-*   It is also used by the ntuple selection mechanism TNtupleFormula.
-
*-*   In version 7 of TFormula, the usage of fOper has been changed
*-*   to improve the performance of TFormula::EvalPar.
*-*   Conceptually, fOper was changed from a simple array of Int_t
*-*   to an array of composite values.
*-*   For example a 'ylandau(5)' operation used to be encoded as 4105;
*-*   it is now encoded as (klandau >> kTFOperShit) + 5
*-*   Any class inheriting from TFormula and using directly fOper (which
*-*   is now a private data member), needs to be updated to take this
*-*   in consideration.  The member functions recommended to set and
*-*   access fOper are:  SetAction, GetAction, GetActionParam
*-*   TFormula::EvalPar
-
*-*   CHANGING DEFAULT SETTINGS
*-*   =========================
*-*   When creating complex formula , it may be necessary to increase
*-*   some default parameters. see static function TFormula::SetMaxima
-
*-*   WHY TFormula CANNOT ACCEPT A CLASS MEMBER FUNCTION ?
*-*   ====================================================
*-* This is a frequently asked question.
*-* C++ is a strongly typed language. There is no way for TFormula (without
*-* recompiling this class) to know about all possible user defined data types.
*-* This also apply to the case of a static class function.
*-* Because TMath is a special and frequent case, TFormula is aware
*-* of all TMath functions.
-
-
```

## Function Members (Methods)

public:
protected:
 virtual Bool_t CheckOperands(Int_t operation, Int_t& err) virtual Bool_t CheckOperands(Int_t leftoperand, Int_t rightoperartion, Int_t& err) void ClearFormula(Option_t* option = "") virtual void Convert(UInt_t fromVersion) virtual void TObject::DoError(int level, const char* location, const char* fmt, va_list va) const Double_t EvalParFast(const Double_t* x, const Double_t* params) Double_t EvalPrimitive(const Double_t* x, const Double_t* params) Double_t EvalPrimitive0(const Double_t* x, const Double_t* params) Double_t EvalPrimitive1(const Double_t* x, const Double_t* params) Double_t EvalPrimitive2(const Double_t* x, const Double_t* params) Double_t EvalPrimitive3(const Double_t* x, const Double_t* params) Double_t EvalPrimitive4(const Double_t* x, const Double_t* params) Short_t GetAction(Int_t code) const Short_t GetActionOptimized(Int_t code) const Int_t GetActionParam(Int_t code) const Int_t GetActionParamOptimized(Int_t code) const Int_t* GetOper() const Int_t* GetOperOptimized() const virtual Bool_t IsString(Int_t oper) const void MakePrimitive(const char* expr, Int_t pos) void TObject::MakeZombie() Int_t PreCompile() void SetAction(Int_t code, Int_t value, Int_t param = 0) void SetActionOptimized(Int_t code, Int_t value, Int_t param = 0) virtual Bool_t StringToNumber(Int_t code)

## Data Members

public:
 enum { kEnd kAdd kSubstract kMultiply kDivide kModulo kcos ksin ktan kacos kasin katan katan2 kfmod kpow ksq ksqrt kstrstr kmin kmax klog kexp klog10 kpi kabs ksign kint kSignInv krndm kAnd kOr kEqual kNotEqual kLess kGreater kLessThan kGreaterThan kNot kcosh ksinh ktanh kacosh kasinh katanh kStringEqual kStringNotEqual kBitAnd kBitOr kLeftShift kRightShift kJumpIf kJump kexpo kxexpo kyexpo kzexpo kxyexpo kgaus kxgaus kygaus kzgaus kxygaus klandau kxlandau kylandau kzlandau kxylandau kpol kxpol kypol kzpol kParameter kConstant kBoolOptimize kStringConst kVariable kFunctionCall kData kUnary kBinary kThree kDefinedVariable kDefinedString kPlusD kPlusDD kMultD kMultDD kBoolOptimizeOr kBoolOptimizeAnd kBoolSet kFDM kFD0 kFD1 kFD2 kFD3 kNotGlobal kNormalized kLinear }; enum TObject::EStatusBits { kCanDelete kMustCleanup kObjInCanvas kIsReferenced kHasUUID kCannotPick kNoContextMenu kInvalidObject }; enum TObject::[unnamed] { kIsOnHeap kNotDeleted kZombie kBitMask kSingleKey kOverwrite kWriteDelete };
protected:
 TBits fAlreadyFound ! cache for information Double_t* fConst [fNconst] Array of fNconst formula constants TString* fExpr [fNoper] List of expressions TString* fExprOptimized ![fNOperOptimized] List of expressions TObjArray fFunctions Array of function calls to make TObjArray fLinearParts Linear parts if the formula is linear (contains '|' or "++") Int_t fNOperOptimized !Number of operators after optimization TString TNamed::fName object identifier TString* fNames [fNpar] Array of parameter names Int_t fNconst Number of constants Int_t fNdim Dimension of function (1=1-Dim, 2=2-Dim,etc) Int_t fNoper Number of operators Int_t fNpar Number of parameters Int_t fNstring Number of different constants character strings Int_t fNumber formula number identifier Int_t fNval Number of different variables in expression TOperOffset* fOperOffset ![fNOperOptimized] Offsets of operrands Int_t* fOperOptimized ![fNOperOptimized] List of operators. (See documentation for changes made at version 7) G__p2memfunc fOptimal !pointer to optimal function Double_t* fParams [fNpar] Array of fNpar parameters TFormulaPrimitive** fPredefined ![fNPar] predefined function TString TNamed::fTitle object title
private:
 Int_t* fOper [fNoper] List of operators. (See documentation for changes made at version 7)

## Function documentation

TFormula()
```Formula default constructor*-*-*-
*-*                  ============================
```
TFormula(const char* name, const char* formula)
```Normal Formula constructor*-*-*-
*-*                  ==========================
```
TFormula(const TFormula& formula)
``` Default constructor.
```
TFormula& operator=(const TFormula& rhs)
``` Operator =
```

```Formula default destructor*-*-*-
*-*                  ===========================
```
Bool_t AnalyzeFunction(TString& chaine, Int_t& err, Int_t offset = 0)
```Check if the chain as function call *-*-
*-*              =======================================
-
*-*   If you overload this member function, you also HAVE TO
*-*   never call the constructor:
-
*-*     TFormula::TFormula(const char *name,const char *expression)
-
*-*   and write your own constructor
-
*-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
-
*-*   which has to call the TFormula default constructor and whose implementation
*-*   should be similar to the implementation of the normal TFormula constructor
-
*-*   This is necessary because the normal TFormula constructor call indirectly
*-*   the virtual member functions Analyze, DefaultString, DefaultValue
*-*   and DefaultVariable.
-
```
void Analyze(const char* schain, Int_t& err, Int_t offset = 0)
```Analyze a sub-expression in one formula*-*-
*-*              =======================================
-
*-*   Expressions in one formula are recursively analyzed.
*-*   Result of analysis is stored in the object tables.
-
*-*                  Table of function codes and errors
*-*                  ==================================
-
*-*   * functions :
-
*-*     +           1                   pow          20
*-*     -           2                   sq           21
*-*     *           3                   sqrt         22
*-*     /           4                   strstr       23
*-*     %           5                   min          24
*-*                                     max          25
*-*                                     log          30
*-*     cos         10                  exp          31
*-*     sin         11                  log10        32
*-*     tan         12
*-*     acos        13                  abs          41
*-*     asin        14                  sign         42
*-*     atan        15                  int          43
*-*     atan2       16
*-*     fmod        17                  rndm         50
-
*-*     cosh        70                  acosh        73
*-*     sinh        71                  asinh        74
*-*     tanh        72                  atanh        75
-
*-*     expo       100                  gaus        110     gausn  (see note below)
*-*     expo(0)    100 0                gaus(0)     110 0   gausn(0)
*-*     expo(1)    100 1                gaus(1)     110 1   gausn(1)
*-*     xexpo      100 x                xgaus       110 x   xgausn
*-*     yexpo      101 x                ygaus       111 x   ygausn
*-*     zexpo      102 x                zgaus       112 x   zgausn
*-*     xyexpo     105 x                xygaus      115 x   xygausn
*-*     yexpo(5)   102 5                ygaus(5)    111 5   ygausn(5)
*-*     xyexpo(2)  105 2                xygaus(2)   115 2   xygausn(2)
-
*-*     landau      120 x   landaun (see note below)
*-*     landau(0)   120 0   landaun(0)
*-*     landau(1)   120 1   landaun(1)
*-*     xlandau     120 x   xlandaun
*-*     ylandau     121 x   ylandaun
*-*     zlandau     122 x   zlandaun
*-*     xylandau    125 x   xylandaun
*-*     ylandau(5)  121 5   ylandaun(5)
*-*     xylandau(2) 125 2   xylandaun(2)
-
*-*     pol0        130 x               pol1        130 1xx
*-*     pol0(0)     130 0               pol1(0)     130 100
*-*     pol0(1)     130 1               pol1(1)     130 101
*-*     xpol0       130 x               xpol1       130 101
*-*     ypol0       131 x               ypol1       131 101
*-*     zpol0       132 x               zpol1       132 1xx
*-*     ypol0(5)    131 5               ypol1(5)    131 105
-
*-*     pi          40
-
*-*     &&          60                  <            64
*-*     ||          61                  >            65
*-*     ==          62                  <=           66
*-*     !=          63                  =>           67
*-*     !           68
*-*     ==(string)  76                  &            78
*-*     !=(string)  77                  |            79
*-*     <<(shift)   80                  >>(shift)    81
*_*     ? :         82
-
*-*   * constants (kConstants) :
-
*-*    c0  141 1      c1  141 2  etc..
-
*-*   * strings (kStringConst):
-
*-*    sX  143 x
-
*-*   * variables (kFormulaVar) :
-
*-*     x    144 0      y    144 1      z    144 2      t    144 3
-
*-*   * parameters :
-
*-*     [1]        140 1
*-*     [2]        140 2
*-*     etc.
-
*-*   special cases for normalized gaussian or landau distributions
*-*   =============================================================
*-*   the expression "gaus" is a substitute for
*-*     [0]*exp(-0.5*((x-[1])/[2])**2)
*-*   to obtain a standard normalized gaussian, use "gausn" instead of "gaus"
*-*   the expression "gausn" is a substitute for
*-*     [0]*exp(-0.5*((x-[1])/[2])**2)/(sqrt(2*pi)*[2]))
-
*-*   In the same way the expression "landau" is a substitute for
*-*     [0]*TMath::Landau(x,[1],[2],kFALSE)
*-*   to obtain a standard normalized landau, use "landaun" instead of "landau"
*-*   the expression "landaun" is a substitute for
*-*     [0]*TMath::Landau(x,[1],[2],kTRUE)
-
*-*   boolean optimization (kBoolOptmize) :
*-*   =====================================
-
*-*     Those pseudo operation are used to implement lazy evaluation of
*-*     && and ||.  When the left hand of the expression if false
*-*     (respectively true), the evaluation of the right is entirely skipped
*-*     (since it would not change the value of the expreession).
-
*-*     &&   142 11 (one operation on right) 142 21 (2 operations on right)
*-*     ||   142 12 (one operation on right) 142 22 (2 operations on right)
-
*-*   * functions calls (kFunctionCall) :
-
*-*    f0 145  0  f1 145  1  etc..
-
*-*   errors :
*-*   ========
-
*-*     1  : Division By Zero
*-*     2  : Invalid Floating Point Operation
*-*     4  : Empty String
*-*     5  : invalid syntax
*-*     6  : Too many operators
*-*     7  : Too many parameters
*-*    10  : z specified but not x and y
*-*    11  : z and y specified but not x
*-*    12  : y specified but not x
*-*    13  : z and x specified but not y
*-*    20  : non integer value for parameter number
*-*    21  : atan2 requires two arguments
*-*    22  : pow requires two arguments
*-*    23  : degree of polynomial not specified
*-*    24  : Degree of polynomial must be positive
*-*    25  : Degree of polynomial must be less than 20
*-*    26  : Unknown name
*-*    27  : Too many constants in expression
*-*    28  : strstr requires two arguments
*-*    29  : interpreted or compiled function have to return a numerical type
*-*    30  : Bad numerical expression
*-*    31  : Part of the variable exist but some of it is not accessible or useable
*-*    40  : '(' is expected
*-*    41  : ')' is expected
*-*    42  : '[' is expected
*-*    43  : ']' is expected

```
/* */
```-
*-*  Special functions
*-*  -----------------
*-*  By default, the formula is assigned fNumber=0. However, the following
*-*  formula built with simple functions are assigned  fNumber:
*-*    "gaus"      100  (or gausn)
*-*    "xygaus"    110
*-*    "expo"      200
*-*    "polN"      300+N
*-*    "landau"    400
*-*    "xylandau"  410
*-*  Note that expressions like gaus(0), expo(1) will force fNumber=0
-
*-*  Warning when deriving a class from TFormula
*-*  -------------------------------------------
*-*   If you overload this member function, you also HAVE TO
*-*   never call the constructor:
-
*-*     TFormula::TFormula(const char *name,const char *expression)
-
*-*   and write your own constructor
-
*-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
-
*-*   which has to call the TFormula default constructor and whose implementation
*-*   should be similar to the implementation of the normal TFormula constructor
-
*-*   This is necessary because the normal TFormula constructor call indirectly
*-*   the virtual member functions Analyze, DefaultString, DefaultValue
*-*   and DefaultVariable.
-
-
```
Bool_t CheckOperands(Int_t operation, Int_t& err)
``` Check whether the operand at 'oper-1' is compatible with the operation at 'oper'.
```
Bool_t CheckOperands(Int_t leftoperand, Int_t rightoperartion, Int_t& err)
``` Check whether the operands at 'leftoper' and 'oper-1' are compatible with the operation at 'oper'.
```

``` Try to 'demote' a string into an array bytes.  If this is not possible,
return false.
```
void Clear(Option_t* option = "")
```Resets the objects*-*-
*-*              ==================
-
*-* Resets the object to its state before compilation.
-
```
void ClearFormula(Option_t* option = "")
```Resets the objects*-*-
*-*              ==================
-
*-* Resets the object to its state before compilation.
-
```
Int_t Compile(const char* expression = "")
```-*-*-*-*-*Compile expression already stored in fTitle
*-*                  ===========================================
-
*-*   Loop on all subexpressions of formula stored in fTitle
-
*-*   If you overload this member function, you also HAVE TO
*-*   never call the constructor:
-
*-*     TFormula::TFormula(const char *name,const char *expression)
-
*-*   and write your own constructor
-
*-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
-
*-*   which has to call the TFormula default constructor and whose implementation
*-*   should be similar to the implementation of the normal TFormula constructor
-
*-*   This is necessary because the normal TFormula constructor call indirectly
*-*   the virtual member functions Analyze, DefaultString, DefaultValue
*-*   and DefaultVariable.
-

```
/* */
```-
-
```
void Copy(TObject& formula) const
```Copy this formula*-*-*-*-*-*-*-*-
*-*                  =================
```
char * DefinedString(Int_t code)
```Return address of string corresponding to special code
*-*        ======================================================
-
*-*   This member function is inactive in the TFormula class.
*-*   It may be redefined in derived classes.
-
*-*   If you overload this member function, you also HAVE TO
*-*   never call the constructor:
-
*-*     TFormula::TFormula(const char *name,const char *expression)
-
*-*   and write your own constructor
-
*-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
-
*-*   which has to call the TFormula default constructor and whose implementation
*-*   should be similar to the implementation of the normal TFormula constructor
-
*-*   This is necessary because the normal TFormula constructor call indirectly
*-*   the virtual member functions Analyze, DefaultString, DefaultValue
*-*   and DefaultVariable.
-
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
```

```Return value corresponding to special code*-*-*-
*-*        ==========================================
-
*-*   This member function is inactive in the TFormula class.
*-*   It may be redefined in derived classes.
-
*-*   If you overload this member function, you also HAVE TO
*-*   never call the constructor:
-
*-*     TFormula::TFormula(const char *name,const char *expression)
-
*-*   and write your own constructor
-
*-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
-
*-*   which has to call the TFormula default constructor and whose implementation
*-*   should be similar to the implementation of the normal TFormula constructor
-
*-*   This is necessary because the normal TFormula constructor call indirectly
*-*   the virtual member functions Analyze, DefaultString, DefaultValue
*-*   and DefaultVariable.
-
*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
```
Int_t DefinedVariable(TString& variable, Int_t& action)
```-*Check if expression is in the list of defined variables
*-*        =======================================================
-
*-*   This member function can be overloaded in derived classes
-
*-*   If you overload this member function, you also HAVE TO
*-*   never call the constructor:
-
*-*     TFormula::TFormula(const char *name,const char *expression)
-
*-*   and write your own constructor
-
*-*     MyClass::MyClass(const char *name,const char *expression) : TFormula()
-
*-*   which has to call the TFormula default constructor and whose implementation
*-*   should be similar to the implementation of the normal TFormula constructor
-
*-*   This is necessary because the normal TFormula constructor call indirectly
*-*   the virtual member functions Analyze, DefaultString, DefaultValue
*-*   and DefaultVariable.
-
*-*   The expected returns values are
*-*     -2 :  the name has been recognized but won't be usable
*-*     -1 :  the name has not been recognized
*-*    >=0 :  the name has been recognized, return the action parameter.
-
-
```
Double_t Eval(Double_t x, Double_t y = 0, Double_t z = 0, Double_t t = 0) const
```Evaluate this formula*-*-*-*-*-*-
*-*                  =====================
-
*-*   The current value of variables x,y,z,t is passed through x, y, z and t.
*-*   The parameters used will be the ones in the array params if params is given
*-*    otherwise parameters will be taken from the stored data members fParams
-
-
```
Double_t EvalParOld(const Double_t* x, const Double_t* params = 0)
```Evaluate this formula*-*-*-*-*-*-
*-*                  =====================
-
*-*   The current value of variables x,y,z,t is passed through the pointer x.
*-*   The parameters used will be the ones in the array params if params is given
*-*    otherwise parameters will be taken from the stored data members fParams

```
/* */
```-
-
-
```
TString GetExpFormula(Option_t* option = "") const
```Reconstruct the formula expression from*-*-
*-*              the internal TFormula member variables
*-*              =======================================
-
*-*   This function uses the internal member variables of TFormula to
*-*   construct the mathematical expression associated with the TFormula
*-*   instance. This function can be used to get an expanded version of the
*-*   expression originally assigned to the TFormula instance, i.e. that
*-*   the string returned by GetExpFormula() doesn't depend on other
*-*   TFormula object names.
-
*-*  if option contains "p" the returned string will contain the formula
*-*  expression with symbolic parameters, eg [0] replaced by the actual value
*-*  of the parameter. Example:
*-*  if expression in formula is: "[0]*(x>-[1])+[2]*exp(-[3]*x)"
*-*  and parameters are 3.25,-4.01,4.44,-0.04, GetExpFormula("p") will return:
*-*   "(3.25*(x>+4.01))+(4.44*exp(+0.04*x))"
```
const TObject* GetLinearPart(Int_t i)
``` Return linear part.
```

```return value of parameter number ipar
```
Double_t GetParameter(const char *parName)
```return value of parameter named parName
```
const char * GetParName(Int_t ipar) const
```Return name of one parameter*-*-*-*-*-*-*-*-
*-*            ============================
```
Int_t GetParNumber(const char* name) const
``` return parameter number by name
```
Bool_t IsString(Int_t oper) const
``` return true if the expression at the index 'oper' is to be treated as
as string
```
void Print(Option_t* option = "") const
```-*Dump this formula with its attributes
*-*                  =====================================
```
void ProcessLinear(TString& replaceformula)
```if the formula is for linear fitting, change the title to
normal and fill the LinearParts array
```
void SetParameter(const char *name, Double_t value)
```Initialize parameter number ipar*-*-*-*-*-
*-*            ================================
```
void SetParameter(Int_t ipar, Double_t value)
```Initialize parameter number ipar*-*-*-*-*-
*-*            ================================
```
void SetParameters(const Double_t* params)
``` Initialize array of all parameters
```
void SetParameters(Double_t p0, Double_t p1, Double_t p2 = 0, Double_t p3 = 0, Double_t p4 = 0, Double_t p5 = 0, Double_t p6 = 0, Double_t p7 = 0, Double_t p8 = 0, Double_t p9 = 0, Double_t p10 = 0)
``` Initialize up to 10 parameters
All arguments except THE FIRST TWO are optional
In case of a function with only one parameter, call this function with p1=0.
Minimum two arguments are required to differentiate this function
from the SetParameters(cont Double_t *params)
```
void SetParName(Int_t ipar, const char* name)
``` Set name of parameter number ipar
```
void SetParNames(const char* name0 = "p0", const char* name1 = "p1", const char* name2 = "p2", const char* name3 = "p3", const char* name4 = "p4", const char* name5 = "p5", const char* name6 = "p6", const char* name7 = "p7", const char* name8 = "p8", const char* name9 = "p9", const char* name10 = "p10")
```Set up to 10 parameter names*-*-*-*-*-
*-*                ============================
```
void Streamer(TBuffer& b)
```Stream a class object*-*-*-*-*-*-*-
*-*              =========================================
```
void Convert(UInt_t fromVersion)
``` Convert the fOper of a TFormula version fromVersion to the current in memory version
```
void MakePrimitive(const char* expr, Int_t pos)
```  MakePrimitive
find TFormulaPrimitive replacement for some operands

```
void Optimize()
``` MI include

Optimize formula
1.) Minimize the number of operands
a.)  several operanands are glued togther
b.)  some primitive functions glued together - exemp. (x+y) => PlusXY(x,y)
c.)  maximize number of standard calls minimizing number of jumps in Eval cases
d.)  variables, parameters and constants are mapped - using fOperOfssets0
Eval procedure use direct acces to data (only one corresponding case statement in eval procedure)

pdata[operand={Var,Par,Const}][offset]
pdata[fOperOffsets0[i]][fOperOffset1[i+1]]
2.) The fastest evaluation function is choosen at the end
a.) fOptimal := pointer to the fastest function for given evaluation string
switch(GetActionOptimized(0)){
case kData : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive0; break;}
case kUnary : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive1; break;}
case kBinary : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive2; break;}
case kThree : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive3; break;}
case kFDM : {fOptimal= (TFormulaPrimitive::TFuncG)&TFormula::EvalPrimitive4; break;}
}
b.) ex. fOptimal = ::EvalPrimitive0 - if it return only variable, constant or parameter
= ::EvalParameter1 - if only one unary operation
= ::EvalPrimitive2 - if only one binary operation

```
Double_t EvalPrimitive(const Double_t* x, const Double_t* params)
```Evaluate primitive formula

```
Double_t EvalPrimitive0(const Double_t* x, const Double_t* params)
```Evaluate primitive formula

```
Double_t EvalPrimitive1(const Double_t* x, const Double_t* params)
```Evaluate primitive formula

```
Double_t EvalPrimitive2(const Double_t* x, const Double_t* params)
```Evaluate primitive formula

```
Double_t EvalPrimitive3(const Double_t* x, const Double_t* params)
```Evaluate primitive formula

```
Double_t EvalPrimitive4(const Double_t* x, const Double_t* params)
```Evaluate primitive formula

```
Double_t EvalParFast(const Double_t* x, const Double_t* params)
```Evaluate this formula*-*-*-*-*-*-
*-*                  =====================
-
*-*   The current value of variables x,y,z,t is passed through the pointer x.
*-*   The parameters used will be the ones in the array params if params is given
*-*    otherwise parameters will be taken from the stored data members fParams

```
/* */
```-
-
-
```

```Pre compile function

```
void SetMaxima(Int_t maxop = 1000, Int_t maxpar = 1000, Int_t maxconst = 1000)
``` static function to set the maximum value of 3 parameters
-maxop    : maximum number of operations
-maxpar   : maximum number of parameters
-maxconst : maximum number of constants
None of these parameters cannot be less than 10 (default is 1000)
call this function to increase one or all maxima when processing
very complex formula, eg TFormula::SetMaxima(100000,1000,1000000);
If you process many functions with a small number of operations/parameters
you may gain some memory and performance by decreasing these values.
```
Int_t * GetOper() const
`{ return fOper; }`
Short_t GetAction(Int_t code) const
`{ return fOper[code] >> kTFOperShift; }`
Int_t GetActionParam(Int_t code) const
`{ return fOper[code] & kTFOperMask; }`
void SetAction(Int_t code, Int_t value, Int_t param = 0)
Int_t * GetOperOptimized() const
`{ return fOperOptimized; }`
Short_t GetActionOptimized(Int_t code) const
`{ return fOperOptimized[code] >> kTFOperShift; }`
Int_t GetActionParamOptimized(Int_t code) const
`{ return fOperOptimized[code] & kTFOperMask; }`
void SetActionOptimized(Int_t code, Int_t value, Int_t param = 0)
Double_t EvalPar(const Double_t* x, const Double_t* params = 0)
`{return ((*this).*fOptimal)(x,params);}`
Int_t GetNdim() const
`{return fNdim;}`
Int_t GetNpar() const
`{return fNpar;}`
Int_t GetNumber() const
`{return fNumber;}`
Double_t * GetParameters() const
`{return fParams;}`
void GetParameters(Double_t* params)
`{for(Int_t i=0;i<fNpar;i++) params[i] = fParams[i];}`

`{return TestBit(kLinear);}`

`{return TestBit(kNormalized);}`
void SetNumber(Int_t number)
`{fNumber = number;}`
void Update()
`{;}`