Difference between revisions of "SuFac.cin"

Latest revision as of 07:06, 1 December 2018

// Sufac.cin is complex double implementation of superfunction of factorial, constructed with regular iteration at the fixed point 3.

//For argument x, the call is superfac(x); the retunting value is z_type; this type should be defined as complex double.

//

z_type superfac0(z_type z){ int n; z_type s;
// DB K=1.8455686701969342788;
DB k=0.61278745233070836381366079016859252; //k=log(K);
DB u[21]={2.,1., //0,1
.798731835172434541585621072345730147, // 2
.577880975476483235803807592348110833, // 3
.393978809662971757177848639852917378, // 4
.257533958032332679820773329133486586, // 5
.162901958103705249541496101752195514, // 6
.100282419171352371943554511785342142, // 7
.0603184725913977494512136774562415014, // 8
.0355544582258061836048059212969418417, // 9
.0205859954874424134686332481358935023, //10
.0117302279624549548734823541033644211, //11
.00658835541777254650743317221091667507,//12
.00365218351418374834372649788987162842,//13
.00200039479760669665711545138631474960,//14
.00108362752868222808502286098449166985,//15
.000581036636299227699924018045799185045,//16
.000308601963223618214714523083268563975,//17
.000162 ,.000084, 0.000043 //18,19,20
};
z_type e=exp(k*z);
       s=u[20]; for(n=19;n>=0;n--){s*=e; s+=u[n];}
// s=u[15]; for(n=14;n>=0;n--){s*=e; s+=u[n];}
return s;}
z_type superfac(z_type z){
       if(Re(z)>-2.) return fac(superfac(z-1.));
                       return superfac0(z-0.919385965452180);
       }

//

//

Difference between revisions of "SuFac.cin"

Latest revision as of 07:06, 1 December 2018

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@@ Line 1: / Line 1: @@
+// [[Sufac.cin]] is [[complex double]] implementation of superfunction of [[factorial]], constructed with [[regular iteration]] at the fixed point 3.
-// [[SuFac.cin]] defines z_type SuFac(z_type) that evaluates
-// [[Superfunction]] of [[Factorial]] built up at the fixed pont 2.
-// Of order of 14 correct decimal digits are expected in the result.
+//For argument x, the call is superfac(x); the retunting value is z_type; this type should be defined as [[complex double]].
- z_type superfac0(z_type z){ int n; z_type s;
- //      DB K=1.8455686701969342788;
- DB k=0.61278745233070836381366079016859252;  //k=log(K);
- DB u[21]={2.,1., //0,1
- .798731835172434541585621072345730147,  // 2
- .577880975476483235803807592348110833,  // 3
- .393978809662971757177848639852917378,  // 4
- .257533958032332679820773329133486586,  // 5
- .162901958103705249541496101752195514,  // 6
- .100282419171352371943554511785342142,  // 7
- .0603184725913977494512136774562415014, // 8
- .0355544582258061836048059212969418417, // 9
- .0205859954874424134686332481358935023, //10
- .0117302279624549548734823541033644211, //11
- .00658835541777254650743317221091667507,//12
- .00365218351418374834372649788987162842,//13
- .00200039479760669665711545138631474960,//14
- .00108362752868222808502286098449166985,//15
- .000581036636299227699924018045799185045,//16
- .000308601963223618214714523083268563975,//17
- .000162 ,.000084, 0.000043      //18,19,20
- };
- z_type e=exp(k*z);
-        s=u[20]; for(n=19;n>=0;n--){s*=e; s+=u[n];}
- //      s=u[15]; for(n=14;n>=0;n--){s*=e; s+=u[n];}
- return s;}
+//<poem><nomathjax><nowiki>
- z_type SuFac(z_type z){
+z_type superfac0(z_type z){ int n; z_type s;
-        if(Re(z)>-2.)   return fac(SuFac(z-1.));
+//      DB K=1.8455686701969342788;
-                        return superfac0(z);
+DB k=0.61278745233070836381366079016859252;  //k=log(K);
-        }
+DB u[21]={2.,1., //0,1
+.798731835172434541585621072345730147,  // 2
+.577880975476483235803807592348110833,  // 3
+.393978809662971757177848639852917378,  // 4
+.257533958032332679820773329133486586,  // 5
+.162901958103705249541496101752195514,  // 6
+.100282419171352371943554511785342142,  // 7
+.0603184725913977494512136774562415014, // 8
+.0355544582258061836048059212969418417, // 9
+.0205859954874424134686332481358935023, //10
+.0117302279624549548734823541033644211, //11
+.00658835541777254650743317221091667507,//12
+.00365218351418374834372649788987162842,//13
+.00200039479760669665711545138631474960,//14
+.00108362752868222808502286098449166985,//15
+.000581036636299227699924018045799185045,//16
+.000308601963223618214714523083268563975,//17
+.000162 ,.000084, 0.000043      //18,19,20
+};
+z_type e=exp(k*z);
+       s=u[20]; for(n=19;n>=0;n--){s*=e; s+=u[n];}
+//      s=u[15]; for(n=14;n>=0;n--){s*=e; s+=u[n];}
+return s;}
+z_type superfac(z_type z){
+       if(Re(z)>-2.)   return fac(superfac(z-1.));
+                       return superfac0(z-0.919385965452180);
+       }
-// [[Category:SuperFactorial]] [[Category:Factorial]] [[Category:Superfunction]] [[Category:C++]]
+//</nowiki></nomathjax></poem>
+//[[Category:C++]] [[Category:Superfunction]] [[Category:SuFac]]