+ functions fac, cata

pub/src/func.cpp

@@ -92,6 +92,14 @@ double func_coth(double v) { double t=tanh(v); return t==0?0:1/t;}
 
 double func_j0(double v) { return v==0 ? 1 : sin(v)/v;}
 
+double func_fac(double v) { return v>-.5 ? gsl_sf_gamma(round(v+1)) : 0; } 
+double func_cata(double v) {
+    if ( v<=-.5 )
+        return 0;
+    double x = round(v);
+    return exp( gsl_sf_lngamma( 2*x+1 ) - gsl_sf_lngamma( x+1 ) -
+                gsl_sf_lngamma( x+2 ) ); }
+
 double func_gamma(double v) { return v>0 ? gsl_sf_gamma(v) : 0; } 
 double func_lgamma(double v) { return v>0 ? gsl_sf_lngamma(v) : 0; } 
 // could be extended to non-integer negative arguments...
@@ -451,6 +459,10 @@ void NFunctions::initialize(void)
            "(x): hyperbolic tangent of x" ).register_me();
     CFunc( "j0", func_j0, 0, 0,
            "(x): spherical Bessel function x" ).register_me();
+    CFunc( "fac",func_fac, 0, 0,
+           "(x): factorial of nearest integer of x" ).register_me();
+    CFunc( "cata",func_cata, 0, 0,
+           "(x): Catalan number of nearest integer of x" ).register_me();
     CFunc( "gamma",func_gamma, 0, 0,
            "(x): gamma function of x (i.e. factorial of x-1)" ).register_me();
     CFunc( "lgamma",func_lgamma, 0, 0,