[fpc-devel] Nested functions in numlib

[Werner Pamler]

In addition to the incomplete gamma function I am planning to add a 
series of other special functions useful for statistical calculations, 
among them the incomplete beta function and its inverse.

Calculation of the inverse incomplete beta function usually is performed 
in the literature by numerical root finding procedures. Numlib is 
well-equipped for this purpose, it has the unit "roo" with the procedure 
"roof1r" which does a bisection search of the root lying between 
positive and negative guess values. The function for which the zero 
point is to be found must be specified as a procedure variable of type 
rfunc1r (defined in "typ", probably meaning "real function of one real 
variable"); in case of the inverse incomplete beta function, this 
function is the complete beta function, of course, and this depends on 
three parameters, a, b, and x.

In the current state of numlib, parameters must be declared globally so 
that the function passed as a parameter gets access to them:

   var
     _a, _b, _y: ArbFloat;

   function _betai(x: ArbFloat): ArbFloat;
   begin
     Result := betai(_a, _b, x) - _y;
   end;

   function invbetai(a, b, y: ArbFloat): ArbFloat;
   const
     EPS = 1e-7;
   var
     term: ArbInt = 0;
   begin
     _a := a;
     _b := b;
     _y := y;
     roof1r(@_betai, 0, 1, EPS, EPS, Result, term);
   end;

This is not very nice. It would be better if the test function could be 
declared as a nested function inside "invbetai":

   function invbetai(a, b, y: ArbFloat): ArbFloat;

     function _invbetai(x: ArbFloat): ArbFloat;
     begin
       Result := betai(a, b, x) - y;
     end;

   const
     EPS = 1e-7;
   var
     term: ArbInt = 0;
   begin
     roof1r(@_betai(0, 1, EPS, EPS, Result, term);
   end;

In order to make this construction pass the compiler I would like to

- declare another rfuncf1r type, now as "is nested"
     type
       rfuncf1rn = function(x: ArbFloat): ArbFloat is nested;   // 
trailing "n" means "nested"

- modify roof1r to use the nested function
     Procedure roof1r(f: rfunc1rn; a, b, ae, re: ArbFloat; Var x: 
ArbFloat; var term: ArbInt); overload;

- to avoid breaking existing code and to avoid forcing users of the 
original version to add a {$modeswitch nestedprocvars} to their code, I 
want to overload this function with a version using the non-nested 
function, but calling the nested version:

   Procedure roof1r(f: rfunc1r; a, b, ae, re: ArbFloat; Var x: ArbFloat; 
Var term: ArbInt); overload;

     function _f(x: ArbFloat): ArbFloat;
     begin
       Result := f(x);
     end;

   begin
     roof1r(@_f, a, b, ae, re, x, term);
   end;

Is there a chance that such a patch would be accepted?