# [fpc-devel] Nested functions in numlib

Werner Pamler werner.pamler at freenet.de
Mon Apr 3 18:32:25 CEST 2017

```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

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:

- 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;

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?

```