The Wiert Corner – irregular stream of stuff

A while ago on Facebook (it’s a private group, so you cannot see the posts unless you both have a Facebook account and are member of the group), [Archive.is] Niels Tjørnhøj-Thomsen (coming from a C++ templates background) asked why the below method would throw a E2015 Operator not applicable to this operand type in the complex expression:

function TAxis<t>.Calc(const AScalar: T): single;
begin
  Result := fStart + ( ( ( AScalar - fMin ) / fRange ) * fExtent );
end;

The type itself was very simple:

TAxis<T> = record
  fMin, fMax, fRange: T;
  fStart, fEnd, fExtent: single;
  function Calc( const AScalar: T ): single;
end;

He used these small example specialisations that put me on the wrong foot, as the order was TDateTime followed by single:

var
  rXAxis: TAxis<TDateTime>;
  rYAxis: TAxis<single>;

So at first I thought this might be caused by TDateTime to be defined in the System unit as a typed type:

type
  TDateTime = type Double;

It wasn’t.

Splitting the code in 4 lines with assignments of single expression operations would make the error appear in all expressions.

Casting parts of the expression to simple would not help either.

A small test program [Archive.is] might put you, like me, on the wrong foot because the specialisation is in the same source file as the generic type:

program DelphiMathAndGenerics;

type
  TAxis<T> = record
    fMin, fMax, fRange: T;
    fStart, fEnd, fExtent: single;
    function CalcCasted( const AScalar: T ): single;
    function CalcPlain( const AScalar: T ): single;
  end;

function TAxis<T>.CalcCasted(const AScalar: T): single;
var
  Offset: single;
  NormalisedOffset: single;
  ScaledOffset: single;
begin
  // First 2 lines give the same error: E2089 Invalid typecast
  Offset := single(AScalar) - fMin;
  NormalisedOffset := Offset / single(fRange);
  ScaledOffset := NormalisedOffset * fExtent;
  Result := fStart + ScaledOffset;
end;

function TAxis<T>.CalcPlain(const AScalar: T): single;
var
  Offset: T;
  NormalisedOffset: T;
  ScaledOffset: T;
begin
  // All 4 lines give the same error: E2015 Operator not applicable to this operand type
  Offset := AScalar - fMin;
  NormalisedOffset := Offset / fRange;
  ScaledOffset := NormalisedOffset * fExtent;
  Result := fStart + ScaledOffset;
end;

var
  rXAxis: TAxis<TDateTime>;
  rYAxis: TAxis<single>;

begin
end.

Splitting this in two files [Archive.is], a AxisUnit unit having only the TAxis<T> type, and a main program (even without having the specialisations) shows that even the unit itself would not compile.

This shows a major difference between Delphi (and similar C#) generics and C++ templates:

• generics are compiled and fully verified at the generic stage
• templates are pre-processed, then finally verified at specialisation stage

A solution would be that Delphi could constraint the generic type T into something like float or ordinal so the compiler would know that more operators are allowed in the code. But alas, Delphi – like C# – has a very limited number of constraints (C# only would allow a constraint for enumerations in version 7.3): Delphi Constraints in Generics – RAD Studio XE documentation wiki.

This StackOverflow question is very similar, and has the same answer (generics in Delphi work differently than templates in C++): [Source] templates – Arithmetic operations with generic types in Delphi – Stack Overflow

I’m new in Delphi. For a project required by my company, I need to translate some code from our existing C++ classes to Delphi. Some of these classes are templates, such …

Workaround: use the TValue.From<T>() function

There is a workaround though, but it is slow, as you need to convert from the generic T type to the actual (in this case floating point) type you can apply the operators on.

This is possible with the (Delphi 2010 introduced) TValue.From<T>() method which returns a TValue record. That TValue record has instance methods like AsExtended to extract or convert the embedded value as a specific type.

Initially, [Wayback] Delphi 2010 Rtti.TValue documentation had the From method signature wrong, maybe because of many wiki and blog HTML editors kill angle bracket pairs < and > in code blocks:

function From(const Value: T): TValue; static;

Since the [Wayback] Delphi XE System.Rtti.TValue documentation, the From method signature is fixed (see the bold parts):

class function From<T>(const Value: T): TValue; static;

With the [Wayback] Delphi XE2 Rtti.TValue documentation, the unit got renamed from Rtti into System.Rtti and has not changed further.

When using TValue.From<T>(), the AxisUnit becomes this:

unit AxisUnit;

interface

type
  TAxis<T> = record
    fMin, fMax, fRange: T;
    fStart, fEnd, fExtent: single;
    function Calc( const AScalar: T ): single;
  strict private
    function AsSingle(const Value: T): single;
  end;

implementation

uses
  System.Rtti;

function TAxis<T>.AsSingle(const Value: T): single;
begin
  Result := TValue.From<T>(Value).AsExtended
end;

function TAxis<T>.Calc(const AScalar: T): single;
var
  Offset: single;
  NormalisedOffset: single;
  ScaledOffset: single;
begin
  Offset := AsSingle(AScalar) - AsSingle(fMin);
  NormalisedOffset := Offset / AsSingle(fRange);
  ScaledOffset := NormalisedOffset * fExtent;
  Result := fStart + ScaledOffset;
end;

end.

–jeroen

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