Delphi: workaround doing math with generic types preventing “E2015 Operator not applicable to this operand type” with TValue (as there is no way to constraint the generic type to be floating point or ordinal)

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

Syntax highlighted sources

Full program

Split in unit and realisation