How to compare double in delphi?

The Math.pas unit includes functions such as SameValue(), IsZero(), CompareValue() which handle floating type comparisons and equality.

const
  EPSILON = 0.0000001;
begin    
  if CompareValue(p, pMax, EPSILON) = GreaterThanValue then
    ShowMessage('p greater than pMax');

The constant GreaterThanValue is defined in Types.pas

If you’re comparing very large values you shouldn’t use a constant for epsilon, instead your epsilon value should be calculated based on the values you’re comparing.

var
  epsilon: double;
begin    
  epsilon := Max(Min(Abs(p), Abs(pMax)) * 0.000001, 0.000001);
  if CompareValue(p, pMax, epsilon) = GreaterThanValue then
    ShowMessage('p greater than pMax');

Note that if you use CompareValue(a, b, 0) or in XE2 and later CompareValue(a, b), Delphi will automatically fill in a good epsilon for you.

From the Delphi Math unit:

function SameValue(const A, B: Extended; Epsilon: Extended): Boolean;
begin
  if Epsilon = 0 then
    Epsilon := Max(Min(Abs(A), Abs(B)) * ExtendedResolution, ExtendedResolution);
  if A > B then
    Result := (A - B) <= Epsilon
  else
    Result := (B - A) <= Epsilon;
end;

As of Delphi XE2 there are now overloads for all these functions that do not require an epsilon parameter and instead calculate one for you (similar to passing a 0 value for epsilon). For code clarity I would recommend calling these simpler functions and let Delphi handle the epsilon.

The only reason not to use the overloads without epsilon parameters would be when performance is crucial and you want to avoid the overhead of having the epsilon repeatedly calculated.