Модуль и знак числа

function Math.Abs(X: Double): Double;

The Abs function returns the absolute value of a number X. It does this by removing a negative sign, if found.

begin
  a := Math.Abs(b + c);
end;

function Abs(X): Double;

function Math.AbsInt(X: Integer): Integer;

Same as Abs, but works with integer numbers.

function Math.Sign(X: Double): Integer;

Returns -1 if X is negative number, 0 if X=0 and +1 is X is positive number.

begin
  V1 := Math.Sign(5*5);  // V1=1
  V2 := Math.Sign(-5*5); // V2=-1
  V3 := Math.Sign(-5+5); // V3=0
end;

function Sign(X): Integer;

Check Values

function IsInfinite(X: Double): Boolean;

Returns True, if X is "infinite", and False otherwise.

uses Math;

begin
  if IsInfinite(3/0) then
    ShowMessage('∞')       
  else
    ShowMessage('ok');  
end;

function IsNaN(X: Double): Boolean;

Returns True, if X is "not-a-number", and False otherwise.

uses Math;

begin
  if IsNan(0/0) then
    ShowMessage('Not a number!')       
  else
    ShowMessage('ok');  
end;

function IsZero(X, Epsilon: Double): Boolean;

Returns True, if X ~ 0 in accordance with Epsilon tolerance. Otherwise, returns False.

uses Math;

begin
  if IsZero(0.000009, 0.0001) then
    ShowMessage('Zero')       
  else
    ShowMessage('Not zero');    
end;

Extrema

function Math.Max(A, B: Double): Double;

Returns the greater of A, B numbers.

begin
  a := Math.Max(b, c);
end;

function Max(X): Double;

function Math.MaxInt(A, B: Integer): Integer;

Same as Max, but works with integer numbers.

function Math.Min(A, B: Double): Double;

Returns the smaller of A, B numbers.

begin
  a := Math.Min(b, c);
end;

function Min(X): Double;

function Math.MinInt(A, B: Integer): Integer;

Same as Min, but works with integer numbers.

Interpolation

function Math.LInterp(x1, x, x2: Double; y1, y2: Double): Double;

Returns the result of linear interpolation according to the formula:

If x1=x2, then function returns x1.

begin
  X := 1.5;
  Y := Math.LInterp(1, X, 2, 100, 200); // y=150
end;

Other Routins

procedure Dec(var X: Integer);

Decrements a variable X by 1.

var
  X: Integer;

begin
  X := 10;
  Dec(X); // here x=9
end;

procedure DivMod(Dividend: Cardinal; Divisor: Word; var Result, Remainder: Word);

Returns the result of an integer division, including the remainder. Dividend is the integer into which you are dividing. Divisor is the value by which to divide Dividend. Result returns the result of the integer division. Remainder returns the remainder (the difference between Result * Divisor and Dividend).

var
  X, Remainder: Word;
begin
  DivMod(100, 3, X, Remainder); // 100/3=33.333...; x=33; Remainder=1
end;

procedure Inc(var X: Integer);

Increments a variable X by 1.

var
  X: Integer;

begin
  X := 10;
  Inc(X); // here x=11
end;

function Odd(X: Integer): Boolean;

The Odd function returns True if the given Number is odd. Otherwise, returns False.

begin
  if Odd(x) then
    ShowMessage('x - odd number')       
  else
    ShowMessage('x - even number');    
end;

function Math.Random: Double;

Generates random number within the range 0 <= X < 1.

begin
  ShowMessage('Random number: ' + FloatToStr(Math.Random));
end;