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Mathematical procedures and functions

These procedures and functions can be used in all types of documents, regardless of their purpose.

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

Returns the absolute value of X.

Example: Abs(-5.3) returns 5.3.

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

Rounds X up to the nearest integer.

Example: Ceil(3.2) returns 4.

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

Returns the value of e raised to the power of X.

Example: Exp(1) returns 2.718281828459045.

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

Rounds X down to the nearest integer.

Example: Floor(3.9) returns 3.

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

Returns the fractional part of X.

Example: Frac(5.75) returns 0.75.

function Math.FracDigit(X: Double; DigitNo: Integer): Int64;

Returns the specified digit of the fractional part of X.

Example: FracDigit(5.75, 1) returns 7.

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

Returns the integer part of X.

Example: Int(5.75) returns 5.0.

function Math.IntPower(X: Double; Exponent: Integer): Double;

Returns X raised to the power of Exponent.

Example: IntPower(2, 3) returns 8.0.

function Math.Ldexp(X: Double; P: Integer): Double;

Returns X * 2^P.

Example: Ldexp(3, 2) returns 12.0.

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

Returns the natural logarithm of X.

Example: Ln(2.718281828459045) returns 1.0.

function Math.LnXP1(X: Double): Double;

Returns the natural logarithm of X + 1.

Example: LnXP1(1.0) returns 0.6931471805599453.

function Math.Log10(X: Double): Double;

Returns the base-10 logarithm of X.

Example: Log10(100) returns 2.0.

function Math.Log2(X: Double): Double;

Returns the base-2 logarithm of X.

Example: Log2(8) returns 3.0.

function Math.LogN(Base, X: Double): Double;

Returns the logarithm of X with the specified Base.

Example: LogN(3, 9) returns 2.0.

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

Returns the larger of A and B.

Example: Max(5, 10) returns 10.0.

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

Returns the larger of A and B as integers.

Example: MaxInt(5, 10) returns 10.

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

Returns the smaller of A and B.

Example: Min(5, 10) returns 5.0.

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

Returns the smaller of A and B as integers.

Example: MinInt(5, 10) returns 5.

function Math.Power(Base, Exponent: Double): Double;

Returns Base raised to the power of Exponent.

Example: Power(2, 3) returns 8.0.

function Math.Random: Double;

Returns a random floating-point number between 0 and 1.

Example: Random might return 0.123456789.

function Math.Round(X: Double): Int64;

Rounds X to the nearest integer.

Example: Round(3.6) returns 4.

function Math.RoundToEven(X: Double; Digits: Integer): Double;

Rounds X to the nearest even number with the specified number of Digits.

Example: RoundToEven(3.5, 0) returns 4.0.

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

Returns the sign of X (-1, 0, or 1).

Example: Sign(-5) returns -1.

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

Returns the square root of X.

Example: Sqrt(16) returns 4.0.

function Math.Trunc(X: Double): Int64;

Truncates X to an integer by removing the fractional part.

Example: Trunc(5.75) returns 5.

Trigonometric Functions

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

Returns the arccosine of X in radians.

Example: ArcCos(0.5) returns 1.0471975511965976.

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

Returns the hyperbolic arccosine of X.

Example: ArcCosH(1.5) returns 0.9624236501192069.

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

Returns the arccotangent of X in radians.

Example: ArcCot(1) returns 0.7853981633974483.

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

Returns the hyperbolic arccotangent of X.

Example: ArcCotH(1.5) returns 0.8047189562170503.

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

Returns the arccosecant of X in radians.

Example: ArcCsc(2) returns 0.5235987755982989.

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

Returns the hyperbolic arccosecant of X.

Example: ArcCscH(1.5) returns 0.6931471805599453.

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

Returns the arcsecant of X in radians.

Example: ArcSec(2) returns 1.0471975511965976.

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

Returns the hyperbolic arcsecant of X.

Example: ArcSecH(0.5) returns 1.3169578969248166.

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

Returns the arcsine of X in radians.

Example: ArcSin(0.5) returns 0.5235987755982989.

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

Returns the hyperbolic arcsine of X.

Example: ArcSinH(1.5) returns 1.1947632172871094.

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

Returns the arctangent of X in radians.

Example: ArcTan(1) returns 0.7853981633974483.

function Math.ArcTan2(Y, X: Double): Double;

Returns the arctangent of Y/X in radians, considering the quadrant.

Example: ArcTan2(1, 1) returns 0.7853981633974483.

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

Returns the hyperbolic arctangent of X.

Example: ArcTanH(0.5) returns 0.5493061443340549.

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

Returns the cosine of X in radians.

Example: Cos(0) returns 1.0.

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

Returns the hyperbolic cosine of X.

Example: CosH(0) returns 1.0.

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

Returns the cosecant of X in radians.

Example: Cosecant(1) returns 1.1883951057781212.

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

Returns the cotangent of X in radians.

Example: Cot(1) returns 0.6420926159343306.

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

Returns the hyperbolic cotangent of X.

Example: CotH(1) returns 1.3130352854993315.

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

Alias for Cot. Returns the cotangent of X in radians.

Example: Cotan(1) returns 0.6420926159343306.

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

Alias for Cosecant. Returns the cosecant of X in radians.

Example: Csc(1) returns 1.1883951057781212.

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

Returns the hyperbolic cosecant of X.

Example: CscH(1) returns 0.8509181282393216.

function Math.Hypot(X, Y: Double): Double;

Returns the hypotenuse of a right-angled triangle with sides X and Y.

Example: Hypot(3, 4) returns 5.0.

function Math.Pi: Double;

Returns the value of π (pi).

Example: Pi returns 3.141592653589793.

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

Returns the secant of X in radians.

Example: Sec(1) returns 1.8508157176809255.

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

Returns the hyperbolic secant of X.

Example: SecH(1) returns 0.6480542736638853.

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

Alias for Sec. Returns the secant of X in radians.

Example: Secant(1) returns 1.8508157176809255.

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

Returns the sine of X in radians.

Example: Sin(0) returns 0.0.

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

Returns the hyperbolic sine of X.

Example: SinH(1) returns 1.1752011936438014.

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

Returns the tangent of X in radians.

Example: Tan(1) returns 1.5574077246549023.

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

Returns the hyperbolic tangent of X.

Example: TanH(1) returns 0.7615941559557649.

Angle Conversion Functions

function Math.CycleToDeg(Cycles: Double): Double;

Converts cycles to degrees.

Example: CycleToDeg(1) returns 360.0.

function Math.CycleToGrad(Cycles: Double): Double;

Converts cycles to gradians.

Example: CycleToGrad(1) returns 400.0.

function Math.CycleToRad(Cycles: Double): Double;

Converts cycles to radians.

Example: CycleToRad(1) returns 6.283185307179586.

function Math.DegToCycle(Degrees: Double): Double;

Converts degrees to cycles.

Example: DegToCycle(360) returns 1.0.

function Math.DegToGrad(Degrees: Double): Double;

Converts degrees to gradians.

Example: DegToGrad(90) returns 100.0.

function Math.DegToRad(Degrees: Double): Double;

Converts degrees to radians.

Example: DegToRad(180) returns 3.141592653589793.

function Math.GradToCycle(Grads: Double): Double;

Converts gradians to cycles.

Example: GradToCycle(400) returns 1.0.

function Math.GradToDeg(Grads: Double): Double;

Converts gradians to degrees.

Example: GradToDeg(100) returns 90.0.

function Math.GradToRad(Grads: Double): Double;

Converts gradians to radians.

Example: GradToRad(100) returns 1.5707963267948966.

function Math.RadToCycle(Radians: Double): Double;

Converts radians to cycles.

Example: RadToCycle(6.283185307179586) returns 1.0.

function Math.RadToDeg(Radians: Double): Double;

Converts radians to degrees.

Example: RadToDeg(3.141592653589793) returns 180.0.

function Math.RadToGrad(Radians: Double): Double;

Converts radians to gradians.

Example: RadToGrad(1.5707963267948966) returns 100.0.