Mathematical Routines

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This topic lists all mathematical routines used in the Delphi runtime library.

Constants used in math routines

The following table lists all the constants used in mathematical routines found in Delphi:

Routine	Description
System.Math.Infinity	Represents positive infinity.
System.Math.MaxComp	Defines the maximum absolute value for a Comp variable.
System.Math.MaxDouble	Defines the maximum absolute value for a Double variable.
System.Math.MaxExtended	Defines the maximum absolute value for an Extended variable.
System.Math.MaxSingle	Defines the maximum absolute value for a Single variable.
System.Math.MinComp	Defines the smallest absolute value for a Comp variable.
System.Math.MinDouble	Defines the smallest absolute value for a Double variable.
System.Math.MinExtended	Defines the smallest absolute value for an Extended variable.
System.Math.MinSingle	Defines the smallest absolute value for a Single variable.
System.Math.NaN	Represents a value that cannot be represented as a valid number.
Math.NegativeValue (see Math Constants)	Defines a negative number that results from using Sign.
System.Math.NegInfinity	Represents negative infinity.
Math.PositiveValue (see Math Constants)	Defines a positive number that results from using Sign.
Math.ZeroValue (see Math Constants)	Defines a zero-value number that results from using Sign.

Arithmetic routines

The following table lists the arithmetic routines found in Delphi:

Routine	Description
System.Abs	Returns an absolute value.
System.Math.Ceil	Rounds variables up toward positive infinity.
System.Math.DivMod	Returns the result of an integer division, including the remainder.
System.Exp	Returns the exponential of X.
System.Math.Floor	Rounds variables toward negative infinity.
System.Math.Frexp	Separates the Mantissa and Exponent of X.
System.Int	Returns the integer part of a real number.
System.Math.IntPower	Calculates the integral power of a base value.
System.Math.IsInfinite	Indicates when a variable or expression represents an infinite value.
System.Math.IsNan	Indicates when a variable or expression does not evaluate to a numeric value.
System.Math.IsZero	Indicates when a floating-point variable or expression evaluates to zero, or very close to zero.
System.Math.Ldexp	Calculates X times (2 to the power of P).
System.Math.LnXP1	Returns the natural log of (X+1).
System.Math.Log10	Calculates log base 10.
System.Math.Log2	Calculates log base 2.
System.Math.LogN	Calculates the log of X for a specified base.
System.Math.Max	Returns the greater of two numeric values (Delphi only).
System.Math.MaxIntValue	Returns the largest signed value in an integer array.
System.Math.MaxValue	Returns the largest signed value in an array.
System.Math.Mean	Returns the average of all values in an array.
System.Math.Min	Returns the lesser of 2 numeric values (Delphi only).
System.Math.MinIntValue	Returns the smallest signed value in an integer array.
System.Math.MinValue	Returns the smallest signed value in an array.
System.Odd	Returns true if the argument is an odd number.
System.Math.Power	Raises Base to any power.
System.Round	Returns the value of X rounded to the nearest whole number.
System.Math.RoundTo	Rounds a floating-point value to a specified digit or power of 10 using "Banker's rounding".
System.Math.Sign	Indicates whether a numeric value is positive, negative, or zero.
System.Math.SimpleRoundTo	Rounds a floating-point value to a specified digit or power of 10 using asymmetric arithmetic rounding.
System.Sqr	Returns the square of a number.
System.Sqrt	Returns the square root of X.
System.Math.Sum	Returns the sum of the elements in an array.
System.Math.SumInt	Returns the sum of the elements in an integer array.
System.Math.SumOfSquares	Returns the sum of the squared values from a data array.
System.Math.SumsAndSquares	Returns the sum of the values and the sum of the squared values in an array.
System.Trunc	Truncates a real number to an integer.

Trigonometric routines

The following table lists the trigonometric routines found in Delphi:

Routine	Description
System.Math.ArcCos	Calculates the inverse cosine of a given number.
System.Math.ArcCosh	Calculates the inverse hyperbolic cosine of a given number.
System.Math.ArcCot	Calculates the inverse cotangent of a given number.
System.Math.ArcCotH	Calculates the inverse hyperbolic cotangent of a given number.
System.Math.ArcCsc	Calculates the inverse cosecant of a given number.
System.Math.ArcCscH	Calculates the inverse hyperbolic cosecant of a given number.
System.Math.ArcSec	Calculates the inverse secant of a given number.
System.Math.ArcSecH	Calculates the inverse hyperbolic secant of a given number.
System.Math.ArcSin	Calculates the inverse sine of a given number.
System.Math.ArcSinh	Calculates the inverse hyperbolic sine of a given number.
System.ArcTan	Calculates the arc tangent of a given number.
System.Math.ArcTan2	Calculates the arc tangent angle and quadrant of a given number.
System.Math.ArcTanh	Calculates the inverse hyperbolic tangent of a given number.
System.Math.Cosecant	Returns the cosecant of an angle.
System.Math.Cosh	Calculates the hyperbolic cosine of an angle.
System.Math.Cot	Calculates the cotangent of an angle.
System.Math.Cotan	Calculates the cotangent of an angle.
System.Math.CotH	Calculates the hyperbolic cotangent of an angle.
System.Math.Csc	Returns the cosecant of an angle.
System.Math.CscH	Returns the hyperbolic cosecant of an angle.
System.Math.CycleToDeg	Converts an angle measurement from cycles to degrees.
System.Math.CycleToGrad	Converts an angle measurement from cycles to grads.
System.Math.CycleToRad	Converts an angle measurement from cycles to radians.
System.Math.DegToCycle	Returns the value of a degree measurement expressed in cycles.
System.Math.DegToGrad	Returns the value of a degree measurement expressed in grads.
System.Math.DegToRad	Returns the value of a degree measurement expressed in radians.
System.Math.GradToCycle	Converts grad measurements to cycles.
System.Math.GradToDeg	Converts grad measurements to degrees.
System.Math.GradToRad	Converts grad measurements to radians.
System.Math.Hypot	Calculates the length of the hypotenuse.
System.Pi	Returns 3.1415926535897932385.
System.Math.RadToCycle	Converts radians to cycles.
System.Math.RadToDeg	Converts radians to degrees.
System.Math.RadToGrad	Converts radians to grads.
System.Math.Sec	Calculates the secant of an angle.
System.Math.Secant	Calculates the secant of an angle.
System.Math.SecH	Calculates the hyperbolic secant of an angle.
System.Sin	Returns the sine of the angle in radians.
System.Math.SinCos	Returns the sine and cosine of an angle.
System.Math.Sinh	Returns the hyperbolic sine of an angle.
System.Math.Tan	Returns the tangent of X.
System.Math.Tanh	Returns the hyperbolic tangent of X.
System.Trunc	Truncates a real number to an integer.

See Also

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