# Mathematical Routines

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

## Constants used in math routines

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

Routine Description

Represents positive infinity.

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.

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.

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.

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 Object Pascal:

Routine Description

Returns an absolute value.

Rounds variables up toward positive infinity.

Returns the result of an integer division, including the remainder.

Returns the exponential of X.

Rounds variables toward negative infinity.

Separates the Mantissa and Exponent of X.

Returns the integer part of a real number.

Calculates the integral power of a base value.

Indicates when a variable or expression represents an infinite value.

Indicates when a variable or expression does not evaluate to a numeric value.

Indicates when a floating-point variable or expression evaluates to zero, or very close to zero.

Calculates X times (2 to the power of P).

Returns the natural log of (X+1).

Calculates log base 10.

Calculates log base 2.

Calculates the log of X for a specified base.

Returns the greater of two numeric values (Object Pascal only).

Returns the largest signed value in an integer array.

Returns the largest signed value in an array.

Returns the average of all values in an array.

Returns the lesser of 2 numeric values (Object Pascal only).

Returns the smallest signed value in an integer array.

Returns the smallest signed value in an array.

Returns true if the argument is an odd number.

Raises Base to any power.

Returns the value of X rounded to the nearest whole number.

Rounds a floating-point value to a specified digit or power of 10 using "Banker's rounding".

Indicates whether a numeric value is positive, negative, or zero.

Rounds a floating-point value to a specified digit or power of 10 using asymmetric arithmetic rounding.

Returns the square of a number.

Returns the square root of X.

Returns the sum of the elements in an array.

Returns the sum of the elements in an integer array.

Returns the sum of the squared values from a data array.

Returns the sum of the values and the sum of the squared values in an array.

Truncates a real number to an integer.

## Trigonometric routines

The following table lists the trigonometric routines found in Object Pascal:

Routine Description

Calculates the inverse cosine of a given number.

Calculates the inverse hyperbolic cosine of a given number.

Calculates the inverse cotangent of a given number.

Calculates the inverse hyperbolic cotangent of a given number.

Calculates the inverse cosecant of a given number.

Calculates the inverse hyperbolic cosecant of a given number.

Calculates the inverse secant of a given number.

Calculates the inverse hyperbolic secant of a given number.

Calculates the inverse sine of a given number.

Calculates the inverse hyperbolic sine of a given number.

Calculates the arc tangent of a given number.

Calculates the arc tangent angle and quadrant of a given number.

Calculates the inverse hyperbolic tangent of a given number.

Returns the cosecant of an angle.

Calculates the hyperbolic cosine of an angle.

Calculates the cotangent of an angle.

Calculates the cotangent of an angle.

Calculates the hyperbolic cotangent of an angle.

Returns the cosecant of an angle.

Returns the hyperbolic cosecant of an angle.

Converts an angle measurement from cycles to degrees.

Converts an angle measurement from cycles to grads.

Converts an angle measurement from cycles to radians.

Returns the value of a degree measurement expressed in cycles.

Returns the value of a degree measurement expressed in grads.

Returns the value of a degree measurement expressed in radians.

Calculates the length of the hypotenuse.

Returns 3.1415926535897932385.

Calculates the secant of an angle.

Calculates the secant of an angle.

Calculates the hyperbolic secant of an angle.

Returns the sine of the angle in radians.

Returns the sine and cosine of an angle.

Returns the hyperbolic sine of an angle.

Returns the tangent of X.

Returns the hyperbolic tangent of X.

Truncates a real number to an integer.