Math unit

This document describes the math unit. The math unit was initially written by Florian Klaempfl. It provides mathematical functions which aren't covered by the system unit.

This chapter starts out with a definition of all types and constants that are defined, after which an overview is presented of the available functions, grouped by category, and the last part contains a complete explanation of each function.

The following things must be taken into account when using this unit:

1. This unit is compiled in Object Pascal mode so all integers are 32 bit.
2. Some overloaded functions exist for data arrays of integers and floats. When using the address operator (@) to pass an array of data to such a function, make sure the address is typecasted to the right type, or turn on the 'typed address operator' feature. failing to do so, will cause the compiler not be able to decide which function you want to call.

Classes and records

EInvalidArgument

class

Exception raised when invalid arguments are passed to a function.

Procedures and functions

ArcCos	function	Return inverse cosine.
ArcCosH	function	Return inverse hyperbolic cosine.
ArcCot	function
ArcCotH	function
ArcCsc	function
ArcCscH	function
ArCosH	function	Return inverse hyperbolic cosine.
ArcSec	function
ArcSecH	function
ArcSin	function	Return inverse sine.
ArcSinH	function	Return inverse hyperbolic sine.
ArcTan2	function	Return arctangent of (y/x).
ArcTanH	function	Return inverse hyperbolic tangent.
ArSinH	function	Return inverse hyperbolic sine.
ArTanH	function	Return inverse hyperbolic tangent.
Ceil	function	Return the lowest integer number greater than or equal to argument.
Ceil64	function	Round to the nearest bigger int64 value.
ClearExceptions	procedure	Clear Floating Point Unit exceptions.
CompareValue	function	Compare 2 values.
Cosecant	function	Calculate cosecant.
cosh	function	Return hyperbolic cosine.
Cot	function	Alias for Cotan.
Cotan	function	Return cotangent.
CotH	function
Csc	function	Alias for cosecant.
CscH	function
CycleToDeg	function
CycleToGrad	function
CycleToRad	function	Convert cycle angle to radians angle.
DegNormalize	function	Normalize an angle measured in degrees.
DegToCycle	function
DegToGrad	function	Convert degree angle to grads angle.
DegToRad	function	Convert degree angle to radians angle.
DivMod	procedure	Return DIV and MOD of arguments.
EnsureRange	function	Change value so it fits in a specified range.
ExpM1	function
Floor	function	Return the largest integer smaller than or equal to argument.
Floor64	function	Round to the nearest smaller int64 value.
FMod	function	Floatin point modulo.
Frexp	procedure	Return mantissa and exponent.
FutureValue	function	Calculate the future value of an investment.
GetExceptionMask	function	Get the Floating Point Unit exception mask.
GetPrecisionMode	function	Return the Floating Point Unit precision mode.
GetRoundMode	function	Return the Floating Point Unit rounding mode.
GradToCycle	function
GradToDeg	function	Convert grads angle to degrees angle.
GradToRad	function	Convert grads angle to radians angle.
Hypot	function	Return hypotenuse of triangle.
IfThen	function	Return one of two values, depending on a boolean condition.
InRange	function	Check whether value is in range.
InterestRate	function	Calculate the interest rate value of an investment.
IntPower	function	Return integer power.
IsInfinite	function	Check whether value is infinite.
IsNan	function	Check whether value is Not a Number.
IsZero	function	Check whether value is zero.
Ldexp	function	Return (2 to the power p) times x.
LnXP1	function	Return natural logarithm of 1+X.
Log10	function	Return 10-Based logarithm.
Log2	function	Return 2-based logarithm.
LogN	function	Return N-based logarithm.
Max	function	Returns the largest of two values.
MaxIntValue	function	Return largest element in integer array.
MaxValue	function	Return largest value in array.
Mean	function	Return mean value of array.
MeanAndStdDev	procedure	Return mean and standard deviation of array.
Min	function	Return smallest of two values.
MinIntValue	function	Return smallest value in integer array.
MinValue	function	Return smallest value in array.
modulus(Float,Float):Float	operator	Floating point modulo.
MomentSkewKurtosis	procedure	Return 4 first moments of distribution.
Norm	function	Return Euclidean norm.
NumberOfPeriods	function	Calculate the number of periods for an investment.
Payment	function	Calculate the payment for an investment.
PopnStdDev	function	Return Population standard deviation.
PopnVariance	function	Return population variance.
Power	function	Return real power.
power(Float,Float):Float	operator	Raise base to the power exponent.
power(Int64,Int64):Int64	operator	Raise base to the power exponent.
PresentValue	function	Calculate the present value given the future value of an investment.
RadToCycle	function	Convert radians angle to cycle angle.
RadToDeg	function	Convert radians angle to degrees angle.
RadToGrad	function	Convert radians angle to grads angle.
RandG	function	Return gaussian distributed random number.
RandomFrom	function	Return a random element of an array of numbers.
RandomRange	function	Return a random number in a range.
RoundTo	function	Round to the specified number of digits.
SameValue	function	Check whether 2 float values are the same.
Sec	function	Alias for secant.
Secant	function	Calculate secant.
SecH	function
SetExceptionMask	function	Set the Floating Point Unit exception mask.
SetPrecisionMode	function	Set the Floating Point Unit precision mode.
SetRoundMode	function	Set the Floating Point Unit rounding mode.
Sign	function	Return sign of argument.
SimpleRoundTo	function	Round to the specified number of digits (rounding up if needed).
SinCos	procedure	Return sine and cosine of argument.
sinh	function	Return hyperbolic sine.
StdDev	function	Return standard deviation of data.
Sum	function	Return sum of values.
SumInt	function	Return the sum of an array of integers.
SumOfSquares	function	Return sum of squares of values.
SumsAndSquares	procedure	Return sum and sum of squares of values.
Tan	function	Return tangent.
tanh	function	Return hyperbolic tangent.
TotalVariance	function	Return total variance of values.
Variance	function	Return variance of values.

Types

Float	type	Float type used in all calls.
PFloat	type	Pointer to type.
PInteger	type	Pointer to integer type.
TFPUException	type	Type describing Floating Point processor exceptions.
TFPUExceptionMask	type	Type to set the Floating Point Unit exception mask.
TFPUPrecisionMode	type	Type describing the default precision for the Floating Point processor.
TFPURoundingMode	type	Type describing the rounding mode for the Floating Point processor.
TPaymentTime	enumeration	Type used in financial (interest) calculations.
TRoundToRange	type	Range with valid range of digits in RoundTo.
TValueRelationship	type	Type to describe relational order between values.
TValueSign	type	Type indicating sign of a value.

Constants

EqualsValue	constant	Values are the same.
GreaterThanValue	constant	First values is greater than second value.
Infinity	constant	Value is infinity.
LessThanValue	constant	First value is less than second value.
MaxFloat	constant	Maximum value of float type.
MinFloat	constant	Minimum value (closest to zero) of float type.
NaN	constant	Value is Not a Number.
NegativeValue	constant	Value is negative.
NegInfinity	constant	Value is negative (minus) infinity.
PositiveValue	constant	Value is positive.
ZeroValue	constant	Value is zero.

Topics

AngleConversionRoutines	topic	Angle unit conversion.
CashFlowFunctions	topic	Cash flow functions.
ExpLogRoutines	topic	Exponential and logarithmic functions.
GeometricalRoutines	topic	Geometrical functions.
HyperbolicRoutines	topic	Hyperbolic functions.
MinMaxRoutines	topic	Min/max determination.
NumberConversionRoutines	topic	Number converting.
StatisticalRoutines	topic	Statistical functions.
TrigoniometricRoutines	topic	Trigonometric functions.

Uses

• sysutils
• Types