System.Math

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Defines classes, routines, types, variables, and constants related to mathematical operations, vectors and matrixes.

Package	rtl.bpl

Units

System.Math	Defines classes, routines, types, variables, and constants related to mathematical operations, vectors and matrixes.
System.Math.Vectors	Defines classes, routines, types and variables for using vectors and matrixes.

Classes

EInvalidArgument

EInvalidArgument is the exception class for out-of-range parameters in specialized math and accounting functions.

Routines

ArcCos	Calculates the inverse cosine of a given number.
ArcCosh	Calculates the inverse hyperbolic cosine of a given number.
ArcCot	Calculates the inverse cotangent of a given number.
ArcCotH	Calculates the inverse hyperbolic cotangent of a given number.
ArcCsc	Calculates the inverse cosecant of a given number.
ArcCscH	Calculates the inverse hyperbolic cosecant of a given number.
ArcSec	Calculates the inverse secant of a given number.
ArcSecH	Calculates the inverse hyperbolic secant of a given number.
ArcSin	Calculates the inverse sine of a given number.
ArcSinh	Calculates the inverse hyperbolic sine of a given number.
ArcTan2	Calculates the arctangent angle and quadrant of a given number.
ArcTanh	Calculates the inverse hyperbolic tangent of a given number.
Ceil	Rounds variables up toward positive infinity.
ClearExceptions	Clears floating-point number's cumulative exception flags and raises cumulative floating-point number's exceptions if RaisePending is True.
ClearFPUExceptions	Clears all exception bits in the FPU status word.
ClearSSEExceptions	Clears all exception bits in the SSE’s MXCSR register.
CompareValue	Returns the relationship between two numeric values.
Cosecant	Returns the cosecant of an angle.
Cosh	Calculates the hyperbolic cosine of an angle.
Cot	Calculates the cotangent of an angle.
Cotan	Calculates the cotangent of an angle.
CotH	Calculates the hyperbolic cotangent of an angle.
Csc	Returns the cosecant of an angle.
CscH	Returns the hyperbolic cosecant of an angle.
CycleToDeg	Converts an angle measurement from cycles to degrees.
CycleToGrad	Converts an angle measurement from cycles to grads.
CycleToRad	Converts an angle measurement from cycles to radians.
DegNormalize
DegToCycle	Returns the value of a degree measurement expressed in cycles.
DegToGrad	Returns the value of a degree measurement expressed in grads.
DegToRad	Returns the value of a degree measurement expressed in radians.
DivMod	Returns the result of an integer division, including the remainder.
DoubleDecliningBalance	Calculates the depreciation of an asset using the double-declining balance method.
EnsureRange	Returns the closest value to a specified value within a specified range.
Floor	Rounds variables toward negative infinity.
FMod	Returns the remainder of ANumerator / ADenominator (like mod in integers) with the same sign as ANumerator.
Frexp	Separates the Mantissa and Exponent of X
FutureValue	Calculates the future value of an investment.
GetExceptionMask	Returns the current floating-point exception mask.
GetExceptions	Retrieves the set of active floating-point exceptions.
GetFPUExceptionMask	Returns the set of masked FPU floating-point arithmetic exceptions.
GetFPURoundMode	Gets the Intel FPU's rounding mode.
GetPrecisionMode	Returns the Intel FPU precision control mode.
GetRoundMode	Returns the current floating-point rounding mode.
GetSSEExceptionMask	Returns the set of masked Intel SSE arithmetic exceptions.
GetSSERoundMode	Gets the Intel SSE's rounding mode.
GradToCycle	Converts grad measurements to cycles.
GradToDeg	Converts grad measurements to degrees.
GradToRad	Converts grad measurements to radians.
Hypot	Calculates the length of the hypotenuse.
IfThen	Conditionally returns one of two specified values.
InRange	Indicates whether a value falls within a specified range.
InterestPayment	Calculates the interest portion of a loan payment.
InterestRate	Returns the interest rate required to increase PresentValue to FutureValue.
InternalRateOfReturn	Calculates the internal rate of return for an investment.
IntPower	Calculates the integral power of a base value.
IsInfinite	Indicates when a variable or expression represents an infinite value.
IsNan	Indicates when a variable or expression does not evaluate to a numeric value.
IsZero	Indicates when a floating-point variable or expression evaluates to zero, or very close to zero.
Ldexp	Calculates X times (2 to the power of P).
LnXP1	Returns the natural log of (X+1)
Log10	Calculates log base 10.
Log2	Calculates log base 2.
LogN	Calculates the log of X for a specified base.
Max	Returns the greater of two numeric values.
MaxIntValue	Returns the largest signed value in an integer array.
MaxValue	Returns the largest signed value in an array.
Mean	Returns the average of all values in an array.
MeanAndStdDev	Calculates the mean and standard deviation of array elements.
Min	Returns the lesser of two numeric values.
MinIntValue	Returns the smallest signed value in an integer array.
MinValue	Returns smallest signed value in an array.
MomentSkewKurtosis	Calculates the mean, variance, skew, and kurtosis.
NetPresentValue	Calculates the current value from an array of estimated cash flow values.
Norm	Returns the Euclidean 'L-2' norm.
NumberOfPeriods	Returns the number of payment periods for an investment.
Payment	Calculates a fully amortized payment.
PeriodPayment	Returns the principal amount from a full payment.
Poly	Evaluates a uniform polynomial of one variable at the value X.
PopnStdDev	Calculates the population standard deviation.
PopnVariance	Calculates the population variance.
Power	Raises Base to any Exponent power.
PresentValue	Calculates the present value of an investment.
RadToCycle	Converts radians to cycles.
RadToDeg	Converts radians to degrees.
RadToGrad	Converts radians to grads.
RaiseExceptions	Raises cumulative floating-point number's exceptions.
RandG	Generates random numbers with Gaussian distribution.
RandomFrom	Returns a randomly selected element from an array.
RandomRange	Returns a random integer from a specified range.
RoundTo	Rounds a floating-point value to a specified digit or power of ten using "Banker's rounding".
SameValue	Indicates whether two floating-point values are (approximately) equal.
Sec	Calculates the secant of an angle.
Secant	Calculates the secant of an angle.
SecH	Calculates the hyperbolic secant of an angle.
SetExceptionMask	Sets the exception mask for the floating-point exceptions.
SetExceptions	Sets the floating-point exceptions specified in Exceptions.
SetFPUExceptionMask	Sets the floating-point exception masks TFPUExceptionMask in the Intel FPU control word.
SetFPURoundMode	Sets the Intel X87 FPU's rounding mode.
SetPrecisionMode	Sets the Intel FPU precision control mode.
SetRoundMode	Sets the rounding mode for floating-point calculations.
SetSSEExceptionMask	Sets the floating-point exception masks TSSEExceptionMask in the Intel SSE’s MXCSR register.
SetSSERoundMode	Sets the Intel SSE's rounding mode.
Sign	Indicates whether a numeric value is positive, negative, or zero.
SimpleRoundTo	Rounds a floating-point value to a specified digit or power of ten using symmetric arithmetic rounding.
SinCos	Returns sine and cosine of an angle.
Sinh	Returns the hyperbolic sine of an angle.
SLNDepreciation	Returns the straight-line depreciation allowance of an asset.
StdDev	Returns the sample standard deviation for elements in an array.
Sum	Returns the sum of the elements in an array.
SumInt	Returns the sum of the elements in an integer array.
SumOfSquares	Returns the sum of the squared values from a data array.
SumsAndSquares	Returns the sum of the values and the sum of the squared values in an array.
SYDDepreciation	Calculates depreciation for an asset.
Tan	Returns the tangent of X.
Tanh	Returns the hyperbolic tangent of X.
TotalVariance	Returns the statistical variance from an array of values.
Variance	Calculates statistical sample variance from an array of data.

Types

TArithmeticException	Enumeration that holds values representing floating-point exceptions.
TArithmeticExceptionMask	Specifies a set of masked floating-point exceptions.
TArithmeticExceptions	Specifies a set of handled floating-point exceptions.
TFPUException	Enumeration that holds values representing FPU floating-point exceptions.
TFPUExceptionMask	Specifies a set of masked FPU floating-point exceptions.
TFPUPrecisionMode	TFPUPrecisionMode defines how the FPU handles precision.
TFPURoundingMode	Enumerates the FPU's floating-point rounding modes.
TPaymentTime	TPaymentTime is an enumerated type used as a parameter in financial functions.
TRoundingMode	Enumerates the floating-point rounding modes.
TRoundToEXRangeExtended	Represents the permitted range for a power of ten used by System.Math.RoundTo.
TRoundToRange	TRoundToRange defines the RoundTo rounding limits.
TSSEException	Enumeration that holds values representing SSE floating-point exceptions.
TSSEExceptionMask	Specifies a set of masked SSE floating-point exceptions.
TSSERoundingMode	Enumerates the SSE's floating-point rounding modes.
TValueSign	TValueSign defines the Sign returned value.

Variables

Infinity	Infinity represents positive infinity.
MaxComp	MaxComp represents the maximum absolute value for a Comp variable.
MinComp	MinComp represents the minimum value for a Comp variable.
NaN	NaN represents a value that cannot be represented as a valid number.
NegInfinity	NegInfinity represents negative infinity.

Constants

DefaultExceptionFlags	DefaultExceptionFlags: Set = [exInvalidOp,exZeroDivide..exOverflow];
exAllArithmeticExceptions	exAllArithmeticExceptions: Set = [exInvalidOp..exPrecision];
MaxDouble	MaxDouble: Extended = 1.798e+308;
MaxExtended	MaxExtended: Extended = 1.19e+4932;
MaxExtended80	MaxExtended80: Extended = 1.19e+4932;
MaxSingle	MaxSingle: Extended = 3.403e+38;
MinDouble	MinDouble: Extended = 2.225e-308;
MinDoubleDenormal	MinDoubleDenormal: Extended = 4.941e-324;
MinExtended	MinExtended: Extended = 3.362e-4932;
MinExtended80	MinExtended80: Extended = 3.362e-4932;
MinExtended80Denormal	MinExtended80Denormal: Extended = 3.645e-4951;
MinExtendedDenormal	MinExtendedDenormal: Extended = 3.645e-4951;
MinSingle	MinSingle: Extended = 1.175e-38;
MinSingleDenormal	MinSingleDenormal: Extended = 1.401e-45;
NegativeValue	NegativeValue: Integer = $FFFFFFFF;
PositiveValue	PositiveValue: Integer = 1;
seAESNI	seAESNI: Integer = $80;
sePCLMULQDQ	sePCLMULQDQ: Integer = $100;
sePOPCNT	sePOPCNT: Integer = $40;
seSSE	seSSE: Integer = 1;
seSSE2	seSSE2: Integer = 2;
seSSE3	seSSE3: Integer = 4;
seSSE41	seSSE41: Integer = $10;
seSSE42	seSSE42: Integer = $20;
seSSSE3	seSSSE3: Integer = 8;
ZeroValue	ZeroValue: Integer = 0;