efg's Delphi Math Functions: Constants

Constant Name	Description	Source(s)
Cbrt2, Cbrt3, Cbrt10, Cbrt100, CbrtPi	cube roots of various values	ESBMaths
e (natural constant)	e = ESBe, e^2 = ESBe2, e^PI = ESBePi, e^(PI/2) = ESBePiOn2, e^(PI/4) = ESBePiOn4	ESBMaths
exp(1.0)	natural constant (e) e = 2.718281828459045	system
Euler's Gamma	Gamma	ESBMaths
High(OrdinalType)	where OrdinalType can be Byte, Word, Integer, LongInt, LongWord, Int64, High(Byte) = 255 High(Word) = 65535 High(LongInt) = 2,147,483,647 High(LongWord) = 4,294,967,295 High(Int64) = 9,223,372,036,854,775,807	ESBMaths
INF	Infinity: See Exploring Numbers, Not-A-Number, and Infinity
Infinity, NegInfinity	CONST Infinity = 1.0 / 0.0; NegInfinity = -1.0 / 0.0; These constants should *only* be used in assignments. Use the IsInfinity function to compare a value with Infinity.	Kylix math
InvSqrt2, InvSqrt3, InvSqrt5, InvSqrtPi, InvCbrtPi	Inverse square roots 2, 3, 5 and SQRT(PI), cube root of PI	ESBMaths
Ln2, Ln10, LnPi	natural logarithms of 2, 10, PI	ESBMaths
Ln2	natural logarithm of 2 // Ln(2) = 0.693147180559945344 FUNCTION Ln2: Extended; ASM FLDLN2 FWAIT END;
Log10Base2	Base 2 logarithm of 10	ESBMaths
Log102	Base-10 logarithm of 2 // Log10(2) = 0.301029995663981184 FUNCTION Log102: Extended; ASM FLDLG2 FWAIT END;
Log2Base10	Base-10 logarithm of 2	ESBMaths
Log210	// Log2(10) = 3.321928094887362560 FUNCTION Log210: Extended; ASM FLDL2T FWAIT END;
Log2E	// Log2(E) = 1.442695040888963520 FUNCTION Log2E: Extended; ASM FLDL2E FWAIT END;
Log3Base10	Base 10 Log of 3	ESBMaths
LogEBase10	Base 10 Log of e	ESBMaths
LogPiBase10	Base 10 Log of PI	ESBMaths
Low(OrdinalType)	where OrdinalType can be Byte, Word, Integer, LongInt, LongWord, Int64, Low(Byte) = 0 Low(Word) = 0 Low(LongInt) = -2,147,483,648 Low(LongWord) = 0 Low(Int64) = -9,223,372,036,854,775,808
MACHEP	1.08420217248550444E-19, machine precision = 2^-63	TPmath1(fmath)
MaxComp	9.223372036854775807E+18	math
MaxDouble	1.7E+308 {$J-} CONST MaxDoubleBits: Int64 = $7FEFFFFFFFFFFFFF; VAR MaxDoubleValue: Double ABSOLUTE MaxDoubleBits; 1.79769313486232E308	math
MaxExtended	1.1E+4932	math
MaxFac	1754, highest argument for factorial	TPmath1(fmath)
MaxGam	1755.455, highest argument for gamma	TPmath1(fmath)
MaxLGm	1.04848146839019521E+4928	TPmath1(fmath)
MaxLog	11356.5234062941439, highest argument for Exp Ln(MaxNum)	TPmath1(fmath)
MaxNormal	{$J-} CONST MaxNormalBits: Int64 = $7FEFFFFFFFFFFFFF; VAR MaxNormal: Double ABSOLUTE MaxNormalBits; 1.7976931348623157E308
MaxNum	1.18973149535723103E+4932 2¹⁶³⁸⁴	TPmath1(fmath)
MaxSingle	3.4E+38	math
MaxSubNormal	{$J-} CONST MaxSubNormalBits: Int64 = $000FFFFFFFFFFFFF; VAR MaxSubNormal: Double ABSOLUTE MaxSubNormalBits; 2.2250738585072009E-308
MinComp	-9.223372036854775807E+18	math
MinDouble	5.0E-324	math
MinExtended	3.4E-4932	math
MinLog	-11355.137111933024, lowest argument for Exp Ln(MinNum)	TPmath1(fmath)
MinNormal	{$J-} CONST MinNormalBits: Int64 = $0010000000000000; VAR MinNormal: Double ABSOLUTE MinNormalBits; 2.2250738585072014E-308
MinNum	3.36210314311209558E-4932 2^-16382	TPmath1(fmath)
MinSingle	1.5E-45	math
MinSubNormal	{$J-} CONST MinSubNormalBits: Int64 = $0000000000000001; VAR MinSubNormal: Double ABSOLUTE MinSubNormalBits; 4.9406564584124654E-324
NaN	NaN = Not a Number: CONST NaN = 0.0 / 0.0; The NaN constant should *only* be used in assignments. Use the IsNan function to compare a value with a NaN. See Exploring Numbers, Not-A-Number, and Infinity	Kylix math
One	// 1.000000000000000000 FUNCTION One: Extended; ASM FLD1 FWAIT END;
OneDegree	One degree in radians: 0.017453292519943295769	ESBMaths
OneMinute	One minute in radians:	ESBMaths
OneRadian	One radian in degrees: 57.295779513082320877	ESBMaths
OneSecond	One second in radians	ESBMaths
pi	pi ~ 3.14159 26535 89793 23846 26433 ... The verifiable FPU value is 3.14159 26535 89793 28 (decimal) or $4000C90FDAA22168C235 (hex). // 3.141592653589793280 // Note: %25.19f gives the same result as %25.2f // Memo1.Lines.Add( Format('%25.18f', [PI]) ); // 3.141592653589793280 FUNCTION InLinePi: Extended; ASM FLDPI FWAIT END; Ray Lischner in a 29 Aug 1999 UseNet post: "...the compiler generates inline code with hardwired integer values to represent the floating point numbers. You get the same results as the FLDPI instruction, but it's faster because you don't have to move data out of the FPU and you don't have to use the FWAIT instruction." Delphi uses "compiler magic" for the pi "function," which is evaluated at compile time and not at run time.	inline
pi constants	ESBPi, InvPi, TwoPi, ThreePi, Pi^2 = Pi2, Pi^e = PiE, Pi/2 = PiOn2, Pi/3 = PiOn3, Pi/4 = Pi/4, 3Pi/2 = ThreePiOn2, 4Pi/3 = FourPiOn3	ESBMaths
Sqrt2, Sqrt3, Sqrt5, Sqrt10, SqrtPi	square roots of various values	ESBMaths
TwoToPower63	9223372036854775808	ESBMaths
Zero	// Zero = 0.000000000000000000 FUNCTION Zero: Extended; ASM FLDZ FWAIT END;