Machine constants

• The MachineConstants class - contains constants for floating-point arithmetic because the CLS System.Single and Double floating-point types do not follow the standard conventions and are useless. machine constants for the Double type:
  • machine precision: Epsilon , SqrtEpsilon CubeRootEpsilon
  • largest possible value: MaxDouble , SqrtMaxDouble, LogMaxDouble
  • smallest Double-precision floating point number that is greater than zero: MinDouble , SqrtMinDouble , LogMinDouble
• A similar set of constants is available for the Single Datatype

Mathematical Constants

• The Constants class contains static fields for many mathematical constants and common expressions involving small integers – if you are doing thousands of iterations, you wouldn't want to calculate OneOverSqrtTwoPi , Sqrt17 or Log17 !!!
• Fundamental constants
  • E - The base for the natural logarithm, e (2.718...).
  • EulersConstant - (0.577...).
  • GoldenRatio - (1.618...).
  • Pi - the ratio between the circumference and the diameter of a circle (3.1415...).
• Expressions involving fundamental constants: TwoPi, PiOverTwo, PiOverFour, LogTwoPi, PiSquared, SqrPi, SqrtTwoPi, OneOverSqrtPi, OneOverSqrtTwoPi
• Square roots of small integers: Sqrt2, Sqrt3, Sqrt5, Sqrt7, Sqrt17
• Logarithms of small integers: Log2, Log3, Log10, Log17, InvLog10

Elementary Functions

• The IterativeAlgorithm<T> class in the Extreme.Mathematics namespace defines many elementary functions that are missing from System.Math.
• Hyperbolic Trig Functions: Cosh, Coth, Csch, Sinh, Sech, Tanh
• Inverse Hyperbolic Trig Functions: Acosh, Acoth, Acsch, Asinh, Asech, Atanh
• Exponential, Logarithmic and Miscellaneous Functions:
  • ExpMinus1 - The exponential function minus one, e^x-1.
  • Hypot - The hypotenuse of a right-angled triangle with specified sides.
  • LambertW - Lambert's W function, the (real) solution W of x=We^W.
  • Log1PlusX - The natural logarithm of 1+x.
  • Pow - A number raised to an integer power.