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Josh Reuben

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, ex-1.
    • Hypot - The hypotenuse of a right-angled triangle with specified sides.
    • LambertW - Lambert's W function, the (real) solution W of x=WeW.
    • Log1PlusX - The natural logarithm of 1+x.
    • Pow - A number raised to an integer power.
Posted on Thursday, January 6, 2011 7:57 PM Numerical Computing | Back to top

Comments on this post: Extreme Optimization –Mathematical Constants and Basic Functions

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New information provides useful idea that we can use in most of our projects. - Antiquities of California
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