# Module math

Constructive mathematics is naturally typed. -- Simon Thompson

Basic math routines for Nimrod. This module is available for the ECMAScript target.

# Types

    TFloatClass* = enum
      fcNormal,                   ## value is an ordinary nonzero floating point value
      fcSubnormal,                ## value is a subnormal (a very small) floating point value
      fcZero,                     ## value is zero
      fcNegZero,                  ## value is the negative zero
      fcNan,                      ## value is Not-A-Number (NAN)
      fcInf,                      ## value is positive infinity
      fcNegInf                    ## value is negative infinity

  describes the class a floating point value belongs to. This is the type that is returned by classify.

    TRunningStat* {.pure, final.} = object
      n*: int                     ## number of pushed data
      sum*, min*, max*, mean*: float ## self-explaining
      oldM, oldS, newS: float

  an accumulator for statistical data

# Consts

    PI* = 3.1415926535897936e+00

  the circle constant PI (Ludolph's number)

    E* = 2.7182818284590455e+00

  Euler's number

    MaxFloat64Precision* = 16

  maximum number of meaningful digits after the decimal point for Nimrod's `float64` type.

    MaxFloat32Precision* = 8

  maximum number of meaningful digits after the decimal point for Nimrod's `float32` type.

    MaxFloatPrecision* = MaxFloat64Precision

  maximum number of meaningful digits after the decimal point for Nimrod's `float` type.

# Procs

    proc classify*(x: float): TFloatClass

  classifies a floating point value. Returns x's class as specified by TFloatClass.

    proc binom*(n, k: int): int {.noSideEffect.}

  computes the binomial coefficient

    proc fac*(n: int): int {.noSideEffect.}

  computes the faculty function

    proc isPowerOfTwo*(x: int): bool {.noSideEffect.}

  returns true, if x is a power of two, false otherwise. Negative numbers are not a power of two.

    proc nextPowerOfTwo*(x: int): int

  returns the nearest power of two, so that result**2 >= x > (result-1)**2.

    proc countBits32*(n: int32): int {.noSideEffect.}

  counts the set bits in n.

    proc sum*[T](x: openarray[T]): T {.noSideEffect.}

  computes the sum of the elements in x. If x is empty, 0 is returned.

    proc mean*(x: openarray[float]): float {.noSideEffect.}

  computes the mean of the elements in x. If x is empty, NaN is returned.

    proc variance*(x: openarray[float]): float {.noSideEffect.}

  computes the variance of the elements in x. If x is empty, NaN is returned.

    proc random*(max: int): int

  returns a random number in the range 0..max-1. The sequence of random number is always the same, unless randomize is called which initializes the random number generator with a "random" number, i.e. a tickcount.

    proc random*(max: float): float

  returns a random number in the range 0..<max. The sequence of random number is always the same, unless randomize is called which initializes the random number generator with a "random" number, i.e. a tickcount. This is currently not supported for windows.

    proc randomize*()

  initializes the random number generator with a "random" number, i.e. a tickcount. Note: Does nothing for the ECMAScript target, as ECMAScript does not support this.

    proc sqrt*(x: float): float {.importc: "sqrt", header: "<math.h>".}

  computes the square root of x.

    proc ln*(x: float): float {.importc: "log", header: "<math.h>".}

  computes ln(x).

    proc log10*(x: float): float {.importc: "log10", header: "<math.h>".}

    proc log2*(x: float): float

    proc exp*(x: float): float {.importc: "exp", header: "<math.h>".}

  computes e**x.

    proc frexp*(x: float; exponent: var int): float {.importc: "frexp",
        header: "<math.h>".}

  Split a number into mantissa and exponent. frexp calculates the mantissa m (a float greater than or equal to 0.5 and less than 1) and the integer value n such that x (the original float value) equals m * 2**n. frexp stores n in exponent and returns m.

    proc round*(x: float): int {.importc: "lrint", nodecl.}

  converts a float to an int by rounding.

    proc arccos*(x: float): float {.importc: "acos", header: "<math.h>".}

    proc arcsin*(x: float): float {.importc: "asin", header: "<math.h>".}

    proc arctan*(x: float): float {.importc: "atan", header: "<math.h>".}

    proc arctan2*(y, x: float): float {.importc: "atan2", header: "<math.h>".}

  Calculate the arc tangent of y / x. atan2 returns the arc tangent of y / x; it produces correct results even when the resulting angle is near pi/2 or -pi/2 (x near 0).

    proc cos*(x: float): float {.importc: "cos", header: "<math.h>".}

    proc cosh*(x: float): float {.importc: "cosh", header: "<math.h>".}

    proc hypot*(x, y: float): float {.importc: "hypot", header: "<math.h>".}

  same as `sqrt(x*x + y*y)`.

    proc sinh*(x: float): float {.importc: "sinh", header: "<math.h>".}

    proc sin*(x: float): float {.importc: "sin", header: "<math.h>".}

    proc tan*(x: float): float {.importc: "tan", header: "<math.h>".}

    proc tanh*(x: float): float {.importc: "tanh", header: "<math.h>".}

    proc pow*(x, y: float): float {.importc: "pow", header: "<math.h>".}

  computes x to power raised of y.

    proc trunc*(x: float): float {.importc: "trunc", nodecl.}

    proc floor*(x: float): float {.importc: "floor", nodecl.}

    proc ceil*(x: float): float {.importc: "ceil", nodecl.}

    proc fmod*(x, y: float): float {.importc: "fmod", header: "<math.h>".}

    proc `mod`*(x, y: float): float

    proc random*[T](x: TSlice[T]): T

    proc push*(s: var TRunningStat; x: float)

  pushes a value x for processing

    proc push*(s: var TRunningStat; x: int)

  pushes a value x for processing. x is simply converted to `float` and the other push operation is called.

    proc variance*(s: TRunningStat): float

  computes the current variance of s

    proc standardDeviation*(s: TRunningStat): float

  computes the current standard deviation of s

Generated: 2012-09-23 21:47:54 UTC