complex

This module implements complex numbers. Complex numbers are currently implemented as generic on a 64-bit or 32-bit float.

Imports

math

Types

Complex[T] = object
  re*, im*: T                ## A complex number, consisting of a real and an imaginary part.

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Complex64 = Complex[float64]

Alias for a pair of 64-bit floats. Source Edit

Complex32 = Complex[float32]

Alias for a pair of 32-bit floats. Source Edit

Procs

proc complex[T: SomeFloat](re: T; im: T = 0.0): Complex[T]

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proc complex32(re: float32; im: float32 = 0.0): Complex[float32] {...}{.raises: [],
    tags: [].}

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proc complex64(re: float64; im: float64 = 0.0): Complex[float64] {...}{.raises: [],
    tags: [].}

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proc abs[T](z: Complex[T]): T

Returns the distance from (0,0) to z. Source Edit

proc abs2[T](z: Complex[T]): T

Returns the squared distance from (0,0) to z. Source Edit

proc conjugate[T](z: Complex[T]): Complex[T]

Conjugates of complex number z. Source Edit

proc inv[T](z: Complex[T]): Complex[T]

Multiplicatives inverse of complex number z. Source Edit

proc `==`[T](x, y: Complex[T]): bool

Compares two complex numbers x and y for equality. Source Edit

proc `+`[T](x: T; y: Complex[T]): Complex[T]

Adds a real number to a complex number. Source Edit

proc `+`[T](x: Complex[T]; y: T): Complex[T]

Adds a complex number to a real number. Source Edit

proc `+`[T](x, y: Complex[T]): Complex[T]

Adds two complex numbers. Source Edit

proc `-`[T](z: Complex[T]): Complex[T]

Unary minus for complex numbers. Source Edit

proc `-`[T](x: T; y: Complex[T]): Complex[T]

Subtracts a complex number from a real number. Source Edit

proc `-`[T](x: Complex[T]; y: T): Complex[T]

Subtracts a real number from a complex number. Source Edit

proc `-`[T](x, y: Complex[T]): Complex[T]

Subtracts two complex numbers. Source Edit

proc `/`[T](x: Complex[T]; y: T): Complex[T]

Divides complex number x by real number y. Source Edit

proc `/`[T](x: T; y: Complex[T]): Complex[T]

Divides real number x by complex number y. Source Edit

proc `/`[T](x, y: Complex[T]): Complex[T]

Divides x by y. Source Edit

proc `*`[T](x: T; y: Complex[T]): Complex[T]

Multiplies a real number and a complex number. Source Edit

proc `*`[T](x: Complex[T]; y: T): Complex[T]

Multiplies a complex number with a real number. Source Edit

proc `*`[T](x, y: Complex[T]): Complex[T]

Multiplies x with y. Source Edit

proc `+=`[T](x: var Complex[T]; y: Complex[T])

Adds y to x. Source Edit

proc `-=`[T](x: var Complex[T]; y: Complex[T])

Subtracts y from x. Source Edit

proc `*=`[T](x: var Complex[T]; y: Complex[T])

Multiplies y to x. Source Edit

proc `/=`[T](x: var Complex[T]; y: Complex[T])

Divides x by y in place. Source Edit

proc sqrt[T](z: Complex[T]): Complex[T]

Square root for a complex number z. Source Edit

proc exp[T](z: Complex[T]): Complex[T]

e raised to the power z. Source Edit

proc ln[T](z: Complex[T]): Complex[T]

Returns the natural log of z. Source Edit

proc log10[T](z: Complex[T]): Complex[T]

Returns the log base 10 of z. Source Edit

proc log2[T](z: Complex[T]): Complex[T]

Returns the log base 2 of z. Source Edit

proc pow[T](x, y: Complex[T]): Complex[T]

x raised to the power y. Source Edit

proc pow[T](x: Complex[T]; y: T): Complex[T]

Complex number x raised to the power y. Source Edit

proc sin[T](z: Complex[T]): Complex[T]

Returns the sine of z. Source Edit

proc arcsin[T](z: Complex[T]): Complex[T]

Returns the inverse sine of z. Source Edit

proc cos[T](z: Complex[T]): Complex[T]

Returns the cosine of z. Source Edit

proc arccos[T](z: Complex[T]): Complex[T]

Returns the inverse cosine of z. Source Edit

proc tan[T](z: Complex[T]): Complex[T]

Returns the tangent of z. Source Edit

proc arctan[T](z: Complex[T]): Complex[T]

Returns the inverse tangent of z. Source Edit

proc cot[T](z: Complex[T]): Complex[T]

Returns the cotangent of z. Source Edit

proc arccot[T](z: Complex[T]): Complex[T]

Returns the inverse cotangent of z. Source Edit

proc sec[T](z: Complex[T]): Complex[T]

Returns the secant of z. Source Edit

proc arcsec[T](z: Complex[T]): Complex[T]

Returns the inverse secant of z. Source Edit

proc csc[T](z: Complex[T]): Complex[T]

Returns the cosecant of z. Source Edit

proc arccsc[T](z: Complex[T]): Complex[T]

Returns the inverse cosecant of z. Source Edit

proc sinh[T](z: Complex[T]): Complex[T]

Returns the hyperbolic sine of z. Source Edit

proc arcsinh[T](z: Complex[T]): Complex[T]

Returns the inverse hyperbolic sine of z. Source Edit

proc cosh[T](z: Complex[T]): Complex[T]

Returns the hyperbolic cosine of z. Source Edit

proc arccosh[T](z: Complex[T]): Complex[T]

Returns the inverse hyperbolic cosine of z. Source Edit

proc tanh[T](z: Complex[T]): Complex[T]

Returns the hyperbolic tangent of z. Source Edit

proc arctanh[T](z: Complex[T]): Complex[T]

Returns the inverse hyperbolic tangent of z. Source Edit

proc sech[T](z: Complex[T]): Complex[T]

Returns the hyperbolic secant of z. Source Edit

proc arcsech[T](z: Complex[T]): Complex[T]

Returns the inverse hyperbolic secant of z. Source Edit

proc csch[T](z: Complex[T]): Complex[T]

Returns the hyperbolic cosecant of z. Source Edit

proc arccsch[T](z: Complex[T]): Complex[T]

Returns the inverse hyperbolic cosecant of z. Source Edit

proc coth[T](z: Complex[T]): Complex[T]

Returns the hyperbolic cotangent of z. Source Edit

proc arccoth[T](z: Complex[T]): Complex[T]

Returns the inverse hyperbolic cotangent of z. Source Edit

proc phase[T](z: Complex[T]): T

Returns the phase of z. Source Edit

proc polar[T](z: Complex[T]): tuple[r, phi: T]

Returns z in polar coordinates. Source Edit

proc rect[T](r, phi: T): Complex[T]

Returns the complex number with polar coordinates r and phi.

result.re = r * cos(phi)
result.im = r * sin(phi)

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proc `$`(z: Complex): string

Returns z's string representation as "(re, im)". Source Edit

Templates

template im(arg: typedesc[float32]): Complex32

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template im(arg: typedesc[float64]): Complex64

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template im(arg: float32): Complex32

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template im(arg: float64): Complex64

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