Module complex

This module implements complex numbers.

Imports

math

Types

Complex = tuple[re, im: float]

a complex number, consisting of a real and an imaginary part

Consts

im: Complex = (re: 0.0, im: 1.0)

The imaginary unit. √-1.

Procs

proc toComplex(x: SomeInteger): Complex

Convert some integer x to a complex number.

proc `==`(x, y: Complex): bool {...}{.raises: [], tags: [].}

Compare two complex numbers x and y for equality.

proc `=~`(x, y: Complex): bool {...}{.raises: [], tags: [].}

Compare two complex numbers x and y approximately.

proc `+`(x, y: Complex): Complex {...}{.raises: [], tags: [].}

Add two complex numbers.

proc `+`(x: Complex; y: float): Complex {...}{.raises: [], tags: [].}

Add complex x to float y.

proc `+`(x: float; y: Complex): Complex {...}{.raises: [], tags: [].}

Add float x to complex y.

proc `-`(z: Complex): Complex {...}{.raises: [], tags: [].}

Unary minus for complex numbers.

proc `-`(x, y: Complex): Complex {...}{.raises: [], tags: [].}

Subtract two complex numbers.

proc `-`(x: Complex; y: float): Complex {...}{.raises: [], tags: [].}

Subtracts float y from complex x.

proc `-`(x: float; y: Complex): Complex {...}{.raises: [], tags: [].}

Subtracts complex y from float x.

proc `/`(x, y: Complex): Complex {...}{.raises: [], tags: [].}

Divide x by y.

proc `/`(x: Complex; y: float): Complex {...}{.raises: [], tags: [].}

Divide complex x by float y.

proc `/`(x: float; y: Complex): Complex {...}{.raises: [], tags: [].}

Divide float x by complex y.

proc `*`(x, y: Complex): Complex {...}{.raises: [], tags: [].}

Multiply x with y.

proc `*`(x: float; y: Complex): Complex {...}{.raises: [], tags: [].}

Multiply float x with complex y.

proc `*`(x: Complex; y: float): Complex {...}{.raises: [], tags: [].}

Multiply complex x with float y.

proc `+=`(x: var Complex; y: Complex) {...}{.raises: [], tags: [].}

Add y to x.

proc `+=`(x: var Complex; y: float) {...}{.raises: [], tags: [].}

Add y to the complex number x.

proc `-=`(x: var Complex; y: Complex) {...}{.raises: [], tags: [].}

Subtract y from x.

proc `-=`(x: var Complex; y: float) {...}{.raises: [], tags: [].}

Subtract y from the complex number x.

proc `*=`(x: var Complex; y: Complex) {...}{.raises: [], tags: [].}

Multiply y to x.

proc `*=`(x: var Complex; y: float) {...}{.raises: [], tags: [].}

Multiply y to the complex number x.

proc `/=`(x: var Complex; y: Complex) {...}{.raises: [], tags: [].}

Divide x by y in place.

proc `/=`(x: var Complex; y: float) {...}{.raises: [], tags: [].}

Divide complex x by float y in place.

proc abs(z: Complex): float {...}{.raises: [], tags: [].}

Return the distance from (0,0) to z.

proc conjugate(z: Complex): Complex {...}{.raises: [], tags: [].}

Conjugate of complex number z.

proc sqrt(z: Complex): Complex {...}{.raises: [], tags: [].}

Square root for a complex number z.

proc exp(z: Complex): Complex {...}{.raises: [], tags: [].}

e raised to the power z.

proc ln(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the natural log of z.

proc log10(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the log base 10 of z.

proc log2(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the log base 2 of z.

proc pow(x, y: Complex): Complex {...}{.raises: [], tags: [].}

x raised to the power y.

proc sin(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the sine of z.

proc arcsin(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse sine of z.

proc cos(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the cosine of z.

proc arccos(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse cosine of z.

proc tan(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the tangent of z.

proc arctan(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse tangent of z.

proc cot(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the cotangent of z.

proc arccot(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse cotangent of z.

proc sec(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the secant of z.

proc arcsec(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse secant of z.

proc csc(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the cosecant of z.

proc arccsc(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse cosecant of z.

proc sinh(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the hyperbolic sine of z.

proc arcsinh(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse hyperbolic sine of z.

proc cosh(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the hyperbolic cosine of z.

proc arccosh(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse hyperbolic cosine of z.

proc tanh(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the hyperbolic tangent of z.

proc arctanh(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse hyperbolic tangent of z.

proc sech(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the hyperbolic secant of z.

proc arcsech(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse hyperbolic secant of z.

proc csch(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the hyperbolic cosecant of z.

proc arccsch(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse hyperbolic cosecant of z.

proc coth(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the hyperbolic cotangent of z.

proc arccoth(z: Complex): Complex {...}{.raises: [], tags: [].}

Returns the inverse hyperbolic cotangent of z.

proc phase(z: Complex): float {...}{.raises: [], tags: [].}

Returns the phase of z.

proc polar(z: Complex): tuple[r, phi: float] {...}{.raises: [], tags: [].}

Returns z in polar coordinates.

proc rect(r: float; phi: float): Complex {...}{.raises: [], tags: [].}

Returns the complex number with polar coordinates r and phi.

proc `$`(z: Complex): string {...}{.raises: [], tags: [].}

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