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cispi

Compute exp(im*π*x), where im is the imaginary unit, return in half-revolutions.

Base.cispi — Function
cispi(x)

More accurate method for cis(pi*x) (especially for large x).

See also cis, sincospi, exp, angle.

Examples

julia> cispi(10000)
1.0 + 0.0im

julia> cispi(0.25 + 1im)
0.030556854645954562 + 0.03055685464595456im
Julia 1.6

This function requires Julia 1.6 or later.

source

Methods

julia> methods(cispi, (Any,), [Base, Base.Math, Base.MathConstants, Base.MPFR])# 2 methods for generic function "cispi" from Base:
 [1] cispi(z::Complex)
     @ complex.jl:617
 [2] cispi(theta::Real)
     @ complex.jl:615

Examples

Real Numbers

julia> cispi(0)
1.0 + 0.0im

julia> cispi(-0.0)
1.0 - 0.0im

julia> cispi(0.5)
0.0 + 1.0im

julia> cispi(1.0)
-1.0 + 0.0im

Complex

julia> cispi(0+0im)
1.0 + 0.0im

Tips

See Also

Extended Inputs

Tech Notes

  • cispi(::Real): by pure julia
  • cispi(::BigFloat): by MPFR

Version History

Introduced in Julia v1.6 (2021)