function ChebCoef(f::Function, h::T, w::Int, ν::Int) where{T<:Union{Float32, Float64}}

This function creates a ChebCoef object for the Chebyshev approximation of function f.

f: the function to be interpolated
h: the grid spacing
w: the number of grid points for the window function cutoff
ν: the number of Chebyshev points

function GridInfo(Nreal::NTuple{N, Int}, w::NTuple{N, Int}, periodicity::NTuple{N, Bool}, extrapad::NTuple{N, Int}, L::NTuple{N, T}) where{N, T<:Union{Float32, Float64}}

This function creates a GridBox object with two mutable Array.

N_real: the number of real grid points in each direction
w: the number of grid points in each direction for the window function cutoff
periodicity: a tuple of three boolean values indicating whether the grid is periodic in each direction, to decide padding or not
extra_pad: the number of extra grid points in each direction for padding
L: the length of the box in each direction
h: the grid spacing in each direction, the first point is at [h/2, 3h/2, ..., L - h/2]
N_image: the number of grid points in each direction for the image grid, given by tuple([2 * w[i] + 2 for i in 1:N]...) .+ N_real
N_pad: the numer of padded grid points in each direction, given by tuple([2 * pad[i] * (periodicity[i] == false) for i in 1:N]...) .+ N_image .+ N_real

function fft!(gridbox::GridBox{N, T}) where{N, T}

calculate the inplace fft on the padded grid

function ifft!(gridbox::GridBox{N, T}) where{N, T}

calculate the inplace ifft on the padded grid

function FWkb(k::T, width::T, β::T) where{T<:Real}

Fourier transform of Wkb kernel function

function Wkb(x::T, width::T, β::T) where{T<:Real}

WKB kernel function, used as window function for the Chebyshev interpolation

function gridrevisepad!(gridbox::GridBox{N, T}) where{N, T}

set all values of gridbox.pad_grid to 0

function horner(x, p)

Evaluate a polynomial using Horner's method.