Fixes

• Fixed imprecision of complex li2 for small arguments (#24)
• preserve sign of zero (#27)

Fixes

• Ensure enough terms are taken into account in the series expansions in li(n,z) when n is of type Int8.

New

• arbitrary precision implementations of li0(z), li1(z), reli1(x), li2(z), reli2(x), li(n,z), reli(n,x),

Changes

• extend range of input values that do not cause a floating-point overflow

Changes

• Added protection against catastrophic cancellation in the real dilogarithm li2 and the real trilogarithm li3 for arguments close to 1. (Such a potential catastrophic cancellation has not been observed yet, though.)

Changes

• performance improvement of real dilogarithm reli2(x)

Changes

• performance improvement of reli4(x)
• performance improvement of digamma(n)
• file CITATION.cff has been added with structured citation information

Changes

• performance improvement of real trilogarithm reli3(x::Real)

Changes

The real polylogarithm functions have been renamed in order to avoid bugs when a non-zero imaginary part would actually occur (which is omitted in the real polylogarithm functions):

• rename real li1 -> reli1
• rename real li2 -> reli2
• rename real li3 -> reli3
• rename real li4 -> reli4
• rename real li(n,x) -> reli(n,x)

The complex polylogarithm functions li* now accept real arguments and always return a complex number.

Changes

• performance improvement of the complex li3(z), li4(z) and li(n,z) for imag(z) == 0

New

The polylogarithm functions can now be evaluated for all standard numeric types.

Example for li2:

using PolyLog

li2(1.0)
li2(1.0f0)
li2(Float16(1.0))
li2(1//1)
li2(1)

li2(1.0 + 0.0im)
li2(1.0f0 + 0.0f0im)
li2(ComplexF16(1.0 + 0.0im))
li2(1//1 + 0//1im)
li2(1 + 0im)

Changes

• small performance improvement of complex polylogarithms li2, li3, li4, li5, li6

New

• general complex polylogarithm function li(n,z) for all integers n and complex z of type ComplexF64
• extension of the general real polylogarithm function li(n,x) to all integers n (now including n < 0) and real x of type Float64

New

• general real polylogarithm function li(n,x) for all integers n >= 0 and real x of type Float64

New

• real trilogarithm Li3(x) for x of type Float64
• real polylogarithm of 4th order Li4(x) for x of type Float64

Changes

• ~5% performance improvement of the real dilogarithm li2

Fixes

• increased precision of complex dilogarithm li2 for z values with z^2 < machine epsilon

New

• added implementation of complex 6th order polylogarithm li6

Changes

• The functions li2, ..., li6 are now exported and can be called without the PolyLog. prefix. An example can be found in the README file.

New

• added implementation of 5th order polylogarithm li5

New

• PolyLog.jl is now a Julia package.

New

• Implementation of complex 4th order polylogarithm li4