From d4e7aa649aa95b1be555d03a174bcbca19db4005 Mon Sep 17 00:00:00 2001
From: Alexander Voigt <ahgvoigt@gmail.com>
Date: Thu, 5 Oct 2023 16:28:15 +0200
Subject: [PATCH] type-stabilize reli(n,x)

---
 src/Eta.jl       | 2 +-
 src/Factorial.jl | 4 ++--
 src/Harmonic.jl  | 2 +-
 src/Li.jl        | 6 ++++--
 src/Zeta.jl      | 2 +-
 5 files changed, 9 insertions(+), 7 deletions(-)

diff --git a/src/Eta.jl b/src/Eta.jl
index 704d4bd..bc39e2e 100644
--- a/src/Eta.jl
+++ b/src/Eta.jl
@@ -61,7 +61,7 @@ const MINUS_ETA_NEG = (
 )
 
 # returns Li(n,-1) = (2^(1 - n) - 1)*zeta(n)
-function neg_eta(n::Integer, T)
+function neg_eta(n::Integer, ::Type{T})::T where T
     if issimplefloat(T)
         convert(T, neg_eta_f46(n))
     else
diff --git a/src/Factorial.jl b/src/Factorial.jl
index b4b86f6..40caba2 100644
--- a/src/Factorial.jl
+++ b/src/Factorial.jl
@@ -121,7 +121,7 @@ const INVERSE_FACTORIALS = (
 )
 
 # returns n! for n >= 0
-function fac(n::Integer, T)
+function fac(n::Integer, ::Type{T})::T where T
     if issimplefloat(T)
         convert(T, fac_f64(n))
     else
@@ -148,7 +148,7 @@ function fac_big(n::Integer)::BigFloat
 end
 
 # returns 1/n! for n >= 0
-function inv_fac(n::Integer, T)
+function inv_fac(n::Integer, ::Type{T})::T where T
     if issimplefloat(T)
         convert(T, inv_fac_f64(n))
     else
diff --git a/src/Harmonic.jl b/src/Harmonic.jl
index b829f06..e335c6a 100644
--- a/src/Harmonic.jl
+++ b/src/Harmonic.jl
@@ -1,5 +1,5 @@
 # returns n-th harmonic number, n > 0
-function harmonic(n::Integer, T)
+function harmonic(n::Integer, ::Type{T})::T where T
     if issimplefloat(T)
         convert(T, harmonic_f64(n))
     else
diff --git a/src/Li.jl b/src/Li.jl
index 2b9ee89..a7fd0bd 100644
--- a/src/Li.jl
+++ b/src/Li.jl
@@ -29,7 +29,7 @@ _reli(n::Integer, x::Float16) = oftype(x, _reli(n, Float32(x)))
 
 _reli(n::Integer, x::Float32) = oftype(x, _reli(n, Float64(x)))
 
-function _reli(n::Integer, x::Real)::Real
+function _reli(n::Integer, x::Real)
     isnan(x) && return oftype(x, NaN)
     isinf(x) && return oftype(x, -Inf)
     x == zero(x) && return zero(x)
@@ -157,7 +157,9 @@ function _li(n::Integer, z::ComplexF64)::ComplexF64
 end
 
 # returns -(-1)^n of type T
-oddsgn(n, T) = isodd(n) ? one(T) : -one(T)
+function oddsgn(n, ::Type{T})::T where T
+    isodd(n) ? one(T) : -one(T)
+end
 
 # returns r.h.s. of inversion formula for complex z:
 #
diff --git a/src/Zeta.jl b/src/Zeta.jl
index ed60ecd..adccae4 100644
--- a/src/Zeta.jl
+++ b/src/Zeta.jl
@@ -63,7 +63,7 @@ const ZETA_NEG = (
 )
 
 # Riemann zeta function for integer arguments
-function zeta(n::Integer, T)
+function zeta(n::Integer, ::Type{T})::T where T
     if issimplefloat(T)
         convert(T, zeta_f64(n))
     else