update docs + remove abuses of word cardinal

Author: mattsignorelli

docs/src/functions_list.md

@@ -151,3 +151,9 @@ ellipe
 eta
 zeta
 ```
+
+## Special Trigonometric Functions
+```@docs
+sincu
+sinhcu
+```

docs/src/functions_overview.md

@@ -118,3 +118,11 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi
 |:-------- |:----------- |
 | [`eta(x)`](@ref SpecialFunctions.eta) | [Dirichlet eta function](https://en.wikipedia.org/wiki/Dirichlet_eta_function) at `x` |
 | [`zeta(x)`](@ref SpecialFunctions.zeta) | [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function) at `x` |
+
+## Special Trigonometric Functions
+
+| Function | Description |
+|:-------- |:----------- |
+| [`sincu(x)`](@ref SpecialFunctions.sincu) | [Unnormalized sine cardinal function](https://en.wikipedia.org/wiki/Sinc_function) at `x` |
+| [`sinhcu(x)`](@ref SpecialFunctions.sinhcu) | [Unnormalized hyperbolic sinc function](https://mathworld.wolfram.com/SinhcFunction.html) at `x` |
+

src/SpecialFunctions.jl

@@ -107,7 +107,7 @@ include("gamma.jl")
 include("gamma_inc.jl")
 include("betanc.jl")
 include("beta_inc.jl")
-include("trigcardinal.jl")
+include("trig.jl")
 
 if !isdefined(Base, :get_extension)
     include("../ext/SpecialFunctionsChainRulesCoreExt.jl")

src/trigcardinal.jl src/trig.jlsrc/trigcardinal.jl renamed to src/trig.jl

@@ -8,14 +8,20 @@ isinf_real(x::Number) = isinf(real(x)) && isfinite(imag(x))
 isinf_imag(x::Real) = false
 isinf_imag(x::Number) = isfinite(real(x)) && isinf(imag(x))
 
-# sincu copied exactly from Boost library
+# sincu copied from Boost library and correct limit behavior added
 # https://www.boost.org/doc/libs/1_87_1/boost/math/special_functions/sinc.hpp
+"""
+    sincu(x)
+
+Compute the unnormalized sinc function ``\\operatorname{sincu}(x) = \\sin(x) / (x)`` 
+with accuracy near the origin.
+"""
 sincu(x) = _sinc(float(x))
 function _sinc(x::Union{T,Complex{T}}) where {T}
     if isinf_real(x)
         return zero(x)
     end
-    
+
     nrm = fastabs(x)
     if nrm >= 3.3*sqrt(sqrt(eps(T)))
         return sin(x)/x
@@ -25,8 +31,15 @@ function _sinc(x::Union{T,Complex{T}}) where {T}
     end
 end
 
-# sinhcu copied exactly from Boost library 
+# sinhcu copied from Boost library and correct limit behavior added
 # https://www.boost.org/doc/libs/1_87_1/boost/math/special_functions/sinhc.hpp
+
+"""
+    sinhcu(x)
+
+Compute the unnormalized sinhc function ``\\operatorname{sinhcu}(x) = \\sinh(x) / (x)`` 
+with accuracy accuracy near the origin.
+"""
 sinhcu(x) = _sinhcu(float(x))
 function _sinhcu(x::Union{T,Complex{T}}) where {T}
     taylor_0_bound = eps(T)

test/runtests.jl

@@ -34,7 +34,7 @@ tests = [
     "sincosint",
     "other_tests",
     "chainrules",
-    "trigcardinal"
+    "trig"
 ]
 
 const testdir = dirname(@__FILE__)

test/trigcardinal.jl test/trig.jltest/trigcardinal.jl renamed to test/trig.jl

@@ -1,4 +1,4 @@
-@testset "Cardinal trigonometric" begin
+@testset "Special trigonometric functions" begin
     @testset "sincu (unnormalized sinc)" begin
         a = 1.0
         @test sincu(a) ≈ sin(a)/a