Define gamma and lgamma for Float16 (#132)

Also make other AbstractFloat inputs result in a MethodError.

Author: ararslan

src/gamma.jl

@@ -555,8 +555,10 @@ export gamma, lgamma, beta, lbeta, lfactorial
 
 ## from base/special/gamma.jl
 
-gamma(x::Float64) = nan_dom_err(ccall((:tgamma,libm),  Float64, (Float64,), x), x)
-gamma(x::Float32) = nan_dom_err(ccall((:tgammaf,libm),  Float32, (Float32,), x), x)
+gamma(x::Float64) = nan_dom_err(ccall((:tgamma, libm), Float64, (Float64,), x), x)
+gamma(x::Float32) = nan_dom_err(ccall((:tgammaf, libm), Float32, (Float32,), x), x)
+gamma(x::Float16) = Float16(gamma(Float32(x)))
+gamma(x::AbstractFloat) = throw(MethodError(gamma, x))
 
 """
     gamma(x)
@@ -760,7 +762,9 @@ end
 
 @inline lgamma(x::Float64) = nan_dom_err(ccall((:lgamma, libm), Float64, (Float64,), x), x)
 @inline lgamma(x::Float32) = nan_dom_err(ccall((:lgammaf, libm), Float32, (Float32,), x), x)
+@inline lgamma(x::Float16) = Float16(lgamma(Float32(x)))
 @inline lgamma(x::Real) = lgamma(float(x))
+lgamma(x::AbstractFloat) = throw(MethodError(lgamma, x))
 
 ## from base/numbers.jl
 

test/runtests.jl

@@ -565,6 +565,10 @@ end
 
 @test sprint(showerror, AmosException(1)) == "AmosException with id 1: input error."
 
+# Used to check method existence below
+struct NotAFloat <: AbstractFloat
+end
+
 @testset "gamma and friends" begin
     @testset "gamma, lgamma (complex argument)" begin
         if Base.Math.libm == "libopenlibm"
@@ -628,6 +632,17 @@ end
         @test lgamma(-Inf*im) === -Inf - Inf*im
         @test lgamma(Inf + Inf*im) === lgamma(NaN + 0im) === lgamma(NaN*im) === NaN + NaN*im
     end
+
+    @testset "Other float types" begin
+        let x = one(Float16)
+            @test gamma(x) ≈ one(Float16)
+            @test gamma(x) isa Float16
+            @test lgamma(x) ≈ zero(Float16)
+            @test lgamma(x) isa Float16
+        end
+        @test_throws MethodError gamma(NotAFloat())
+        @test_throws MethodError lgamma(NotAFloat())
+    end
 end
 
 @testset "beta, lbeta" begin