diff --git a/Project.toml b/Project.toml
index 5a71cfc..32f5bd1 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "StatsFuns"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.10"
+version = "0.9.11"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
@@ -13,7 +13,7 @@ SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 [compat]
 ChainRulesCore = "1"
 IrrationalConstants = "0.1"
-LogExpFunctions = "0.3"
+LogExpFunctions = "0.3.2"
 Reexport = "1"
 Rmath = "0.4, 0.5, 0.6, 0.7"
 SpecialFunctions = "0.8, 0.9, 0.10, 1.0"
diff --git a/README.md b/README.md
index 555965a..65e40d7 100644
--- a/README.md
+++ b/README.md
@@ -40,6 +40,7 @@ log4π,      # log(4π)
 # basicfuns
 xlogx,          # x * log(x), or 0 when x is zero
 xlogy,          # x * log(y), or 0 when x is zero
+xlog1py,        # x * log(1 + y) for x > 0, or 0 when x == 0
 logistic,       # 1 / (1 + exp(-x))
 logit,          # log(x / (1 - x))
 log1psq,        # log(1 + x^2)
diff --git a/src/StatsFuns.jl b/src/StatsFuns.jl
index 2ff3414..cc4e0e0 100644
--- a/src/StatsFuns.jl
+++ b/src/StatsFuns.jl
@@ -35,6 +35,7 @@ import ChainRulesCore
 @reexport using LogExpFunctions:
     xlogx,          # x * log(x) for x > 0, or 0 when x == 0
     xlogy,          # x * log(y) for x > 0, or 0 when x == 0
+    xlog1py,        # x * log(1 + y) for x > 0, or 0 when x == 0
     logistic,       # 1 / (1 + exp(-x))
     logit,          # log(x / (1 - x))
     log1psq,        # log(1 + x^2)
diff --git a/src/chainrules.jl b/src/chainrules.jl
index f405c21..7f6040f 100644
--- a/src/chainrules.jl
+++ b/src/chainrules.jl
@@ -12,9 +12,9 @@ ChainRulesCore.@scalar_rule(
     binomlogpdf(n::Real, p::Real, k::Real),
     @setup(z = digamma(n - k + 1)),
     (
-        digamma(n + 2) - z + log1p(-p) - 1 / (1 + n),
+        ChainRulesCore.NoTangent(),
         (k / p - n) / (1 - p),
-        z - digamma(k + 1) + logit(p),
+        ChainRulesCore.NoTangent(),
     ),
 )
 
@@ -59,7 +59,7 @@ ChainRulesCore.@scalar_rule(
 
 ChainRulesCore.@scalar_rule(
     poislogpdf(λ::Number, x::Number),
-    ((iszero(x) && iszero(λ) ? zero(x / λ) : x / λ) - 1, log(λ) - digamma(x + 1)),
+    ((iszero(x) && iszero(λ) ? zero(x / λ) : x / λ) - 1, ChainRulesCore.NoTangent()),
 )
 
 ChainRulesCore.@scalar_rule(
diff --git a/src/distrs/beta.jl b/src/distrs/beta.jl
index 3d1bfae..6328c4e 100644
--- a/src/distrs/beta.jl
+++ b/src/distrs/beta.jl
@@ -1,8 +1,8 @@
 # functions related to beta distributions
 
-import .RFunctions:
-    betapdf,
-    betalogpdf,
+# R implementations
+# For pdf and logpdf we use the Julia implementation
+using .RFunctions:
     betacdf,
     betaccdf,
     betalogcdf,
@@ -12,8 +12,13 @@ import .RFunctions:
     betainvlogcdf,
     betainvlogccdf
 
-# pdf for numbers with generic types
-betapdf(α::Real, β::Real, x::Number) = x^(α - 1) * (1 - x)^(β - 1) / beta(α, β)
+# Julia implementations
+betapdf(α::Real, β::Real, x::Real) = exp(betalogpdf(α, β, x))
 
-# logpdf for numbers with generic types
-betalogpdf(α::Real, β::Real, x::Number) = (α - 1) * log(x) + (β - 1) * log1p(-x) - logbeta(α, β)
+betalogpdf(α::Real, β::Real, x::Real) = betalogpdf(promote(α, β, x)...)
+function betalogpdf(α::T, β::T, x::T) where {T<:Real}
+    # we ensure that `log(x)` and `log1p(-x)` do not error
+    y = clamp(x, 0, 1)
+    val = xlogy(α - 1, y) + xlog1py(β - 1, -y) - logbeta(α, β)
+    return x < 0 || x > 1 ? oftype(val, -Inf) : val
+end
diff --git a/src/distrs/binom.jl b/src/distrs/binom.jl
index e1237f1..09b1c2a 100644
--- a/src/distrs/binom.jl
+++ b/src/distrs/binom.jl
@@ -1,8 +1,8 @@
 # functions related to binomial distribution
 
-import .RFunctions:
-    binompdf,
-    binomlogpdf,
+# R implementations
+# For pdf and logpdf we use the Julia implementation
+using .RFunctions:
     binomcdf,
     binomccdf,
     binomlogcdf,
@@ -12,8 +12,13 @@ import .RFunctions:
     binominvlogcdf,
     binominvlogccdf
 
-# pdf for numbers with generic types
+
+# Julia implementations
 binompdf(n::Real, p::Real, k::Real) = exp(binomlogpdf(n, p, k))
 
-# logpdf for numbers with generic types
-binomlogpdf(n::Real, p::Real, k::Real) = -log1p(n) - logbeta(n - k + 1, k + 1) + k * log(p) + (n - k) * log1p(-p)
+binomlogpdf(n::Real, p::Real, k::Real) = binomlogpdf(promote(n, p, k)...)
+function binomlogpdf(n::T, p::T, k::T) where {T<:Real}
+    m = clamp(k, 0, n)
+    val = betalogpdf(m + 1, n - m + 1, p) - log(n + 1)
+    return 0 <= k <= n && isinteger(k) ? val : oftype(val, -Inf)
+end
diff --git a/src/distrs/chisq.jl b/src/distrs/chisq.jl
index 25a069d..467fa08 100644
--- a/src/distrs/chisq.jl
+++ b/src/distrs/chisq.jl
@@ -1,8 +1,8 @@
 # functions related to chi-square distribution
 
-import .RFunctions:
-    chisqpdf,
-    chisqlogpdf,
+# R implementations
+# For pdf and logpdf we use the Julia implementation
+using .RFunctions:
     chisqcdf,
     chisqccdf,
     chisqlogcdf,
@@ -12,14 +12,11 @@ import .RFunctions:
     chisqinvlogcdf,
     chisqinvlogccdf
 
-# pdf for numbers with generic types
-function chisqpdf(k::Real, x::Number)
-  hk = k / 2  # half k
-  1 / (2^(hk) * gamma(hk)) * x^(hk - 1) * exp(-x / 2)
-end
+# Julia implementations
+# promotion ensures that we do forward e.g. `chisqpdf(::Int, ::Float32)` to
+# `gammapdf(::Float32, ::Int, ::Float32)` but not `gammapdf(::Float64, ::Int, ::Float32)`
+chisqpdf(k::Real, x::Real) = chisqpdf(promote(k, x)...)
+chisqpdf(k::T, x::T) where {T<:Real} = gammapdf(k / 2, 2, x)
 
-# logpdf for numbers with generic types
-function chisqlogpdf(k::Real, x::Number)
-  hk = k / 2  # half k
-  -hk * logtwo - loggamma(hk) + (hk - 1) * log(x) - x / 2
-end
+chisqlogpdf(k::Real, x::Real) = chisqlogpdf(promote(k, x)...)
+chisqlogpdf(k::T, x::T) where {T<:Real} = gammalogpdf(k / 2, 2, x)
diff --git a/src/distrs/fdist.jl b/src/distrs/fdist.jl
index b3041e3..1f11c16 100644
--- a/src/distrs/fdist.jl
+++ b/src/distrs/fdist.jl
@@ -1,8 +1,8 @@
 # functions related to F distribution
 
-import .RFunctions:
-    fdistpdf,
-    fdistlogpdf,
+# R implementations
+# For pdf and logpdf we use the Julia implementation
+using .RFunctions:
     fdistcdf,
     fdistccdf,
     fdistlogcdf,
@@ -12,8 +12,14 @@ import .RFunctions:
     fdistinvlogcdf,
     fdistinvlogccdf
 
-# pdf for numbers with generic types
-fdistpdf(ν1::Real, ν2::Real, x::Number) = sqrt((ν1 * x)^ν1 * ν2^ν2 / (ν1 * x + ν2)^(ν1 + ν2)) / (x * beta(ν1 / 2, ν2 / 2))
+# Julia implementations
+fdistpdf(ν1::Real, ν2::Real, x::Real) = exp(fdistlogpdf(ν1, ν2, x))
 
-# logpdf for numbers with generic types
-fdistlogpdf(ν1::Real, ν2::Real, x::Number) = (ν1 * log(ν1 * x) + ν2 * log(ν2) - (ν1 + ν2) * log(ν1 * x + ν2)) / 2 - log(x) - logbeta(ν1 / 2, ν2 / 2)
+fdistlogpdf(ν1::Real, ν2::Real, x::Real) = fdistlogpdf(promote(ν1, ν2, x)...)
+function fdistlogpdf(ν1::T, ν2::T, x::T) where {T<:Real}
+    # we ensure that `log(x)` does not error if `x < 0`
+    ν1ν2 = ν1 / ν2
+    y = max(x, 0)
+    val = (xlogy(ν1, ν1ν2) + xlogy(ν1 - 2, y) - xlogy(ν1 + ν2, 1 + ν1ν2 * y)) / 2 - logbeta(ν1 / 2, ν2 / 2)
+    return x < 0 ? oftype(val, -Inf) : val
+end
diff --git a/src/distrs/gamma.jl b/src/distrs/gamma.jl
index 26dbef6..15b3975 100644
--- a/src/distrs/gamma.jl
+++ b/src/distrs/gamma.jl
@@ -1,8 +1,8 @@
 # functions related to gamma distribution
 
-import .RFunctions:
-    gammapdf,
-    gammalogpdf,
+# R implementations
+# For pdf and logpdf we use the Julia implementation
+using .RFunctions:
     gammacdf,
     gammaccdf,
     gammalogcdf,
@@ -12,8 +12,13 @@ import .RFunctions:
     gammainvlogcdf,
     gammainvlogccdf
 
-# pdf for numbers with generic types
-gammapdf(k::Real, θ::Real, x::Number) = 1 / (gamma(k) * θ^k) * x^(k - 1) * exp(-x / θ)
+# Julia implementations
+gammapdf(k::Real, θ::Real, x::Real) = exp(gammalogpdf(k, θ, x))
 
-# logpdf for numbers with generic types
-gammalogpdf(k::Real, θ::Real, x::Number) = -loggamma(k) - k * log(θ) + (k - 1) * log(x) - x / θ
+gammalogpdf(k::Real, θ::Real, x::Real) = gammalogpdf(promote(k, θ, x)...)
+function gammalogpdf(k::T, θ::T, x::T) where {T<:Real}
+    # we ensure that `log(x)` does not error if `x < 0`
+    xθ = max(x, 0) / θ
+    val = -loggamma(k) + xlogy(k - 1, xθ) - log(θ) - xθ
+    return x < 0 ? oftype(val, -Inf) : val
+end
diff --git a/src/distrs/hyper.jl b/src/distrs/hyper.jl
index 5d62bd6..6c2869f 100644
--- a/src/distrs/hyper.jl
+++ b/src/distrs/hyper.jl
@@ -1,6 +1,7 @@
 # functions related to hyper-geometric distribution
 
-import .RFunctions:
+# R implementations
+using .RFunctions:
     hyperpdf,
     hyperlogpdf,
     hypercdf,
diff --git a/src/distrs/nbeta.jl b/src/distrs/nbeta.jl
index 9007f7e..33c59cf 100644
--- a/src/distrs/nbeta.jl
+++ b/src/distrs/nbeta.jl
@@ -1,6 +1,7 @@
 # functions related to noncentral beta distribution
 
-import .RFunctions:
+# R implementations
+using .RFunctions:
     nbetapdf,
     nbetalogpdf,
     nbetacdf,
diff --git a/src/distrs/nbinom.jl b/src/distrs/nbinom.jl
index 6ffae35..5f80b1e 100644
--- a/src/distrs/nbinom.jl
+++ b/src/distrs/nbinom.jl
@@ -1,6 +1,7 @@
 # functions related to negative binomial distribution
 
-import .RFunctions:
+# R implementations
+using .RFunctions:
     nbinompdf,
     nbinomlogpdf,
     nbinomcdf,
diff --git a/src/distrs/nchisq.jl b/src/distrs/nchisq.jl
index 942b7d5..9382d04 100644
--- a/src/distrs/nchisq.jl
+++ b/src/distrs/nchisq.jl
@@ -1,6 +1,7 @@
 # functions related to noncentral chi-square distribution
 
-import .RFunctions:
+# R implementations
+using .RFunctions:
     nchisqpdf,
     nchisqlogpdf,
     nchisqcdf,
diff --git a/src/distrs/nfdist.jl b/src/distrs/nfdist.jl
index e38c2f2..3f2e735 100644
--- a/src/distrs/nfdist.jl
+++ b/src/distrs/nfdist.jl
@@ -1,6 +1,7 @@
 # functions related to noncentral F distribution
 
-import .RFunctions:
+# R implementations
+using .RFunctions:
     nfdistpdf,
     nfdistlogpdf,
     nfdistcdf,
diff --git a/src/distrs/ntdist.jl b/src/distrs/ntdist.jl
index 99cae2b..b1bbb1b 100644
--- a/src/distrs/ntdist.jl
+++ b/src/distrs/ntdist.jl
@@ -1,6 +1,7 @@
 # functions related to noncentral T distribution
 
-import .RFunctions:
+# R implementations
+using .RFunctions:
     ntdistpdf,
     ntdistlogpdf,
     ntdistcdf,
diff --git a/src/distrs/pois.jl b/src/distrs/pois.jl
index 3caffc2..ed6192b 100644
--- a/src/distrs/pois.jl
+++ b/src/distrs/pois.jl
@@ -1,8 +1,8 @@
 # functions related to Poisson distribution
 
-import .RFunctions:
-    poispdf,
-    poislogpdf,
+# R implementations
+# For pdf and logpdf we use the Julia implementation
+using .RFunctions:
     poiscdf,
     poisccdf,
     poislogcdf,
@@ -12,19 +12,11 @@ import .RFunctions:
     poisinvlogcdf,
     poisinvlogccdf
 
-# generic versions
+# Julia implementations
 poispdf(λ::Real, x::Real) = exp(poislogpdf(λ, x))
 
-poislogpdf(λ::T, x::T) where {T <: Real} = xlogy(x, λ) - λ - loggamma(x + 1)
-
-poislogpdf(λ::Number, x::Number) = poislogpdf(promote(float(λ), x)...)
-
-#=
-function poislogpdf(λ::Union{Float32,Float64}, x::Union{Float64,Float32,Integer})
-    if iszero(λ)
-        iszero(x) ? zero(λ) : oftype(λ, -Inf)
-    elseif iszero(x)
-        -λ
-    else
-        -lstirling_asym(x + 1)
-=#
+poislogpdf(λ::Real, x::Real) = poislogpdf(promote(λ, x)...)
+function poislogpdf(λ::T, x::T) where {T <: Real}
+    val = xlogy(x, λ) - λ - loggamma(x + 1)
+    return x >= 0 && isinteger(x) ? val : oftype(val, -Inf)
+end
diff --git a/src/distrs/srdist.jl b/src/distrs/srdist.jl
index 8d1e180..4399f45 100644
--- a/src/distrs/srdist.jl
+++ b/src/distrs/srdist.jl
@@ -1,6 +1,7 @@
 # functions related to studentized range distribution
 
-import .RFunctions:
+# R implementations
+using .RFunctions:
     srdistcdf,
     srdistccdf,
     srdistlogcdf,
diff --git a/src/distrs/tdist.jl b/src/distrs/tdist.jl
index 5dc83e9..b7aefbc 100644
--- a/src/distrs/tdist.jl
+++ b/src/distrs/tdist.jl
@@ -1,8 +1,8 @@
 # functions related to student's T distribution
 
-import .RFunctions:
-    tdistpdf,
-    tdistlogpdf,
+# R implementations
+# For pdf and logpdf we use the Julia implementation
+using .RFunctions:
     tdistcdf,
     tdistccdf,
     tdistlogcdf,
@@ -12,8 +12,11 @@ import .RFunctions:
     tdistinvlogcdf,
     tdistinvlogccdf
 
-# pdf for numbers with generic types
-tdistpdf(ν::Real, x::Number) = gamma((ν + 1) / 2) / (sqrt(ν * pi) * gamma(ν / 2)) * (1 + x^2 / ν)^(-(ν + 1) / 2)
+# Julia implementations
+tdistpdf(ν::Real, x::Real) = exp(tdistlogpdf(ν, x))
 
-# logpdf for numbers with generic types
-tdistlogpdf(ν::Real, x::Number) = loggamma((ν + 1) / 2) - log(ν * pi) / 2 - loggamma(ν / 2) + (-(ν + 1) / 2) * log1p(x^2 / ν)
+tdistlogpdf(ν::Real, x::Real) = tdistlogpdf(promote(ν, x)...)
+function tdistlogpdf(ν::T, x::T) where {T<:Real}
+    νp12 = (ν + 1) / 2
+    return loggamma(νp12) - (logπ + log(ν)) / 2 - loggamma(ν / 2) - νp12 * log1p(x^2 / ν)
+end
diff --git a/src/rmath.jl b/src/rmath.jl
index 0a24ca3..595babf 100644
--- a/src/rmath.jl
+++ b/src/rmath.jl
@@ -57,7 +57,7 @@ function _import_rmath(rname::Symbol, jname::Symbol, pargs)
         rtypes = Expr(:tuple, _pts...)
     end
 
-    pdecls = [Expr(:(::), ps, :(Union{Float64,Int})) for ps in pargs] # [:(p1::Union{Float64, Int}), :(p2::Union{...}), ...]
+    pdecls = [Expr(:(::), ps, :Real) for ps in pargs] # [:(p1::Real), :(p2::Real), ...]
 
     if is_tukey
         # ptukey and qtukey have an extra literal 1 argument
@@ -67,36 +67,56 @@ function _import_rmath(rname::Symbol, jname::Symbol, pargs)
     # Function implementation
     quote
         if $(!is_tukey)
-            $pdf($(pdecls...), x::Union{Float64,Int}) =
-                ccall(($dfun, libRmath), Float64, $dtypes, x, $(pargs...), 0)
-
-            $logpdf($(pdecls...), x::Union{Float64,Int}) =
-                ccall(($dfun, libRmath), Float64, $dtypes, x, $(pargs...), 1)
+            function $pdf($(pdecls...), x::Real)
+                T = float(Base.promote_typeof($(pargs...), x))
+                return convert(T, ccall(($dfun, libRmath), Float64, $dtypes, x, $(pargs...), 0))
+            end
+
+            function $logpdf($(pdecls...), x::Real)
+                T = float(Base.promote_typeof($(pargs...), x))
+                return convert(T, ccall(($dfun, libRmath), Float64, $dtypes, x, $(pargs...), 1))
+            end
         end
 
-        $cdf($(pdecls...), x::Union{Float64,Int}) =
-            ccall(($pfun, libRmath), Float64, $ptypes, x, $(pargs...), 1, 0)
+        function $cdf($(pdecls...), x::Real)
+            T = float(Base.promote_typeof($(pargs...), x))
+            return convert(T, ccall(($pfun, libRmath), Float64, $ptypes, x, $(pargs...), 1, 0))
+        end
 
-        $ccdf($(pdecls...), x::Union{Float64,Int}) =
-            ccall(($pfun, libRmath), Float64, $ptypes, x, $(pargs...), 0, 0)
+        function $ccdf($(pdecls...), x::Real)
+            T = float(Base.promote_typeof($(pargs...), x))
+            return convert(T, ccall(($pfun, libRmath), Float64, $ptypes, x, $(pargs...), 0, 0))
+        end
 
-        $logcdf($(pdecls...), x::Union{Float64,Int}) =
-            ccall(($pfun, libRmath), Float64, $ptypes, x, $(pargs...), 1, 1)
+        function $logcdf($(pdecls...), x::Real)
+            T = float(Base.promote_typeof($(pargs...), x))
+            return convert(T, ccall(($pfun, libRmath), Float64, $ptypes, x, $(pargs...), 1, 1))
+        end
 
-        $logccdf($(pdecls...), x::Union{Float64,Int}) =
-            ccall(($pfun, libRmath), Float64, $ptypes, x, $(pargs...), 0, 1)
+        function $logccdf($(pdecls...), x::Real)
+            T = float(Base.promote_typeof($(pargs...), x))
+            return convert(T, ccall(($pfun, libRmath), Float64, $ptypes, x, $(pargs...), 0, 1))
+        end
 
-        $invcdf($(pdecls...), q::Union{Float64,Int}) =
-            ccall(($qfun, libRmath), Float64, $qtypes, q, $(pargs...), 1, 0)
+        function $invcdf($(pdecls...), q::Real)
+            T = float(Base.promote_typeof($(pargs...), q))
+            return convert(T, ccall(($qfun, libRmath), Float64, $qtypes, q, $(pargs...), 1, 0))
+        end
 
-        $invccdf($(pdecls...), q::Union{Float64,Int}) =
-            ccall(($qfun, libRmath), Float64, $qtypes, q, $(pargs...), 0, 0)
+        function $invccdf($(pdecls...), q::Real)
+            T = float(Base.promote_typeof($(pargs...), q))
+            return convert(T, ccall(($qfun, libRmath), Float64, $qtypes, q, $(pargs...), 0, 0))
+        end
 
-        $invlogcdf($(pdecls...), lq::Union{Float64,Int}) =
-            ccall(($qfun, libRmath), Float64, $qtypes, lq, $(pargs...), 1, 1)
+        function $invlogcdf($(pdecls...), lq::Real)
+            T = float(Base.promote_typeof($(pargs...), lq))
+            return convert(T, ccall(($qfun, libRmath), Float64, $qtypes, lq, $(pargs...), 1, 1))
+        end
 
-        $invlogccdf($(pdecls...), lq::Union{Float64,Int}) =
-            ccall(($qfun, libRmath), Float64, $qtypes, lq, $(pargs...), 0, 1)
+        function $invlogccdf($(pdecls...), lq::Real)
+            T = float(Base.promote_typeof($(pargs...), lq))
+            return convert(T, ccall(($qfun, libRmath), Float64, $qtypes, lq, $(pargs...), 0, 1))
+        end
 
         if $has_rand
             $rand($(pdecls...)) =
@@ -109,7 +129,6 @@ macro import_rmath(rname, jname, pargs...)
     esc(_import_rmath(rname, jname, pargs))
 end
 
-
 ### Import specific functions
 
 @import_rmath beta beta α β
diff --git a/test/chainrules.jl b/test/chainrules.jl
index e469ebf..d59b5ea 100644
--- a/test/chainrules.jl
+++ b/test/chainrules.jl
@@ -32,25 +32,22 @@ using Random
     test_frule(tdistlogpdf, x, y)
     test_rrule(tdistlogpdf, x, y)
 
-    # use `BigFloat` to avoid Rmath implementation in finite differencing check
-    # (returns `NaN` for non-integer values)
-    n = rand(1:100)
-    x = BigFloat(n)
-    y = big(logistic(randn()))
-    z = BigFloat(rand(1:n))
+    x = rand(1:100)
+    y = logistic(randn())
+    z = rand(1:x)
     test_frule(binomlogpdf, x, y, z)
     test_rrule(binomlogpdf, x, y, z)
 
-    x = big(exp(randn()))
-    y = BigFloat(rand(1:100))
+    x = exp(randn())
+    y = rand(1:100)
     test_frule(poislogpdf, x, y)
     test_rrule(poislogpdf, x, y)
 
     # test special case λ = 0
-    _, pb = rrule(StatsFuns.poislogpdf, 0.0, 0.0)
+    _, pb = rrule(poislogpdf, 0.0, 0)
     _, x̄1, _ = pb(1)
     @test x̄1 == -1
-    _, pb = rrule(StatsFuns.poislogpdf, 0.0, 1.0)
+    _, pb = rrule(poislogpdf, 0.0, 1)
     _, x̄1, _ = pb(1)
     @test x̄1 == Inf
 end
diff --git a/test/generic.jl b/test/generic.jl
index 1b4bf0e..473d6cd 100644
--- a/test/generic.jl
+++ b/test/generic.jl
@@ -1,9 +1,10 @@
 using StatsFuns
+using StatsFuns: RFunctions
 using ForwardDiff: Dual
 
-function check_rmath(fname, statsfun, params, aname, a, isprob, rtol)
-    v = statsfun(params..., a)
-    rv = statsfun(params..., Dual(a)).value
+function check_rmath(fname, statsfun, rmathfun, params, aname, a, isprob, rtol)
+    v = @inferred(rmathfun(params..., a))
+    rv = @inferred(statsfun(params..., Dual(a))).value
     if isprob
         rd = abs(v / rv - 1.0)
         if rd > rtol
@@ -27,10 +28,12 @@ function genericcomp(basename, params, X::AbstractArray, rtol=100eps(float(one(e
   logpdf = string(basename, "logpdf")
   stats_pdf = eval(Symbol(pdf))
   stats_logpdf = eval(Symbol(logpdf))
+  rmath_pdf = eval(Meta.parse(string("RFunctions.", pdf)))
+  rmath_logpdf = eval(Meta.parse(string("RFunctions.", logpdf)))
   for i = 1:length(X)
     x = X[i]
-    check_rmath(pdf, stats_pdf, params, "x", x, true, rtol)
-    check_rmath(logpdf, stats_logpdf, params, "x", x, false, rtol)
+    check_rmath(pdf, stats_pdf, rmath_pdf, params, "x", x, true, rtol)
+    check_rmath(logpdf, stats_logpdf, rmath_logpdf, params, "x", x, false, rtol)
   end
 end
 
diff --git a/test/rmath.jl b/test/rmath.jl
index 138cce8..f3c5829 100644
--- a/test/rmath.jl
+++ b/test/rmath.jl
@@ -1,9 +1,12 @@
-using StatsFuns, Test
-import StatsFuns.RFunctions
+using StatsFuns
+using StatsFuns: RFunctions
+using Test
 
 function check_rmath(fname, statsfun, rmathfun, params, aname, a, isprob, rtol)
-    v = statsfun(params..., a)
-    rv = rmathfun(params..., a)
+    v = @inferred(statsfun(params..., a))
+    rv = @inferred(rmathfun(params..., a))
+    @test v isa float(Base.promote_typeof(params..., a))
+    @test rv isa float(Base.promote_typeof(params..., a))
     if isprob
         @test v ≈ rv rtol=rtol nans=true
     else
@@ -116,12 +119,35 @@ end
 
 @testset "RMath" begin
     rmathcomp_tests("beta", [
-        ((1.0, 1.0), 0.01:0.01:0.99),
-        ((2.0, 3.0), 0.01:0.01:0.99),
-        ((10.0, 2.0), 0.01:0.01:0.99),
-        ((10, 2), 0.01:0.01:0.99),
+        ((0.1, 1.0), 0.0:0.01:1.0),
+        ((1.0, 1.0), 0.0:0.01:1.0),
+        ((2.0, 3.0), 0.0:0.01:1.0),
+        ((10.0, 2.0), 0.0:0.01:1.0),
+        ((10, 2), 0.0:0.01:1.0),
+        ((1f0, 1f0), 0f0:0.01f0:1f0),
+        ((1.0, 1.0), 0f0:0.01f0:1f0),
+        ((Float16(1), Float16(1)), Float16(0):Float16(0.01):Float16(1)),
+        ((1f0, 1f0), Float16(0):Float16(0.01):Float16(1)),
+        ((10, 2), [0, 1]),
+        ((10, 2), 0//1:1//100:1//1),
     ])
 
+    # We test the following extreme parameters separately since
+    # a slightly larger tolerance is needed.
+    #
+    # For `betapdf(1000, 2, 0.58)`:
+    # StatsFuns:   1.9419987107407202e-231
+    # Rmath:       1.941998710740941e-231
+    # Mathematica: 1.941998710742487e-231
+    # For `betapdf(1000, 2, 0.68)`:
+    # StatsFuns:   1.5205049885199752e-162
+    # Rmath:       1.5205049885200616e-162
+    # Mathematica: 1.520504988521358e-162
+    @testset "Beta(1000, 2)" begin
+        rmathcomp("beta", (1000, 2), setdiff(0.0:0.01:1.0, (0.58, 0.68)))
+        rmathcomp("beta", (1000, 2), [0.58, 0.68], 1e-12)
+    end
+
     rmathcomp_tests("binom", [
         ((1, 0.5), 0.0:1.0),
         ((1, 0.7), 0.0:1.0),
@@ -129,6 +155,11 @@ end
         ((20, 0.1), 0.0:20.0),
         ((20, 0.9), 0.0:20.0),
         ((20, 0.9), 0:20),
+        ((1, 0.5f0), 0f0:1f0),
+        ((1, 0.5), 0f0:1f0),
+        ((1, Float16(0.5)), Float16(0):Float16(1)),
+        ((1, 0.5f0), Float16(0):Float16(1)),
+        ((10, 1//2), 0//1:10//1),
     ])
 
     rmathcomp_tests("chisq", [
@@ -136,6 +167,9 @@ end
         ((4,), 0.0:0.1:8.0),
         ((9,), 0.0:0.1:8.0),
         ((9,), 0:8),
+        ((1,), 0f0:0.1f0:8f0),
+        ((1,), Float16(0):Float16(0.1):Float16(8)),
+        ((9,), 0//1:8//1),
     ])
 
     rmathcomp_tests("fdist", [
@@ -145,20 +179,31 @@ end
         ((10, 1), (0.0:0.1:5.0)),
         ((10, 3), (0.0:0.1:5.0)),
         ((10, 3), (0:5)),
+        ((1, 1), (0f0:0.1f0:5f0)),
+        ((1, 1), (Float16(0):Float16(0.1):Float16(5))),
+        ((10, 3), 0//1:5//1),
     ])
 
     rmathcomp_tests("gamma", [
-        ((1.0, 1.0), (0.05:0.05:12.0)),
-        ((0.5, 1.0), (0.05:0.05:12.0)),
-        ((3.0, 1.0), (0.05:0.05:12.0)),
-        ((9.0, 1.0), (0.05:0.05:12.0)),
-        ((2.0, 3.0), (0.05:0.05:12.0)),
-        ((2, 3), (1:12)),
+        ((1.0, 1.0), (0.0:0.05:12.0)),
+        ((0.5, 1.0), (0.0:0.05:12.0)),
+        ((3.0, 1.0), (0.0:0.05:12.0)),
+        ((9.0, 1.0), (0.0:0.05:12.0)),
+        ((2.0, 3.0), (0.0:0.05:12.0)),
+        ((2, 3), (0:12)),
+        ((1f0, 1f0), (0f0:0.05f0:12f0)),
+        ((1.0, 1.0), (0f0:0.05f0:12f0)),
+        ((Float16(1), Float16(1)), (Float16(0):Float16(0.05):Float16(12))),
+        ((1f0, 1f0), (Float16(0):Float16(0.05):Float16(12))),
+        ((2, 3), (0//1:12//1)),
     ])
 
     rmathcomp_tests("hyper", [
         ((2, 3, 4), 0.0:4.0),
-        ((2, 3, 4), 0:4)
+        ((2, 3, 4), 0:4),
+        ((2, 3, 4), 0f0:4f0),
+        ((2, 3, 4), Float16(0):Float16(4)),
+        ((2, 3, 4), 0//1:4//1),
     ])
 
     rmathcomp_tests("nbeta", [
@@ -167,6 +212,11 @@ end
         ((1.0, 1.0, 2.0), 0.01:0.01:0.99),
         ((3.0, 4.0, 2.0), 0.01:0.01:0.99),
         ((3, 4, 2), 0.01:0.01:0.99),
+        ((1f0, 1f0, 0f0), 0.01f0:0.01f0:0.99f0),
+        ((1.0, 1.0, 0.0), 0.01f0:0.01f0:0.99f0),
+        ((Float16(1), Float16(1), Float16(0)), Float16(0.01):Float16(0.01):Float16(0.99)),
+        ((1f0, 1f0, 0f0), Float16(0.01):Float16(0.01):Float16(0.99)),
+        ((3, 4, 2), 1//100:1//100:99//100),
     ])
 
     rmathcomp_tests("nbinom", [
@@ -174,7 +224,11 @@ end
         ((3, 0.5), 0.0:20.0),
         ((3, 0.2), 0.0:20.0),
         ((3, 0.8), 0.0:20.0),
+        ((1, 0.5f0), 0f0:20f0),
+        ((1, 0.5), 0f0:20f0),
+        ((1, Float16(0.5)), Float16(0):Float16(20)),
         ((3, 0.8), 0:20),
+        ((3, 1//2), 0//1:20//1),
     ])
 
     rmathcomp_tests("nchisq", [
@@ -183,6 +237,9 @@ end
         ((4, 1), 0.0:0.2:8.0),
         ((4, 3), 0.0:0.2:8.0),
         ((4, 3), 0:8),
+        ((2, 1), 0f0:0.2f0:8f0),
+        ((2, 1), Float16(0):Float16(0.2):Float16(8)),
+        ((2, 1), 0//1:1//5:8//1),
     ])
 
     rmathcomp_tests("nfdist", [
@@ -190,6 +247,11 @@ end
         ((1.0, 1.0, 2.0), 0.1:0.1:10.0),
         ((2.0, 3.0, 1.0), 0.1:0.1:10.0),
         ((2, 3, 1), 1:10),
+        ((1f0, 1f0, 0f0), 0.1f0:0.1f0:10f0),
+        ((1.0, 1.0, 0.0), 0.1f0:0.1f0:10f0),
+        ((Float16(1), Float16(1), Float16(0)), Float16(0.1):Float16(0.1):Float16(10)),
+        ((1f0, 1f0, 0f0), Float16(0.1):Float16(0.1):Float16(10)),
+        ((2, 3, 1), 1//1:10//1),
     ])
 
     rmathcomp_tests("norm", [
@@ -200,6 +262,11 @@ end
         ((0, 1), -3.0:0.01:3.0),
         ((0, 1), -3:3),
         ((0.0, 0.0), -6.0:0.1:6.0),
+        ((0f0, 1f0), -6f0:0.01f0:6f0),
+        ((0.0, 1.0), -6f0:0.01f0:6f0),
+        # Fail since `SpecialFunctions.erfcx` is not implemented for `Float16`
+        #((Float16(0), Float16(1)), -Float16(6):Float16(0.01):Float16(6)),
+        #((0f0, 1f0), -Float16(6):Float16(0.01):Float16(6)),
     ])
 
     rmathcomp_tests("ntdist", [
@@ -208,6 +275,9 @@ end
         ((2, 1), -4.0:0.1:10.0),
         ((2, 4), -4.0:0.1:10.0),
         ((2, 4), -4:10),
+        ((0, 1), -4f0:0.1f0:10f0),
+        ((0, 1), -Float16(4):Float16(0.1):Float16(10)),
+        ((0, 1), -4//1:1//10:10//1),
     ])
 
     rmathcomp_tests("pois", [
@@ -216,6 +286,11 @@ end
         ((2.0,), 0.0:20.0),
         ((10.0,), 0.0:20.0),
         ((10,), 0:20),
+        ((0.5f0,), 0f0:20f0),
+        ((0.5,), 0f0:20f0),
+        ((Float16(0.5),), Float16(0):Float16(20)),
+        ((0.5f0,), Float16(0):Float16(20)),
+        ((1//2,), 0//1:20//1),
     ])
 
     rmathcomp_tests("tdist", [
@@ -223,6 +298,9 @@ end
         ((2,), -5.0:0.1:5.0),
         ((5,), -5.0:0.1:5.0),
         ((5,), -5:5),
+        ((1,), -5f0:0.1f0:5f0),
+        ((1,), -Float16(5):Float16(0.1):Float16(5)),
+        ((1,), -5//1:5//1),
     ])
 
     rmathcomp_tests("srdist", [
@@ -230,7 +308,10 @@ end
         ((2,2), (0.0:0.2:5.0)),
         ((5,3), (0.0:0.2:5.0)),
         ((10,2), (0.0:0.2:5.0)),
-        ((10,5), (0.0:0.2:5.0))
+        ((10,5), (0.0:0.2:5.0)),
+        ((1,2), (0f0:0.2f0:5f0)),
+        ((1,2), (Float16(0):Float16(0.2):Float16(5))),
+        ((1,2), (0//1:1//5:5//1)),
     ])
 
     # Note: Convergence fails in srdist with cdf values below 0.16 with df = 10, k = 5.
@@ -240,4 +321,31 @@ end
     rx = srdistinvcdf(10, 5, q)
     rtol = 100eps(1.0)
     @test_broken x ≈ rx atol=rtol rtol=rtol nans=true
+
+    # Test values outside of the support
+    rmathcomp_tests("beta", [
+        ((1.0, 1.0), [-10.0, -6.3, 2.1, 23.5]),
+        ((1//1, 1//1), [-10//1, -63//10, 21//10, 47//2]),
+        ((1, 1), [-10, -6, 2, 24]),
+    ])
+    rmathcomp_tests("binom", [
+        ((5, 0.5), [-8, -2.3, 1.2, 5.4, 11.9]),
+        ((5, 1//2), [-8, -23//10, 6//5, 27//5, 119//10]),
+        ((5, 1//2), [-8, -2, 6, 12]),
+    ])
+    rmathcomp_tests("fdist", [
+        ((1.0, 1.0), [-10.0, -6.3]),
+        ((1//1, 1//1), [-10//1, -63//10]),
+        ((1, 1), [-10, -6]),
+    ])
+    rmathcomp_tests("gamma", [
+        ((1.0, 1.0), [-10.0, -6.3]),
+        ((1//1, 1//1), [-10//1, -63//10]),
+        ((1, 1), [-10, -6]),
+    ])
+    rmathcomp_tests("pois", [
+        ((0.5,), [-10, -2.5, 1.3, 8.7]),
+        ((1//2,), [-10, -5//2, 13//10, 87//10]),
+        ((1,), [-10, -3]),
+    ])
 end