Merge files from StatsFuns and LogExpFunctions

Does not affect implementations.

Author: devmotion

src/LogExpFunctions.jl

@@ -7,284 +7,7 @@ using DocStringExtensions: SIGNATURES
 
 using Base: Math.@horner, @irrational
 
-####
-#### constants
-####
-
-@irrational loghalf -0.6931471805599453094 log(big(0.5))
-@irrational logtwo 0.6931471805599453094 log(big(2.))
-@irrational logπ   1.1447298858494001741 log(big(π))
-@irrational log2π  1.8378770664093454836 log(big(2.)*π)
-@irrational log4π  2.5310242469692907930 log(big(4.)*π)
-
-####
-#### functions
-####
-
-"""
-$(SIGNATURES)
-
-Return `x * log(x)` for `x ≥ 0`, handling ``x = 0`` by taking the downward limit.
-
-```jldoctest
-julia> xlogx(0)
-0.0
-```
-"""
-function xlogx(x::Number)
-    result = x * log(x)
-    ifelse(iszero(x), zero(result), result)
-end
-
-"""
-$(SIGNATURES)
-
-Return `x * log(y)` for `y > 0` with correct limit at ``x = 0``.
-
-```jldoctest
-julia> xlogy(0, 0)
-0.0
-```
-"""
-function xlogy(x::Number, y::Number)
-    result = x * log(y)
-    ifelse(iszero(x) && !isnan(y), zero(result), result)
-end
-
-"""
-$(SIGNATURES)
-
-The [logistic](https://en.wikipedia.org/wiki/Logistic_function) sigmoid function mapping a
-real number to a value in the interval ``[0,1]``,
-
-```math
-\\sigma(x) = \\frac{1}{e^{-x} + 1} = \\frac{e^x}{1+e^x}.
-```
-
-Its inverse is the [`logit`](@ref) function.
-"""
-logistic(x::Real) = inv(exp(-x) + one(x))
-
-# The following bounds are precomputed versions of the following abstract
-# function, but the implicit interface for AbstractFloat doesn't uniformly
-# enforce that all floating point types implement nextfloat and prevfloat.
-# @inline function _logistic_bounds(x::AbstractFloat)
-#     (
-#         logit(nextfloat(zero(float(x)))),
-#         logit(prevfloat(one(float(x)))),
-#     )
-# end
-
-@inline _logistic_bounds(::Float16) = (Float16(-16.64), Float16(7.625))
-@inline _logistic_bounds(::Float32) = (-103.27893f0, 16.635532f0)
-@inline _logistic_bounds(::Float64) = (-744.4400719213812, 36.7368005696771)
-
-function logistic(x::Union{Float16, Float32, Float64})
-    e = exp(x)
-    lower, upper = _logistic_bounds(x)
-    ifelse(
-        x < lower,
-        zero(x),
-        ifelse(
-            x > upper,
-            one(x),
-            e / (one(x) + e)
-        )
-    )
-end
-
-"""
-$(SIGNATURES)
-
-The [logit](https://en.wikipedia.org/wiki/Logit) or log-odds transformation,
-
-```math
-\\log\\left(\\frac{x}{1-x}\\right), \\text{where} 0 < x < 1
-```
-
-Its inverse is the [`logistic`](@ref) function.
-"""
-logit(x::Real) = log(x / (one(x) - x))
-
-"""
-$(SIGNATURES)
-
-Return `log(1+x^2)` evaluated carefully for `abs(x)` very small or very large.
-"""
-log1psq(x::Real) = log1p(abs2(x))
-function log1psq(x::Union{Float32,Float64})
-    ax = abs(x)
-    ax < maxintfloat(x) ? log1p(abs2(ax)) : 2 * log(ax)
-end
-
-"""
-$(SIGNATURES)
-
-Return `log(1+exp(x))` evaluated carefully for largish `x`.
-
-This is also called the ["softplus"](https://en.wikipedia.org/wiki/Rectifier_(neural_networks))
-transformation, being a smooth approximation to `max(0,x)`. Its inverse is [`logexpm1`](@ref).
-"""
-log1pexp(x::Real) = x < 18.0 ? log1p(exp(x)) : x < 33.3 ? x + exp(-x) : oftype(exp(-x), x)
-log1pexp(x::Float32) = x < 9.0f0 ? log1p(exp(x)) : x < 16.0f0 ? x + exp(-x) : oftype(exp(-x), x)
-
-"""
-$(SIGNATURES)
-
-Return `log(1 - exp(x))`
-
-See:
- * Martin Maechler (2012) [“Accurately Computing log(1 − exp(− |a|))”](http://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf)
-
-Note: different than Maechler (2012), no negation inside parentheses
-"""
-log1mexp(x::Real) = x < loghalf ? log1p(-exp(x)) : log(-expm1(x))
-
-"""
-$(SIGNATURES)
-
-Return `log(2 - exp(x))` evaluated as `log1p(-expm1(x))`
-"""
-log2mexp(x::Real) = log1p(-expm1(x))
-
-"""
-$(SIGNATURES)
-
-Return `log(exp(x) - 1)` or the “invsoftplus” function.  It is the inverse of
-[`log1pexp`](@ref) (aka “softplus”).
-"""
-logexpm1(x::Real) = x <= 18.0 ? log(expm1(x)) : x <= 33.3 ? x - exp(-x) : oftype(exp(-x), x)
-
-logexpm1(x::Float32) = x <= 9f0 ? log(expm1(x)) : x <= 16f0 ? x - exp(-x) : oftype(exp(-x), x)
-
-const softplus = log1pexp
-const invsoftplus = logexpm1
-
-"""
-$(SIGNATURES)
-
-Return `log(1 + x) - x`.
-
-Use naive calculation or range reduction outside kernel range.  Accurate ~2ulps for all `x`.
-"""
-function log1pmx(x::Float64)
-    if !(-0.7 < x < 0.9)
-        return log1p(x) - x
-    elseif x > 0.315
-        u = (x-0.5)/1.5
-        return _log1pmx_ker(u) - 9.45348918918356180e-2 - 0.5*u
-    elseif x > -0.227
-        return _log1pmx_ker(x)
-    elseif x > -0.4
-        u = (x+0.25)/0.75
-        return _log1pmx_ker(u) - 3.76820724517809274e-2 + 0.25*u
-    elseif x > -0.6
-        u = (x+0.5)*2.0
-        return _log1pmx_ker(u) - 1.93147180559945309e-1 + 0.5*u
-    else
-        u = (x+0.625)/0.375
-        return _log1pmx_ker(u) - 3.55829253011726237e-1 + 0.625*u
-    end
-end
-
-"""
-$(SIGNATURES)
-
-Return `log(x) - x + 1` carefully evaluated.
-"""
-function logmxp1(x::Float64)
-    if x <= 0.3
-        return (log(x) + 1.0) - x
-    elseif x <= 0.4
-        u = (x-0.375)/0.375
-        return _log1pmx_ker(u) - 3.55829253011726237e-1 + 0.625*u
-    elseif x <= 0.6
-        u = 2.0*(x-0.5)
-        return _log1pmx_ker(u) - 1.93147180559945309e-1 + 0.5*u
-    else
-        return log1pmx(x - 1.0)
-    end
-end
-
-# The kernel of log1pmx
-# Accuracy within ~2ulps for -0.227 < x < 0.315
-function _log1pmx_ker(x::Float64)
-    r = x/(x+2.0)
-    t = r*r
-    w = @horner(t,
-                6.66666666666666667e-1, # 2/3
-                4.00000000000000000e-1, # 2/5
-                2.85714285714285714e-1, # 2/7
-                2.22222222222222222e-1, # 2/9
-                1.81818181818181818e-1, # 2/11
-                1.53846153846153846e-1, # 2/13
-                1.33333333333333333e-1, # 2/15
-                1.17647058823529412e-1) # 2/17
-    hxsq = 0.5*x*x
-    r*(hxsq+w*t)-hxsq
-end
-
-"""
-$(SIGNATURES)
-
-Return `log(exp(x) + exp(y))`, avoiding intermediate overflow/undeflow, and handling
-non-finite values.
-"""
-function logaddexp(x::Real, y::Real)
-    # ensure Δ = 0 if x = y = ± Inf
-    Δ = ifelse(x == y, zero(x - y), abs(x - y))
-    max(x, y) + log1pexp(-Δ)
-end
-
-Base.@deprecate logsumexp(x::Real, y::Real) logaddexp(x, y)
-
-"""
-$(SIGNATURES)
-
-Return `log(abs(exp(x) - exp(y)))`, preserving numerical accuracy.
-"""
-logsubexp(x::Real, y::Real) = max(x, y) + log1mexp(-abs(x - y))
-
-"""
-$(SIGNATURES)
-
-Overwrite `r` with the `softmax` (or _normalized exponential_) transformation of `x`
-
-That is, `r` is overwritten with `exp.(x)`, normalized to sum to 1.
-
-See the [Wikipedia entry](https://en.wikipedia.org/wiki/Softmax_function)
-"""
-function softmax!(r::AbstractArray{R}, x::AbstractArray{T}) where {R<:AbstractFloat,T<:Real}
-    n = length(x)
-    length(r) == n || throw(DimensionMismatch("Inconsistent array lengths."))
-    u = maximum(x)
-    s = 0.
-    @inbounds for i = 1:n
-        s += (r[i] = exp(x[i] - u))
-    end
-    invs = convert(R, inv(s))
-    @inbounds for i = 1:n
-        r[i] *= invs
-    end
-    r
-end
-
-"""
-$(SIGNATURES)
-
-Return the [`softmax transformation`](https://en.wikipedia.org/wiki/Softmax_function)
-applied to `x` *in place*.
-"""
-softmax!(x::AbstractArray{<:AbstractFloat}) = softmax!(x, x)
-
-"""
-$(SIGNATURES)
-
-Return the [`softmax transformation`](https://en.wikipedia.org/wiki/Softmax_function)
-applied to `x`.
-"""
-softmax(x::AbstractArray{<:Real}) = softmax!(similar(x, Float64), x)
-
-include("logsumexp.jl")
+include("constants.jl")
+include("basicfuns.jl")
 
 end # module