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add logabstanh #86

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add logabstanh #86

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e8d075a
add logabstanh
oscardssmith Nov 16, 2024
528545d
export
oscardssmith Nov 16, 2024
5cf0058
Update src/basicfuns.jl
oscardssmith Nov 16, 2024
95639d1
Update src/basicfuns.jl
oscardssmith Nov 16, 2024
3364d20
Update src/basicfuns.jl
oscardssmith Nov 16, 2024
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Update src/basicfuns.jl
oscardssmith Nov 16, 2024
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2 changes: 1 addition & 1 deletion src/LogExpFunctions.jl
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Expand Up @@ -8,7 +8,7 @@ import LinearAlgebra

export xlogx, xlogy, xlog1py, xexpx, xexpy, logistic, logit, log1psq, log1pexp, log1mexp, log2mexp, logexpm1,
softplus, invsoftplus, log1pmx, logmxp1, logaddexp, logsubexp, logsumexp, logsumexp!, softmax,
softmax!, logcosh, logabssinh, cloglog, cexpexp,
softmax!, logcosh, logabssinh, logabstanh, cloglog, cexpexp,
loglogistic, logitexp, log1mlogistic, logit1mexp

# expm1(::Float16) is not defined in older Julia versions,
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25 changes: 25 additions & 0 deletions src/basicfuns.jl
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Expand Up @@ -149,6 +149,31 @@ end
"""
$(SIGNATURES)

Return `log(abs(tanh(x)))`, carefully evaluated without intermediate calculation of `tanh(x)`.

The implementation ensures `logabstanh(-x) = logabstanh(x)`.
"""
function logabstanh(x::Real)
return log1p(-2/((exp(2abs(x))+1)))
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As indicated by the special cases close to 0 for Float32 and Float64, maybe a safer default would be

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return log1p(-2/((exp(2abs(x))+1)))
return log(abs(tanh(x)))

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I think the version I wrote stays more accurate overall but I'll do a test

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I don't think it's possible to do such an analysis? You can't realistically test any subtype of Real.

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for any AbstractFloat log(tanh(x)) will be inaccurate for large x since tanh(x) will be very close to 1.

end
function logabstanh(x::Float32)
abs_x = abs(x)
if abs_x < 0.0625f0
return log(abs_x) - x*x*(1f0/3)
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end
return log1p(-2/((exp(2abs_x)+1)))
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end
function logabstanh(x::Float64)
abs_x = abs(x)
if abs_x < 0x1p-5
return log(abs_x) + evalpoly(x*x, (0, -1/3, 7/90, -62/2835))
end
return log1p(-2/((exp(2abs_x)+1)))
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end

"""
$(SIGNATURES)

Return `log(1+x^2)` evaluated carefully for `abs(x)` very small or very large.
"""
log1psq(x::Real) = log1p(abs2(x))
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