Precision and time

gistfile1.txt

# Adapted from https://tpapp.github.io/post/log1p/
# consistent random numbers
T = Float32
srand(UInt32[0xfd909253, 0x7859c364, 0x7cd42419, 0x4c06a3b6])

"""
    err(x, [prec])

Return two values, which are the log2 relative errors for calculating
`log(x)`, using `Base.log` and `Base.Math.JuliaLibm.log`.

The errors are calculated by compating to `BigFloat` calculations with the given
precision `prec`.1½
"""
function err(x, prec = 1024)
    yb = log(BigFloat(x, prec))
    e2(y) = Float64(log2(abs(y-yb)/abs(yb)))
    e2(log(x)), e2(Base.Math.JuliaLibm.log(x))
end

x = exp.(randn(Float32, 20000)*T(10))       # z > 0, Lognormal(0, 10)
es = map(err, x)                # errors

using Plots; gr()               # plots

p = scatter(log2.(x), first.(es), xlab = "log2(x)", ylab = "log2 error of Base.log",
        legend = false)
hline!(log2(eps())-[0,1])
Plots.png("Base_log_error_$(T).png")
scatter(log2.(x), last.(es) .- first.(es), xlab = "log2(x)",
        ylab = "improvement (Base.Math.JuliaLibm.log)", legend = false)
Plots.png("JuliaLibm_improvement_$(T).png")
q = scatter(log2.(x), last.(es), xlab = "log2(x)",
        ylab = "log2 error of Base.Math.JuliaLibm.log", legend = false)
hline!(log2(eps())-[0,1])
Plots.png("JuliaLibm_log_error_$(T).png")

######################################################################
# WARNING: these run for a very long time
######################################################################
using BenchmarkTools

x = exp.(vcat(randn(T,200)*T(10), rand(T,200)*T(0.1)) # z > 0, more values around 
b1 = [@belapsed log($x) for x in x]        # WARNING: takes forever
b2 = [@belapsed Base.Math.JuliaLibm.log($x) for x in x] # ditto

scatter(log2.(x), b2 ./ b1, xlab = "log2(x)",
        ylab = "time Math.JuliaLibm.log / log", legend = false, yticks = 0:0.2:1.2)
hline!([1])
Plots.png("relative_time_$(T).png")