use newton method to count logarithms; monte-carlo method to compute pi digits; compute square roots with given precision

logarithm.jl

#!/usr/bin/julia
using Test
const EPS = 1e-11


function log_core(base::Float64, n::Float64)
	x = 1
	step = 1
	while step > EPS
		while base ^ x < n
			x += step
		end
		x -= step
		step = step / 10
	end
	return x + step
end


function log(base::Float64, n::Float64)
	if base < 0 || n < 0
		return "error"
	end
	if base < 1 && n < 1
		return log_core(1/base, 1/n)
	elseif base > 1 && n > 1
		return log_core(base, n)
	elseif base < 1 && n > 1
		return - log_core(1/base, n)
	elseif base > 1 && n < 1
		return log_core(base, 1/n)
	end
end


@testset "log" begin
	@test 6 < div(log(Float64(2), Float64(128)), 1) < 8
end;
println(log(Float64(5), Float64(8)))
println(log(Float64(3), Float64(27)))
println(log(Float64(3), Float64(81)))
println(log(Float64(5), Float64(125)))
println(log(Float64(0.5), Float64(1/128)))

pi.jl

#!/usr/bin/julia

function calc_pi()
	Ox, Oy = 100000, 100000
	inside = 0
	attempts = 10000000
	for i = 1:attempts
		x, y = rand(0:Ox), rand(0:Oy)
		if (x ^ 2 + y ^ 2) ^ 0.5 < Ox
			inside = inside + 1
		end
	end
	return inside / attempts * 4
end

print(calc_pi())

sqrt.jl

#!/usr/bin/julia
const eps = 1e-15;

function sqrt(n::Int64)
	x = 1;
	while abs(x * x - n) > eps
		x = (x + n / x) / 2;
	end
	return x;
end

println(sqrt(7));