# L-25 MCS 572 Wed 23 Oct 2024 : leibnizunrolled.jl

using BenchmarkTools

"""
The Leibniz series approximates pi/4 as
1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

This example is based on section 3.2.2 on loop unrolling in 
Scientific Programming and Computer Architecture
by Divakar Viswanath, Springer-Verlag, 2017.

The branching in the straighforward code below prevents
a pipelined execution of the floating-point operations.
"""
function leibniz1(N::Int)
    s = 1.0
    for i=1:N
        if(i%2 == 1)
            s = s - 1.0/(2.0*i + 1.0)
        else
            s = s + 1.0/(2.0*i + 1.0)
        end
    end
    return s
end

"""
The Leibniz series approximates pi/4 as
1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...

This example is based on section 3.2.2 on loop unrolling in 
Scientific Programming and Computer Architecture
by Divakar Viswanath, Springer-Verlag, 2017.

This second implementation (see leibniz1.jl for the first one)
allows a pipelined execution of the floating-point operations.
"""
function leibniz2(N::Int)
    s = 1.0
    for i=2:2:N
        s = s + 1.0/(2.0*i + 1.0)
    end
    for i=1:2:N
        s = s - 1.0/(2.0*i + 1.0)
    end
    return s
end

println(4.0*leibniz1(10^8))
@btime leibniz1(10^8)

println(4.0*leibniz2(10^8))
@btime leibniz2(10^8)