#!/usr/bin/env julia

# Jacek Poziemski 272389

"""
    macheps(T::Type{<: AbstractFloat})::T

Calculate the machine epsilon iteratively
for the given IEEE 754 floating point type.

# Arguments
- `T`: the floating point type
"""
function macheps(T::Type{<: AbstractFloat})::T
    one_T::T = one(T)
    ret::T = one_T
    while one_T + (ret / T(2)) > one_T
        ret /= T(2)
    end

    return ret
end

"""
    eta(T::Type{<: AbstractFloat})::T

Calculate the eta number iteratively
for the given IEEE 754 floating point type.

# Arguments
- `T`: the floating point type
"""
function eta(T::Type{<: AbstractFloat})::T
    ret::T = one(T)

    while ret / T(2) > zero(T)
        ret /= T(2)
    end

    return ret
end

"""
    max(T::Type{<: AbstractFloat})::T

Calculate the largest possible value
for the given IEEE 754 floating type.

# Arguments
- `T`: the floating point type
"""
function max(T::Type{<: AbstractFloat})::T
    ret::T = one(T)

    while isfinite(ret * T(2))
        ret *= T(2)
    end

    x::T = ret / T(2)
    while isfinite(ret + x)
        ret += x
        x /= T(2)
    end

    return ret
end

for T::Type{<: AbstractFloat} in [Float16, Float32, Float64]
    println("me - macheps($T): $(macheps(T))")
    println("julia - eps($T): $(eps(T))")

    println()

    println("me - eta($T): $(eta(T))")
    println("julia - nextfloat($T(0.0)): $(nextfloat(T(0.0)))")

    println()

    println("me - max($T): $(max(T))")
    println("julia - floatmax($T): $(floatmax(T))")

    println()

    println("julia - floatmin($T): $(floatmin(T))")

    println()
end