e_calcul_SALE_all_base.jl

# calculates Euler e in different bases
# aprroximation for m!,increasing m from on an
# Stirling: ln(n!) = 0.5*ln(2πn) + n(ln(n)-1)
# initial value of 4 until m! > 10^(n+1)
# ln(10) = 2.302585092994046, ln(2pi)=ln(6.283185307179586)
# Eulerin luvun e desimaalit ( n kpl)
# Juhani Kaukoranta 13.2.2022
function e_calcul(n,b)
    # n digits, b base
    nro="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
    print("base ",b," : ",)
    m = 5 # laskentatermien määrä
    test = (n+1)*2.302585092994046
    while m*(log(m)-1.0) + 0.5*log(6.283185307179586*m) <= test
        m += 1
    end
    if b == 2
        print("10.",) # eka e:n numero
    else print("2.",) # eka e:n numero
    end
    coef = fill(1,m) # array coef contains only 1
    for i in 1:n
        carry = 0
        for j in reverse(2:m)
            temp = coef[j]*b + carry # in base:bin 2,oct 8,dec 10,hex 16
            carry = div(temp,j)
            coef[j] = temp - carry*j
        end # of digit generation

        print(nro[carry+1],) # prints e digits, on by one
    end
    println()
end