#include "windows.bi"

Type prime_factor
    p As Ulong
    e As Ulong
End Type

' Arrays and their counters
Dim Shared primes(1 Shl 15) As Ulong
Dim Shared primeCount As Integer = 0

Function get_prime_factors(n As Ulong, factors() As prime_factor) As Integer
    Static As Ulong e, p, i
    Dim factorCount As Integer = 0

    ' Handle even numbers specially
    If (n And 1) = 0 Then
        e = 0
        While (n And 1) = 0
            e += 1
            n Shr= 1
        Wend
        factors(factorCount).p = 2
        factors(factorCount).e = e
        factorCount += 1
    End If

    ' Now we only need to check odd numbers
    For i = 1 To primeCount - 1
        p = primes(i)
        If p * p > n Then Exit For

        If (n Mod p) = 0 Then
            e = 0
            Do
                e += 1
                n \= p
            Loop While (n Mod p) = 0

            factors(factorCount).p = p
            factors(factorCount).e = e
            factorCount += 1
        End If
    Next

    If n > 1 Then
        factors(factorCount).p = n
        factors(factorCount).e = 1
        factorCount += 1
    End If

    Return factorCount
End Function

Function get_factors(n As Ulong, factors() As Ulong) As Integer
    Dim As Ulong i, k
    Dim As Integer p, j, prevLen
    Dim As prime_factor prime_factors(100)
    Dim As Integer factorCount = get_prime_factors(n, prime_factors())

    factors(0) = 1
    Dim As Integer len2 = 1
    Dim As Integer totalFactors = 1

    For i = 0 To factorCount - 1
        p = prime_factors(i).p
        prevLen = totalFactors

        For j = 0 To prime_factors(i).e - 1
            For k = 0 To prevLen - 1
                factors(totalFactors) = factors(k) * p
                totalFactors += 1
            Next
            p *= prime_factors(i).p
        Next
    Next

    ' Sort the factors
    For i = 0 To totalFactors - 2
        For p = i + 1 To totalFactors - 1
            If factors(i) > factors(p) Then Swap factors(i), factors(p)
        Next
    Next

    Return totalFactors
End Function

Function mpow(a As Ulongint, p As Ulongint, m As Ulongint) As Ulongint
    Dim r As Ulongint = 1
    While p > 0
        If (p And 1) Then r = (r * a) Mod m
        a = (a * a) Mod m
        p Shr= 1
    Wend
    Return r
End Function

Function ipow(a As Ulongint, p As Ulongint) As Ulongint
    Dim r As Ulongint = 1
    While p > 0
        If (p And 1) Then r *= a
        a *= a
        p Shr= 1
    Wend
    Return r
End Function

Function GCD(n As Ulongint, d As Ulongint) As Ulongint
    Return Iif(d = 0, n, GCD(d, n Mod d))
End Function

Function lcm(r As Ulongint, s As Ulongint) As Ulongint
    Return (r * s) / GCD(r, s)
End Function

Function multi_order_p(a As Ulong, p As Ulong, e As Ulong) As Ulong
    Dim As Ulong m = ipow(p, e)
    Dim As Ulong t = (m \ p) * (p - 1)
    Dim As Ulong fac(1000)
    Dim As Integer facCount = get_factors(t, fac())

    For i As Integer = 0 To facCount - 1
        If mpow(a, fac(i), m) = 1 Then Return fac(i)
    Next

    Return 0
End Function

Function multi_order(a As Ulong, m As Ulong) As Ulong
    Dim pf(100) As prime_factor
    Dim pfCount As Integer = get_prime_factors(m, pf())
    Dim res As Ulong = 1

    For i As Integer = 0 To pfCount - 1
        res = lcm(res, multi_order_p(a, pf(i).p, pf(i).e))
    Next

    Return res
End Function

Sub sieve()
    Dim As Integer i, j
    Const SIZE = 1 Shl 15
    Static bits(0 To SIZE-1) As Boolean

    ' Fill with True's (faster than loop)
    FillMemory(@bits(0), SIZE, True)

    bits(0) = False
    bits(1) = False

    ' Only need to check up to sqrt(SIZE)
    For i = 2 To Int(Sqr(SIZE))
        If bits(i) Then
            For j = i * i To SIZE-1 Step i
                bits(j) = False
            Next
        End If
    Next

    ' Store primes in array
    For i = 2 To SIZE-1
        If bits(i) Then
            primes(primeCount) = i
            primeCount += 1
        End If
    Next
End Sub

' Main program
sieve()
Print multi_order(37, 1000)    ' Prints 100
Print multi_order(37, 3343)    ' Prints 1114
Print multi_order(54, 100001)  ' Prints 9090
Print multi_order(3047753288, 2257683301)  ' Prints 62713425

Sleep