Converting a number to base64 in Python

So I am trying to program (in Python 3 WITHOUT strings) this cool project that I found.

Return the 6-character string representation of the 36-bit number n as a base-64 number in reverse order where the order of the 64 numerals is: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz-+

For example,

encode(0) → '000000'

encode(9876543210) → 'gR1iC9'

encode(68719476735) → '++++++'

What I have so far is:

def encode(n):
  SYM = {'0': 0,
         '1': 1,
         '2': 2,
         '3': 3,
         '4': 4,
         '5': 5,
         '6': 6,
         '7': 7,
         '8': 8,
         '9': 9,
         'A': 10,
         'B': 11,
         'C': 12,
         'D': 13,
         'E': 14,
         'F': 15,
         'G': 16,
         'H': 17,
         'I': 18,
         'J': 19,
         'K': 20,
         'L': 21,
         'M': 22,
         'N': 23,
         'O': 24,
         'P': 25,
         'Q': 26,
         'R': 27,
         'S': 28,
         'T': 29,
         'U': 30,
         'V': 31,
         'W': 32,
         'X': 33,
         'Y': 34,
         'Z': 35,
         'a': 36,
         'b': 37,
         'c': 38,
         'd': 39,
         'e': 40,
         'f': 41,
         'g': 42,
         'h': 43,
         'i': 44,
         'j': 45,
         'k': 46,
         'l': 47,
         'm': 48,
         'n': 49,
         'o': 50,
         'p': 51,
         'q': 52,
         'r': 53,
         's': 54,
         't': 55,
         'u': 56,
         'v': 57,
         'w': 58,
         'x': 59,
         'y': 60,
         'z': 61,
         '-': 62,
         '+': 63,}

But now I am not sure what to do next. I do not want to use strings and concatenation etc, I would like to do this using modulus and the standard number theory + for/while/else methods.

My thoughts were to define

r1 = n % 63
r2 = r1 % 63
r3 = r2 % 63
r4 = r3 % 63
r5 = r4 % 63
r6 = r5 % 63

But I'm not sure what to do from there.

How should I convert n to base 64?

At the end, to reverse the digits after I have found the new representation, I am thinking that I will just mod each power of 10 to isolate each individual digit and then put them back together backwards.

How should I go about programming this?

Thanks!

Here's some code that does what you want. The get_digit function uses a bunch of if... elif tests to convert an integer d in 0 <= d < 64 into its corresponding character number, and then uses the standard chr function to convert that number to the actual character. The encode function does the actual remainder calculations, calling get_digit to do the character conversion, and saving the results into the out list. We append that list with '0' characters to make its length 6.

def get_digit(d):
    ''' Convert a base 64 digit to the desired character '''
    if 0 <= d <= 9:
        # 0 - 9
        c = 48 + d
    elif 10 <= d <= 35:
        # A - Z
        c = 55 + d
    elif 36 <= d <= 61:
        # a - z
        c = 61 + d
    elif d == 62:
        # -
        c = 45
    elif d == 63:
        # +
        c = 43
    else:
        # We should never get here
        raise ValueError('Invalid digit for base 64: ' + str(d)) 
    return chr(c)

# Test `digit`
print(''.join([get_digit(d) for d in range(64)]))

def encode(n):
    ''' Convert integer n to base 64 '''
    out = []
    while n:
        n, r = n // 64, n % 64
        out.append(get_digit(r))
    while len(out) < 6:
        out.append('0')
    return ''.join(out)

# Test `encode`
for i in (0, 9876543210, 68719476735):
    print(i, encode(i))

output

0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz-+
0 000000
9876543210 gR1iC9
68719476735 ++++++

Since we're working with a base that's a power of 2, an alternative to

n, r = n // 64, n % 64

is to use bitwise operations

n, r = n >> 64, n & 63

which are slightly faster, but I guess that doesn't make much difference here, and the previous code is more readable. OTOH, it can be useful to understand why the bitwise version produces the correct result.