Divmod, yeah?

bigjoyints/divmod.py

@@ -0,0 +1,108 @@
+'''
+Let's grok division (and modulus.)
+
+For now we will deal with both positive
+(or at least of the same sign.)
+
+
+'''
+
+def div_mod(A, B):
+    '''
+    A and B are lists of digits, LSB->MSB.
+    '''
+    if not A:
+        return [], []
+    if not B:
+        raise ZeroDivisionError()
+    a_len, b_len = len(A), len(B)
+    if a_len < b_len or A[-1] < B[-1]:
+        return [], A
+
+    # Whew! Okay, we got all that out of the way.
+    # A > B
+
+    A_digits = A[-b_len:]
+    if -1 == cmp_digits(A_digits, B):
+        # Because we know
+        #   A > B  AND a_len >= b_len (aka len(A_digits))
+        # if A_digits < B there must be at least one more
+        # digit in A:
+        assert a_len > b_len
+        A_digits = A[-(b_len + 1):]
+        assert -1 < cmp_digits(A_digits, B)
+    q, r = lil_divmod(A_digits, B)
+
+def lil_divmod(A, B):
+    assert -1 < cmp_digits(A, B)
+    assert A and B
+    # There is a greatest digit between 0..9 such that:
+    # B * digit <= A
+    # The obvious thing to do here is a bisect search,
+    # if we were really just doing 0..9 we could go linear.
+    digit = 9
+    Q = mul_digit_by_list_of_digits(digit, B)
+    while 1 == cmp_digits(Q, A):
+        digit = digit - 1
+        if not digit:
+            raise ValueError('huh?')
+        Q = mul_digit_by_list_of_digits(digit, B)
+    return digit, subtract(A, Q)
+
+def mul_digit_by_list_of_digits(digit, A):
+    assert 0 <= digit <= 9
+    for n in A:
+        assert 0 <= n <= 9
+    return int_to_list(list_to_int(A) * digit)
+
+def int_to_list(i):
+    assert i >= 0
+    return list(map(int, str(i)[::-1]))
+
+def list_to_int(A):
+    i = int(''.join(map(str, A[::-1])))
+    assert i >= 0
+    return i
+
+def cmp_digits(A, B):
+    if len(A) > len(B):
+        return 1
+    if len(A) < len(B):
+        return -1
+    for a, b in zip(reversed(A), reversed(B)):
+        if a > b: return 1
+        if a < b: return -1
+    else:
+        return 0
+
+
+def subtract(A, B):
+    return int_to_list(list_to_int(A) - list_to_int(B))
+
+
+##A = int_to_list(123)
+##B = int_to_list(72)
+##print(A, B)
+##Q = mul_digit_by_list_of_digits(9, A)
+##print(Q)
+
+A = int_to_list(145)
+B = int_to_list(72)
+q, R = lil_divmod(A, B)
+print(f'divmod({list_to_int(A)}, {list_to_int(B)}) = ',
+      q, list_to_int(R))
+
+
+##print(cmp_digits([], []))
+##print(cmp_digits([], [1]))
+##print(cmp_digits([1], []))
+##print(cmp_digits([1], [1]))
+##print(cmp_digits([0,1], [1]))
+
+
+
+
+
+
+
+