Flush out and squash some bugs.
This commit is contained in:
Simon Forman
parent
df42bbcb7d
commit
634ff157bc
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@ -6,6 +6,8 @@ For now we will deal with both positive
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'''
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from random import randint
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def div_mod(A, B):
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'''
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@ -16,7 +18,7 @@ def div_mod(A, B):
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if not B:
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raise ZeroDivisionError()
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a_len, b_len = len(A), len(B)
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if a_len < b_len or (a_len == b_len and A[-1] < B[-1]):
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if -1 == cmp_digits(A, B): # A < B
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return [], A
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# Whew! Okay, we got all that out of the way.
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@ -30,8 +32,11 @@ def div_mod(A, B):
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# digit in A:
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assert a_len > b_len
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A_digits.insert(0, A.pop())
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assert -1 < cmp_digits(A_digits, B)
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assert -1 < cmp_digits(A_digits, B) # A_digits >= B
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q, R = lil_divmod(A_digits, B)
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# So we have divided a prefix of A by B
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# resulting in a digit q of the answer Q
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# and a remainder R that must be extended
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@ -59,7 +64,7 @@ def div_mod(A, B):
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def foo(Digits, Divisor, Prefix):
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'''
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'''E.g.:
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___2___
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72)145000
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@ -70,13 +75,16 @@ def foo(Digits, Divisor, Prefix):
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Digits = 000
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Divisor = 72
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Prefix = 1
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'''
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Q = []
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while Prefix < Divisor and Digits isn't empty:
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take a digit from Digits
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append it to Prefix
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add a zero to Q <-- but only if new Prefix < Divisor
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Quotient = []
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while Digits:
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Prefix.insert(0, Digits.pop())
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if -1 < cmp_digits(Prefix, Divisor): # Prefix >= Divisor
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break
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Quotient.insert(0, 0)
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'''
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One iteration through the while loop:
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___20__
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@ -87,7 +95,7 @@ def foo(Digits, Divisor, Prefix):
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Another iteration through the while loop:
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___20?_
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___20__
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72)145000
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-144|| = 72 * 2
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---||
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@ -98,16 +106,27 @@ def foo(Digits, Divisor, Prefix):
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Prefix = 100
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At this point Prefix >= Divisor OR Digits == [] OR BOTH
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if Prefix < Divisor AND not Digits:
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the remainder is Prefix
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return Q, Prefix
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return Quotient, Prefix
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'''
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if -1 == cmp_digits(Prefix, Divisor) and not Digits:
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return Quotient, Prefix
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'''
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if Prefix < Divisor AND Digits:
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Can't get here
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assert Prefix >= Divisor
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'''
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q, R = lil_divmod(Prefix, Divisor)
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assert -1 < cmp_digits(Prefix, Divisor) # Prefix >= Divisor
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___200q
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q, Remainder = lil_divmod(Prefix, Divisor)
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Quotient.insert(0, q)
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'''
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___20q_
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72)145000
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-144|| = 72 * 2
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---||
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@ -116,41 +135,38 @@ def foo(Digits, Divisor, Prefix):
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---
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28 = (100 - N) = (100 - 72q)
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R = 28
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New_Prefix = R
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Remainder = 28
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New_Prefix = Remainder
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Digits = 0 (still)
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Divisor = 72 (still)
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'''
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if Digits:
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Q, Remainder = foo(Digits, Divisor, Remainder)
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Quotient = Q + Quotient
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return Quotient, Remainder
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## Q = []
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## N = R
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## while A and -1 == cmp_digits(N, B):
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## N.insert(0, A.pop())
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## Q.insert(0, 0)
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## Q.append(q)
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## if not A:
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## return Q, N
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##
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## Qz, R = div_mod(N, B)
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## return Qz + Q, R
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def lil_divmod(A, B):
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assert -1 < cmp_digits(A, B)
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assert -1 < cmp_digits(A, B) # A >= B
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assert A and B
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# There is a greatest digit between 0..9 such that:
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# There is a greatest digit in 1..9 such that:
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# B * digit <= A
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# The obvious thing to do here is a bisect search,
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# if we were really just doing 0..9 we could go linear.
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# if we were really just doing 1..9 we could go linear.
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# Maybe drive it by the bits in digit?
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digit = 9
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Q = mul_digit_by_list_of_digits(digit, B)
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while 1 == cmp_digits(Q, A):
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while 1 == cmp_digits(Q, A): # Q > A
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digit = digit - 1
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if not digit:
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raise ValueError('huh?')
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Q = mul_digit_by_list_of_digits(digit, B)
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return digit, subtract(A, Q)
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assert -1 < cmp_digits(A, Q)
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assert list_to_int(A) >= list_to_int(Q)
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remainder = subtract(A, Q)
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assert -1 == cmp_digits(remainder, B) # Remainder < Divisor
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return digit, remainder
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def mul_digit_by_list_of_digits(digit, A):
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assert 0 <= digit <= 9
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@ -169,16 +185,17 @@ def list_to_int(A):
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return i
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def cmp_digits(A, B):
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if len(A) > len(B):
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return 1
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if len(A) < len(B):
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return -1
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for a, b in zip(reversed(A), reversed(B)):
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if a > b: return 1
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if a < b: return -1
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else:
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return 0
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a, b = list_to_int(A), list_to_int(B)
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return 1 if a > b else 0 if a == b else -1
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## if len(A) > len(B):
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## return 1
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## if len(A) < len(B):
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## return -1
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## for a, b in zip(reversed(A), reversed(B)):
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## if a > b: return 1
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## if a < b: return -1
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## else:
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## return 0
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def subtract(A, B):
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return int_to_list(list_to_int(A) - list_to_int(B))
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@ -200,12 +217,28 @@ B = int_to_list(72)
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def try_it(a, b):
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A = int_to_list(a)
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B = int_to_list(b)
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print(f'divmod({list_to_int(A)}, {list_to_int(B)}) = ', end='')
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Q, R = div_mod(A, B)
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print(f'divmod({list_to_int(A)}, {list_to_int(B)}) = {list_to_int(Q)}, {list_to_int(R)}')
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q, r = divmod(a, b)
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assert q == list_to_int(Q)
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assert r == list_to_int(R)
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print(f'{list_to_int(Q)}, {list_to_int(R)}')
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try_it(145, 72)
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try_it(1450, 72)
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try_it(145000, 72)
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for _ in range(20):
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try_it(
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randint(0, 10**30),
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randint(0, 10**4)
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)
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#div_mod(int_to_list(829569806932507641866449807296), int_to_list(296))
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##try_it(145, 72)
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##try_it(1450, 72)
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##try_it(14500, 72)
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##try_it(145000, 72)
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##try_it(1450000, 72)
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##try_it(14500000, 72)
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##try_it(100000000000000, 3)
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##print(cmp_digits([], []))
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@ -213,11 +246,3 @@ try_it(145000, 72)
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##print(cmp_digits([1], []))
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##print(cmp_digits([1], [1]))
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##print(cmp_digits([0,1], [1]))
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