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TWEET # My complete test a guest Aug 21st, 2018 79 Never
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1. def test(b:int) -> int:
2.     """
3.     `//` does "floor division", meaning it performs the division and then
4.     does a true floor operation - unlike C and Python2 which do "integer"
5.     division that merely truncates the remainder.
6.     """
7.     return (b + 16383) // 16384
8.
9. def foo(b:int) -> int:
10.     """
11.     Nothing to explain here, just the second of your three expressions.
12.     """
13.     return ( (b - 1) // 16384) + 1
14.
15. def quest(b:int) -> int:
16.     """
17.     "An upside-down ceiling is a floor" is the advice that led me to this;
18.     in Python3 `-(-x//y)` is ceil(x/y) because of the aforementioned
19.     "floor division" that will result in e.g. `-1//2` = `-1` and then a
20.     correcting inversion gives `-(-1//2) = -(-1) = 1 == ceil(1/2)`.
21.     """
22.     return -(-b // 16384)
23.
24.
25. # this checks for any differences in the outputs by testing with each integer
26. # on the interval from 0 (inclusive) to 163840 (exclusive), because
27. # `NOT(x = y) or NOT(x = z)` is equivalent to `NOT( x = y AND x = z)` which by
28. # transitive property covers all cases where any one output is different.
29. for i in range(163840):
30.     if test(i) != quest(i) or test(i) != foo(i):
31.             print("i=", i, " test(i)=", test(i), " quest(i)=", quest(i), " foo(i)=", foo(i), sep='')
32.             break
33.
34. # At this point, nothing is output, meaning the entire loop was executed without
35. # finding any differing outputs.
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