How can I best make a function which functions similar as modulus but stops at max without using conditionals?

Question

I want to create a function which will function like this:

def ceil(i: int, max: int) -> int:
    return max if i > max else i

I am wondering if it is possible to do this without using conditions.

I think it should be possible to do the function with simple math. But I can't figure out how.

I don't want to use any built in functions.

`max` is poor name - it's built-in function. if I get what you want - `return min(i, ceil_value)` — buran, Jan 29 '22 at 21:50

Lukasz Wiecek · Answer 1 · 2022-01-29T22:37:20.083

2

The following function will do the trick:

def ceil(i: int, max: int) -> int:
    return min(i, max)

But at this point you don't event need the function! :)

ceil = min

and that's it.

P.S. I agree with the comment saying max is not a great name choice.

Based on the discussion from the comment section:

To avoid conditionals that min or abs builin functions have in Python you could do:

custom_abs = lambda v: v * ((v>0) - (v<0))
ceil = lambda a, b: (a + b - custom_abs(a-b)) / 2

However, I still think you would have conditionals in CPython implementation due to type checking etc.

edited Jan 29 '22 at 22:37

answered Jan 29 '22 at 21:50

Lukasz Wiecek

414
2
8

1

are you sure the min functions does not contain any conditions? – mama Jan 29 '22 at 22:02
@mama Why do you care? – Kelly Bundy Jan 29 '22 at 22:07
because I don't want to use if statements – mama Jan 29 '22 at 22:07
@mama Why not ? – Kelly Bundy Jan 29 '22 at 22:08
Do you allow your CPU to use branching? :> – Lukasz Wiecek Jan 29 '22 at 22:08
I think its possible to do it with math. – mama Jan 29 '22 at 22:09
1

`ceil = lambda a, b: (a + b - abs(a-b)) / 2` from https://stackoverflow.com/a/7424900/1577204 – Lukasz Wiecek Jan 29 '22 at 22:12
https://github.com/python/cpython/blob/77195cd44b2506cda88a3cfc98918526068b1d46/Python/bltinmodule.c#L1708 – mama Jan 29 '22 at 22:15
Thats the source code for min and max - there is too many if statements – mama Jan 29 '22 at 22:15
And here is the sourcecode for abs which also is using if statements https://github.com/python/cpython/blob/31ff96712e8f89ac1056c2da880b44650002219f/Objects/abstract.c#L1377 – mama Jan 29 '22 at 22:18
@LukaszWiecek The absolute value function still probably contains the conditional unfortunately. – Richard K Yu Jan 29 '22 at 22:28
1

`abs = lambda v: v * ((v>0) - (v<0))` how about this one? – Lukasz Wiecek Jan 29 '22 at 22:29
That's clever, I think it works now without conditionals if you combine both of those! I would put it in the answer. I hope there's no more conditionals lurking anywhere – Richard K Yu Jan 29 '22 at 22:35
1

@RichardKYu I suspect that **many** conditionals get used to evaluate those. Or **anything** written in Python. They're asking about the wrong language. – Kelly Bundy Jan 29 '22 at 22:58

Yuri Ginsburg · Answer 2 · 2022-01-31T02:53:47.667

1

Code below works for -2**32 <= |a - b| <= 2**32 In this case, the sign bit of the integer is the 31st bit (counting from 0)

def ceil(a: int, b: int):
    return -a * ((a - b) >> 31) - b * ((b - a) >> 31)

edited Jan 31 '22 at 02:53

answered Jan 30 '22 at 23:43

Yuri Ginsburg

2,302
2
13
16

mama · Answer 3 · 2022-01-30T00:03:36.773

-1

So this is what I came up with - it is not pretty but it works.

def ceil(x, top=10): return (
    1-1//(1+x))*(1-(
        top-top//x
    )//top)*x+(
        top-top//x
    )//top*top

for i in range(1,21):
    print(ceil(i))

edited Jan 30 '22 at 00:03

answered Jan 29 '22 at 23:58

mama

2,046
1
7
24

How can I best make a function which functions similar as modulus but stops at max without using conditionals?

3 Answers3