Floor-integer-div and integer sign operations?

I'm looking for ways to do some basic operations without using branches.

The key operation I want is a floored/round-to-negative-infinity integer
division (as opposed to the default round-to-zero).

7 floordiv 5 = 1
\-3 floordiv 5 = \-1
\-6 floordiv 5 = \-2

As I guess that doesn't exist, the operation can be constructed as:

(a/b) + (a>>31)

Assuming a is 32 bits. I can probably check the bit count, but perhaps
there's an op that does this already.

I'm also looking for a `sign(a) => (-1,0,1)` operation. Is there some
easy way to do this without branches? That is, have I overlooked from IR

Hacker's Delight or this web page are probably the best references for tricks like this:



I should note that your flooring division is incorrect for exact cases, e.g. a = –2, b = 1 should produce –2 but you’ll get –3. Assuming you know b > 0 you want something more like:

mask = a >> 31
(a – (b–1 & mask)) / b

and you may or may not need to handle the possibility of the subtract overflowing, depending on how robust you need to be.

– Steve