bpf: add special smin32/smax32 derivation from 64-bit bounds

Add a special case where we can derive valid s32 bounds from umin/umax
or smin/smax by stitching together negative s32 subrange and
non-negative s32 subrange. That requires upper 32 bits to form a [N, N+1]
range in u32 domain (taking into account wrap around, so 0xffffffff
to 0x00000000 is a valid [N, N+1] range in this sense). See code comment
for concrete examples.

Eduard Zingerman also provided an alternative explanation ([0]) for more
mathematically inclined readers:

Suppose:
. there are numbers a, b, c
. 2**31 <= b < 2**32
. 0 <= c < 2**31
. umin = 2**32 * a + b
. umax = 2**32 * (a + 1) + c

The number of values in the range represented by [umin; umax] is:
. N = umax - umin + 1 = 2**32 + c - b + 1
. min(N) = 2**32 + 0 - (2**32-1) + 1 = 2, with b = 2**32-1, c = 0
. max(N) = 2**32 + (2**31 - 1) - 2**31 + 1 = 2**32, with b = 2**31, c = 2**31-1

Hence [(s32)b; (s32)c] forms a valid range.

  [0] https://lore.kernel.org/bpf/[email protected]/

Acked-by: Eduard Zingerman <[email protected]>
Acked-by: Shung-Hsi Yu <[email protected]>
Signed-off-by: Andrii Nakryiko <[email protected]>
Link: https://lore.kernel.org/r/[email protected]
Signed-off-by: Alexei Starovoitov <[email protected]>

0 files changed, 0 insertions, 0 deletions