bpf: representation and basic operations on circular numbers

This commit adds basic definitions for cnum32/cnum64.
This is a unified numeric range representation for signed and unsigned
domains. Inspired by an old post from Shung-Hsi Yu [1] and paper [2].
Operations correctness is verified using cbmc model checker,
tests source code can be found in a separate repo [3].

The cnum64_cnum32_intersect() function is notable, because it handled
several cases verifier.c:deduce_bounds_64_from_32() does not.
Given:
- a is a 64-bit range
- b is a 32-bit range
- t is a refined 64-bit range, such that ∀ v ∈ a, (u32)v ∈ b: v ∈ t.
cnum64_cnum32_intersect() makes the following deductions:

(A): 'b' is a sub-range of the first or the last 32-bit
     sub-range of 'a':

                                                         64-bit number axis --->

 N*2^32                   (N+1)*2^32                (N+2)*2^32                (N+3)*2^32
 ||------|---|=====|-------||----------|=====|-------||----------|=====|----|--||
         |   |< b >|                   |< b >|                   |< b >|    |
         |   |                                                         |    |
         |<--+--------------------------- a ---------------------------+--->|
             |                                                         |
             |<-------------------------- t -------------------------->|

(B) 'b' does not intersect with the first of the last 32-bit
    sub-range of 'a':

N*2^32                   (N+1)*2^32                (N+2)*2^32                (N+3)*2^32
||--|=====|----|----------||--|=====|---------------||--|=====|------------|--||
    |< b >|    |              |< b >|                   |< b >|            |
               |              |                               |            |
               |<-------------+--------- a -------------------|----------->|
                              |                               |
                              |<-------- t ------------------>|

(C) 'b' crosses 0/U32_MAX boundary:

N*2^32                   (N+1)*2^32                (N+2)*2^32                (N+3)*2^32
||===|---------|------|===||===|----------------|===||===|---------|------|===||
 |b >|         |      |< b||b >|                |< b||b >|         |      |< b|
               |      |                                  |         |
               |<-----+----------------- a --------------+-------->|
                      |                                  |
                      |<---------------- t ------------->|

Current implementation of deduce_bounds_64_from_32() only handles
case (A).

[1] https://lore.kernel.org/all/ZTZxoDJJbX9mrQ9w@u94a/
[2] https://jorgenavas.github.io/papers/ACM-TOPLAS-wrapped.pdf
[3] https://github.com/eddyz87/cnum-verif/tree/master

Signed-off-by: Eduard Zingerman <eddyz87@gmail.com>
Link: https://lore.kernel.org/r/20260424-cnums-everywhere-rfc-v1-v3-1-ca434b39a486@gmail.com
Signed-off-by: Alexei Starovoitov <ast@kernel.org>

0 files changed, 0 insertions, 0 deletions