[dpdk-dev] [PATCH 2/3] mem: remove redundant check in optimize_object_size

[Julien Cretin <julien.cretin@trust-in-soft.com>]

The second condition of this logical OR:
    (get_gcd(new_obj_size, nrank * nchan) != 1 ||
    get_gcd(nchan, new_obj_size) != 1)
is redundant with the first condition.

We can show that the first condition is equivalent to its disjunction
with the second condition using these two results:

- R1: For all conditions A and B, if B implies A, then (A || B) is
  equivalent to A.

- R2: (get_gcd(nchan, new_obj_size) != 1) implies
  (get_gcd(new_obj_size, nrank * nchan) != 1)

We can show R1 with the following truth table (0 is false, 1 is true):
        +-----+-----++----------+-----+-------------+
        |  A  |  B  || (A || B) |  A  | B implies A |
        +-----+-----++----------+-----+-------------+
        |  0  |  0  ||     0    |  0  |      1      |
        |  0  |  1  ||     1    |  0  |      0      |
        |  1  |  0  ||     1    |  1  |      1      |
        |  1  |  1  ||     1    |  1  |      1      |
        +-----+-----++----------+-----+-------------+
                Truth table of (A || B) and A

We can show R2 by looking at the code of optimize_object_size and
get_gcd.

We see that:
- S1: (nchan >= 1) and (nrank >= 1).
- S2: get_gcd returns 0 only when both arguments are 0.

Let:
- X be get_gcd(new_obj_size, nrank * nchan).
- Y be get_gcd(nchan, new_obj_size).

Suppose:
- H1: get_gcd returns the greatest common divisor of its arguments.
- H2: (nrank * nchan) does not exceed UINT_MAX.

We prove (Y != 1) implies (X != 1) with the following steps:
- Suppose L0: (Y != 1). We have to show (X != 1).
- By H1, Y is the greatest common divisor of nchan and new_obj_size.
  In particular, we have L1: Y divides nchan and new_obj_size.
- By H2, we have L2: nchan divides (nrank * nchan)
- By L1 and L2, we have L3: Y divides (nrank * nchan) and
  new_obj_size.
- By H1 and L3, we have L4: (Y <= X).
- By S1 and S2, we have L5: (Y != 0).
- By L0 and L5, we have L6: (Y > 1).
- By L4 and L6, we have (X > 1) and thus (X != 1), which concludes.

R2 was also tested for all values of new_obj_size, nrank, and nchan
between 0 and 2000.

This redundant condition was found using TrustInSoft Analyzer.

Signed-off-by: Julien Cretin <julien.cretin@trust-in-soft.com>
---
 lib/librte_mempool/rte_mempool.c | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/lib/librte_mempool/rte_mempool.c b/lib/librte_mempool/rte_mempool.c
index fdc1586..8e6c86a 100644
--- a/lib/librte_mempool/rte_mempool.c
+++ b/lib/librte_mempool/rte_mempool.c
@@ -114,8 +114,7 @@ static unsigned optimize_object_size(unsigned obj_size)
 
 	/* process new object size */
 	new_obj_size = (obj_size + CACHE_LINE_MASK) / CACHE_LINE_SIZE;
-	while (get_gcd(new_obj_size, nrank * nchan) != 1 ||
-			get_gcd(nchan, new_obj_size) != 1)
+	while (get_gcd(new_obj_size, nrank * nchan) != 1)
 		new_obj_size++;
 	return new_obj_size * CACHE_LINE_SIZE;
 }
-- 
1.9.1