Drop the value-mask decomposition technique and adopt straightforward long-multiplication with a twist: when LSB(a) is uncertain, find the two partial products (for LSB(a) = known 0 and LSB(a) = known 1) and take a union. Experiment shows that applying this technique in long multiplication improves the precision in a significant number of cases (at the cost of losing precision in a relatively lower number of cases). Signed-off-by: Nandakumar Edamana Acked-by: Eduard Zingerman Reviewed-by: Harishankar Vishwanathan --- include/linux/tnum.h | 3 +++ kernel/bpf/tnum.c | 55 +++++++++++++++++++++++++++++++++----------- 2 files changed, 45 insertions(+), 13 deletions(-) diff --git a/include/linux/tnum.h b/include/linux/tnum.h index 57ed3035cc30..68e9cdd0a2ab 100644 --- a/include/linux/tnum.h +++ b/include/linux/tnum.h @@ -54,6 +54,9 @@ struct tnum tnum_mul(struct tnum a, struct tnum b); /* Return a tnum representing numbers satisfying both @a and @b */ struct tnum tnum_intersect(struct tnum a, struct tnum b); +/* Returns a tnum representing numbers satisfying either @a or @b */ +struct tnum tnum_union(struct tnum t1, struct tnum t2); + /* Return @a with all but the lowest @size bytes cleared */ struct tnum tnum_cast(struct tnum a, u8 size); diff --git a/kernel/bpf/tnum.c b/kernel/bpf/tnum.c index fa353c5d550f..a47183ddbfdb 100644 --- a/kernel/bpf/tnum.c +++ b/kernel/bpf/tnum.c @@ -116,31 +116,47 @@ struct tnum tnum_xor(struct tnum a, struct tnum b) return TNUM(v & ~mu, mu); } -/* Generate partial products by multiplying each bit in the multiplier (tnum a) - * with the multiplicand (tnum b), and add the partial products after - * appropriately bit-shifting them. Instead of directly performing tnum addition - * on the generated partial products, equivalenty, decompose each partial - * product into two tnums, consisting of the value-sum (acc_v) and the - * mask-sum (acc_m) and then perform tnum addition on them. The following paper - * explains the algorithm in more detail: https://arxiv.org/abs/2105.05398. +/* Perform long multiplication, iterating through the bits in a using rshift: + * - if LSB(a) is a known 0, keep current accumulator + * - if LSB(a) is a known 1, add b to current accumulator + * - if LSB(a) is unknown, take a union of the above cases. + * + * For example: + * + * acc_0: acc_1: + * + * 11 * -> 11 * -> 11 * -> union(0011, 1001) == x0x1 + * x1 01 11 + * ------ ------ ------ + * 11 11 11 + * xx 00 11 + * ------ ------ ------ + * ???? 0011 1001 */ struct tnum tnum_mul(struct tnum a, struct tnum b) { - u64 acc_v = a.value * b.value; - struct tnum acc_m = TNUM(0, 0); + struct tnum acc = TNUM(0, 0); while (a.value || a.mask) { /* LSB of tnum a is a certain 1 */ if (a.value & 1) - acc_m = tnum_add(acc_m, TNUM(0, b.mask)); + acc = tnum_add(acc, b); /* LSB of tnum a is uncertain */ - else if (a.mask & 1) - acc_m = tnum_add(acc_m, TNUM(0, b.value | b.mask)); + else if (a.mask & 1) { + /* acc = tnum_union(acc_0, acc_1), where acc_0 and + * acc_1 are partial accumulators for cases + * LSB(a) = certain 0 and LSB(a) = certain 1. + * acc_0 = acc + 0 * b = acc. + * acc_1 = acc + 1 * b = tnum_add(acc, b). + */ + + acc = tnum_union(acc, tnum_add(acc, b)); + } /* Note: no case for LSB is certain 0 */ a = tnum_rshift(a, 1); b = tnum_lshift(b, 1); } - return tnum_add(TNUM(acc_v, 0), acc_m); + return acc; } /* Note that if a and b disagree - i.e. one has a 'known 1' where the other has @@ -155,6 +171,19 @@ struct tnum tnum_intersect(struct tnum a, struct tnum b) return TNUM(v & ~mu, mu); } +/* Returns a tnum with the uncertainty from both a and b, and in addition, new + * uncertainty at any position that a and b disagree. This represents a + * superset of the union of the concrete sets of both a and b. Despite the + * overapproximation, it is optimal. + */ +struct tnum tnum_union(struct tnum a, struct tnum b) +{ + u64 v = a.value & b.value; + u64 mu = (a.value ^ b.value) | a.mask | b.mask; + + return TNUM(v & ~mu, mu); +} + struct tnum tnum_cast(struct tnum a, u8 size) { a.value &= (1ULL << (size * 8)) - 1; -- 2.39.5 Add new selftest to test the abstract multiplication technique(s) used by the verifier, following the recent improvement in tnum multiplication (tnum_mul). One of the newly added programs, verifier_mul/mul_precise, results in a false positive with the old tnum_mul, while the program passes with the latest one. Signed-off-by: Nandakumar Edamana Acked-by: Eduard Zingerman Reviewed-by: Harishankar Vishwanathan --- .../selftests/bpf/prog_tests/verifier.c | 2 + .../selftests/bpf/progs/verifier_mul.c | 38 +++++++++++++++++++ 2 files changed, 40 insertions(+) create mode 100644 tools/testing/selftests/bpf/progs/verifier_mul.c diff --git a/tools/testing/selftests/bpf/prog_tests/verifier.c b/tools/testing/selftests/bpf/prog_tests/verifier.c index 77ec95d4ffaa..e35c216dbaf2 100644 --- a/tools/testing/selftests/bpf/prog_tests/verifier.c +++ b/tools/testing/selftests/bpf/prog_tests/verifier.c @@ -59,6 +59,7 @@ #include "verifier_meta_access.skel.h" #include "verifier_movsx.skel.h" #include "verifier_mtu.skel.h" +#include "verifier_mul.skel.h" #include "verifier_netfilter_ctx.skel.h" #include "verifier_netfilter_retcode.skel.h" #include "verifier_bpf_fastcall.skel.h" @@ -194,6 +195,7 @@ void test_verifier_may_goto_1(void) { RUN(verifier_may_goto_1); } void test_verifier_may_goto_2(void) { RUN(verifier_may_goto_2); } void test_verifier_meta_access(void) { RUN(verifier_meta_access); } void test_verifier_movsx(void) { RUN(verifier_movsx); } +void test_verifier_mul(void) { RUN(verifier_mul); } void test_verifier_netfilter_ctx(void) { RUN(verifier_netfilter_ctx); } void test_verifier_netfilter_retcode(void) { RUN(verifier_netfilter_retcode); } void test_verifier_bpf_fastcall(void) { RUN(verifier_bpf_fastcall); } diff --git a/tools/testing/selftests/bpf/progs/verifier_mul.c b/tools/testing/selftests/bpf/progs/verifier_mul.c new file mode 100644 index 000000000000..7145fe3351d5 --- /dev/null +++ b/tools/testing/selftests/bpf/progs/verifier_mul.c @@ -0,0 +1,38 @@ +// SPDX-License-Identifier: GPL-2.0 +/* Copyright (c) 2025 Nandakumar Edamana */ +#include +#include +#include +#include "bpf_misc.h" + +/* Intended to test the abstract multiplication technique(s) used by + * the verifier. Using assembly to avoid compiler optimizations. + */ +SEC("fentry/bpf_fentry_test1") +void BPF_PROG(mul_precise, int x) +{ + /* First, force the verifier to be uncertain about the value: + * unsigned int a = (bpf_get_prandom_u32() & 0x2) | 0x1; + * + * Assuming the verifier is using tnum, a must be tnum{.v=0x1, .m=0x2}. + * Then a * 0x3 would be m0m1 (m for uncertain). Added imprecision + * would cause the following to fail, because the required return value + * is 0: + * return (a * 0x3) & 0x4); + */ + asm volatile ("\ + call %[bpf_get_prandom_u32];\ + r0 &= 0x2;\ + r0 |= 0x1;\ + r0 *= 0x3;\ + r0 &= 0x4;\ + if r0 != 0 goto l0_%=;\ + r0 = 0;\ + goto l1_%=;\ +l0_%=:\ + r0 = 1;\ +l1_%=:\ +" : + : __imm(bpf_get_prandom_u32) + : __clobber_all); +} -- 2.39.5