A More Precise Algorithm for Tnum Multiplication

This repo contains the test programs to benchmark a rewritten version of tnum_mul, the function used in the Linux kernel to multiply tristate numbers. The new algorithm addresses a challenge ("How can we incorporate correlation in unknown bits across partial products?") pointed out by Harishankar et al. in their paper.

UPDATE: The tnum_mul presented by this repo has been merged to the upstream Linux kernel (version 6.18).

Overview of the Improvement

As an example, at 6 bits, the new algorithm achieved optimality in in 81% cases compared to the 38% obtained by the current algorithm.

While work is underway on a detailed explanation on the new algorithm and its soundness proof, please refer to the following to get an initial picture:

1. The comments for my_tnum_mul in lib.c
2. Quote from the paper by Harishankar et al., given in this section
3. An example given in this section

From the paper by Harishankar et al.:

While our_mul is sound, it is not optimal. Key questions remain in designing a sound and optimal algorithm with O(n) or faster run time. (1) How can we incorporate correlation in unknown bits across partial products? For example, multiplying P = 11, Q = 𝜇1 produces the partial products T1 = 11, T2 = 𝜇𝜇0. However, the two 𝜇 trits in T2 are concretely either both 0 or both 1, resulting from the same 𝜇 trit in Q. Failing to consider this in the addition makes the result imprecise. ...

Example showing the above-mentioned imprecision with the current tnum_mul(a, b), with a = 𝜇1 and b = 11.

    11 *
    x1
------
    11
   xx
------
  xxx1

The same example with the new algorithm:

    11 *
    x1
------
    11
   xx
------
  ????

acc_0:

    11 *
    01
------
    11
   00
------
  0011

acc_1:

    11 *
    11
------
    11
   11
------
  1001

Union:

Value = 0011 & 1001 = 0001
Mask  = (0011 ^ 1001) | 0000 | 0000 = 1010

Result = x0x1 (more precise compared to xxx1)

Kernel Version

This repo contains the code for "the current algorithm" from the kernel, which is taken from:

commit 0cc53520e68bea7fb80fdc6bdf8d226d1b6a98d9 (origin/master, origin/HEAD, master)
Merge: dfc0f6373094 e2f9ae91619a
Author: Linus Torvalds <torvalds@linux-foundation.org>
Date:   Wed Aug 13 20:23:32 2025 -0700

    Merge tag 'probes-fixes-v6.17-rc1' of git://git.kernel.org/pub/scm/linux/kernel/git/trace/linux-trace

Copyright

Copyright 2025, 2026 Nandakumar Edamana; lib.c (multiple copies) contains snippets from the Linux kernel. Released under the terms of the GNU General Public License version 2 only.