set parameters which guarantee all tests pass

[jacksonwalters]

appears n=16 is necessary for tests to pass

[jacksonwalters]

(n = 16, q = 1073741824, t = 1024) sometimes passes, sometimes fails. $\Delta = q / t = 2^{30} / 2^{10} = 2^{20}$.

[jacksonwalters]

it looks like with $q$ set this high, we're going to have $q^2 \approx 2^{60}$, which is close to the i64 max of $\approx 2^{64}$.

---- test::tests::test_hom_prod stdout ----
thread 'test::tests::test_hom_prod' panicked at /Users/jacksonwalters/.cargo/registry/src/index.crates.io-6f17d22bba15001f/polynomial-ring-0.5.0/src/ops.rs:102:9:
attempt to add with overflow
note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace

[jacksonwalters]

so it's really just line 55 in lib.rs, which is polymul:

let mut r = x*y;

This multiplication of polynomials occurs first, then we reduce modulo q. This causes an overflow for large q.

We can use i128, but we're probably missing something obvious.

[jacksonwalters]

for now, the largest set of parameters that seem to pass are $n = 16, q = 1073741824, t = 512$.

[jacksonwalters]

one thing to note is that with q fixed, increasing t by powers of 2 causes the error to increase by powers of 2. so the constant term will be correct (= 6) but you'll get other terms either zero or say 16. If you increase t by a power of 2, you'll get e.g. [6,...,0,...,32,32,0,32,...,0,0,...,32]. This also holds for non-powers of 2, say primes q, t where you get some small constant error term or zero.