`poly.c`: arithmetic shift right instead of logical shift right leads to hang

[Juul-Mc-Goa]

I've been trying to use Lazer for image modifications, which means I tend to aggregate many statements (one for each pixel). Here's a simplified example for applying grayscale:

deg = 512
VBIG = 0

# grayscale ring
BIGMOD_RING = polyring_t(deg, LAB_RING_40.mod)
PRIMESIZE = str(ceil(log2(BIGMOD_RING.mod)))

# int version of grayscale coefficients
r_int = 3566836
g_int = 11999065
b_int = 1211315
# poly version of grayscale coefficients
r_poly = int_to_poly(r_int, BIGMOD_RING)
g_poly = int_to_poly(g_int, BIGMOD_RING)
b_poly = int_to_poly(b_int, BIGMOD_RING)

ID = int_to_poly(1, BIGMOD_RING)

width = 512
height = 1024
poly_nb = ceil(width * height / float(deg))

rgb_img = [random_pixels_poly() for _ in range(3 * poly_nb)]
grayscale_img = img_float_gr(rgb_img)
grayscale_error = img_diff_gr(rgb_img)

max_l2_u8 = (255**2) * deg
max_l2_diff = (418**2) * deg # difference between exact and floating point computations
norms = [max_l2_u8] * 3 + [max_l2_diff]

deg_list = [deg] * len(norms) * poly_nb
num_pols_list = [1] * len(norms) * poly_nb
norm_list = norms * poly_nb
num_constraints = poly_nb
PS = proof_statement(deg_list, num_pols_list, norm_list, num_constraints, PRIMESIZE)

j = 0
stat_left = [
    r_poly,
    g_poly,
    b_poly,
    ID,
]

while j < grayscale_nb:
    wit = witness(rgb_img, grayscale_error, j)

    if is_witness_small(wit):
        rhs = right_hand_side(grayscale_img, j)
        PS.fresh_statement(stat_left, wit, rhs)
        j += 1
    else:
        print("Too BIG in ", j)
        VBIG += 1

stmnt = PS.output_statement()
PS.smpl_verify()

When width = 512 and height = 1024, the program often hangs (but not always), and I have to kill my terminal.

This seems to be caused by an infinite loop in the labrador.c:project function: the condition jlproj_normsq(pi->p) > normsq here is always verified.

This in turn seems to result from a faulty computation of iwt->normsq: sometimes for some i, iwt->normsq[i] < 0.

It seems to boil down to the polyvec_sprodz function, which uses arithmetic shift right here instead of logical shift right.
Changing the poly.c file to have:

    g = _mm512_srli_epi64(h,32);
    f = _mm512_srli_epi64(f,32);

solves the issue.

[Juul-Mc-Goa]

Actually doing the above breaks the correctness of the polyvec_sprodz function.

What can be done instead is create a new function unsigned_polyvec_sprodz, then call this new function here and here.