Bug: ChebyshevTT rank caps overflow for high-dimensional grids

[0xC000005]

Related C# issue: 0xC000005/ChebyshevSharp#23

Summary

ChebyshevTT has a high-dimensional integer overflow bug in the TT-Cross rank-cap path. The cache-key design is already safe because _tt_cross uses tuple multi-indices, but rank-cap products still use np.prod, which overflows as numpy.int64 for large grids before being converted to Python int.

This is the Python-side analogue of the ChebyshevSharp high-dimensional TT issue, though the C# issue also includes a flattened long cache-key problem.

Evidence

Relevant code:

• src/pychebyshev/tensor_train.py, _tt_cross: left_size = int(np.prod(n[:k])), right_size = int(np.prod(n[k:]))
• Similar full-grid products appear in diagnostics such as compression_ratio, get_num_evaluation_points, and __str__

Minimal overflow check:

python -c "import numpy as np; x=np.prod([7]*35); print(x, type(x), getattr(x,'dtype',None)); print(int(x))"

Observed:

-6870017497503494569 <class 'numpy.int64'> int64
-6870017497503494569

Minimal ChebyshevTT repro:

import sys
sys.path.insert(0, "/home/max/Documents/PyChebyshev/src")
from pychebyshev import ChebyshevTT

N = 35
n = 7

def f(x, data=None):
    return float(sum(x))

tt = ChebyshevTT(
    f,
    N,
    [[-1.0, 1.0] for _ in range(N)],
    [n] * N,
    max_rank=12,
    tolerance=1e-5,
    max_sweeps=1,
)
tt.build(verbose=False, seed=42)

Observed failure:

ValueError: negative dimensions are not allowed

MoCaX comparison

MoCaX Extend handles the same high-dimensional shape differently. A local probe with:

MocaxExtend(35, [7] * 35, [[-1.0, 1.0]] * 35)

reported:

get_tensor_size() == 378818692265664781682717625943

as a Python int. subgrid_by_number(500), set_subgrid_values, gen_train_val_data, a minimal run_rank_adaptive_algo(max_rank=2, max_iters=2, max_rounds=1), and cheb_tensor_evals completed without overflow.

Proposed fix

• Replace np.prod rank-cap products in TT-Cross with Python math.prod or, better, a capped product helper that stops once the product reaches max_rank.
• Keep tuple multi-index cache keys; that part is already the right design.
• Use guarded/full-precision products for diagnostics, and make full-grid materialization APIs fail clearly when the tensor is too large.
• Add a regression test for ChebyshevTT with N=35, n=7, small max_rank, and max_sweeps=1 to verify the build path no longer overflows.