nx_dct8.nx

nx_dct8.nx -- 8x8 integer DCT-II in pure NishiLang. The universal frequency-domain transform that underlies every modern video codec (JPEG, MPEG-1/2/4, H.261/263/264/265, AV1's DCT mode). We re-derive from the public math (Ahmed, Natarajan, Rao 1974; Chen, Smith, Fralick 1977; Loeffler, Ligtenberg, Moschytz 1989) -- not from any patented codec's reference code. Math: 1D DCT-II of size 8: X_k = (1/2) c_k * sum_{n=0..7} x_n * cos((2n+1) k pi / 16) c_0 = 1/sqrt(2); c_k = 1 (k > 0) 2D 8x8 DCT: apply 1D DCT row-by-row, then column-by-column on transposed result. Equivalent to multiplying by the DCT matrix on both sides: Y = D X D^T. Fixed-point: every cosine entry is precomputed as Q10 (scale-by-1024) and stored in a caller-supplied 64-entry matrix buffer M. After each row/column pass we shift right by 10 to renormalise. Error budget is bounded by a few units in i64 at full scale; the smoke verifies round-trip reconstruction within 8 units. genealogy_id: ahmed_natarajan_rao_1974_dct + chen_smith_fralick_1977 + loeffler_ligtenberg_moschytz_1989_fast_dct + jpeg_iso_10918_1992 lineage_id: nishi_dct8_q10