nx_jpeg_idct.nx

nx_jpeg_idct.nx -- 8x8 inverse DCT for JPEG decode. Implements the separable row-then-column inverse DCT-II per the ITU-T Rec. T.81 Annex A.3.3 / IEEE 1180-1990 (Standard Specifications for the Implementations of 8x8 Inverse Discrete Cosine Transform). Math (natural-order coefficients F[u,v], output samples s[x,y]): s[x,y] = (1/4) * sum_{u=0..7} sum_{v=0..7} Cu * Cv * F[u,v] * cos((2x+1) u pi / 16) * cos((2y+1) v pi / 16) where C0 = 1/sqrt(2), Ck = 1 for k > 0 We use the well-known AAN-equivalent fixed-point factorisation: scale the coefficients by per-position constants that fold the 1/4 and Cu Cv factors into the quantization table, then do a pure cosine-sum. This file uses the direct cosine-sum form for clarity + simplicity; performance optimisation is a follow-on stone once nx_jpeg_decode is end-to-end working with real JPEGs. All arithmetic is integer fixed-point: we multiply by 2^12 = 4096 to give cosines 12 fractional bits, do the 16-bit-input * 12-bit-cosine arithmetic in i64 (no overflow), and right-shift the final result back by FX_SHIFT + 3 = 15 bits (the 1/4 = >>2 plus row/col combine shift; AAN literature explains this). Substrate-honesty: this is the unoptimised reference implementation. 1024 muls + 1024 adds per 8x8 block. Real decoders use Loeffler- Lieberknecht-Moschytz (LLM) factorisation for ~16 muls + 26 adds per row. That swap is a future arc once the full JPEG pipeline is proven end-to-end against real images. nx_safety_envelope: intended_use: "Inverse 8x8 DCT for JPEG decode pipeline." sil_target: SIL1 evidence: [t81_annex_a3_3_canonical_basis, ieee1180_1990_conformance_target,