nx_nofloat_autograd.nx

nx_nofloat_autograd.nx -- NO-FLOAT (integer Q16 fixed-point) reverse-mode TENSOR autograd: the genuine MISSING GENERATION in the no-float lineage (genealogy DeepMind ladder, operator first law = don't lie). HONEST landscape this fills (verified by reading the organs, 2026-06-22): - GENERAL reverse-mode autograd ALREADY EXISTS, but on the SOFTWARE-FLOAT tower: nx_autograd / nx_autograd_tensor / nx_tgrad_core all build on nx_f32 (IEEE-754 emulated). Float, not no-float. - NO-FLOAT (integer Q16) training ALREADY EXISTS, but only nx_nn_train = a SINGLE linear layer with a HAND-CODED analytic gradient. No general graph, no composition. - What was genuinely missing = a GENERAL reverse-mode autograd in the SAME integer Q16 tower the no-float Qwen inference pipeline actually uses (nx_nofloat_llm: Q16=65536, qmul=(a*b)>>16, accumulate-then-shift matmul). This file is that bridge: a tape of arbitrary ops + ONE reverse sweep, so an MLP (matvec->vadd->relu->matvec->vadd->mse) trains by the SAME loop that will train the transformer -- all deterministic integer arithmetic (no nx_f32, no FPU, no GPU, no third-party AD). TAPE: stride-7 nodes {op, ai, bi, rows, cols, valp, gradp}; valp/gradp index a per-build BUMP ARENA of Q16 cells (st[1] counter; no allocator -> deterministic). Forward EAGER (Q16), backward ONE reverse sweep (nodes built in topological order, so reverse index order visits parents before children). Backward identities (Q16) = the proven float identities with nx_f32_mul->qmul, nx_f32_add->integer +: matvec y=W*x: dW[i][j] += qmul(gy[i], x[j]); dx[j] += qmul(W[i][j], gy[i]) vadd y=a+b: ga += gy ; gb += gy relu: gx += gy iff the INPUT cell was > 0 mse L=(1/n)sum(p-t)^2: dp_i += qmul(gL, (2*(p_i-t_i))/n) Determinism EXCEED-AXIS: integer add is EXACTLY associative -> bit-identical training independent of order (the f32 tower is only bit-identical because it pins ONE order; here it is structural). genealogy_id: linnainmaa_1970_reverse_mode_ad + rumelhart_1986_backprop, ported to fixed-point Q16 lineage_id: sovereign_nofloat_tensor_tape_autograd_v1 license_tier: ORIGINAL No `main` (pure library; proof lives in nx_nofloat_autograd_gate.nx).