feat(balls): add NliBall — non-uniform linear interpolation for non-linear ops (SiLU)

[chipcrowd]

Implements issue #34: a new NliBall for non-linear operators, using the NLI (Non-uniform Linear Interpolation) methodology from "NLI: Non-uniform Linear Interpolation Approximation of Nonlinear Operations for Efficient LLMs Inference".

What it does

NliBall approximates any non-linear function with 16 piecewise-linear segments whose cutpoints are placed non-uniformly (offline, where the function is most curved). The Ball is function-agnostic — the segment table (cutpoints / slopes / intercepts) is loaded through a coefficient bank with MVIN, so SiLU, GELU, exp, … all run on the same hardware.

Per INT8 lane it selects the segment with a comparator tree, then evaluates one Q7 MAC:

seg = #{ cutpoint <= x }
out = clamp( (slope[seg] * x) >> 7 + intercept[seg], -128, 127 )

Deliverables

• RTL — examples/balls/nli/arch/src/main/scala/NliBall.scala (Chisel, 2 read / 1 write ports, 16 INT8 lanes/row).
• C test — examples/balls/nli/workloads/ctests/nli_test.c (datapath + SiLU accuracy), workloads/isa/nli.h.
• README — examples/balls/nli/README.md (contract, data layout, datapath, results).
• Compiler — NliBall.td, LegalizeForLLVMExport.cpp, AssignPhysicalBankPatterns.cpp.
• Emulator — emu/src/{lib.rs,nli.rs} (BEMU golden model, bit-exact with RTL).
• Offline tablegen — scripts/gen_silu_table.py (cutpoint optimisation).
• Registered in the pebble core: ballNum 11, bid 10, mnemonic NLI, funct7 73.

Results

SiLU over the full INT8 domain [-128, 127] (16 segments):

metric	value
max abs error	1.0 LSB (@ x=37)
mean abs error	0.50 LSB
vs uniform 16-entry LUT	8.0 LSB max / 2.0 LSB mean
vs uniform 256-entry LUT	same 1.0 LSB, but 16x the storage

16 non-uniform linear segments reach the fixed-point quantization floor and match a 256-entry uniform LUT with 16x less table — including the extreme outliers where a coarse uniform LUT collapses.

Validation performed

• validate (ball-domain registration): all checks pass.
• Config derivation (chip.pb) and compiler registry generation: pass; NLI td/legalize/assign all discovered.
• Chisel RTL compiles (mill buckyball.compile).
• Emulator datapath verified bit-exact against an independent reference (max/mean error match the offline model).

Note: full bemu/Verilator simulation requires the buckyball-dev MCP tooling, which was not available in this session (the nix development environment could not be entered under the sandbox), so the on-target sim run is left for CI.