# FOptInf 05 analysis results

Generated by `analysis/build.py` from the vendored inputs (simulator plms 0.3.0 at e3054d1; the series' flop_share.py results). Every computed number on the slides is here.

## 1. Precision needed (precision_needed.py)

Reference signal: the series' length-4096 causal FFT convolution, crest 3.644. ENOB = log2(crest x 2 / (sqrt(12) x rel)); e16 bits = (-20 log10 rel - 1.76)/6.02. The two measures differ by 1.37 bits here.

| Format | Scaling | Bits/value | Rounding error (rel RMS) | ENOB needed (series rule) | Effective bits (e16 measure) |
|---|---|---|---|---|---|
| BF16 | the series' rounding (8 mantissa bits incl. hidden) | 16 | 0.00164 | 10.32 | 8.96 |
| FP8 E4M3 | the series' rounding, per-tensor scale | 8 | 0.0261 | 6.33 | 4.97 |
| INT8 | the series' rounding, per-tensor scale | 8 | 0.00834 | 7.98 | 6.61 |
| FP8 E5M2 | per-tensor scale | 8 | 0.0536 | 5.29 | 3.93 |
| INT4 | symmetric, per-tensor scale | 4 | 0.151 | 3.80 | 2.44 |
| INT4 g32 | symmetric, one scale per 32 values | 4.5 | 0.0986 | 4.41 | 3.05 |
| FP4 E2M1 | per-tensor scale | 4 | 0.114 | 4.20 | 2.84 |
| MXFP4 | E2M1, block 32, E8M0 scale | 4.25 | 0.118 | 4.16 | 2.79 |
| NVFP4 | E2M1, block 16, E4M3 scale | 4.5 | 0.0931 | 4.50 | 3.13 |

The series' values reproduced: BF16 10.3, FP8 E4M3 6.3, INT8 8.0.

## 2. Energy (breakeven.py)

Exact mode at the defaults: 485.9 pJ per 59-bit 4-point transform against 32.35 pJ (ASIC); break-even E_conv -0.1406 pJ/bit.

| S | photonic pJ/butterfly-stage | static part | throughput /s | effective bits | digital matched pJ | ratio |
|---|---|---|---|---|---|---|
| 1 | 34.11 | 1.493 | 1.408e+13 | 2.74 | 0.1333 | 255.9 |
| 2 | 17.8 | 1.493 | 2.724e+13 | 3.061 | 0.2141 | 83.16 |
| 3 | 12.37 | 1.493 | 2.724e+13 | 3.187 | 0.2141 | 57.77 |
| 4 | 9.648 | 1.493 | 2.724e+13 | 3.167 | 0.2141 | 45.07 |
| 5 | 8.017 | 1.493 | 2.724e+13 | 3.125 | 0.2141 | 37.45 |
| 6 | 6.929 | 1.493 | 2.724e+13 | 3.198 | 0.2141 | 32.37 |

Digital 8-bit complex butterfly: 0.7188 pJ.

Static pJ per butterfly-stage (laser + phase shifters, S = 6) by phase-shifter technology:

| technology | pJ |
|---|---|
| thermo 2 mW/π | 0.5531 |
| thermo 10 mW/π | 1.493 |
| thermo 30 mW/π | 3.843 |
| mems | 0.3183 |
| nv | 0.3182 |

Laser pJ per butterfly-stage by laser power (fan-out at 6 dB margin from e14, 4 λ, 112 GBd):

| laser dBm | pJ |
|---|---|
| 13 | 0.3125 |
| 17 | 0.3925 |
| 20 | 0.3182 |
| 23 | 0.3907 |
| 27 | 0.368 |

Conditions for S = 6 to match the matched-precision digital butterfly (0.2141 pJ):

* wall-plug efficiency needed with free heaters and free conversions: 0.4302 (default 0.15)
* E_conv needed with free heaters and a lossless laser (wall plug 1): 0.005926 pJ/bit (default 0.5)
* E_conv needed against the 8-bit digital butterfly with MEMS phase shifters: 0.02787 pJ/bit
* at the defaults: never

Approximate-mode throughput at S = 6 over the exact-mode rate: 59x.