# Equivalence matrix

Every case ran twice on the same machine: unchanged backtrader 1.9.78.123 (A) and the same backtrader
with the TAKT build loaded (C), with the published scripts in `tools/` (`tools/matrix.py`). The complete
canonical result of every parameter set (parameters, the output of every analyzer, every order
notification, every trade notification, final value, cash and positions; `tools/bt_opt.py`) was
compared byte for byte. AMD Ryzen Threadripper PRO 5975WX (Zen 3), Python 3.12.3. Times are single
runs on one CPU each (two cases at a time on two CPUs; the `maxcpus=4` case ran its four worker
processes on both CPUs), for orientation only; the measured factors are in the README.

| Case | Strategy (source; file in `tools/`) | Grid | Data and settings | Parameter sets | Closed trades | Order notifications | Result | Engine in C | A, s | C, s |
|---|---|---|---|---:|---:|---:|---|---|---:|---:|
| smacross_btc1h | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10, 20], "pslow": [30, 60, 120]}` | `BTCUSDT-1h`; default settings (stdstats, optreturn, 7 analyzers) | 9 | 3,323 | 19,959 | identical | TAKT | 21.0 | 5.3 |
| smacross_eth5m | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [10, 20], "pslow": [50, 100]}` | `ETHUSDT-5m`; 5-minute candles, 105,120 bars | 4 | 4,673 | 28,050 | identical | TAKT | 35.9 | 10.3 |
| quickstart_sol_margin | TestStrategy (backtrader documentation (Quickstart, final version); `strats_bt_docs.py`) | `{"maperiod": [10, 15, 20, 25, 30]}` | `SOLUSDT-1h --cash 1000 --comm 0 --sizer fixed10`; quickstart settings: 1,000 cash, no commission, 10-unit fixed size; many orders rejected for margin | 5 | 7,173 | 58,894 | identical | TAKT | 14.9 | 7.1 |
| sigsmacross_sol | SigSmaCross (backtrader samples/sigsmacross/sigsmacross.py; `strats_bt_samples.py`) | `{"sma1": [5, 10, 20], "sma2": [30, 50]}` | `SOLUSDT-1h`; SignalStrategy | 6 | 2,700 | 16,206 | identical | TAKT | 15.6 | 4.9 |
| macdatr_bnb | MacdAtr (backtrader samples/macd-settings; `strats_bt_samples.py`) | `{"macd1": [8, 12], "macd2": [21, 26], "atrdist": [2.0, 3.0]}` | `BNBUSDT-1h` | 8 | 4,012 | 24,084 | identical | TAKT | 21.0 | 5.9 |
| btfd_xrp | Btfd (backtrader samples/btfd; `strats_bt_samples.py`) | `{"fall": [-0.01, -0.02], "hold": [2, 5], "target": [0.9]}` | `XRPUSDT-1h --sizer none`; order_target_percent | 4 | 9,879 | 59,274 | identical | TAKT | 13.4 | 7.0 |
| bkrsi_btc | BkRSI (bukosabino/wrapper-backtrader strategies/rsi.py (MIT); `strats_bukosabino.py`) | `{"period": [21, 28, 35]}` | `BTCUSDT-1h --sizer none --bksize 0.1`; explicit sizes | 3 | 274 | 1,693 | identical | TAKT | 6.2 | 2.0 |
| bkrsi_bracket_btc | BkRSI (bukosabino/wrapper-backtrader strategies/rsi.py (MIT); `strats_bukosabino.py`) | `{"period": [21, 28, 35]}` | `BTCUSDT-1h --sizer none --bksize 0.1 --bracket 1`; bracket orders (limit entry with expiry, stop loss, take profit) | 3 | 351 | 14,821 | identical | TAKT | 6.9 | 2.5 |
| bkaberration_sol | BkAberration (bukosabino/wrapper-backtrader strategies/bbands.py (MIT); `strats_bukosabino.py`) | `{"period": [20, 40], "devfactor": [2, 2.5]}` | `SOLUSDT-1h --sizer none --bksize 10` | 4 | 733 | 4,404 | identical | TAKT | 8.5 | 2.5 |
| bkaberration_bracket_sol | BkAberration (bukosabino/wrapper-backtrader strategies/bbands.py (MIT); `strats_bukosabino.py`) | `{"period": [20, 40]}` | `SOLUSDT-1h --sizer none --bksize 10 --bracket 1`; bracket orders | 2 | 1,040 | 9,886 | identical | TAKT | 4.9 | 2.2 |
| bbadx_xrp_short_stop | BBADX (jasgin/backtrader-backtests BB_ADX.py (MIT); `strats_jasgin.py`) | `{"BB_MA": [20, 30], "ADX_Max": [25, 40]}` | `XRPUSDT-1h --sizer pct50`; short selling, stop orders | 4 | 3,825 | 23,145 | identical | TAKT | 11.8 | 5.3 |
| stochsr_xrp_oco | StochasticSR (jasgin/backtrader-backtests Stochastic_SR_Backtest.py (MIT); `strats_jasgin.py`) | `{"period": [14, 21], "stop_pips": [0.002, 0.01]}` | `XRPUSDT-1h --sizer pct50`; short selling, OCO stop orders | 4 | 5,047 | 48,366 | identical | TAKT | 11.8 | 5.4 |
| dma_btc_signal | DualMovingAverageStrategy (quantrocket-codeload/backtrader-dma (Apache-2.0); `strats_quantrocket.py`) | `{"smavg_window": [50, 100], "lmavg_window": [200, 300]}` | `BTCUSDT-1h`; SignalStrategy | 4 | 274 | 1,650 | identical | TAKT | 10.1 | 2.8 |
| empsma_5pairs | EmpSmaCross (empenoso/backtrader-quickstart-template sma_cross_strategy.py (MIT); `strats_empenoso.py`) | `{"fast_ma": [5, 10], "slow_ma": [30, 60]}` | `BTCUSDT-1h,ETHUSDT-1h,SOLUSDT-1h,BNBUSDT-1h,XRPUSDT-1h --sizer none --cash 500000`; five aligned data feeds, per-feed indicators | 4 | 8,817 | 52,929 | identical | TAKT | 32.2 | 12.7 |
| empsma_5pairs_asauthored | EmpSmaCross (empenoso/backtrader-quickstart-template sma_cross_strategy.py (MIT); `strats_empenoso.py`) | `{"fast_ma": [5, 10], "slow_ma": [30, 60]}` | `BTCUSDT-1h,ETHUSDT-1h,SOLUSDT-1h,BNBUSDT-1h,XRPUSDT-1h --sizer none --cash 500000 --runonce 0 --exactbars -1`; the author's settings: runonce=False, exactbars=-1 | 4 | 8,817 | 52,929 | identical | backtrader's own (fallback) | 53.4 | 53.6 |
| statsreader_btc_observer | StatsReader (ours: reads the broker observer, receives cash/value notifications; `strats_takt.py`) | `{"period": [20, 50]}` | `BTCUSDT-1h`; strategy reads the broker observer | 2 | 14,610 | 87,663 | identical | TAKT | 12.4 | 9.7 |
| smacross_nostdstats | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10], "pslow": [30, 60]}` | `ETHUSDT-1h --stdstats 0 --analyzers min`; stdstats=False, 3 analyzers | 4 | 1,884 | 11,307 | identical | TAKT | 7.0 | 2.3 |
| smacross_optreturn0 | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10], "pslow": [30, 60]}` | `ETHUSDT-1h --optreturn 0`; optreturn=False (full strategy objects returned) | 4 | 1,884 | 11,307 | identical | TAKT | 9.1 | 3.8 |
| smacross_coc_slip | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10], "pslow": [30, 60]}` | `SOLUSDT-1h --coc 1 --slip 0.001`; cheat-on-close, 0.1% slippage | 4 | 1,827 | 10,962 | identical | TAKT | 9.1 | 2.8 |
| smacross_fund_interest | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10], "pslow": [30, 60]}` | `BNBUSDT-1h --fundmode 1 --interest 0.05`; fund mode, 5% credit interest on longs | 4 | 1,916 | 11,508 | identical | TAKT | 9.1 | 2.8 |
| smacross_runnext | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10], "pslow": [30, 60]}` | `BTCUSDT-1h --runonce 0`; runonce=False | 4 | 1,871 | 11,238 | identical | backtrader's own (fallback) | 14.8 | 14.7 |
| smacross_daterange | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10], "pslow": [30, 60]}` | `XRPUSDT-1h --fromdate 2024-06-01 --todate 2025-06-30`; fromdate/todate subset | 4 | 669 | 4,026 | identical | TAKT | 3.8 | 1.2 |
| smacross_lowcash_margin | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10], "pslow": [30, 60]}` | `BTCUSDT-1h --cash 100 --sizer fixed`; 100 cash, 1 BTC fixed size: every order rejected | 4 | 0 | 3,750 | identical | TAKT | 8.3 | 1.9 |
| smacross_2data | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10], "pslow": [30, 60]}` | `ETHUSDT-1h,BTCUSDT-1h`; two aligned data feeds | 4 | 1,884 | 11,307 | identical | TAKT | 12.0 | 3.4 |
| smacross_maxcpus4 | SmaCross (backtrader documentation ("Hello Algotrading!"); `strats_bt_docs.py`) | `{"pfast": [5, 10, 20, 30], "pslow": [40, 80, 120]}` | `BTCUSDT-1h --maxcpus 4`; maxcpus=4 (worker processes) | 12 | 3,539 | 21,255 | identical | TAKT | 13.8 | 5.2 |

Total: 25 cases, 114 parameter sets, 91,022 closed trades, 600,613 order notifications; 25 of 25 identical.
The canonical results (149 MB per side) were compared in full; every case also printed the same
digest line in A and C (`matrix.log`, `matrix_raw.tsv`: the first 16 hex digits of the SHA-256).

Unless stated otherwise: 10,000 USDT cash, 0.1% commission, 95% PercentSizer, `stdstats=True`,
`optreturn=True`, `maxcpus=1`, analyzers TradeAnalyzer, DrawDown, SharpeRatio, Returns, SQN,
Transactions and TimeReturn (days) plus the three recording analyzers of `tools/bt_opt.py`; data
Binance spot 1-hour candles 2023-10-01 to 2026-09-30 (26,304 bars).

Order outcomes that occur in these cases (from the recorded notifications of A): Completed; Margin
(7,928 in `quickstart_sol_margin`, 23 in `bkrsi_btc`, 21 in `bbadx_xrp_short_stop`, every order in
`smacross_lowcash_margin`); Rejected, Canceled, Expired and Margin (bracket orders with a validity
date in `bkrsi_bracket_btc`; Canceled and Expired in `bkaberration_bracket_sol`); Canceled by OCO
(`stochsr_xrp_oco`); short positions and stop orders (`bbadx_xrp_short_stop`, `stochsr_xrp_oco`).

"Engine in C": TAKT where the TAKT build ran every parameter set itself; "backtrader's own
(fallback)" where the setting is one the TAKT build does not cover and backtrader's own engine ran
it (`runonce=False`, `exactbars`), at backtrader's own speed and with the same result.