Reed-Solomon error correction over GF(2^8)
Upgrade to ocamlformat 0.29.0; fix csvt/sexpt streaming; reformat
- Update .ocamlformat to 0.29.0 across all 591 files
- csvt: reuse single Buffer.t for field reads (no alloc per field)
- sexpt: Obj members decoded from stream into Dict, typed Variant GADT
- Reformat all source files for 0.29.0
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lib/gf256.mli
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-8
lib/gf256.mli
···
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{2 Usage}
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{[
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(* CCSDS field: polynomial 0x187, primitive element 11 *)
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let module F = Gf256.Make (struct
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let primitive_poly = 0x187
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let primitive_element = 11
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end) in
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let product = F.mul 0xA3 0x7B in
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let inverse = F.inv 0xA3 in
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assert (F.mul product inverse = 0x7B)
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(* CCSDS field: polynomial 0x187, primitive element 11 *)
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let module F = Gf256.Make (struct
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let primitive_poly = 0x187
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let primitive_element = 11
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end) in
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let product = F.mul 0xA3 0x7B in
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let inverse = F.inv 0xA3 in
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assert (F.mul product inverse = 0x7B)
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]}
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{2 References}
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lib/reed_solomon.mli
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lib/reed_solomon.mli
···
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{2 Usage}
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{[
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let data = Bytes.of_string "Hello, Reed-Solomon!" in
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(* Pad to 223 bytes for CCSDS RS(255,223) *)
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let padded = Bytes.make 223 '\x00' in
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Bytes.blit data 0 padded 0 (Bytes.length data);
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let codeword = Reed_solomon.encode_systematic ccsds padded in
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(* Inject up to 16 symbol errors... *)
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Bytes.set codeword 0 '\xff';
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Bytes.set codeword 42 '\xab';
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match Reed_solomon.decode ccsds codeword with
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| Ok recovered -> assert (recovered = padded)
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| Error e -> Printf.eprintf "decode failed: %s\n" e
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let data = Bytes.of_string "Hello, Reed-Solomon!" in
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(* Pad to 223 bytes for CCSDS RS(255,223) *)
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let padded = Bytes.make 223 '\x00' in
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Bytes.blit data 0 padded 0 (Bytes.length data);
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let codeword = Reed_solomon.encode_systematic ccsds padded in
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(* Inject up to 16 symbol errors... *)
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Bytes.set codeword 0 '\xff';
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Bytes.set codeword 42 '\xab';
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match Reed_solomon.decode ccsds codeword with
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| Ok recovered -> assert (recovered = padded)
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| Error e -> Printf.eprintf "decode failed: %s\n" e
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]}
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{2 References}
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test/interop/dune
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test/interop/dune
···
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(test
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(name test)
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(libraries reed_solomon alcotest)
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(deps
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(source_tree traces)
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(source_tree scripts)))
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(rule
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(alias regen-traces)
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(enabled_if
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(= %{env:REGEN_TRACES=0} 1))
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(deps
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(source_tree scripts))
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(action
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(with-stdout-to
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rs_vectors.hex
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(run python3 scripts/generate_rs.py))))
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(rule
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(alias regen-traces)
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(enabled_if
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(= %{env:REGEN_TRACES=0} 1))
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(action
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(diff traces/rs_vectors.hex rs_vectors.hex)))
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test/interop/regenerate.sh
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test/interop/regenerate.sh
···
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#!/bin/bash
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# Regenerate Reed-Solomon interop test traces.
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#
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# Requires: pip install reedsolo
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# Usage: ./regenerate.sh
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#
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# Preferred method: REGEN_TRACES=1 dune build @regen-traces
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# Then: dune promote
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set -euo pipefail
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SCRIPT_DIR="$(cd "$(dirname "$0")/scripts" && pwd)"
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TRACE_DIR="$(cd "$(dirname "$0")/traces" && pwd)"
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echo "Scripts: $SCRIPT_DIR"
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echo "Traces: $TRACE_DIR"
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echo
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python3 "$SCRIPT_DIR/generate_rs.py" > "$TRACE_DIR/rs_vectors.hex"
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echo "Regenerated $TRACE_DIR/rs_vectors.hex"
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echo "Review with: git diff $TRACE_DIR"
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test/interop/scripts/generate_rs.py
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test/interop/scripts/generate_rs.py
···
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#!/usr/bin/env python3
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"""Generate Reed-Solomon test vectors using Python reedsolo.
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Outputs pipe-delimited lines:
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name|data_hex|codeword_hex
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Uses CCSDS RS(255,223) parameters:
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- Field polynomial: 0x187 (x^8 + x^7 + x^2 + x + 1)
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- Primitive element (alpha): 11
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- First consecutive root: 112
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- t = 16 (corrects up to 16 symbol errors)
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NOTE: reedsolo defaults to alpha=2 and fcr=0. The CCSDS standard uses
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alpha=11, primitive poly 0x187, and fcr=112. We configure reedsolo with
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these parameters explicitly.
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Requires: pip install reedsolo
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"""
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try:
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from reedsolo import RSCodec, init_tables
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except ImportError:
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print("ERROR: reedsolo not installed. Run: pip install reedsolo", flush=True)
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raise SystemExit(1)
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# CCSDS RS(255,223) parameters
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NSYM = 32 # 2*t = 2*16 = 32 parity symbols
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PRIM = 0x187 # primitive polynomial
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ALPHA = 11 # primitive element
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FCR = 112 # first consecutive root
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# Initialize with CCSDS field parameters
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rs = RSCodec(NSYM, prim=PRIM, generator=ALPHA, fcr=FCR)
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messages = [
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("zeros", bytes(223)),
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("ones", bytes([0x01] * 223)),
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("ascending", bytes([i % 256 for i in range(223)])),
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("hello", b"Hello, Reed-Solomon!" + bytes(203)),
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]
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for name, data in messages:
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codeword = rs.encode(data)
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print(f"{name}|{data.hex()}|{bytes(codeword).hex()}")
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test/interop/test.ml
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test/interop/test.ml
···
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(** Python reedsolo interop tests for ocaml-reed-solomon.
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Reads committed traces from [traces/rs_vectors.hex] and verifies that the
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OCaml RS(255,223) encoder produces identical codewords.
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Traces generated by: [REGEN_TRACES=1 dune build @regen-traces] Oracle:
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Python reedsolo (configured with CCSDS parameters) *)
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let trace path = Filename.concat "traces" path
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let read_file path =
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let ic = open_in path in
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let n = in_channel_length ic in
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let s = Bytes.create n in
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really_input ic s 0 n;
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close_in ic;
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Bytes.to_string s
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let bytes_of_hex hex =
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let len = String.length hex / 2 in
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Bytes.init len (fun i ->
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Char.chr (int_of_string ("0x" ^ String.sub hex (i * 2) 2)))
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let hex_of_bytes b =
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let buf = Buffer.create (Bytes.length b * 2) in
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Bytes.iter
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(fun c -> Buffer.add_string buf (Printf.sprintf "%02x" (Char.code c)))
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b;
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Buffer.contents buf
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type vector = { name : string; data : bytes; expected_codeword : bytes }
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let parse_vectors path =
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let content = read_file path in
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let lines = String.split_on_char '\n' content in
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List.filter_map
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(fun line ->
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let line = String.trim line in
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if line = "" then None
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else
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match String.split_on_char '|' line with
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| [ name; data_hex; codeword_hex ] ->
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Some
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{
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name;
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data = bytes_of_hex data_hex;
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expected_codeword = bytes_of_hex codeword_hex;
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}
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| _ -> Alcotest.failf "bad vector line: %s" line)
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lines
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let test_encode vec () =
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let cfg = Reed_solomon.ccsds in
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let got = Reed_solomon.encode_systematic cfg vec.data in
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if got <> vec.expected_codeword then
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Alcotest.failf "%s: codeword mismatch\n expected: %s\n got: %s"
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vec.name
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(hex_of_bytes vec.expected_codeword)
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(hex_of_bytes got)
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let test_roundtrip vec () =
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let cfg = Reed_solomon.ccsds in
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let codeword = Reed_solomon.encode_systematic cfg vec.data in
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match Reed_solomon.decode cfg codeword with
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| Ok decoded ->
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if decoded <> vec.data then
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Alcotest.failf "%s: decode mismatch after clean roundtrip" vec.name
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| Error _ -> Alcotest.failf "%s: decode failed on clean codeword" vec.name
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let test_error_correction vec () =
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let cfg = Reed_solomon.ccsds in
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let codeword = Bytes.copy vec.expected_codeword in
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(* Inject 8 symbol errors (well within t=16 correction capability) *)
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for i = 0 to 7 do
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let pos = i * 30 in
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let orig = Bytes.get codeword pos in
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Bytes.set codeword pos (Char.chr (Char.code orig lxor 0xFF))
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done;
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match Reed_solomon.decode cfg codeword with
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| Ok decoded ->
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if decoded <> vec.data then
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Alcotest.failf "%s: decode mismatch after error correction" vec.name
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| Error _ -> Alcotest.failf "%s: decode failed with 8 errors (t=16)" vec.name
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let () =
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let vectors = parse_vectors (trace "rs_vectors.hex") in
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Alcotest.run "rs-interop"
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[
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( "encode",
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List.map
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(fun v -> Alcotest.test_case v.name `Quick (test_encode v))
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vectors );
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( "roundtrip",
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List.map
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(fun v -> Alcotest.test_case v.name `Quick (test_roundtrip v))
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vectors );
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( "error-correction",
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List.map
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(fun v -> Alcotest.test_case v.name `Quick (test_error_correction v))
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vectors );
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]
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test/interop/traces/rs_vectors.hex
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test/interop/traces/rs_vectors.hex
···
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zeros|00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000|000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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ones|01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101|010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
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ascending|000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f303132333435363738393a3b3c3d3e3f404142434445464748494a4b4c4d4e4f505152535455565758595a5b5c5d5e5f606162636465666768696a6b6c6d6e6f707172737475767778797a7b7c7d7e7f808182838485868788898a8b8c8d8e8f909192939495969798999a9b9c9d9e9fa0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebfc0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcddde|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hello|48656c6c6f2c20526565642d536f6c6f6d6f6e210000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000|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