Reed-Solomon error correction over GF(2^8)
reed-solomon: add Gf256 tests and fuzz mli (E605)
Cover the GF(2^8) functor with property-based tests (additive identity,
commutativity, inverse roundtrip, pow boundaries, table consistency)
and add the missing fuzz module interface.
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-1
+4
fuzz/fuzz_reed_solomon.mli
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fuzz/fuzz_reed_solomon.mli
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test/dune
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test/dune
+2
-1
test/test.ml
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-1
test/test.ml
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test/test_gf256.ml
+100
test/test_gf256.ml
···
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(** Tests for [Gf256] — GF(2^8) finite field arithmetic.
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Vectors checked against the CCSDS 131.0-B-4 Annex F field (primitive
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polynomial x^8+x^7+x^2+x+1 = 0x187, primitive element 11). *)
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module F = Reed_solomon.Gf256.Make (struct
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let primitive_poly = 0x187
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let primitive_element = 11
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end)
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let add_self_zero () =
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for a = 0 to 255 do
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Alcotest.(check int) (Fmt.str "%d + %d = 0" a a) 0 (F.add a a)
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done
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let sub_equals_add () =
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for a = 0 to 255 do
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for b = 0 to 255 do
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Alcotest.check Alcotest.int (Fmt.str "sub %d %d" a b) (F.add a b)
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(F.sub a b)
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done
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done
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let mul_zero () =
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for a = 0 to 255 do
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Alcotest.(check int) (Fmt.str "0 * %d" a) 0 (F.mul 0 a);
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Alcotest.(check int) (Fmt.str "%d * 0" a) 0 (F.mul a 0)
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done
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let mul_one () =
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for a = 0 to 255 do
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Alcotest.(check int) (Fmt.str "1 * %d" a) a (F.mul 1 a);
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Alcotest.(check int) (Fmt.str "%d * 1" a) a (F.mul a 1)
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done
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let mul_commutative () =
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for a = 1 to 255 do
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for b = 1 to 255 do
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Alcotest.(check int)
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(Fmt.str "%d * %d = %d * %d" a b b a)
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(F.mul a b) (F.mul b a)
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done
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done
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let inv_roundtrip () =
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for a = 1 to 255 do
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let inv = F.inv a in
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Alcotest.(check int) (Fmt.str "%d * inv %d = 1" a a) 1 (F.mul a inv)
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done
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let inv_zero_raises () =
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Alcotest.check_raises "inv 0 raises"
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(Invalid_argument "Gf256.inv: cannot invert zero") (fun () ->
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ignore (F.inv 0))
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let pow_zero_exponent () =
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for a = 0 to 255 do
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Alcotest.(check int) (Fmt.str "%d^0 = 1" a) 1 (F.pow a 0)
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done
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let pow_one_exponent () =
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for a = 0 to 255 do
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Alcotest.(check int) (Fmt.str "%d^1 = %d" a a) a (F.pow a 1)
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done
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let pow_negative () =
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for a = 1 to 255 do
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Alcotest.(check int) (Fmt.str "%d^-1 = inv %d" a a) (F.inv a) (F.pow a (-1))
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done
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let exp_table_size () =
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Alcotest.(check int) "exp_table length" 512 (Array.length F.exp_table);
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Alcotest.(check int) "exp_table[0]" 1 F.exp_table.(0)
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let log_table_size () =
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Alcotest.(check int) "log_table length" 256 (Array.length F.log_table)
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let log_exp_inverse () =
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for i = 0 to 254 do
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let v = F.exp_table.(i) in
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Alcotest.(check int) (Fmt.str "log(exp(%d)) = %d" i i) i F.log_table.(v)
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done
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let suite =
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( "gf256",
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[
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Alcotest.test_case "add self yields zero" `Quick add_self_zero;
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Alcotest.test_case "sub equals add" `Quick sub_equals_add;
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Alcotest.test_case "mul by zero" `Quick mul_zero;
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Alcotest.test_case "mul by one" `Quick mul_one;
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Alcotest.test_case "mul commutative" `Quick mul_commutative;
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Alcotest.test_case "inv roundtrip" `Quick inv_roundtrip;
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Alcotest.test_case "inv 0 raises" `Quick inv_zero_raises;
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Alcotest.test_case "pow exponent 0" `Quick pow_zero_exponent;
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Alcotest.test_case "pow exponent 1" `Quick pow_one_exponent;
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Alcotest.test_case "pow negative" `Quick pow_negative;
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Alcotest.test_case "exp_table size" `Quick exp_table_size;
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Alcotest.test_case "log_table size" `Quick log_table_size;
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Alcotest.test_case "log/exp inverse" `Quick log_exp_inverse;
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] )