0408ab8857
Fixes an issue where a GF(256) remainder used for reed-solomon error correction bytes is a codeword short on return from division. This may not be the final resolution to the wider issue.
75 lines
1.8 KiB
Erlang
75 lines
1.8 KiB
Erlang
%% Copyright 2011 Steve Davis <steve@simulacity.com>
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%
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% Licensed under the Apache License, Version 2.0 (the "License");
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% you may not use this file except in compliance with the License.
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% You may obtain a copy of the License at
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%
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% http://www.apache.org/licenses/LICENSE-2.0
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%
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% Unless required by applicable law or agreed to in writing, software
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% distributed under the License is distributed on an "AS IS" BASIS,
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% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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% See the License for the specific language governing permissions and
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% limitations under the License.
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-module(qrcode_reedsolomon).
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-export([encode/2, bch_code/2]).
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-define(QRCODE_GF256_PRIME_MODULUS, 285). % 16#011D = 2^8 + 2^4 + 2^3 + 2^2 + 2^0
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%%
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encode(Bin, Degree) when Degree > 0 ->
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Field = gf256:field(?QRCODE_GF256_PRIME_MODULUS),
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Generator = generator(Field, Degree),
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Data = binary_to_list(Bin),
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Coeffs = gf256:monomial_product(Field, Data, 1, Degree),
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{_Quotient, Remainder} = gf256:divide(Field, Coeffs, Generator),
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Remainder0 = zero_pad(Degree, Remainder),
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ErrorCorrectionBytes = list_to_binary(Remainder0),
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<<ErrorCorrectionBytes/binary>>.
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zero_pad(Length, R) when length(R) < Length ->
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zero_pad(Length, [0|R]);
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zero_pad(_, R) ->
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R.
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%%
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bch_code(Byte, Poly) ->
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MSB = msb(Poly),
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Byte0 = Byte bsl (MSB - 1),
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bch_code(Byte0, Poly, MSB).
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%% Internal
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%%
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generator(F, D) when D > 0 ->
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generator(F, [1], D, 0).
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%
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generator(_, P, D, D) ->
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P;
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generator(F, P, D, Count) ->
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P0 = gf256:polynomial_product(F, P, [1, gf256:exponent(F, Count)]),
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generator(F, P0, D, Count + 1).
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%
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bch_code(Byte, Poly, MSB) ->
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case msb(Byte) >= MSB of
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true ->
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Byte0 = Byte bxor (Poly bsl (msb(Byte) - MSB)),
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bch_code(Byte0, Poly, MSB);
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false ->
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Byte
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end.
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%%
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msb(0) ->
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0;
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msb(Byte) ->
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msb(Byte, 0).
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msb(0, Count) ->
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Count;
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msb(Byte, Count) ->
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msb(Byte bsr 1, Count + 1).
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