From 596656536a727ebe434cf5fc9c79c952b172edec Mon Sep 17 00:00:00 2001
From: Steven Charles Davis <steven.charles.davis@gmail.com>
Date: Mon, 20 Jan 2014 11:45:31 -0600
Subject: [PATCH] Issue #2 - correct resolution to RFC3339 date encoding

Reverts provisional commit and applies the correct fixes to gf256 math
module. This resolves incorrect ECC generation for a large number of
cases where the most significant polynomial in a remainder resolves to
0 at any point during the generation of intermediate remainder values.
---
 src/gf256.erl              | 22 ++++++----------------
 src/qrcode_reedsolomon.erl |  7 +------
 2 files changed, 7 insertions(+), 22 deletions(-)

diff --git a/src/gf256.erl b/src/gf256.erl
index 5c0bde6..0a274f0 100644
--- a/src/gf256.erl
+++ b/src/gf256.erl
@@ -75,8 +75,6 @@ add(F, [H|T], [], Acc) ->
 	add(F, T, [], [H|Acc]);
 add(F, [], [H|T], Acc) ->
 	add(F, [], T, [H|Acc]);
-add(F, [], [], [0|Acc]) ->
-	add(F, [], [], Acc);
 add(_, [], [], Acc) ->
 	Acc.
 
@@ -85,17 +83,13 @@ subtract(F = #gf256{}, A, B) ->
 	add(F, A, B).
 
 %%
-multiply(#gf256{}, 0, _) ->
-	0;
-multiply(#gf256{}, _, 0) ->
-	0;
 multiply(#gf256{}, 1, B) ->
 	B;
 multiply(#gf256{}, A, 1) ->
 	A;
-multiply(#gf256{exponent = E, log = L}, A, B) ->
-	X = (lists:nth(A + 1, L) + lists:nth(B + 1, L)) rem ?RANGE,
-	lists:nth(X + 1, E).
+multiply(F = #gf256{}, A, B) ->
+	X = (log(F, A) + log(F, B)) rem ?RANGE,
+	exponent(F, X).
 
 %%
 exponent(#gf256{exponent = E}, X) ->
@@ -106,8 +100,8 @@ log(#gf256{log = L}, X) ->
 	lists:nth(X + 1, L).
 	
 %%
-inverse(#gf256{exponent = E, log = L}, X) ->
-	lists:nth(256 - lists:nth(X + 1, L), E).
+inverse(F = #gf256{}, X) ->
+	exponent(F, ?RANGE - log(F, X)).
 
 %%
 value(#gf256{}, Poly, 0) ->
@@ -131,8 +125,6 @@ monomial(#gf256{}, Coeff, Degree) when Degree >= 0 ->
 	[Coeff|lists:duplicate(Degree, 0)].
 
 %%
-monomial_product(#gf256{}, _, 0, _) ->
-	[0];
 monomial_product(F, Poly, Coeff, Degree) ->
 	monomial_product(F, Poly, Coeff, Degree, []).
 %	
@@ -184,9 +176,7 @@ divide(F, IDLT, B, Q, R = [H|_]) when length(R) >= length(B), R =/= [0] ->
 	M = monomial(F, Scale, Diff),
 	Q0 = add(F, Q, M),
 	Coeffs = monomial_product(F, B, Scale, Diff),
-	R0 = add(F, R, Coeffs),
+	[_|R0] = add(F, R, Coeffs),
 	divide(F, IDLT, B, Q0, R0);
 divide(_, _, _, Q, R) ->
 	{Q, R}.
-	
-
diff --git a/src/qrcode_reedsolomon.erl b/src/qrcode_reedsolomon.erl
index 8a4cda8..62edfaf 100644
--- a/src/qrcode_reedsolomon.erl
+++ b/src/qrcode_reedsolomon.erl
@@ -25,14 +25,9 @@ encode(Bin, Degree) when Degree > 0 ->
 	Data = binary_to_list(Bin),
 	Coeffs = gf256:monomial_product(Field, Data, 1, Degree),
 	{_Quotient, Remainder} = gf256:divide(Field, Coeffs, Generator),
-	Remainder0 = zero_pad(Degree, Remainder),
-	ErrorCorrectionBytes = list_to_binary(Remainder0),
+	ErrorCorrectionBytes = list_to_binary(Remainder),
 	<<ErrorCorrectionBytes/binary>>.
 
-zero_pad(Length, R) when length(R) < Length ->
-	zero_pad(Length, [0|R]);
-zero_pad(_, R) ->
-	R.
 %%
 bch_code(Byte, Poly) ->
 	MSB = msb(Poly),