rsecbinary: Require caller-prepared tables

Each caller's gencoeffs procedure delivers the generator coefficients
reversed and in the log domain with -1 denoting a zero coefficient, so
that the FIFO caches hold the form consumed by the inner loop, and the
anti-log tables are built spanning two periods during lazy
initialisation so that log-sums resolve without a modulo reduction.
Each inner-loop iteration is a single get, log-add, anti-log get, xor
and put. The field order parameter is dropped from the interface along
with the ECC codeword count, which is the length of the coefficient
array.

Author: terryburton

src/azteccode.ps.src

@@ -252,7 +252,14 @@ begin
         coeffs 0 2 copy get 3 index rsprod put   % coeffs[0] = coeffs[0] * ai
         pop  % ai
     } for
-    coeffs
+
+    %
+    % Deliver the coefficients reversed and in the log domain, with -1
+    % denoting a zero coefficient, as rsecbinary requires
+    %
+    [ rsnc 1 sub -1 0 {
+        coeffs exch get dup 0 ne { rslog exch get } { pop -1 } ifelse
+    } for ]
 } bind def
 
 /azteccode.coeffscache azteccode.coeffscachemax azteccode.coeffscachelimit //fifocache exec def
@@ -289,13 +296,15 @@ begin
     /charvals charvals readonly def
 
     %
-    % Calculate the log and anti-log tables for each GF
+    % Calculate the log and anti-log tables for each GF, the anti-log
+    % tables spanning two periods so that log-sums resolve without a
+    % modulo reduction
     %
     /rstables [
         //azteccode.rsparams {
             dup length 0 ne {
                 aload pop /rspm exch def /rsgf exch def
-                /rsalog [ 1 rsgf 1 sub { dup 2 mul dup rsgf ge {rspm xor} if } repeat ] def
+                /rsalog [ 1 rsgf 2 mul 2 sub { dup 2 mul dup rsgf ge {rspm xor} if } repeat ] def
                 /rslog rsgf array def
                 1 1 rsgf 1 sub {dup rsalog exch get exch rslog 3 1 roll put} for
                 [ rslog rsalog ]
@@ -1013,17 +1022,16 @@ begin
         /rscws exch def
 
         %
-        % Lookup the Reed Solomon error correction parameters for the codeword size
+        % Lookup the Reed Solomon log tables for the codeword size
         %
-        //azteccode.rsparams rsbt get aload pop /rspm exch def /rsgf-1 exch 1 sub def
         rstables rsbt get aload pop /rsalog exch def /rslog exch def
 
         %
         % Function to calculate the product in the field
         %
         /rsprod {
             dup 0 ne { 1 index 0 ne {
-               rslog exch get exch rslog exch get add rsgf-1 mod rsalog exch get
+               rslog exch get exch rslog exch get add rsalog exch get
             } { pop pop 0 } ifelse } { pop pop 0 } ifelse
         } def
 
@@ -1032,7 +1040,7 @@ begin
         (ecc.coeffs) //azteccode.after exec
 
         /lfsr rsnc array def
-        {rscws exch get} rscws length coeffs rsnc lfsr rslog rsalog rsgf-1 //rsecbinary exec
+        {rscws exch get} rscws length coeffs lfsr rslog rsalog //rsecbinary exec
         lfsr
 
         (ecc.cws) //azteccode.after exec

src/codeone.ps.src

@@ -284,13 +284,15 @@ begin
     /encvals [ avals cvals tvals xvals -1 bvals ] readonly def
 
     %
-    % Calculate the log and anti-log tables for each Galois field
+    % Calculate the log and anti-log tables for each Galois field, the
+    % anti-log tables spanning two periods so that log-sums resolve
+    % without a modulo reduction
     %
     /rstables [
         //codeone.rsparams {
             dup length 0 ne {
                 aload pop /rspm exch def /rsgf exch def
-                /rsalog [ 1 rsgf 1 sub { dup 2 mul dup rsgf ge {rspm xor} if } repeat ] def
+                /rsalog [ 1 rsgf 2 mul 2 sub { dup 2 mul dup rsgf ge {rspm xor} if } repeat ] def
                 /rslog rsgf array def
                 1 1 rsgf 1 sub {dup rsalog exch get exch rslog 3 1 roll put} for
                 [ rslog rsalog ]
@@ -321,7 +323,7 @@ begin
 %
 /codeone.rsprod {
     dup 0 ne { 1 index 0 ne {
-        rslog exch get exch rslog exch get add gf-1 mod rsalog exch get
+        rslog exch get exch rslog exch get add rsalog exch get
     } { pop pop 0 } ifelse } { pop pop 0 } ifelse
 } bind def
 
@@ -346,7 +348,13 @@ begin
         //codeone.rsprod exec put                 % coeffs[0] = coeffs[0] * ai
         pop  % ai
     } for
-    coeffs 0 coeffs length 1 sub getinterval
+    %
+    % Deliver the coefficients reversed and in the log domain, with -1
+    % denoting a zero coefficient, as rsecbinary requires
+    %
+    [ ecpb 1 sub -1 0 {
+        coeffs exch get dup 0 ne { rslog exch get } { pop -1 } ifelse
+    } for ]
 } bind def
 
 %
@@ -369,8 +377,6 @@ begin
     /ecpb exch def
     /rslog rstables rsbt get 0 get def
     /rsalog rstables rsbt get 1 get def
-    /gf rsalog length def
-    /gf-1 gf 1 sub def
     rsbt 10000 mul ecpb add  % key = rsbt * 10000 + ecpb
     { //codeone.gencoeffs exec }
     { length }
@@ -1106,7 +1112,7 @@ begin
         /blk exch def
         ecbs blk
         /lfsr ecpb array def
-        {cws exch rsbl mul blk add get} dcpb coeffs ecpb lfsr rslog rsalog gf-1 //rsecbinary exec
+        {cws exch rsbl mul blk add get} dcpb coeffs lfsr rslog rsalog //rsecbinary exec
         lfsr
         put
     } for

src/datamatrix.ps.src

@@ -283,9 +283,11 @@ begin
     /encvals [ Avals Cvals Tvals Xvals Evals Bvals ] readonly def
 
     %
-    % Calculate the Reed-Solomon log and anti-log tables for GF(256) with prime polynomial 301
+    % Calculate the Reed-Solomon log and anti-log tables for GF(256) with
+    % prime polynomial 301, the anti-log table spanning two periods so that
+    % log-sums resolve without a modulo reduction
     %
-    /rsalog [ 1 255 { dup 2 mul dup 256 ge {301 xor} if } repeat ] readonly def
+    /rsalog [ 1 510 { dup 2 mul dup 256 ge {301 xor} if } repeat ] readonly def
     /rslog 256 array def
     1 1 255 {dup rsalog exch get exch rslog 3 1 roll put} for
     /rslog rslog readonly def
@@ -311,7 +313,7 @@ begin
 %
 /datamatrix.rsprod {
     dup 0 ne { 1 index 0 ne {
-        rslog exch get exch rslog exch get add 255 mod rsalog exch get
+        rslog exch get exch rslog exch get add rsalog exch get
     } { pop pop 0 } ifelse } { pop pop 0 } ifelse
 } bind def
 
@@ -335,7 +337,13 @@ begin
         //datamatrix.rsprod exec put             % coeffs[0] = coeffs[0] * ai
         pop  % ai
     } for
-    coeffs 0 coeffs length 1 sub getinterval
+    %
+    % Deliver the coefficients reversed and in the log domain, with -1
+    % denoting a zero coefficient, as rsecbinary requires
+    %
+    [ k 1 sub -1 0 {
+        coeffs exch get dup 0 ne { rslog exch get } { pop -1 } ifelse
+    } for ]
 } bind def
 
 %
@@ -1052,7 +1060,7 @@ begin
         } ifelse
         ecbs blk
         /lfsr ecpb array def
-        {cws exch rsbl mul blk add get} cwbsize coeffs ecpb lfsr rslog rsalog 255 //rsecbinary exec
+        {cws exch rsbl mul blk add get} cwbsize coeffs lfsr rslog rsalog //rsecbinary exec
         lfsr
         put
     } for

src/hanxin.ps.src

@@ -501,13 +501,15 @@ begin
     //hanxin.latevars begin
 
     %
-    % Calculate the log and anti-log tables for each Galois field
+    % Calculate the log and anti-log tables for each Galois field, the
+    % anti-log tables spanning two periods so that log-sums resolve
+    % without a modulo reduction
     %
     /rstables [
         //hanxin.rsparams {
             dup length 0 ne {
                 aload pop /rspm exch def /rsgf exch def
-                /rsalog [ 1 rsgf 1 sub { dup 2 mul dup rsgf ge {rspm xor} if } repeat ] def
+                /rsalog [ 1 rsgf 2 mul 2 sub { dup 2 mul dup rsgf ge {rspm xor} if } repeat ] def
                 /rslog rsgf array def
                 1 1 rsgf 1 sub {dup rsalog exch get exch rslog 3 1 roll put} for
                 [ rslog rsalog ]
@@ -538,7 +540,7 @@ begin
 %
 /hanxin.rsprod {
     dup 0 ne { 1 index 0 ne {
-        rslog exch get exch rslog exch get add rsgf-1 mod rsalog exch get
+        rslog exch get exch rslog exch get add rsalog exch get
     } { pop pop 0 } ifelse } { pop pop 0 } ifelse
 } bind def
 
@@ -562,7 +564,13 @@ begin
         //hanxin.rsprod exec put                 % coeffs[0] = coeffs[0] * ai
         pop  % ai
     } for
-    coeffs 0 coeffs length 1 sub getinterval
+    %
+    % Deliver the coefficients reversed and in the log domain, with -1
+    % denoting a zero coefficient, as rsecbinary requires
+    %
+    [ rsnc 1 sub -1 0 {
+        coeffs exch get dup 0 ne { rslog exch get } { pop -1 } ifelse
+    } for ]
 } bind def
 
 %
@@ -584,7 +592,6 @@ begin
     /rsbt exch def
     /rsnc exch def
     rstables rsbt get aload pop /rsalog exch def /rslog exch def
-    /rsgf-1 rsalog length 1 sub def
     rsbt 10000 mul rsnc add  % key = rsbt * 10000 + rsnc
     { //hanxin.gencoeffs exec }
     { length }
@@ -972,7 +979,7 @@ begin
         %
         (ecc.cws) //hanxin.before exec
         /lfsr rsnc array def
-        {rscws exch get} rscws length coeffs rsnc lfsr rslog rsalog rsgf-1 //rsecbinary exec
+        {rscws exch get} rscws length coeffs lfsr rslog rsalog //rsecbinary exec
         lfsr
         (ecc.cws) //hanxin.after exec
 

src/maxicode.ps.src

@@ -221,7 +221,7 @@ begin
 %
 /maxicode.rsprod {
     2 copy 0 ne exch 0 ne and {
-        rslog exch get exch rslog exch get add 63 mod rsalog exch get
+        rslog exch get exch rslog exch get add rsalog exch get
     } { pop pop 0 } ifelse
 } bind def
 
@@ -244,7 +244,13 @@ begin
         //maxicode.rsprod exec put               % coeffs[0] = coeffs[0] * ai
         pop  % ai
     } for
-    coeffs 0 k getinterval
+    %
+    % Deliver the coefficients reversed and in the log domain, with -1
+    % denoting a zero coefficient, as rsecbinary requires
+    %
+    [ k 1 sub -1 0 {
+        coeffs exch get dup 0 ne { rslog exch get } { pop -1 } ifelse
+    } for ]
 } bind def
 
 %
@@ -300,9 +306,11 @@ begin
     /charvals charvals readonly def
 
     %
-    % Calculate the Reed-Solomon log and anti-log tables for GF(64)
+    % Calculate the Reed-Solomon log and anti-log tables for GF(64), the
+    % anti-log table spanning two periods so that log-sums resolve without
+    % a modulo reduction
     %
-    /rsalog [ 1 63 { dup 2 mul dup 64 ge {67 xor} if } repeat ] readonly def
+    /rsalog [ 1 126 { dup 2 mul dup 64 ge {67 xor} if } repeat ] readonly def
     /rslog 64 array def
     1 1 63 {dup rsalog exch get exch rslog 3 1 roll put} for
     /rslog rslog readonly def
@@ -1081,7 +1089,7 @@ begin
         % Calculate the error correction codewords
         %
         /lfsr rsnum array def
-        {cwb exch get} cwb length coeffs rsnum lfsr rslog rsalog 63 //rsecbinary exec
+        {cwb exch get} cwb length coeffs lfsr rslog rsalog //rsecbinary exec
         lfsr
 
     } def

src/qrcode.ps.src

@@ -562,9 +562,11 @@ begin
     /charvals charvals readonly def
 
     %
-    % Calculate the Reed-Solomon log and anti-log tables
+    % Calculate the Reed-Solomon log and anti-log tables, the latter
+    % spanning two periods so that log-sums resolve without a modulo
+    % reduction
     %
-    /rsalog [ 1 255 { dup 2 mul dup 256 ge {285 xor} if } repeat ] readonly def
+    /rsalog [ 1 510 { dup 2 mul dup 256 ge {285 xor} if } repeat ] readonly def
     /rslog 256 array def
     1 1 255 {dup rsalog exch get exch rslog 3 1 roll put} for
     /rslog rslog readonly def
@@ -641,7 +643,7 @@ begin
 %
 /qrcode.rsprod {
     dup 0 ne { 1 index 0 ne {
-        rslog exch get exch rslog exch get add 255 mod rsalog exch get
+        rslog exch get exch rslog exch get add rsalog exch get
     } { pop pop 0 } ifelse } { pop pop 0 } ifelse
 } bind def
 
@@ -666,7 +668,13 @@ begin
         //qrcode.rsprod exec put                  % coeffs[0] = coeffs[0] * ai
         pop  % ai
     } for
-    coeffs 0 coeffs length 1 sub getinterval
+    %
+    % Deliver the coefficients reversed and in the log domain, with -1
+    % denoting a zero coefficient, as rsecbinary requires
+    %
+    [ ecpb 1 sub -1 0 {
+        coeffs exch get dup 0 ne { rslog exch get } { pop -1 } ifelse
+    } for ]
 } bind def
 
 %
@@ -1352,7 +1360,7 @@ begin
     /rscodes {
         /rscws exch def
         /lfsr ecpb array def
-        {rscws exch get} rscws length coeffs ecpb lfsr rslog rsalog 255 //rsecbinary exec
+        {rscws exch get} rscws length coeffs lfsr rslog rsalog //rsecbinary exec
         lfsr
     } def