rsecprime: Require caller-reversed coefficients

Callers deliver the generator coefficients reversed from their cached
gencoeffs procedures, matching the rsecbinary interface; the ECC
codeword count is the length of the coefficient array.

Author: terryburton

src/dotcode.ps.src

@@ -218,9 +218,9 @@ begin
         } for
         pop  % i
     } for
-    % Flip to standard g(x) form: drop the leading 1 and reverse coeffs[1..NC]
-    % so the constant term ends up at index 0.
-    NC -1 1 { coeffs exch get } for
+    % Drop the leading 1, delivering the coefficients reversed as rsecprime
+    % requires
+    1 1 NC { coeffs exch get } for
     NC array astore
 } bind def
 
@@ -1184,7 +1184,7 @@ begin
             % spec's negated form in lfsr[0..NC), so no post-pass is needed.
             %
             /lfsr NC array def
-            {step mul start add rscws exch get} ND coeffs NC lfsr 113 //rsecprime exec
+            {step mul start add rscws exch get} ND coeffs lfsr 113 //rsecprime exec
             0 1 NC 1 sub {
                 /j exch def
                 rscws ND j add offset lfsr j get put

src/micropdf417.ps.src

@@ -564,7 +564,11 @@ begin
     } for
     /coeffs coeffs 0 coeffs length 1 sub getinterval def
     coeffs length 1 sub -2 0 { coeffs exch 2 copy get 929 exch sub put } for
-    coeffs
+
+    %
+    % Deliver the coefficients reversed, as rsecprime requires
+    %
+    [ k 1 sub -1 0 { coeffs exch get } for ]
 } bind def
 
 %
@@ -1273,7 +1277,7 @@ begin
     %
     % Derive the error codewords directly into cws[n..n+k)
     %
-    {cws exch get} n coeffs k cws n k getinterval 929 //rsecprime exec
+    {cws exch get} n coeffs cws n k getinterval 929 //rsecprime exec
 
     options /debugecc known
     /uk.co.terryburton.bwipp.global_ctx dup where {exch get /enabledebug known} {pop false} ifelse

src/pdf417.ps.src

@@ -433,7 +433,11 @@ begin
     } for
     /coeffs coeffs 0 k getinterval def
     k 1 sub -2 0 { coeffs exch 2 copy get 929 exch sub put } for
-    coeffs
+
+    %
+    % Deliver the coefficients reversed, as rsecprime requires
+    %
+    [ k 1 sub -1 0 { coeffs exch get } for ]
 } bind def
 
 %
@@ -1167,7 +1171,7 @@ begin
     %
     % Derive the error codewords directly into cws[n..n+k)
     %
-    {cws exch get} n coeffs k cws n k getinterval 929 //rsecprime exec
+    {cws exch get} n coeffs cws n k getinterval 929 //rsecprime exec
 
     options /debugecc known
     /uk.co.terryburton.bwipp.global_ctx dup where {exch get /enabledebug known} {pop false} ifelse

src/rsecprime.ps.src

@@ -42,33 +42,25 @@ begin
 %
 % Reed-Solomon encoder for prime-field GF(p).
 %
-% Runs a streaming LFSR over nd data codewords using the generator polynomial
-% coeffs. The caller-owned lfsr is the shift register; on return, its first
-% nc cells are the ECC codewords in the negated form expected by callers
-% (pdf417, micropdf417, ultracode): this fuses what used to be a separate
-% post-pass of (p - cws[i]) mod p into the inner update.
+% Runs a streaming LFSR over nd data codewords using the generator
+% polynomial. The caller-owned lfsr is the shift register; on return, its
+% first nc cells are the ECC codewords, where nc is the length of
+% coeffsrev, negated ((p - c) mod p) as the callers expect. The caller
+% must supply the generator coefficients reversed.
 %
 /rsecprime {
 
     8 dict begin
 
-    /p exch def        % Prime modulus
-    /lfsr exch def     % Workspace of length at least nc
-    /nc exch def       % Number of ECC codewords to produce
-    /coeffs exch def   % Generator polynomial coefficients
-    /nd exch def       % Number of data codewords
-    /getdata exch def  % Implements fetching nth codeword
+    /p exch def          % Prime modulus
+    /lfsr exch def       % Workspace of length at least nc
+    /coeffsrev exch def  % Reversed generator polynomial coefficients
+    /nd exch def         % Number of data codewords
+    /getdata exch def    % Implements fetching nth codeword
 
-    0 1 nc 1 sub {lfsr exch 0 put} for  % Zero LFSR
+    /nc coeffsrev length def  % Number of ECC codewords to produce
 
-    %
-    % Reverse coeffs to simplify the inner loop
-    %
-    /coeffsrev nc array def
-    0 1 nc 1 sub {
-        /j exch def
-        coeffsrev j coeffs nc 1 sub j sub get put
-    } for
+    0 1 nc 1 sub {lfsr exch 0 put} for  % Zero LFSR
 
     0 1 nd 1 sub {  % m
         getdata exec lfsr 0 get sub p add p mod   % fb = (data[m] - S[0]) mod p

src/ultracode.ps.src

@@ -196,7 +196,11 @@ begin
     } for
     /coeffs coeffs 0 coeffs length 1 sub getinterval def
     coeffs length 1 sub -2 0 { coeffs exch 2 copy get 283 exch sub put } for
-    coeffs
+
+    %
+    % Deliver the coefficients reversed, as rsecprime requires
+    %
+    [ k 1 sub -1 0 { coeffs exch get } for ]
 } bind def
 
 %
@@ -430,7 +434,7 @@ begin
     %
     /rsdata [ start mcc acc dcws aload pop ] def
     /ecws k array def
-    {rsdata exch get} n coeffs k ecws 283 //rsecprime exec
+    {rsdata exch get} n coeffs ecws 283 //rsecprime exec
 
     options /debugecc known
     /uk.co.terryburton.bwipp.global_ctx dup where {exch get /enabledebug known} {pop false} ifelse