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array_v_CCT.pl
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#!/bin/sh --# perl, to stop looping
eval 'exec /usr/local/bin/perl $0 ${1+"${@}"}'
if 0;
# Perl script to generate truncated array multiplier (Constant Correction)
# Last update: 08/23/02
use Getopt::Std;
# options are
# -x <bits> the number of x bits
# -y <bits> the number of y bits
# -z <bits> the number of output bits
# -k <int> number of columns to keep
# -m <string> module name
getopts('x:y:z:k:m:');
$XBITS=$opt_x;
$YBITS=$opt_y;
$ZBITS=$opt_z;
$K=$opt_k;
$MODULE=$opt_m;
if($XBITS<=0 || $YBITS<=0 || $ZBITS<=0 || $K<0){
print("Input parameters:\n");
print(" -x <bits> the number of x bits\n");
print(" -y <bits> the number of y bits\n");
print(" -z <bits> the number of output bits\n");
print(" -k <int> number of columns to keep\n");
print(" -m <string> module name (optional)\n");
exit(1);
}
if($ZBITS+$K>$XBITS+$YBITS) {
print("Error: z+k must be smaller than or equal to x+y\n\n");
exit(1);
}
$pp_label=1;
$ha_label=1;
$fa_label=1;
$cpa_label=1;
$instcnt=1;
# Calculation of the correction constant
# --------------------------------------
$err_red = 0;
for($q = $ZBITS+$K+1; $q <= $XBITS+$YBITS; $q++) {
$err_red += ($XBITS+$YBITS+1-$q)/&pow2($q); # reduction error
# printf("%s %s %s %s\n",$q,&pow2($q),$err_red,$XBITS+$YBITS+1-$q);
}
$err_rnd = 1/pow2($ZBITS)*(1 - 1/&pow2($K)); # rounding error
$err_tot = 0.25*$err_red + 0.5*$err_rnd;
printf("\n// Correction constant value: %s (",$err_tot);
# Rounding of that constant
$err_tot_rnd = $err_tot * &pow2($ZBITS+$K);
$err_tot_rnd = &round_near($err_tot_rnd);
$err_tot_rnd = $err_tot_rnd / &pow2($ZBITS+$K);
# Conversion into binary format
@carray;
$rem = $err_tot_rnd;
for($j=1;$j<=$ZBITS+$K;$j++){
$mod = $rem * &pow2($j);
if($mod>=1){
$rem = $rem - 1/&pow2($j);
@carray[$XBITS+$YBITS-$j] = 1;
}
else{
@carray[$XBITS+$YBITS-$j] = 0;
}
}
# Display the value of the constant correction
for($j=$XBITS+$YBITS-1;$j>=$XBITS+$YBITS-$ZBITS-$K;$j--){
printf("%s",@carray[$j]);
}
printf(")\n\n");
# Calculation of the number of bits required for the constant correction
# ----------------------------------------------------------------------
$nbitscon=0;
for($j=$XBITS+$YBITS-$ZBITS-$K;$j<$XBITS+$YBITS;$j++){
$nbitscon += @carray[$j]*&pow2($j-($XBITS+$YBITS-$ZBITS-$K));
}
# calculation of which partial products have to be generated
# ----------------------------------------------------------
if($XBITS<$ZBITS+$K){
$x_pp_size=$XBITS;
$h_pp_size=$K+$ZBITS-$XBITS;
}
else{
$x_pp_size=$ZBITS+$K;
$h_pp_size=0;
}
if($YBITS<=$ZBITS+$K){
$y_pp_size=$YBITS;
}
else{
$y_pp_size=$ZBITS+$K-1;
}
# Calculation of the number of bits available for correction
# (number of HA located on the diagonal and on the second line)
# -------------------------------------------------------------
$nha=0;
$nhadiag=0;
for($y=$YBITS-$y_pp_size; $y < $YBITS ; $y++) {
for($x=$XBITS-2; $x >= $XBITS-$x_pp_size; $x--) {
if($x+$y>=$XBITS+$YBITS-$ZBITS-$K){
if($y==$YBITS-$y_pp_size+1){
$nha++;
}
}
if($x+$y==$XBITS+$YBITS-$ZBITS-$K && $y>$YBITS-$y_pp_size+1){
$nhadiag++;
}
}
}
# Check if the constant correction can be done
# --------------------------------------------
$sum_max=$nhadiag;
for($i=0;$i<$nha;$i++){
$sum_max += &pow2($i);
}
$sum_req=$nbitscon;
if($sum_req>$sum_max || ($XBITS+$YBITS==$ZBITS+$K && @carray[$XBITS+$YBITS-$ZBITS-$K]==1)){
$optimize=0;
}
else{
$optimize=1;
}
# Write the header of the verilog file (variables definition)
# -----------------------------------------------------------
if(length($MODULE)==0){
printf("module CCTarray%s_%s_%s_%s (Z2, X, Y);\n", $XBITS, $YBITS, $ZBITS, $K);
}
else{
printf("module $MODULE (Z2, X, Y);\n", $XBITS, $YBITS, $ZBITS, $K);
}
printf("\t\n");
printf("\tinput [%s:0] Y;\n",$YBITS-1);
printf("\tinput [%s:0] X;\n",$XBITS-1);
printf("\toutput [%s:0] Z2;\n",$ZBITS-1);
printf("\n\n");
for($y=0; $y < $YBITS ; $y++) {
printf("\twire [%s:0] P%s;\n", $XBITS-1, $y);
printf("\twire [%s:0] carry%s;\n", $XBITS-1, $y+1);
printf("\twire [%s:0] sum%s;\n", $XBITS-1, $y+1);
}
printf("\twire [%s:0] carry%s;\n",$ZBITS+$K-2,$YBITS+1);
printf("\twire [%s:0] Z;\n",$ZBITS+$K-1);
print "\n\n";
# Generate the partial products
# -----------------------------
print "\t// generate the partial products.\n";
for($y=$YBITS-$y_pp_size; $y < $YBITS ; $y++) {
for($x=$XBITS-1; $x >= $XBITS-$x_pp_size; $x--) {
if($x+$y>=$XBITS+$YBITS-$ZBITS-$K){
if($y>$YBITS-$y_pp_size && $x==$XBITS-1) {
printf ("\tand pp%s(sum%s[%s], X[%s], Y[%s]);\n", $pp_label, $y, $x, $x, $y);
$pp_label++;
}
else {
printf ("\tand pp%s(P%s[%s], X[%s], Y[%s]);\n", $pp_label, $y, $x, $x, $y);
$pp_label++;
}
}
}
}
print "\n";
# $optimize=0;
if($optimize==0 || $XBITS+$YBITS==$ZBITS){
goto NO_OPTIMIZE;
}
# Array Reduction
# ---------------
$nbitsvarused=0;
$nbitsconused=0;
print "\t// Array Reduction\n";
for($y=$YBITS-$y_pp_size; $y < $YBITS ; $y++) {
for($x=$XBITS-2; $x >= $XBITS-$x_pp_size; $x--) {
if($x+$y>=$XBITS+$YBITS-$ZBITS-$K){
if($y==$YBITS-$y_pp_size+1){
if($nbitsconused+&pow2($x-($XBITS+$YBITS-$ZBITS-$K-$y))<=$nbitscon){
if($K>=2 && $x==0){
printf("\tassign carry%s[%s] = P%s[%s] & P%s[%s];\n",$y,$x,$y,$x,$y-1,$x+1);
$nbitsconused++;
}
else{
printf("\tspecialized_half_adder SHA%s(carry%s[%s],sum%s[%s],P%s[%s],P%s[%s]);\n",$sha_label,$y,$x,$y,$x,$y,$x,$y-1,$x+1);
$sha_label++;
$nbitsconused += &pow2($x-($XBITS+$YBITS-$ZBITS-$K-$y));
}
}
else{
if($K>=2 && $x==0){
printf("\tassign carry%s[%s] = P%s[%s] | P%s[%s];\n",$y,$x,$y,$x,$y-1,$x+1);
}
else{
printf("\thalf_adder HA%s(carry%s[%s],sum%s[%s],P%s[%s],P%s[%s]);\n",$ha_label,$y,$x,$y,$x,$y,$x,$y-1,$x+1);
$ha_label++;
}
}
}
if($y>$YBITS-$y_pp_size+1){
if($x+$y==$XBITS+$YBITS-$ZBITS-$K){
if($nbitsconused<$nbitscon){
if($x==0 && $y<$YBITS-$h_pp_size+$K){
printf("\tassign carry%s[%s] = P%s[%s] | sum%s[%s];\n",$y,$x,$y,$x,$y-1,$x+1);
$nbitsconused++;
}
else{
printf("\tspecialized_half_adder SHA%s(carry%s[%s],sum%s[%s],P%s[%s],sum%s[%s]);\n",$sha_label,$y,$x,$y,$x,$y,$x,$y-1,$x+1);
$sha_label++;
$nbitsconused++;
}
}
else{
if($x==0 && $y<$YBITS-$h_pp_size+$K){
printf("\tassign carry%s[%s] = P%s[%s] & sum%s[%s];\n",$y,$x,$y,$x,$y-1,$x+1);
}
else{
printf("\thalf_adder HA%s(carry%s[%s],sum%s[%s],P%s[%s],sum%s[%s]);\n",$ha_label,$y,$x,$y,$x,$y,$x,$y-1,$x+1);
$ha_label++;
}
}
}
else{
if($x==0 && $y<$YBITS-$h_pp_size+$K){
printf("\treduced_full_adder RFA%s(carry%s[%s],P%s[%s],sum%s[%s],carry%s[%s]);\n",$rfa_label,$y,$x,$y,$x,$y-1,$x+1,$y-1,$x);
$rfa_label++;
}
else{
printf("\tfull_adder FA%s(carry%s[%s],sum%s[%s],P%s[%s],sum%s[%s],carry%s[%s]);\n",$fa_label,$y,$x,$y,$x,$y,$x,$y-1,$x+1,$y-1,$x);
$fa_label++;
}
}
}
}
}
}
print "\n";
# Generate lower order product
print "\t// Generate lower product bits YBITS \n";
$Zpin=0;
if($ZBITS>$XBITS){
for($y=$YBITS+$XBITS-$ZBITS; $y < $YBITS ; $y++){
if($y==0){
printf("\tbuf b1(Z2[0], P0[0]);\n");
$Zpin++;
}
else{
printf ("\tassign Z2[%s] = sum%s[0];\n",$Zpin,$y);
$Zpin++;
}
}
}
print "\n";
# Generate higher order product
print "\t// Final Carry Propagate Addition\n";
print "\t// Generate higher product bits\n";
if($ZBITS>$XBITS){
$nhop=$XBITS;
}
else{
$nhop=$ZBITS;
}
if($ZBITS+$K>$XBITS){
$xstart=0;
}
else{
$xstart=$XBITS-$ZBITS-$K;;
}
for($x=$xstart; $x < $XBITS ; $x++) {
if($x==$xstart) {
if($x==$XBITS-$nhop){
if($ZBITS+$K>$XBITS){
printf("\thalf_adder CPA%s(carry%s[%s],Z2[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$YBITS,$x,$Zpin,$YBITS-1,$x,$YBITS-1,$x+1);
$cpa_label++;
}
else{
printf("\tassign carry%s[%s] = 0;\n",$YBITS,$x);
printf("\tassign Z2[%s] = sum%s[%s];\n",$Zpin,$YBITS-1,$x+1);
}
$Zpin++;
}
else{
if($ZBITS+$K>$XBITS){
printf("\tassign carry%s[%s] = carry%s[%s] & sum%s[%s];\n",$YBITS,$x,$YBITS-1,$x,$YBITS-1,$x+1);
}
else{
printf("\tassign carry%s[%s] = 0;\n",$YBITS,$x);
}
}
}
else{
if($x==$XBITS-2) {
printf("\tfull_adder CPA%s(Z2[%s],Z2[%s],carry%s[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$Zpin+1,$Zpin,$YBITS-1,$x,$YBITS,$x-1,$YBITS-1,$x+1);
}
else{
if($x>=$XBITS-$nhop && $x<$XBITS-2) {
printf("\tfull_adder CPA%s(carry%s[%s],Z2[%s],carry%s[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$YBITS,$x,$Zpin,$YBITS-1,$x,$YBITS,$x-1,$YBITS-1,$x+1);
$cpa_label++;
$Zpin++;
}
if($x<$XBITS-$nhop && $x>$xstart && $x<$XBITS-2){
printf("\treduced_full_adder CPA%s(carry%s[%s],carry%s[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$YBITS,$x,$YBITS-1,$x,$YBITS,$x-1,$YBITS-1,$x+1);
$cpa_label++;
}
}
}
}
goto END;
NO_OPTIMIZE: printf("// FAILED TO OPTIMIZE THE CORRECTION!\n");
# Array Reduction
# ---------------
print "\t// Array Reduction\n";
for($y=$YBITS-$y_pp_size; $y < $YBITS ; $y++) {
for($x=$XBITS-2; $x >= $XBITS-$x_pp_size; $x--) {
if($x+$y>=$XBITS+$YBITS-$ZBITS-$K){
if($y==$YBITS-$y_pp_size+1){
printf("\thalf_adder HA%s(carry%s[%s],sum%s[%s],P%s[%s],P%s[%s]);\n",$ha_label,$y,$x,$y,$x,$y,$x,$y-1,$x+1);
$ha_label++;
}
if($y>$YBITS-$y_pp_size+1){
if($x+$y==$XBITS+$YBITS-$ZBITS-$K){
printf("\thalf_adder HA%s(carry%s[%s],sum%s[%s],P%s[%s],sum%s[%s]);\n",$ha_label,$y,$x,$y,$x,$y,$x,$y-1,$x+1);
$ha_label++;
}
else{
printf("\tfull_adder FA%s(carry%s[%s],sum%s[%s],P%s[%s],sum%s[%s],carry%s[%s]);\n",$fa_label,$y,$x,$y,$x,$y,$x,$y-1,$x+1,$y-1,$x);
$fa_label++;
}
}
}
}
}
print "\n";
if($XBITS+$YBITS>$ZBITS){
# Generate lower order product
print "\t// Generate lower product bits YBITS \n";
$Zpin=0;
if($ZBITS+$K>$XBITS){
for($y=$YBITS-$ZBITS-$K+$XBITS; $y < $YBITS ; $y++){
if($y==0){
printf("\tbuf b1(Z[0], P0[0]);\n");
$Zpin++;
}
else{
printf ("\tassign Z[%s] = sum%s[0];\n",$Zpin,$y);
$Zpin++;
}
}
}
print "\n";
# Generate higher order product
print "\t// Final Carry Propagate Addition\n";
print "\t// Generate higher product bits\n";
if($ZBITS+$K>$XBITS){
$nhop=$XBITS;
}
else{
$nhop=$ZBITS+$K;
}
for($x=$XBITS-$nhop; $x < $XBITS ; $x++) {
if($x==$XBITS-$nhop) {
if($ZBITS+$K>$XBITS){
printf("\thalf_adder CPA%s(carry%s[%s],Z[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$YBITS,$x,$Zpin,$YBITS-1,$x,$YBITS-1,$x+1);
}
else{
printf("\tassign carry%s[%s] = 0;\n",$YBITS,$x);
printf("\tassign Z[%s] = sum%s[%s];\n",$Zpin,$YBITS-1,$x+1);
}
$cpa_label++;
$Zpin++;
}
if($x==$XBITS-2) {
printf("\tfull_adder CPA%s(Z[%s],Z[%s],carry%s[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$Zpin+1,$Zpin,$YBITS-1,$x,$YBITS,$x-1,$YBITS-1,$x+1);
$cpa_label++;
$Zpin++;
}
if($x>$XBITS-$nhop && $x<$XBITS-2) {
printf("\tfull_adder CPA%s(carry%s[%s],Z[%s],carry%s[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$YBITS,$x,$Zpin,$YBITS-1,$x,$YBITS,$x-1,$YBITS-1,$x+1);
$cpa_label++;
$Zpin++;
}
}
print "\n";
# Add the constant to the sum previously calculated
print "\t// Add the constant\n";
for($x=0;$x<$ZBITS+$K;$x++){
if($x==0) {
if(@carray[$XBITS+$YBITS-$ZBITS-$K+$x]==0){
if($K==0){
printf("\tassign Z2[%s] = Z[%s];\n",$x,$x);
}
printf("\tassign carry%s[%s] = 0;\n",$YBITS+1,$x);
}
else{
if($K==0){
printf("\tassign Z2[%s] = !Z[%s];\n",$x,$x);
}
printf("\tassign carry%s[%s] = Z[%s];\n",$YBITS+1,$x,$x);
}
}
if($x==$ZBITS+$K-1) {
if(@carray[$XBITS+$YBITS-$ZBITS-$K+$x]==0){
printf("\tassign Z2[%s] = Z[%s] ^ carry%s[%s];\n",$x-$K,$x,$YBITS+1,$x-1);
}
else{
printf("\tassign Z2[%s] = !Z[%s] ^ carry%s[%s];\n",$x-$K,$x,$YBITS+1,$x-1);
}
$cpa_label++;
}
if($x>0 && $x<$ZBITS+$K-1) {
if($x>=$K){
if(@carray[$XBITS+$YBITS-$ZBITS-$K+$x]==0){
printf("\thalf_adder CPA%s(carry%s[%s],Z2[%s],Z[%s],carry%s[%s]);\n",$cpa_label,$YBITS+1,$x,$x-$K,$x,$YBITS+1,$x-1);
}
else{
printf("\tspecialized_half_adder CPA%s(carry%s[%s],Z2[%s],Z[%s],carry%s[%s]);\n",$cpa_label,$YBITS+1,$x,$x-$K,$x,$YBITS+1,$x-1);
}
}
else{
if(@carray[$XBITS+$YBITS-$ZBITS-$K+$x]==0){
printf("\tand CPA%s(carry%s[%s],Z[%s],carry%s[%s]);\n",$cpa_label,$YBITS+1,$x,$x,$YBITS+1,$x-1);
}
else{
printf("\tor CPA%s(carry%s[%s],Z[%s],carry%s[%s]);\n",$cpa_label,$YBITS+1,$x,$x,$YBITS+1,$x-1);
}
}
$cpa_label++;
}
}
}
else{ # if $XBITS+$YBITS=$ZBITS
# Generate lower order product
print "\t// Generate lower product bits YBITS \n";
$Zpin=0;
if($ZBITS>$XBITS){
for($y=$YBITS-$ZBITS+$XBITS; $y < $YBITS ; $y++){
if($y==0){
printf("\tbuf b1(Z2[0], P0[0]);\n");
$Zpin++;
}
else{
printf ("\tassign Z2[%s] = sum%s[0];\n",$Zpin,$y);
$Zpin++;
}
}
}
print "\n";
# Generate higher order product
print "\t// Final Carry Propagate Addition\n";
print "\t// Generate higher product bits\n";
if($ZBITS>$XBITS){
$nhop=$XBITS;
}
else{
$nhop=$ZBITS;
}
if($XBITS-$ZBITS-$K>0){
$xstart=$XBITS-$ZBITS-$K;
}
else{
$xstart=0;
}
for($x=$xstart; $x < $XBITS ; $x++) {
if($x==$xstart) {
if($x==$XBITS-$nhop){
printf("\thalf_adder CPA%s(carry%s[%s],Z2[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$YBITS,$x,$Zpin,$YBITS-1,$x,$YBITS-1,$x+1);
$cpa_label++;
$Zpin++;
}
else{
printf("\tassign carry%s[%s] = carry%s[%s] & sum%s[%s];\n",$YBITS,$x,$YBITS-1,$x,$YBITS-1,$x+1);
}
}
else{
if($x==$XBITS-2) {
printf("\tfull_adder CPA%s(Z2[%s],Z2[%s],carry%s[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$Zpin+1,$Zpin,$YBITS-1,$x,$YBITS,$x-1,$YBITS-1,$x+1);
$cpa_label++;
$Zpin++;
}
else{
if($x>=$XBITS-$nhop && $x<$XBITS-2) {
printf("\tfull_adder CPA%s(carry%s[%s],Z2[%s],carry%s[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$YBITS,$x,$Zpin,$YBITS-1,$x,$YBITS,$x-1,$YBITS-1,$x+1);
$cpa_label++;
$Zpin++;
}
if($x<$XBITS-$nhop && $x>$xstart && $x<$XBITS-2){
printf("\treduced_full_adder CPA%s(carry%s[%s],carry%s[%s],carry%s[%s],sum%s[%s]);\n",$cpa_label,$YBITS,$x,$YBITS-1,$x,$YBITS,$x-1,$YBITS-1,$x+1);
$cpa_label++;
}
}
}
}
}
END: print "endmodule";
sub pow2 {
($p) = @_;
$res = 1;
for($i=1;$i<=$p;$i++){
$res = $res * 2;
}
return($res);
}
sub round_near {
($num) = @_;
$rnd = 0;
while($num>$rnd+0.5){
$rnd = $rnd + 1;
}
return($rnd);
}