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- Bug 6919.  For multi-part problems containing perl script blocks inside
  part(s), if question type = randomizetry, the first call to &random()
  for each part needs to set the new seed.

# The LearningOnline Network with CAPA 
# used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
#
# $Id: default_homework.lcpm,v 1.177 2019/11/06 16:20:06 raeburn Exp $
#
# Copyright Michigan State University Board of Trustees
#
# This file is part of the LearningOnline Network with CAPA (LON-CAPA).
#
# LON-CAPA is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# LON-CAPA is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with LON-CAPA; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#
# /home/httpd/html/adm/gpl.txt
#
# http://www.lon-capa.org/
#
#

#init some globals
$hidden::RANDOMINIT=0;
$hidden::RANDOMINITTRYPART='';
$pi=atan2(1,1)*4;
$rad2deg=180.0/$pi;
$deg2rad=$pi/180.0;
$"=' ';
use strict;
{
    my $n = 0;
    my $total = 0;
    my $num_left = 0;
    my @order;
    my $type;

    sub init_permutation {
	my ($size,$requested_type) = @_;
	@order = (0..$size-1);
	$n = $size;
	$type = $requested_type;
	if ($type eq 'ordered') {
	    $total = $num_left = 1;
	} elsif ($type eq 'unordered') {
	    $total = $num_left = &factorial($size);
	} else {
	    die("Unkown type: $type");
	}
    }

    sub get_next_permutation {
	if ($num_left == $total) {
	    $num_left--;
	    return \@order;
	}

	# Find largest index j with a[j] < a[j+1]

	my $j = scalar(@order) - 2;
	while ($order[$j] > $order[$j+1]) {
	    $j--;
	}

	# Find index k such that a[k] is smallest integer
	# greater than a[j] to the right of a[j]

	my $k = scalar(@order) - 1;
	while ($order[$j] > $order[$k]) {
	    $k--;
	}

	# Interchange a[j] and a[k]

	@order[($k,$j)] = @order[($j,$k)];

	# Put tail end of permutation after jth position in increasing order

	my $r = scalar(@order) - 1;
	my $s = $j + 1;

	while ($r > $s) {
	    @order[($s,$r)]=@order[($r,$s)];
	    $r--;
	    $s++;
	}

	$num_left--;
	return(\@order);
    }
    
    sub get_permutations_left {
	return $num_left;
    }
}

sub check_commas {
    my ($response)=@_;
    #print("$response ");
    my @numbers=split(',',$response);
    #print(" numbers ".join('-',@numbers)." ");
    if (scalar(@numbers) > 1) {
        #print(" numbers[0] ".$numbers[0]." "); 
	if (length($numbers[0]) > 3 || length($numbers[0]) == 0) { return -1; }
	shift(@numbers);
	#print(" numbers ".scalar(@numbers)." ");
	while (scalar(@numbers) > 1) {
	    #print(" numbers ".join('-',@numbers)." ");
	    if (length($numbers[0]) != 3) { return -2; }
	    shift(@numbers);
	}
	my ($number)=split('\.',$numbers[0]);
	#print(" number ".$number." ");
	#print(" numbers[0] ".$numbers[0]." ");
	if (length($number) != 3) { return -3; }
    } else {
	my ($number)=split('\.',$numbers[0]);
	if (length($number) > 3) { return -4; }
    }
    return 1;
}


sub caparesponse_check {
    my ($answer,$response)=@_;
    #not properly used yet: calc
    #not to be used: $ans_fmt
    my $type=$LONCAPA::CAPAresponse_args{'type'};
    my $tol=$LONCAPA::CAPAresponse_args{'tol'};
    my $sig=$LONCAPA::CAPAresponse_args{'sig'};
    my $ans_fmt=$LONCAPA::CAPAresponse_args{'format'};
    my $unit=$LONCAPA::CAPAresponse_args{'unit'};
    my $calc=$LONCAPA::CAPAresponse_args{'calc'};
    my $samples=$LONCAPA::CAPAresponse_args{'samples'};
    
    my $tol_type=''; # gets it's value from whether tol has a % or not done
    my $sig_lbound=''; #done
    my $sig_ubound=''; #done

    #type's definitons come from capaParser.h

    #remove leading and trailing whitespace
    if (!defined($response)) {
	$response='';
    }
    if ($response=~ /^\s|\s$/) {
	$response=~ s:^\s+|\s+$::g;
    }

    if ($type eq 'cs' || $type eq 'ci') {
	#for string answers make sure all places spaces occur, there is 
        #really only 1 space, in both the answer and the response
	$answer=~s/ +/ /g;
	$response=~s/ +/ /g;
    } elsif ($type eq 'mc') {
	$answer=~s/[\s,]//g;
	$response=~s/[\s,]//g;
    }
    if ($type eq 'float' && $unit=~/\$/) {
	if ($response!~/^\$|\$$/)  { return ('NO_UNIT', undef); }
	$response=~s/\$//g;
    }
    if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) {
	return "COMMA_FAIL:";
    }
    $ans_fmt=~s/\W//g;
    $unit=~s/[\$,]//g;
    if ($type eq 'float') { $response=~s/,//g; }

    if (length($response) > 500) { return ('TOO_LONG',undef); }

    if ($type eq '' ) {
	if ( $answer eq ($answer *1.0)) { $type = 2;
				      } else { $type = 3; }
    } else {
	if    ($type eq 'cs')    { $type = 4; }
	elsif ($type eq 'ci')    { $type = 3 }
	elsif ($type eq 'mc')    { $type = 5; }
	elsif ($type eq 'fml')   { $type = 8; }
        elsif ($type eq 'math')  { $type = 9; }
	elsif ($type eq 'subj')  { $type = 7; }
	elsif ($type eq 'float') { $type = 2; }
	elsif ($type eq 'int')   { $type = 1; }
	else { return ('ERROR', "Unknown type of answer: $type") }
    }

    my $points;
    my $id_list;
    #formula type setup the sample points
    if ($type eq '8') {
	($id_list,$points)=split(/@/,$samples);
    }
    if ($tol eq '') {
	$tol=0.0;
	$tol_type=1; #TOL_ABSOLUTE
    } else {
	if ($tol =~ /%$/) {
	    chop $tol;
	    $tol_type=2; #TOL_PERCENTAGE
	} else {
	    $tol_type=1; #TOL_ABSOLUTE
	}
    }

    ($sig_ubound,$sig_lbound)=&LONCAPA_INTERNAL_get_sigrange($sig);

    my $reterror="";
    my $result;
    if (($type eq '9') || ($type eq '8')) {
        if ($response=~/\=/) {
            return ('BAD_FORMULA','Please submit just an expression, not an equation.');
        } elsif ($response =~ /\,/ and $response !~ /^\s*\{.*\}\s*$/) {
            return ('BAD_FORMULA');
        }
    }
    if ($type eq '9') {
      $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror);
    } else {
	if ($type eq '8') { # fml type
	    $response = &capa_formula_fix($response);
	    $answer   = &capa_formula_fix($answer);
	}
       $result = &caparesponse_capa_check_answer($response,$answer,$type,
						 $tol_type,$tol,
						 $sig_lbound,$sig_ubound,
						 $ans_fmt,$unit,$calc,$id_list,
						 $points,$external::randomseed,
						 \$reterror);
    }
    if    ($result == '1') { $result='EXACT_ANS'; } 
    elsif ($result == '2') { $result='APPROX_ANS'; }
    elsif ($result == '3') { $result='SIG_FAIL'; }
    elsif ($result == '4') { $result='UNIT_FAIL'; }
    elsif ($result == '5') { $result='NO_UNIT'; }
    elsif ($result == '6') { $result='UNIT_OK'; }
    elsif ($result == '7') { $result='INCORRECT'; }
    elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
    elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
    elsif ($result =='10') { $result='SUB_RECORDED'; }
    elsif ($result =='11') { $result='BAD_FORMULA'; }
    elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; }
    elsif ($result =='12') { $result='WANTED_NUMERIC'; }
    elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; }
    elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; }
    elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; }
    elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
    elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
    else  {$result = "ERROR: Unknown Result:$result:$@:";}

    return ($result,$reterror);
}


sub caparesponse_check_list {
    my $responses=$LONCAPA::CAPAresponse_args{'response'};
    &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
    my $type = $LONCAPA::CAPAresponse_args{'type'};
    my $answerunit=$LONCAPA::CAPAresponse_args{'unit'};
    &LONCAPA_INTERNAL_DEBUG("Got type :$type: answer unit :$answerunit:\n");
   
    my $preprocess=$LONCAPA::CAPAresponse_args{'preprocess'};
    $preprocess=~s/^\&//;

    my $num_input_lines =
	scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
    
    if ($type ne '' ) {
	if (scalar(@$responses) < $num_input_lines) {
	    return 'MISSING_ANSWER';
	}
	if (scalar(@$responses) > $num_input_lines) {
	    return 'EXTRA_ANSWER';
	}

    }

    foreach my $which (0..($num_input_lines-1)) {
	my $answer_size = 
	    scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
	if ($type ne '' 
	    && $answer_size > 1) {
	    $responses->[$which]=[split(/,/,$responses->[$which])];
	} else {
	    $responses->[$which]=[$responses->[$which]];
	}
    }
    foreach my $which (0..($num_input_lines-1)) {
	my $answer_size = 
	    scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
	my $response_size = 
	    scalar(@{$responses->[$which]});
	if ($answer_size > $response_size) {
	    return 'MISSING_ANSWER';
	}
	if ($answer_size < $response_size) {
	    return 'EXTRA_ANSWER';
	}
    }

    my $unit;
    my ($allowalgebra)=($LONCAPA::CAPAresponse_args{'allowalgebra'}=~/^(yes|1|on)$/i);
    if ($type eq 'float' || $type eq '') {
	#for numerical problems split off the unit
        my $part1;
        my $part2;
        my $match_algebra = qr{^(.*[^\s])\s+([^\s]+)$};
        # FIXME: with the above regexp, algebra with spaces will not be evaluated correctly
        my $match_numerical_units = qr{^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d+)([\$\s\w\^\*\/\(\)\+\-]*[^\d\.\s\,][\$\s\w\^\*\/\(\)\+\-]*)$};
        if ($allowalgebra) {
           ($part1,$part2) = ($responses->[0][-1] =~ /$match_algebra/); 
        } else {
           ($part1,$part2) = ($responses->[0][-1] =~ /$match_numerical_units/);
        }
        if (defined($part1) && defined($part2)) {
	    $responses->[0][-1]=$part1;
	    $unit=&capa_formula_fix($part2);
            my $customunits=$LONCAPA::CAPAresponse_args{'customunits'};
            if ($customunits =~ /\S/) {
                foreach my $replacement (split(/\s*\,\s*/,$customunits)) {
                    my ($which,$what)=split(/\s*\=\s*/,$replacement);
                    if ((defined($which)) && (defined($what))) {
                        $what=&capa_formula_fix($what);
                        $unit=~s/$which/\($what\)/g;
                    }
                }
            }
            if (scalar(@$responses) > 0 && defined $answerunit) {
                # there are several response values, units should be the same for all
                $part2 =~ s/^\s+|\s+$//g;
                for (my $i=1; $i<scalar(@$responses); $i++) {
                    my $element = $responses->[$i][-1];
                    my ($part1i, $part2i);
                    if ($allowalgebra) {
                        ($part1i, $part2i) = ($element =~ /$match_algebra/); 
                    } else {
                        ($part1i, $part2i) = ($element =~ /$match_numerical_units/);
                    }
                    $part2i =~ s/^\s+|\s+$//g;
                    if (!defined $part2i) {
                        return 'NO_UNIT';
                    } elsif ($part2i ne $part2) {
                        return ('UNIT_FAIL', "$part2 $part2i");
                    } else {
                        $responses->[$i][-1] = $part1i;
                    }
                }
            }
	}
    }
    $unit=~s/\s//;
    my $error;
    foreach my $response (@$responses) {
       foreach my $element (@$response) {
          # See if we have preprocessor
          if ($preprocess=~/\S/) {
             if (defined(&$preprocess)) {
                no strict 'refs';
                $element=&$preprocess($element,$unit);
                use strict 'refs';
             }
          }
          if (($type eq 'float') || (($type eq '') && ($unit ne ''))) {
              $element =~ s/\s//g;
          }
          my $appendunit=$unit;
# Deal with percentages
# unit is unit entered by student, answerunit is unit by author
# Deprecated: divide answer by 100 if student entered percent,
# but author did not. Too much confusion
#          if (($unit=~/\%/) && ($answerunit ne '%'))  {
#             $element=$element/100;
#             $appendunit=~s/\%//;
#          }    
# Author entered percent, student did not
          if (($unit!~/\%/) && ($answerunit=~/\%/)) {
             $element=$element*100;
             $appendunit='%'.$appendunit;
          }
# Zero does not need a dimension
          if (($element =~ /^[0\.]+$/) && ($unit!~/\w/) && ($answerunit=~/\w/)) {
             $appendunit=$answerunit;
          }
# Do the math for the student if allowed
          if ($allowalgebra) {
             $element=&cas('maxima',$element);
          }
          if ($appendunit ne '') {
              $element .= " $appendunit";
          }  
          &LONCAPA_INTERNAL_DEBUG("Made response element :$element:");
       }
    }
    
    foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
	if (!defined($thisanswer)) {
	    return ('ERROR','answer was undefined');
	}
    }

    my $allow_control_char = 0;
    my $control_chars_removed = 0;
    my $ansstring;
    if ($type eq 'cs' || $type eq 'ci') {
        if (ref($LONCAPA::CAPAresponse_answer->{'answers'}) eq 'ARRAY') {
            foreach my $strans (@{$LONCAPA::CAPAresponse_answer->{'answers'}}) {
                if (ref($strans) eq 'ARRAY') {
                    $ansstring = join("\0",@{$strans});
                    foreach my $item (@{$strans}) {  
                        if ($item =~ /[\000-\037]/) {
                            $allow_control_char = 1;
                        }
                    }
                }
            }
        }
    }

#    &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
    my %memoized;
    if ($LONCAPA::CAPAresponse_answer->{'type'}  eq 'ordered') {
	for (my $i=0; $i<scalar(@$responses);$i++) {
	    my $answer   = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
	    my $response = $responses->[$i];
	    my $key = "$answer\0$response";
	    my (@awards,@msgs);
	    for (my $j=0; $j<scalar(@$response); $j++) {
                if ($type eq 'cs' || $type eq 'ci') {
                    unless ($allow_control_char) {
                        if ($response->[$j] =~ /[\000-\037]/) { 
                            $response->[$j] =~ s/[\000-\037]//g;
                            $control_chars_removed = 1;
                        }  
                    }
                }
                # See if we have preprocessor for string responses
                if (($preprocess=~/\S/) && ($type eq 'cs' || $type eq 'ci'))  {
                    if (defined(&$preprocess)) {
                        no strict 'refs';
                        $response->[$j]=&$preprocess($response->[$j]);
                        use strict 'refs';
                    }
                }

		my ($award,$msg) = &caparesponse_check($answer->[$j],
						       $response->[$j]);
                if ($type eq 'cs' || $type eq 'ci') {
                    $error = &verify_stringresponse($type,$award,$response->[$j],
                                                    $answer->[$j]);
                }
		push(@awards,$award);
		push(@msgs,  $msg);
	    }
	    my ($award,$msg) = 
		&LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
	    $memoized{$key} = [$award,$msg];
	}
    } else {
	#FIXME broken with unorder responses where one is a <value>
        #      and the other is a <vector> (need to delay parse til
        #      inside the loop?)
	foreach my $response (@$responses) {
	    my $response_size = scalar(@{$response});
	    foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
		my $key = "$answer\0$response";
		my $answer_size =  scalar(@{$answer});
		my ($award,$msg);
		if ($answer_size > $response_size) {
		    $award = 'MISSING_ANSWER';
		} elsif ($answer_size < $response_size) {
		    $award = 'EXTRA_ANSWER';
		} else {
		    my (@awards,@msgs);
		    for (my $j=0; $j<scalar(@$response); $j++) {
                        if ($type eq 'cs' || $type eq 'ci') {
                            unless ($allow_control_char) {
                                if ($response->[$j] =~ /[\000-\037]/) {
                                    $response->[$j] =~ s/[\000-\037]//g;
                                    $control_chars_removed = 1;
                                }
                            }
                        }
                        # See if we have preprocessor
                        if (($preprocess=~/\S/) && ($type eq 'cs' || $type eq 'ci')) {
                            if (defined(&$preprocess)) {
                                no strict 'refs';
                                $response->[$j]=&$preprocess($response->[$j]);
                                use strict 'refs';
                            }
                        }

			my ($award,$msg) = &caparesponse_check($answer->[$j],
							       $response->[$j]);
                        if ($type eq 'cs' || $type eq 'ci') {
                            $error = &verify_stringresponse($type,$award,$response->[$j],
                                                            $answer->[$j]);
                        }
			push(@awards,$award);
			push(@msgs,  $msg);
		    }
		    ($award,$msg) = 
			&LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
		}
		$memoized{$key} = [$award,$msg];
	    }
	}
    }

    my ($final_award,$final_msg);
    &init_permutation(scalar(@$responses),
		      $LONCAPA::CAPAresponse_answer->{'type'});

    # possible FIXMEs
    # - significant time is spent calling non-safe space routine
    #   from safe space
    # - early outs could be possible with classifying awards is to stratas
    #   and stopping as so as hitting the top strata 
    # - some early outs also might be possible with check ing the 
    #   memoized hash of results (is correct even possible? etc.)

    my (@final_awards,@final_msg);
    while( &get_permutations_left() ) {
	my $order = &get_next_permutation();
	my (@awards, @msgs, $i);
	foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
	    my $key = "$thisanswer\0".$responses->[$order->[$i]];
	    push(@awards,$memoized{$key}[0]);
	    push(@msgs,$memoized{$key}[1]);
	    $i++;

	}
	&LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));

	my ($possible_award,$possible_msg) = 
	    &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
	&LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
	push(@final_awards,$possible_award);
	push(@final_msg,$possible_msg);
    }

    &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
    my ($final_award,$final_msg) = 
	&LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
    return ($final_award,$final_msg,$error,$control_chars_removed,$ansstring);
}

sub verify_stringresponse {
    my ($type,$award,$resp,$ans) = @_;
    return if ($award eq 'EXACT_ANS');
    my $error;
    if ($resp =~ /^\s|\s$/) {
        $resp =~ s{^\s+|\s+$}{}g;
    }
    if ($ans =~ /^\s|\s$/) {
        $ans =~ s{^\s+|\s+$}{}g;
    }
    if ($type eq 'ci') {
        $resp = lc($resp);
        $ans = lc($ans);
    }
    if ($resp eq $ans) {
        if ($award eq 'INCORRECT') {
            $error = 'MISGRADED';
        }
    }
    return $error;
}

sub cas {
    my ($system,$input,$library)=@_;
    my $output;
    my $dump;
    if ($system eq 'maxima') {
       $output=&maxima_eval($input,$library);
    } elsif ($system eq 'R') {
       ($output,$dump)=&r_eval($input,$library,0);
    } else {
       $output='Error: unrecognized CAS';
    }
    return $output;
}

sub cas_hashref {
    my ($system,$input,$library)=@_;
    if ($system eq 'maxima') {
       return 'Error: unsupported CAS';
    } elsif ($system eq 'R') {
       return &r_eval($input,$library,1);
    } else {
       return 'Error: unrecognized CAS';
    }
}

#
# cas_hashref_entry takes a list of indices and gets the entry in a hash generated by Rreturn.
# Call: cas_hashref_entry(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn.
# Rentry will return the first scalar value it encounters (ignoring excess indices).
# If an invalid key is given, it returns undef.
#
sub cas_hashref_entry {
    return &Rentry(@_);
}

#
# cas_hashref_array takes a list of indices and gets a column array from a hash generated by Rreturn.
# Call: cas_hashref_array(Rvalue, index1, index2, ...) where Rvalue is a hash returned by Rreturn.
# If an invalid key is given, it returns undef.
#
sub cas_hashref_array {
    return &Rarray(@_);
}

sub tex {
    if ( $external::target eq "tex" ) {
	return $_[0];
    } else {
	return $_[1];
    }
}

sub var_in_tex {
    if ( $external::target eq "tex" ) {
	return $_[0];
    } else {
	return "";
    }
}

sub web {
    if ( $external::target eq "tex" ) {
	return $_[1];
    } else {
	if ( $external::target eq "web" || $external::target eq "answer") {
	    return $_[2];
	} else {
	    return $_[0];
	}
    }
}

sub html {
    if ( $external::target eq "web" ) {
	return shift;
    }
}

sub hinton {
    return 0;
}

sub random {
    my ($start,$end,$step)=@_;
    if (( ! $hidden::RANDOMINIT ) ||
        (($external::randomizetrypart ne '') &&
         ($hidden::RANDOMINITTRYPART ne $external::randomizetrypart))) {
        if ($external::randomseed == 0) { $external::randomseed=1; }
        if ($external::randomseed =~/,/) {
            my ($num1,$num2) = map { abs($_); } split(/,/,$external::randomseed);
            if ((!$num1) || ($num1 > 2147483398)) {
                &random_set_seed_from_phrase($external::randomseed);
            } else {
                &random_set_seed(1,$num1);
            }
        } elsif ($external::randomseed =~/:/) {
            my ($num1,$num2) = map { abs($_); } split(/:/,$external::randomseed);
            if ((!$num1) || (!$num2) || ($num1 > 2147483562) || ($num2 > 2147483398)) {
                &random_set_seed_from_phrase($external::randomseed);
            } else {
                &random_set_seed($num1,$num2);
            }
        } else {
            my $num1 = int(abs($external::randomseed));
            if ((!$num1) || ($num1 > 2147483398)) {
                &random_set_seed_from_phrase($external::randomseed);
            } else {
                &random_set_seed(1,$num1);
            }
        }
	&math_random_uniform();
	$hidden::RANDOMINIT=1;
        $hidden::RANDOMINITTRYPART=$external::randomizetrypart;
    }
    if (!defined($step)) { $step=1; }
    my $num=1+int(($end-$start)/$step);
    my $result=$start + int(&math_random_uniform() * $num)*$step;
    return $result;
}

sub random_normal {
    my ($item_cnt,$seed,$av,$std_dev) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_normal($item_cnt,$av,$std_dev);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_beta {
    my ($item_cnt,$seed,$aa,$bb) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_beta($item_cnt,$aa,$bb);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_gamma {
    my ($item_cnt,$seed,$a,$r) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_gamma($item_cnt,$a,$r);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_exponential {
    my ($item_cnt,$seed,$av) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_exponential($item_cnt,$av);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_poisson {
    my ($item_cnt,$seed,$mu) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_poisson($item_cnt,$mu);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_chi {
    my ($item_cnt,$seed,$df) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_chi_square($item_cnt,$df);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_noncentral_chi {
    my ($item_cnt,$seed,$df,$nonc) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_f {
    my ($item_cnt,$seed,$dfn,$dfd) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_f($item_cnt,$dfn,$dfd);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_noncentral_f {
    my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_multivariate_normal {
    my ($item_cnt,$seed,$mean,$covar) = @_;
    my @oldseed=&random_get_seed();
    &random_set_seed_from_phrase($seed);
    my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_multinomial {
    my ($item_cnt,$seed,@p) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    my @retArray=&math_random_multinomial($item_cnt,@p);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_permutation {
    my ($seed,@inArray) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_permutation(@inArray);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_uniform {
    my ($item_cnt,$seed,$low,$high) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_uniform($item_cnt,$low,$high);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_uniform_integer {
    my ($item_cnt,$seed,$low,$high) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_binomial {
    my ($item_cnt,$seed,$nt,$p) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_binomial($item_cnt,$nt,$p);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub random_negative_binomial {
    my ($item_cnt,$seed,$ne,$p) = @_;
    my @oldseed=&random_get_seed();
    my @retArray;
    &random_set_seed_from_phrase($seed);
    @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
    &random_set_seed(@oldseed);
    return @retArray;
}

sub abs { CORE::abs(shift) }
sub sin { CORE::sin(shift) }
sub cos { CORE::cos(shift) }
sub exp { CORE::exp(shift) }
sub int { CORE::int(shift) }
sub log { CORE::log(shift) }
sub ln { CORE::log(shift) }
sub atan2 { CORE::atan2($_[0],$_[1]) }
sub sqrt { CORE::sqrt(shift) }

sub tan  { CORE::sin($_[0]) / CORE::cos($_[0]) }
#sub atan { atan2($_[0], 1); }
#sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
#sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) );  }

sub log10 { CORE::log($_[0])/CORE::log(10); }

sub factorial {
    my $input = CORE::int(shift);
    return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
    return "Error - factorial result is greater than system limit ($input)" if $input > 170;
    return 1 if $input == 0;
    my $result = 1; 
    for (my $i=2; $i<=$input; $i++) { $result *= $i }
    return $result;
}

sub sgn {
    return -1 if $_[0] < 0;
    return 0 if $_[0] == 0;
    return 1 if $_[0] > 0;
}

sub min {
    my @sorted = sort { $a <=> $b || $a cmp $b } @_;
    return shift @sorted;
}

sub max {
    my @sorted = sort { $a <=> $b || $a cmp $b } @_;
    return pop @sorted;
}

sub roundto {
    my ($input,$n) = @_;
    return sprintf('%.'.$n.'f',$input);
}

sub to_string {
    my ($input,$n) = @_;
    return sprintf($input) if $n eq "";
    $n = '.'.$n if $n !~ /^\./;
    return sprintf('%'.$n,$input) if $n ne "";
}

sub sub_string {
    my ($str,$start,$len) = @_;
    return substr($str,$start-1,$len);
}

sub pow   {return $_[0] ** $_[1]; }
sub ceil  {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
sub floor  {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
#sub floor {return int($_[0]); }

sub format {
    my ($value,$fmt)=@_;
    my ($dollarmode,$commamode,$alwaysperiod,$options);
    if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 
    #if ($options =~ /\$/) { $dollamode=1; }
    #if ($options =~ /,/)  { $commamode=1; }
    if ($options =~ /\./) { $alwaysperiod=1; }
    my $result;
    if ($fmt=~/s$/i) {
	$result=&format_significant_figures($value,$fmt);
    } else {
	$fmt=~s/e/E/g;
	$result=sprintf('%.'.$fmt,$value);
	if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
	$result=~s/(E[+-]*)0/$1/;
    }
    #if ($dollarmode) {$result=&dollarformat($result);}
    #if ($commamode) {$result=&commaformat($result);}
    return $result;
}

sub chemparse {
    my ($reaction) = @_;
    my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
    my $formula = '';
    foreach my $token (@tokens) {
	if ($token eq '->' ) {
            if ($external::target eq 'web') {
                $formula .= '&rarr; ';
            } else {
                $formula .= '<m>\ensuremath{\rightarrow}</m> ';
	    }
	    next;
	}
	if ($token eq '<-' ) {
            if ($external::target eq 'web') {
                $formula .= '&larr; ';
            } else {
                $formula .= '<m>\ensuremath{\leftarrow}</m> ';
	    }
	    next;
	}  
	if ($token eq '<=>') {
	    if ($external::target eq 'web' &&
		&EXT('request.browser.unicode')) {
		$formula .= '&#8652; ';
	    } else {
		$formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
				 '&lt;=&gt; ');
	    }
	    next;
	}
	if ($token eq '.') {
	  $formula =~ s/(\&nbsp\;| )$//;
	  $formula .= '&middot;';
	  next;
	}
	$token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
        $formula .= $1 if ($1 ne '1');  # stoichiometric coefficient
	
	my $molecule = $2;
	# subscripts
	$molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
	# superscripts
	$molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
	# strip whitespace
	$molecule =~ s/\s*//g;
	# forced space
	$molecule =~ s/_/ /g;
	$molecule =~ s/-/&minus;/g;
	$formula .= $molecule.'&nbsp;';
    }
    # get rid of trailing space
    $formula =~ s/(\&nbsp\;| )$//;
    return &xmlparse($formula);
}

sub conv_eng_format {
    my ($ans,$baseunit)=@_;
    my ($value,$answer,$unit);
    $baseunit =~ s{[^\w/\-\.]}{}g; 
    eval {
           $value = &number_format_pref($ans);
    };
    my ($answer,$prefix) = ($value=~ /^(.+)(\w)$/);
    my $unit = $prefix.$baseunit;
    return($answer,$unit);
} 

sub prettyprint {
    my ($value,$fmt,$target)=@_;
    my $result;
    if (!$target) { $target = $external::target; }
    if ($fmt =~ /chem/i) { return(&chemparse($value)); }
    my ($dollarmode,$commamode,$alwaysperiod,$options);
    if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 
    if ($options =~ /\$/) { $dollarmode=1; }
    if ($options =~ /,/)  { $commamode=1; }
    if ($options =~ /\./) { $alwaysperiod=1; }
    if ($fmt=~/s$/i) {
	$value=&format_significant_figures($value,$fmt);
    } elsif ($fmt) {
	$value=sprintf('%.'.$fmt,$value);
    }
    if ($alwaysperiod && $fmt eq '0f') {
	if ($target eq 'tex') {
	    $value .='\\ensuremath{.}';
	} else {
	    $value .='.';
	}
    }
    if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
	my $frac=$1;
	if ($dollarmode) { $frac=&dollarformat($frac); }
	if ($commamode) { $frac=&commaformat($frac); }
	my $exponent=$2;
	$exponent=~s/^\+0*//;
	$exponent=~s/^-0*/-/;
	$exponent=~s/^-0*/-/;
	if ($exponent eq '-') { undef($exponent); }
	if ($exponent) {
	    if ($target eq 'web') {
		$result=$frac.'&#215;10<sup>'.$exponent.'</sup>';
	    } elsif ($target eq 'tex') {
		$result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
	    } else {
		$result=$value;
	    }
	} else {
	    $result=$frac;
	}
    } else {
	$result=$value;
	if    ($dollarmode) { $result=&dollarformat($result,$target); }
	elsif ($commamode)  { $result=&commaformat($result,$target); }
    }
    return $result;
}

sub commaformat {
    my ($number,$target) = @_;
    if ($number =~ /\./) {
	while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
	    $number = $1.$2.','.$3.$4;
	}
    } else {
	while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
	    $number = $1.$2.','.$3.$4;
	}
    }
    return $number;
}

sub dollarformat {
    my ($number,$target) = @_;
    if (!$target) { $target = $external::target; }
    $number=&commaformat($number,$target);
    if ($target eq 'tex') {
	$number='\$'.$number; #' stupid emacs
    } else {
	$number='$'.$number; #' stupid emacs
    }
    return $number; 
}

# format of form ns or nS where n is an integer
sub format_significant_figures {
    my ($number,$format) = @_; 
    return '0' if ($number == 0);
    # extract number of significant figures needed
    my ($sig) = ($format =~ /(\d+)s/i);
    # arbitrary choice - suggestions ?? or throw error message?
    $sig = 3 if ($sig eq '');
    # save the minus sign
    my $sign = ($number < 0) ? '-' : '';
    $number = abs($number);
    # needed to correct for a number greater than 1 (or
    my $power = ($number < 1) ? 0 : 1;
    # could round up. Take the integer part of log10.
    my $x10 = int(log($number)/log(10));
    # find number with values left of decimal pt = # of sign figs.
    my $xsig = $number*10**($sig-$x10-$power);
    # get just digits left of decimal pt - also rounds off correctly
    my $xint  = sprintf('%.0f',$xsig);
    # save any trailing zero's
    my ($zeros) = ($xint =~ /(0+)$/);
    # return number to original magnitude
    my $numSig = $xint*10**($x10-$sig+$power);
    if ($numSig =~ /^(\d+)\.(\d+)/) {
        # insert trailing zero's if have decimal point
        my @digarray = split('',$1.$2);
        my $sigcount;
        while (@digarray > 0) {
            my $item = shift(@digarray);
            if ($item) {
                $sigcount = 1 + @digarray;
                last;
            }
        }
        if (($sigcount) && ($sig >= $sigcount)) {
            $zeros = substr($zeros,0,($sig - $sigcount));
        }
        $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
    } else {
        if ($numSig =~ /^(\d+)e([\+\-]\d+)$/i) {
            my $pre_exp = $1;
            my $exponent = $2;
            $numSig = $pre_exp.'.'.$zeros.'E'.$exponent;
        } elsif ($numSig =~ /0$/) {
            # add decimal pt for number ending with 0 and length == # of sig figs
            if (length($numSig) == $sig) {
                $numSig.='.';
            } elsif (length($numSig) > $sig) {
                # exponential form for number ending with 0 and length > # of sig figs
                my $fmtsig = $sig-1;
                if ($fmtsig) {
                    $numSig = sprintf('%.'.$fmtsig.'E',$numSig);
                }
            } elsif (length($numSig) < $sig) {
                $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
            }
        } else {
            if (length($numSig) < $sig) {
                $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
            }
        }
    }
    # return number with sign
    return $sign.$numSig;
}

sub map {
    my ($phrase,$dest,$source)=@_;
    my @oldseed=&random_get_seed();
    my @seed = &random_seed_from_phrase($phrase);
    &random_set_seed(@seed);
    my $destct = scalar(@$dest);
    if (!$source) {
	my @output;
	my @idx = &math_random_permuted_index($destct);
	my $ctr = 0;
	while ($ctr < $destct) {
	    $output[$ctr] = $$dest[$idx[$ctr]];
	    $ctr++;
	}
        &random_set_seed(@oldseed);
	return @output;
    } else {
	my $num = scalar(@$source);
	my @idx = &math_random_permuted_index($num);
	my $ctr = 0;
	my $tot = $num;
	$tot = $destct if $destct < $num;
	if (ref($$dest[0])) {
	    while ($ctr < $tot) {
		${$$dest[$ctr]} = $$source[$idx[$ctr]];
	        $ctr++;
            }
        } else {
	    while ($ctr < $tot) {
		$$dest[$ctr] = $$source[$idx[$ctr]];
		$ctr++;
	    }
	}
    }
    &random_set_seed(@oldseed);
    return '';
}

sub rmap {
    my ($phrase,$dest,$source)=@_;
    my @oldseed=&random_get_seed();
    my @seed = &random_seed_from_phrase($phrase);
    &random_set_seed(@seed);
    my $destct = scalar(@$dest);
    if (!$source) {
	my @idx = &math_random_permuted_index($destct);
	my $ctr = 0;
	my @r_idx;
	while ($ctr < $destct) {
	    $r_idx[$idx[$ctr]] = $ctr;
	    $ctr++;
	}
	my @output;
	$ctr = 0;
	while ($ctr < $destct) {
	    $output[$ctr] = $$dest[$r_idx[$ctr]];
	    $ctr++;
	}
        &random_set_seed(@oldseed);
	return @output;
    } else {
	my $num = scalar(@$source);
	my @idx = &math_random_permuted_index($num);
	my $ctr = 0;
	my $tot = $num;
	$tot = $destct if $destct < $num;
	my @r_idx;
	while ($ctr < $tot) {
	    $r_idx[$idx[$ctr]] = $ctr;
	    $ctr++;
	}
	$ctr = 0;
	if (ref($$dest[0])) {
	    while ($ctr < $tot) {
		${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
	        $ctr++;
            }
        } else {
	    while ($ctr < $tot) {
		$$dest[$ctr] = $$source[$r_idx[$ctr]];
		$ctr++;
	    }
	}
    }
    &random_set_seed(@oldseed);
    return '';
}

sub capa_id { return }

sub problem { return }

sub name{
    my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
    $fullname = "" if $fullname eq ",  ";
    $fullname =~ s/\%2d/-/g;
    return $fullname;
}

sub student_number { 
    my $id = &EXT('environment.id');
    $id = '' if $id eq "";
    return $id;
}

sub class {
    my $course = &EXT('course.description');
    $course = '' if $course eq "";
    return $course;
}

sub classid {
    my $courseid = &EXT('request.course.id');
    $courseid = '' if $courseid eq "";
    return $courseid;
}

sub firstname {
    my $firstname = &EXT('environment.firstname');
    $firstname = '' if $firstname eq "";
    return $firstname;
}

sub middlename {
    my $middlename = &EXT('environment.middlename');
    $middlename = '' if $middlename eq "";
    return $middlename;
}

sub lastname {
    my $lastname = &EXT('environment.lastname');
    $lastname = '' if $lastname eq "";
    return $lastname;
}

sub sec { 
    my $sec = &EXT('request.course.sec');
    $sec = '' if $sec eq "";
    return $sec;
}

sub submission {
   my ($partid,$responseid,$subnumber,$encode,$cleanupnum,$mapalias)=@_;
   my $sub='';
   if ($subnumber) { $sub=$subnumber.':'; }
   my $output =
       &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission',$mapalias);
   if (ref($output) eq 'ARRAY') {
       my @items = @{$output};
       if ($encode) {
           @items = map { &encode_response($_); } @items;
       }
       if (ref($cleanupnum) eq 'HASH') {
           @items = map { &cleanup_numerical_response($cleanupnum,$_); } @items;
       }
       return \@items;
   } else {
       if ($encode) {
           $output = &encode_response($output);
       }
       if (ref($cleanupnum) eq 'HASH') {
           $output = &cleanup_numerical_response($cleanupnum,$output);
       }
       return $output;
   }
}

sub encode_response {
    my ($value) = @_;
    $value =~ s/&/&amp;/g;
    $value =~ s/</&lt;/g;
    $value =~ s/>/&gt;/g;
    $value =~ s/"/&quot;/g;
    return $value;
}

sub cleanup_numerical_response {
    my ($cleanupnum,$value) = @_;
    if (ref($cleanupnum) eq 'HASH') {
        if ($cleanupnum->{exponent}) {
            if ($value =~ m{^(.*)[\*xX]\s*10\s*\^\s*(\+|\-)?\s*(\d+)(.*)$}) {
                my $pre_exp = $1;
                my $sign = $2;
                my $exponent = $3;
                my $post_exp = $4;
                if ($pre_exp !~ /\./) {
                    $pre_exp .= '.';
                }
                if ($sign eq '') {
                    $sign = '+';
                }
                $value = $pre_exp.'E'.$sign.$exponent.$post_exp;
            }
        }
        if ($cleanupnum->{comma}) {
            $value =~ s{(\d+),(\d+)}{$1$2};
        }
        if ($cleanupnum->{letterforzero}) {
            $value =~ s/^\s*o(\.\d+)/0$1/i;
        }
        if ($cleanupnum->{spaces}) {
            $value =~ s{^\s+|\s+$}{}g;
            if ($value =~ m{^(.*)\.\s+(\d+)(.*)$}) {
                my $pre_pt = $1;
                my $decimal = $2;
                my $post_dec = $3;
                $value = $pre_pt.'.'.$decimal.$post_dec;
            }
        }
        if ($cleanupnum->{format} =~ /^\d+s$/i) {
            $value = &format_significant_figures($value,$cleanupnum->{format});
        }
    }
    return $value;
}

sub currentpart {
   return $external::part;
}

sub eval_time {
   my ($timestamp)=@_;
   unless ($timestamp) { return ''; }
   return &locallocaltime($timestamp);
}

sub open_date { 
    my ($partid)=@_;
    unless ($partid) { $partid=0; }
    return &eval_time(&EXT('resource.'.$partid.'.opendate'));
}

sub due_date {
    my ($partid)=@_;
    unless ($partid) { $partid=0; } 
    return &eval_time(&EXT('resource.'.$partid.'.duedate'));
}

sub answer_date { 
    my ($partid)=@_;
    unless ($partid) { $partid=0; }
    return &eval_time(&EXT('resource.'.$partid.'.answerdate'));
}

sub open_date_epoch {
    my ($partid)=@_;
    unless ($partid) { $partid=0; }
    return &EXT('resource.'.$partid.'.opendate');
}

sub due_date_epoch {
    my ($partid)=@_;
    unless ($partid) { $partid=0; }
    return &EXT('resource.'.$partid.'.duedate');
}

sub answer_date_epoch {
    my ($partid)=@_;
    unless ($partid) { $partid=0; }
    return &EXT('resource.'.$partid.'.answerdate');
}

sub parameter_setting {
    my ($which,$partid)=@_;
    unless ($partid) { $partid=0; }
    return &EXT('resource.'.$partid.'.'.$which);
}

sub stored_data {
    my ($which,$partid)=@_;
    unless ($partid) { $partid=0; }
    return &EXT('user.resource.resource.'.$partid.'.'.$which);
}

sub wrong_bubbles {
    my ($correct,$lower,$upper,$step,@given)=@_;
    my @array=();
    my %hash=();
    foreach my $new (@given) {
        $hash{$new}=1;
    }
    my $num=int(&parameter_setting('numbubbles',&currentpart()));
    unless ($num) { $num=8; }
    if ($num>1) {
        for (my $i=0;$i<=500;$i++) {
            my $new=&random($lower,$upper,$step);
            if ($hash{$new}) { next; }
            if (abs($new-$correct)<$step) { next; }
            $hash{$new}=1;
            @array=keys(%hash);
            if ($#array+2>=$num) { last; }
        }
    }
    return @array;
}

sub array_moments {
    my @input=@_;
    my (@output,$N);
    $N=scalar (@input);
    $output[0]=$N;
    if ($N <= 1) {
	$output[1]=$input[0];
	$output[1]="Input array not defined" if ($N == 0);
	$output[2]="variance undefined for N<=1";
	$output[3]="skewness undefined for N<=1";
	$output[4]="kurtosis undefined for N<=1";
	return @output;
    }
    my $sum=0;
    foreach my $line (@input) {
	$sum+=$line;
    }
    $output[1] = $sum/$N;
    my ($x,$sdev,$var,$skew,$kurt) = 0;
    foreach my $line (@input) {
	$x=$line-$output[1];
	$var+=$x**2;
	$skew+=$x**3;
	$kurt+=$x**4;
    }
    $output[2]=$var/($N-1);
    $sdev=CORE::sqrt($output[2]);
    if ($sdev == 0) {
	$output[3]="inf-variance=0";
	$output[4]="inf-variance=0";
	return @output;
    }
    $output[3]=$skew/($sdev**3*$N);
    $output[4]=$kurt/($sdev**4*$N)-3;
    return @output;
}

sub choose {
    my $num = $_[0];
    return $_[$num];
}

#&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
#sub sum1 {
#    my ($start,$end,$sub)=@_;
#    my $sum=0;
#    for (my $i=$start;$i<=$end;$i++) {
#        $sum+=&$sub($i);
#    }
#    return $sum
#}

#&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
#sub sum2 {
#    my ($varname,$start,$end,$line)=@_;
#    my $sum=0;
#    for (my $i=$start;$i<=$end;$i++) {
#	my $func=sub {
#	    eval("\$".$varname."=$i");
#	    eval($line);
#	};
#        $sum+=&$func($i);
#    }
#    return $sum
#}

# expiremental idea
sub proper_path {
    my ($path)=@_;
    if ( $external::target eq "tex" ) {
	return '/home/httpd/html'.$path;
    } else {
	return $path;
    }
}

sub input_id {
    my ($part_id, $response_id, $textline_id) = @_;
    return 'HWVAL_'.$part_id.'_'.$response_id.'_'.$textline_id;
}