File:  [LON-CAPA] / loncom / homework / default_homework.lcpm
Revision 1.139: download - view: text, annotated - select for diffs
Fri Sep 12 09:56:09 2008 UTC (15 years, 6 months ago) by raeburn
Branches: MAIN
CVS tags: HEAD
- Bug 5531 (although should really be a separate bug).
RegExp used to separate units from numerical part of an answer can truncate responses to stringresponse items for which the type has not been explicitly set (as ci, cs, mc or re).

- Include the tagname of the response item in calls to caparesponse_check_list(), so that if the type attribute is unspecified, stringresponse submissions are not subjected to the unit extractor.

Perhaps there is a reason why this ambiguity has not been eliminated previously by passing the tagname to caparesponse_check_list() - run in the safe space?
Testing needed.

# The LearningOnline Network with CAPA 
# used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
#
# $Id: default_homework.lcpm,v 1.139 2008/09/12 09:56:09 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;
$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;
	&LONCAPA_INTERNAL_DEBUG("Removed ws now :$response:");
    }

    #&LONCAPA_INTERNAL_DEBUG(" type is $type ");
    if ($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 ($type eq '' ) {
	&LONCAPA_INTERNAL_DEBUG("Didn't find a type :$type: defaulting");
	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(/@/,$samples);
	&LONCAPA_INTERNAL_DEBUG("Found :$id_list:$points: points in $samples");
    }
    if ($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') || ($type eq '8')) && ($response=~/\=/)) { return ('BAD_FORMULA','Please submit just an expression, not an equation.'); }
    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:$result:$@:";}

    &LONCAPA_INTERNAL_DEBUG("RetError $reterror: Answer $answer: Response $response:  type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|");
    &LONCAPA_INTERNAL_DEBUG(" $answer $response $result ");
    return ($result,$reterror);
}


sub caparesponse_check_list {
    my ($tag) = @_;
    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 $num_input_lines =
	scalar(@{$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';
	}
    }

    &LONCAPA_INTERNAL_DEBUG("Initial final response :$responses->[0][-1]:");
    my $unit;
    if (($type eq 'float') || (($type eq '') && (($tag ne 'stringresponse') && ($tag ne 'stringhint')) ) ) {
	#for numerical problems split off the unit
#	if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
        if ( $responses->[0][-1]=~ /^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d+)([\$\s\w\^\*\/\(\)\+\-]*[^\d\.\s\,][\$\s\w\^\*\/\(\)\+\-]*)$/ ) {
	    $responses->[0][-1]=$1;
	    $unit=&capa_formula_fix($2);
            &LONCAPA_INTERNAL_DEBUG("Found unit :$unit:");
	}
    }
    &LONCAPA_INTERNAL_DEBUG("Final final response :$responses->[0][-1]:$unit:");
    $unit=~s/\s//;
    foreach my $response (@$responses) {
       foreach my $element (@$response) {	
          if (($type eq 'float') || (($type eq '') && ($unit ne ''))) {
              $element =~ s/\s//g;
          }
          my $appendunit=$unit;
          if ($unit=~/\%/) {
             $element=$element/100;
             $appendunit=~s/\%//;
          }    
          if (($element==0) && ($unit!~/\w/) && ($answerunit=~/\w/)) {
             $appendunit=$answerunit;
          }
          $element .= " $appendunit";
          &LONCAPA_INTERNAL_DEBUG("Made response element :$element:");
       }
    }
    
    foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
	if (!defined($thisanswer)) {
	    return ('ERROR','answer was undefined');
	}
    }


#    &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); $j++) { 
		my ($award,$msg) = &caparesponse_check($answer->[$j],
						       $response->[$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); $j++) {
			my ($award,$msg) = &caparesponse_check($answer->[$j],
							       $response->[$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);
}

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

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 ( ! $hidden::RANDOMINIT ) {
	if ($external::randomseed == 0) { $external::randomseed=1; }
	if ($external::randomseed =~/,/) {
	    my ($num1,$num2)=split(/,/,$external::randomseed);
	    &random_set_seed(1,abs($num1));
	} elsif ($external::randomseed =~/:/) {
	    my ($num1,$num2)=split(/:/,$external::randomseed);
	    &random_set_seed(abs($num1),abs($num2));
	} else {
	    &random_set_seed(1,int(abs($external::randomseed)));
	}
	&math_random_uniform();
	$hidden::RANDOMINIT=1;
    }
    if (!defined($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 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 '->' ) {
	    $formula .= '<m>\ensuremath{\rightarrow}</m> ';
	    next;
	}
	if ($token eq '<-' ) {
	    $formula .= '<m>\ensuremath{\leftarrow}</m> ';
	    next;
	}  
	if ($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 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);
    # insert trailing zero's if have decimal point
    $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
    # put a decimal pt for number ending with 0 and length = # of sig fig
    $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
    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 firstname {
    my $firstname = &EXT('environment.firstname');
    $firstname = '' if $firstname eq "";
    return $firstname;
}
                                                                                
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)=@_;
   my $sub='';
   if ($subnumber) { $sub=$subnumber.':'; }
   return &EXT('user.resource.'.$sub.'resource.'.$partid.'.'.$responseid.'.submission');
}

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 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;
    }
}


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