Annotation of loncom/homework/default_homework.lcpm, revision 1.129
1.42 albertel 1: # The LearningOnline Network with CAPA
1.1 harris41 2: # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
1.42 albertel 3: #
1.129 ! www 4: # $Id: default_homework.lcpm,v 1.128 2008/03/05 18:05:05 www Exp $
1.42 albertel 5: #
6: # Copyright Michigan State University Board of Trustees
7: #
8: # This file is part of the LearningOnline Network with CAPA (LON-CAPA).
9: #
10: # LON-CAPA is free software; you can redistribute it and/or modify
11: # it under the terms of the GNU General Public License as published by
12: # the Free Software Foundation; either version 2 of the License, or
13: # (at your option) any later version.
14: #
15: # LON-CAPA is distributed in the hope that it will be useful,
16: # but WITHOUT ANY WARRANTY; without even the implied warranty of
17: # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18: # GNU General Public License for more details.
19: #
20: # You should have received a copy of the GNU General Public License
21: # along with LON-CAPA; if not, write to the Free Software
22: # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23: #
24: # /home/httpd/html/adm/gpl.txt
25: #
26: # http://www.lon-capa.org/
27: #
1.20 harris41 28: #
1.76 albertel 29:
1.25 albertel 30: #init some globals
1.38 albertel 31: $hidden::RANDOMINIT=0;
1.22 ng 32: $pi=atan2(1,1)*4;
33: $rad2deg=180.0/$pi;
34: $deg2rad=$pi/180.0;
1.44 matthew 35: $"=' ';
1.116 albertel 36: use strict;
37: {
38: my $n = 0;
39: my $total = 0;
40: my $num_left = 0;
41: my @order;
42: my $type;
43:
44: sub init_permutation {
45: my ($size,$requested_type) = @_;
46: @order = (0..$size-1);
47: $n = $size;
48: $type = $requested_type;
49: if ($type eq 'ordered') {
50: $total = $num_left = 1;
51: } elsif ($type eq 'unordered') {
52: $total = $num_left = &factorial($size);
53: } else {
54: die("Unkown type: $type");
55: }
56: }
57:
58: sub get_next_permutation {
59: if ($num_left == $total) {
60: $num_left--;
1.117 albertel 61: return \@order;
1.116 albertel 62: }
63:
64: # Find largest index j with a[j] < a[j+1]
65:
66: my $j = scalar(@order) - 2;
67: while ($order[$j] > $order[$j+1]) {
68: $j--;
69: }
70:
71: # Find index k such that a[k] is smallest integer
72: # greater than a[j] to the right of a[j]
73:
74: my $k = scalar(@order) - 1;
75: while ($order[$j] > $order[$k]) {
76: $k--;
77: }
78:
79: # Interchange a[j] and a[k]
80:
81: @order[($k,$j)] = @order[($j,$k)];
82:
83: # Put tail end of permutation after jth position in increasing order
84:
85: my $r = scalar(@order) - 1;
86: my $s = $j + 1;
87:
88: while ($r > $s) {
89: @order[($s,$r)]=@order[($r,$s)];
90: $r--;
91: $s++;
92: }
93:
94: $num_left--;
1.117 albertel 95: return(\@order);
1.116 albertel 96: }
97:
98: sub get_permutations_left {
99: return $num_left;
100: }
101: }
1.3 albertel 102:
1.91 albertel 103: sub check_commas {
104: my ($response)=@_;
105: #print("$response ");
106: my @numbers=split(',',$response);
107: #print(" numbers ".join('-',@numbers)." ");
108: if (scalar(@numbers) > 1) {
109: #print(" numbers[0] ".$numbers[0]." ");
110: if (length($numbers[0]) > 3 || length($numbers[0]) == 0) { return -1; }
111: shift(@numbers);
112: #print(" numbers ".scalar(@numbers)." ");
113: while (scalar(@numbers) > 1) {
114: #print(" numbers ".join('-',@numbers)." ");
115: if (length($numbers[0]) != 3) { return -2; }
116: shift(@numbers);
117: }
118: my ($number)=split('\.',$numbers[0]);
119: #print(" number ".$number." ");
120: #print(" numbers[0] ".$numbers[0]." ");
121: if (length($number) != 3) { return -3; }
122: } else {
123: my ($number)=split('\.',$numbers[0]);
124: if (length($number) > 3) { return -4; }
125: }
126: return 1;
127: }
128:
1.117 albertel 129:
1.7 albertel 130: sub caparesponse_check {
1.74 albertel 131: my ($answer,$response)=@_;
1.73 albertel 132: #not properly used yet: calc
133: #not to be used: $ans_fmt
1.74 albertel 134: my $type=$LONCAPA::CAPAresponse_args{'type'};
135: my $tol=$LONCAPA::CAPAresponse_args{'tol'};
136: my $sig=$LONCAPA::CAPAresponse_args{'sig'};
1.88 albertel 137: my $ans_fmt=$LONCAPA::CAPAresponse_args{'format'};
1.74 albertel 138: my $unit=$LONCAPA::CAPAresponse_args{'unit'};
139: my $calc=$LONCAPA::CAPAresponse_args{'calc'};
140: my $samples=$LONCAPA::CAPAresponse_args{'samples'};
1.73 albertel 141:
142: my $tol_type=''; # gets it's value from whether tol has a % or not done
143: my $sig_lbound=''; #done
144: my $sig_ubound=''; #done
145:
146:
147: #type's definitons come from capaParser.h
1.116 albertel 148:
1.73 albertel 149: #remove leading and trailing whitespace
150: if (!defined($response)) {
151: $response='';
152: }
153: if ($response=~ /^\s|\s$/) {
154: $response=~ s:^\s+|\s+$::g;
1.119 albertel 155: &LONCAPA_INTERNAL_DEBUG("Removed ws now :$response:");
1.73 albertel 156: }
1.116 albertel 157:
1.117 albertel 158: #&LONCAPA_INTERNAL_DEBUG(" type is $type ");
1.100 albertel 159: if ($type eq 'cs' || $type eq 'ci') {
1.76 albertel 160: #for string answers make surec all places spaces occur, there is
161: #really only 1 space, in both the answer and the response
162: $answer=~s/ +/ /g;
163: $response=~s/ +/ /g;
1.100 albertel 164: } elsif ($type eq 'mc') {
165: $answer=~s/[\s,]//g;
166: $response=~s/[\s,]//g;
1.76 albertel 167: }
1.91 albertel 168: if ($type eq 'float' && $unit=~/\$/) {
1.126 www 169: if ($response!~/^\$|\$$/) { return ('NO_UNIT', undef); }
1.88 albertel 170: $response=~s/\$//g;
171: }
1.91 albertel 172: if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) {
173: return "COMMA_FAIL:";
174: }
1.88 albertel 175: $ans_fmt=~s/\W//g;
1.91 albertel 176: $unit=~s/[\$,]//g;
177: if ($type eq 'float') { $response=~s/,//g; }
1.88 albertel 178:
1.117 albertel 179: if (length($response) > 500) { return ('TOO_LONG',undef); }
1.73 albertel 180:
181: if ($type eq '' ) {
1.119 albertel 182: &LONCAPA_INTERNAL_DEBUG("Didn't find a type :$type: defaulting");
1.73 albertel 183: if ( $answer eq ($answer *1.0)) { $type = 2;
184: } else { $type = 3; }
185: } else {
1.107 albertel 186: if ($type eq 'cs') { $type = 4; }
1.73 albertel 187: elsif ($type eq 'ci') { $type = 3 }
188: elsif ($type eq 'mc') { $type = 5; }
189: elsif ($type eq 'fml') { $type = 8; }
1.107 albertel 190: elsif ($type eq 'math') { $type = 9; }
1.73 albertel 191: elsif ($type eq 'subj') { $type = 7; }
192: elsif ($type eq 'float') { $type = 2; }
193: elsif ($type eq 'int') { $type = 1; }
1.117 albertel 194: else { return ('ERROR', "Unknown type of answer: $type") }
1.73 albertel 195: }
196:
197: my $points;
198: my $id_list;
199: #formula type setup the sample points
200: if ($type eq '8') {
201: ($id_list,$points)=split(/@/,$samples);
1.119 albertel 202: &LONCAPA_INTERNAL_DEBUG("Found :$id_list:$points: points in $samples");
1.73 albertel 203: }
204: if ($tol eq '') {
205: $tol=0.0;
206: $tol_type=1; #TOL_ABSOLUTE
207: } else {
208: if ($tol =~ /%$/) {
209: chop $tol;
210: $tol_type=2; #TOL_PERCENTAGE
211: } else {
212: $tol_type=1; #TOL_ABSOLUTE
213: }
214: }
215:
1.85 albertel 216: ($sig_ubound,$sig_lbound)=&LONCAPA_INTERNAL_get_sigrange($sig);
217:
1.73 albertel 218: my $reterror="";
1.107 albertel 219: my $result;
1.125 www 220: if ((($type eq '9') || ($type eq '8')) && ($response=~/\=/)) { return ('BAD_FORMULA','Please submit just an expression, not an equation.'); }
1.107 albertel 221: if ($type eq '9') {
1.108 www 222: $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror);
1.107 albertel 223: } else {
1.109 albertel 224: if ($type eq '8') { # fml type
225: $response = &capa_formula_fix($response);
226: $answer = &capa_formula_fix($answer);
227: }
228: $result = &caparesponse_capa_check_answer($response,$answer,$type,
1.73 albertel 229: $tol_type,$tol,
230: $sig_lbound,$sig_ubound,
231: $ans_fmt,$unit,$calc,$id_list,
232: $points,$external::randomseed,
233: \$reterror);
1.107 albertel 234: }
1.73 albertel 235: if ($result == '1') { $result='EXACT_ANS'; }
236: elsif ($result == '2') { $result='APPROX_ANS'; }
237: elsif ($result == '3') { $result='SIG_FAIL'; }
238: elsif ($result == '4') { $result='UNIT_FAIL'; }
239: elsif ($result == '5') { $result='NO_UNIT'; }
240: elsif ($result == '6') { $result='UNIT_OK'; }
241: elsif ($result == '7') { $result='INCORRECT'; }
242: elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
243: elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
244: elsif ($result =='10') { $result='SUB_RECORDED'; }
245: elsif ($result =='11') { $result='BAD_FORMULA'; }
1.94 albertel 246: elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; }
247: elsif ($result =='12') { $result='WANTED_NUMERIC'; }
1.77 albertel 248: elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; }
249: elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; }
250: elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; }
251: elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
252: elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
1.73 albertel 253: else {$result = "ERROR: Unknown Result:$result:$@:";}
254:
1.119 albertel 255: &LONCAPA_INTERNAL_DEBUG("RetError $reterror: Answer $answer: Response $response: type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|");
256: &LONCAPA_INTERNAL_DEBUG(" $answer $response $result ");
1.116 albertel 257: return ($result,$reterror)
1.37 albertel 258: }
259:
1.73 albertel 260:
1.37 albertel 261: sub caparesponse_check_list {
1.119 albertel 262: my $responses=$LONCAPA::CAPAresponse_args{'response'};
1.121 albertel 263: # &LONCAPA_INTERNAL_DEBUG(" answer is ".
264: # &LONCAPA_INTERNAL_Dumper($LONCAPA::CAPAresponse_answer).":\n");
265: # &LONCAPA_INTERNAL_DEBUG(" respons is ".
266: # &LONCAPA_INTERNAL_Dumper($responses).":\n");
1.105 albertel 267: &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
1.74 albertel 268: my $type = $LONCAPA::CAPAresponse_args{'type'};
1.116 albertel 269: &LONCAPA_INTERNAL_DEBUG("Got type :$type:\n");
1.119 albertel 270:
271: my $num_input_lines =
272: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
1.120 albertel 273:
274: if ($type ne '' ) {
1.119 albertel 275: if (scalar(@$responses) < $num_input_lines) {
1.105 albertel 276: return 'MISSING_ANSWER';
277: }
1.119 albertel 278: if (scalar(@$responses) > $num_input_lines) {
279: return 'EXTRA_ANSWER';
280: }
281:
282: }
283:
284: foreach my $which (0..($num_input_lines-1)) {
285: my $answer_size =
286: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
287: if ($type ne ''
288: && $answer_size > 1) {
289: $responses->[$which]=[split(/,/,$responses->[$which])];
290: } else {
291: $responses->[$which]=[$responses->[$which]];
292: }
293: }
1.121 albertel 294: # &LONCAPA_INTERNAL_DEBUG(" parsed response is ".
295: # &LONCAPA_INTERNAL_Dumper($responses).":\n");
1.119 albertel 296: foreach my $which (0..($num_input_lines-1)) {
297: my $answer_size =
298: scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
299: my $response_size =
300: scalar(@{$responses->[$which]});
301: if ($answer_size > $response_size) {
302: return 'MISSING_ANSWER';
303: }
304: if ($answer_size < $response_size) {
1.105 albertel 305: return 'EXTRA_ANSWER';
306: }
1.73 albertel 307: }
1.119 albertel 308:
309: &LONCAPA_INTERNAL_DEBUG("Initial final response :$responses->[0][-1]:");
1.105 albertel 310: my $unit;
1.73 albertel 311: if ($type eq '' || $type eq 'float') {
312: #for numerical problems split off the unit
1.128 www 313: # if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
1.129 ! www 314: if ( $responses->[0][-1]=~ /^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d)([\w\s][\$\s\w\^\*\/\(\)\+\-]*\D[\$\s\w\^\*\/\(\)\+\-]*)$/ ) {
1.119 albertel 315: $responses->[0][-1]=$1;
1.128 www 316: $unit=&capa_formula_fix($2);
317: &LONCAPA_INTERNAL_DEBUG("Found unit :$unit:");
1.73 albertel 318: }
319: }
1.119 albertel 320: &LONCAPA_INTERNAL_DEBUG("Final final response :$responses->[0][-1]:$unit:");
1.73 albertel 321: $unit=~s/\s//;
1.119 albertel 322: if ($unit ne '') {
323: foreach my $response (@$responses) {
1.127 www 324: foreach my $element (@$response) {
325: $element =~ s/\s//g;
1.119 albertel 326: $element .= " $unit";
327: }
328: }
329: }
330:
1.117 albertel 331: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
332: if (!defined($thisanswer)) {
333: return ('ERROR','answer was undefined');
334: }
335: }
336:
337:
1.121 albertel 338: # &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
1.117 albertel 339: my %memoized;
340: if ($LONCAPA::CAPAresponse_answer->{'type'} eq 'ordered') {
1.119 albertel 341: for (my $i=0; $i<scalar(@$responses);$i++) {
1.117 albertel 342: my $answer = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
1.119 albertel 343: my $response = $responses->[$i];
1.117 albertel 344: my $key = "$answer\0$response";
1.119 albertel 345: my (@awards,@msgs);
346: for (my $j=0; $j<scalar(@$response); $j++) {
347: my ($award,$msg) = &caparesponse_check($answer->[$j],
348: $response->[$j]);
349: push(@awards,$award);
350: push(@msgs, $msg);
351: }
352: my ($award,$msg) =
353: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
354: $memoized{$key} = [$award,$msg];
1.117 albertel 355: }
356: } else {
1.119 albertel 357: #FIXME broken with unorder responses where one is a <value>
358: # and the other is a <vector> (need to delay parse til
359: # inside the loop?)
360: foreach my $response (@$responses) {
361: my $response_size = scalar(@{$response});
1.117 albertel 362: foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
363: my $key = "$answer\0$response";
1.119 albertel 364: my $answer_size = scalar(@{$answer});
365: my ($award,$msg);
366: if ($answer_size > $response_size) {
367: $award = 'MISSING_ANSWER';
368: } elsif ($answer_size < $response_size) {
369: $award = 'EXTRA_ANSWER';
370: } else {
371: my (@awards,@msgs);
372: for (my $j=0; $j<scalar(@$response); $j++) {
373: my ($award,$msg) = &caparesponse_check($answer->[$j],
374: $response->[$j]);
375: push(@awards,$award);
376: push(@msgs, $msg);
377: }
378: ($award,$msg) =
379: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
380: }
381: $memoized{$key} = [$award,$msg];
1.117 albertel 382: }
383: }
384: }
385:
1.116 albertel 386: my ($final_award,$final_msg);
1.119 albertel 387: &init_permutation(scalar(@$responses),
1.116 albertel 388: $LONCAPA::CAPAresponse_answer->{'type'});
1.117 albertel 389:
1.118 albertel 390: # possible FIXMEs
391: # - significant time is spent calling non-safe space routine
392: # from safe space
393: # - early outs could be possible with classifying awards is to stratas
394: # and stopping as so as hitting the top strata
395: # - some early outs also might be possible with check ing the
396: # memoized hash of results (is correct even possible? etc.)
397:
1.117 albertel 398: my (@final_awards,@final_msg);
1.116 albertel 399: while( &get_permutations_left() ) {
1.117 albertel 400: my $order = &get_next_permutation();
1.116 albertel 401: my (@awards, @msgs, $i);
402: foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
1.119 albertel 403: my $key = "$thisanswer\0".$responses->[$order->[$i]];
1.117 albertel 404: push(@awards,$memoized{$key}[0]);
405: push(@msgs,$memoized{$key}[1]);
1.116 albertel 406: $i++;
1.119 albertel 407:
1.116 albertel 408: }
1.119 albertel 409: &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));
410:
1.116 albertel 411: my ($possible_award,$possible_msg) =
412: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
1.119 albertel 413: &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
1.117 albertel 414: push(@final_awards,$possible_award);
415: push(@final_msg,$possible_msg);
1.73 albertel 416: }
1.117 albertel 417:
1.119 albertel 418: &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
1.117 albertel 419: my ($final_award,$final_msg) =
420: &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
1.116 albertel 421: return ($final_award,$final_msg);
1.7 albertel 422: }
423:
1.124 www 424: sub cas {
425: my ($system,$input)=@_;
426: my $output;
427: if ($system eq 'maxima') {
428: $output=&maxima_eval($input);
429: }
430: return $output;
431: }
432:
1.4 albertel 433: sub tex {
1.73 albertel 434: if ( $external::target eq "tex" ) {
435: return $_[0];
436: } else {
437: return $_[1];
438: }
1.4 albertel 439: }
440:
1.24 ng 441: sub var_in_tex {
1.73 albertel 442: if ( $external::target eq "tex" ) {
443: return $_[0];
444: } else {
445: return "";
446: }
1.24 ng 447: }
448:
1.4 albertel 449: sub web {
1.73 albertel 450: if ( $external::target eq "tex" ) {
451: return $_[1];
1.26 ng 452: } else {
1.73 albertel 453: if ( $external::target eq "web" || $external::target eq "answer") {
454: return $_[2];
455: } else {
456: return $_[0];
457: }
1.4 albertel 458: }
459: }
460:
1.24 ng 461: sub html {
1.73 albertel 462: if ( $external::target eq "web" ) {
463: return shift;
464: }
1.24 ng 465: }
466:
1.1 harris41 467: sub hinton {
1.73 albertel 468: return 0;
1.1 harris41 469: }
470:
471: sub random {
1.61 albertel 472: my ($start,$end,$step)=@_;
473: if ( ! $hidden::RANDOMINIT ) {
474: if ($external::randomseed == 0) { $external::randomseed=1; }
475: if ($external::randomseed =~/,/) {
1.84 albertel 476: my ($num1,$num2)=split(/,/,$external::randomseed);
477: &random_set_seed(1,abs($num1));
478: } elsif ($external::randomseed =~/:/) {
479: my ($num1,$num2)=split(/:/,$external::randomseed);
1.61 albertel 480: &random_set_seed(abs($num1),abs($num2));
481: } else {
482: &random_set_seed(1,int(abs($external::randomseed)));
483: }
484: &math_random_uniform();
485: $hidden::RANDOMINIT=1;
486: }
487: if (!defined($step)) { $step=1; }
488: my $num=1+int(($end-$start)/$step);
489: my $result=$start + int(&math_random_uniform() * $num)*$step;
490: return $result;
1.1 harris41 491: }
492:
1.26 ng 493: sub random_normal {
1.73 albertel 494: my ($item_cnt,$seed,$av,$std_dev) = @_;
495: my @oldseed=&random_get_seed();
496: my @retArray;
497: &random_set_seed_from_phrase($seed);
498: @retArray=&math_random_normal($item_cnt,$av,$std_dev);
499: &random_set_seed(@oldseed);
500: return @retArray;
1.26 ng 501: }
502:
503: sub random_beta {
1.73 albertel 504: my ($item_cnt,$seed,$aa,$bb) = @_;
505: my @oldseed=&random_get_seed();
506: my @retArray;
507: &random_set_seed_from_phrase($seed);
508: @retArray=&math_random_beta($item_cnt,$aa,$bb);
509: &random_set_seed(@oldseed);
510: return @retArray;
1.26 ng 511: }
512:
513: sub random_gamma {
1.73 albertel 514: my ($item_cnt,$seed,$a,$r) = @_;
515: my @oldseed=&random_get_seed();
516: my @retArray;
517: &random_set_seed_from_phrase($seed);
518: @retArray=&math_random_gamma($item_cnt,$a,$r);
519: &random_set_seed(@oldseed);
520: return @retArray;
1.26 ng 521: }
522:
523: sub random_exponential {
1.73 albertel 524: my ($item_cnt,$seed,$av) = @_;
525: my @oldseed=&random_get_seed();
526: my @retArray;
527: &random_set_seed_from_phrase($seed);
528: @retArray=&math_random_exponential($item_cnt,$av);
529: &random_set_seed(@oldseed);
530: return @retArray;
1.26 ng 531: }
532:
533: sub random_poisson {
1.73 albertel 534: my ($item_cnt,$seed,$mu) = @_;
535: my @oldseed=&random_get_seed();
536: my @retArray;
537: &random_set_seed_from_phrase($seed);
538: @retArray=&math_random_poisson($item_cnt,$mu);
539: &random_set_seed(@oldseed);
540: return @retArray;
1.26 ng 541: }
542:
543: sub random_chi {
1.73 albertel 544: my ($item_cnt,$seed,$df) = @_;
545: my @oldseed=&random_get_seed();
546: my @retArray;
547: &random_set_seed_from_phrase($seed);
548: @retArray=&math_random_chi_square($item_cnt,$df);
549: &random_set_seed(@oldseed);
550: return @retArray;
1.26 ng 551: }
552:
553: sub random_noncentral_chi {
1.73 albertel 554: my ($item_cnt,$seed,$df,$nonc) = @_;
555: my @oldseed=&random_get_seed();
556: my @retArray;
557: &random_set_seed_from_phrase($seed);
558: @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
559: &random_set_seed(@oldseed);
560: return @retArray;
1.26 ng 561: }
562:
563: sub random_f {
1.73 albertel 564: my ($item_cnt,$seed,$dfn,$dfd) = @_;
565: my @oldseed=&random_get_seed();
566: my @retArray;
567: &random_set_seed_from_phrase($seed);
568: @retArray=&math_random_f($item_cnt,$dfn,$dfd);
569: &random_set_seed(@oldseed);
570: return @retArray;
1.26 ng 571: }
572:
573: sub random_noncentral_f {
1.73 albertel 574: my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
575: my @oldseed=&random_get_seed();
576: my @retArray;
577: &random_set_seed_from_phrase($seed);
578: @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
579: &random_set_seed(@oldseed);
580: return @retArray;
1.26 ng 581: }
582:
583: sub random_multivariate_normal {
1.73 albertel 584: my ($item_cnt,$seed,$mean,$covar) = @_;
585: my @oldseed=&random_get_seed();
586: &random_set_seed_from_phrase($seed);
1.87 albertel 587: my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
1.73 albertel 588: &random_set_seed(@oldseed);
589: return @retArray;
1.26 ng 590: }
591:
592: sub random_multinomial {
1.73 albertel 593: my ($item_cnt,$seed,@p) = @_;
594: my @oldseed=&random_get_seed();
595: my @retArray;
596: &random_set_seed_from_phrase($seed);
1.87 albertel 597: my @retArray=&math_random_multinomial($item_cnt,@p);
1.73 albertel 598: &random_set_seed(@oldseed);
599: return @retArray;
1.26 ng 600: }
601:
602: sub random_permutation {
1.73 albertel 603: my ($seed,@inArray) = @_;
604: my @oldseed=&random_get_seed();
605: my @retArray;
606: &random_set_seed_from_phrase($seed);
607: @retArray=&math_random_permutation(@inArray);
608: &random_set_seed(@oldseed);
609: return @retArray;
1.26 ng 610: }
611:
612: sub random_uniform {
1.73 albertel 613: my ($item_cnt,$seed,$low,$high) = @_;
614: my @oldseed=&random_get_seed();
615: my @retArray;
616: &random_set_seed_from_phrase($seed);
617: @retArray=&math_random_uniform($item_cnt,$low,$high);
618: &random_set_seed(@oldseed);
619: return @retArray;
1.26 ng 620: }
621:
622: sub random_uniform_integer {
1.73 albertel 623: my ($item_cnt,$seed,$low,$high) = @_;
624: my @oldseed=&random_get_seed();
625: my @retArray;
626: &random_set_seed_from_phrase($seed);
627: @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
628: &random_set_seed(@oldseed);
629: return @retArray;
1.26 ng 630: }
631:
632: sub random_binomial {
1.73 albertel 633: my ($item_cnt,$seed,$nt,$p) = @_;
634: my @oldseed=&random_get_seed();
635: my @retArray;
636: &random_set_seed_from_phrase($seed);
637: @retArray=&math_random_binomial($item_cnt,$nt,$p);
638: &random_set_seed(@oldseed);
639: return @retArray;
1.26 ng 640: }
641:
642: sub random_negative_binomial {
1.73 albertel 643: my ($item_cnt,$seed,$ne,$p) = @_;
644: my @oldseed=&random_get_seed();
645: my @retArray;
646: &random_set_seed_from_phrase($seed);
647: @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
648: &random_set_seed(@oldseed);
649: return @retArray;
1.26 ng 650: }
651:
1.103 albertel 652: sub abs { CORE::abs(shift) }
653: sub sin { CORE::sin(shift) }
654: sub cos { CORE::cos(shift) }
655: sub exp { CORE::exp(shift) }
656: sub int { CORE::int(shift) }
657: sub log { CORE::log(shift) }
658: sub atan2 { CORE::atan2($_[0],$_[1]) }
659: sub sqrt { CORE::sqrt(shift) }
1.23 ng 660:
1.59 albertel 661: sub tan { CORE::sin($_[0]) / CORE::cos($_[0]) }
1.21 harris41 662: #sub atan { atan2($_[0], 1); }
663: #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
664: #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) ); }
1.22 ng 665:
1.59 albertel 666: sub log10 { CORE::log($_[0])/CORE::log(10); }
1.22 ng 667:
1.20 harris41 668: sub factorial {
1.59 albertel 669: my $input = CORE::int(shift);
1.20 harris41 670: return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
671: return "Error - factorial result is greater than system limit ($input)" if $input > 170;
672: return 1 if $input == 0;
673: my $result = 1;
674: for (my $i=2; $i<=$input; $i++) { $result *= $i }
675: return $result;
676: }
677:
678: sub sgn {
679: return -1 if $_[0] < 0;
680: return 0 if $_[0] == 0;
681: return 1 if $_[0] > 0;
682: }
683:
684: sub min {
685: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
686: return shift @sorted;
687: }
688:
689: sub max {
690: my @sorted = sort { $a <=> $b || $a cmp $b } @_;
691: return pop @sorted;
692: }
1.1 harris41 693:
1.20 harris41 694: sub roundto {
695: my ($input,$n) = @_;
696: return sprintf('%.'.$n.'f',$input);
697: }
698:
699: sub to_string {
700: my ($input,$n) = @_;
1.26 ng 701: return sprintf($input) if $n eq "";
702: $n = '.'.$n if $n !~ /^\./;
1.20 harris41 703: return sprintf('%'.$n,$input) if $n ne "";
704: }
705:
706: sub sub_string {
707: my ($str,$start,$len) = @_;
708: return substr($str,$start-1,$len);
709: }
1.1 harris41 710:
711: sub pow {return $_[0] ** $_[1]; }
1.59 albertel 712: sub ceil {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
713: sub floor {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
1.27 ng 714: #sub floor {return int($_[0]); }
1.1 harris41 715:
1.2 albertel 716: sub format {
1.73 albertel 717: my ($value,$fmt)=@_;
1.81 albertel 718: my ($dollarmode,$commamode,$alwaysperiod,$options);
719: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
720: #if ($options =~ /\$/) { $dollamode=1; }
721: #if ($options =~ /,/) { $commamode=1; }
1.82 albertel 722: if ($options =~ /\./) { $alwaysperiod=1; }
1.99 ng 723: my $result;
1.97 albertel 724: if ($fmt=~/s$/i) {
725: $result=&format_significant_figures($value,$fmt);
726: } else {
727: $fmt=~s/e/E/g;
1.99 ng 728: $result=sprintf('%.'.$fmt,$value);
1.97 albertel 729: if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
730: $result=~s/(E[+-]*)0/$1/;
731: }
1.81 albertel 732: #if ($dollarmode) {$result=&dollarformat($result);}
733: #if ($commamode) {$result=&commaformat($result);}
1.73 albertel 734: return $result;
1.46 albertel 735: }
736:
1.75 albertel 737: sub chemparse {
738: my ($reaction) = @_;
1.96 albertel 739: my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
1.75 albertel 740: my $formula = '';
741: foreach my $token (@tokens) {
742: if ($token eq '->' ) {
743: $formula .= '<m>\ensuremath{\rightarrow}</m> ';
744: next;
745: }
1.96 albertel 746: if ($token eq '<-' ) {
747: $formula .= '<m>\ensuremath{\leftarrow}</m> ';
748: next;
749: }
1.75 albertel 750: if ($token eq '<=>') {
751: if ($external::target eq 'web' &&
752: &EXT('request.browser.unicode')) {
1.76 albertel 753: $formula .= '⇌ ';
1.75 albertel 754: } else {
755: $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
1.95 albertel 756: '<=> ');
1.75 albertel 757: }
758: next;
759: }
1.96 albertel 760: if ($token eq '.') {
761: $formula =~ s/(\ \;| )$//;
762: $formula .= '·';
763: next;
764: }
765: $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
1.90 albertel 766: $formula .= $1 if ($1 ne '1'); # stoichiometric coefficient
1.75 albertel 767:
768: my $molecule = $2;
769: # subscripts
1.78 albertel 770: $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
1.75 albertel 771: # superscripts
772: $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
773: # strip whitespace
774: $molecule =~ s/\s*//g;
775: # forced space
776: $molecule =~ s/_/ /g;
1.96 albertel 777: $molecule =~ s/-/−/g;
1.75 albertel 778: $formula .= $molecule.' ';
779: }
780: # get rid of trailing space
1.87 albertel 781: $formula =~ s/(\ \;| )$//;
1.75 albertel 782: return &xmlparse($formula);
783: }
784:
1.46 albertel 785: sub prettyprint {
1.73 albertel 786: my ($value,$fmt,$target)=@_;
787: my $result;
788: if (!$target) { $target = $external::target; }
1.75 albertel 789: if ($fmt =~ /chem/i) { return(&chemparse($value)); }
1.81 albertel 790: my ($dollarmode,$commamode,$alwaysperiod,$options);
791: if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; }
1.86 albertel 792: if ($options =~ /\$/) { $dollarmode=1; }
1.81 albertel 793: if ($options =~ /,/) { $commamode=1; }
794: if ($options =~ /\./) { $alwaysperiod=1; }
1.97 albertel 795: if ($fmt=~/s$/i) {
796: $value=&format_significant_figures($value,$fmt);
797: } elsif ($fmt) {
798: $value=sprintf('%.'.$fmt,$value);
799: }
1.81 albertel 800: if ($alwaysperiod && $fmt eq '0f') {
801: if ($target eq 'tex') {
802: $value .='\\ensuremath{.}';
803: } else {
804: $value .='.';
805: }
806: }
1.73 albertel 807: if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
808: my $frac=$1;
809: if ($dollarmode) { $frac=&dollarformat($frac); }
1.80 albertel 810: if ($commamode) { $frac=&commaformat($frac); }
1.73 albertel 811: my $exponent=$2;
812: $exponent=~s/^\+0*//;
813: $exponent=~s/^-0*/-/;
814: $exponent=~s/^-0*/-/;
815: if ($exponent eq '-') { undef($exponent); }
816: if ($exponent) {
817: if ($target eq 'web') {
818: $result=$frac.'×10<sup>'.$exponent.'</sup>';
819: } elsif ($target eq 'tex') {
820: $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
821: } else {
822: $result=$value;
823: }
824: } else {
825: $result=$frac;
826: }
827: } else {
1.48 albertel 828: $result=$value;
1.86 albertel 829: if ($dollarmode) { $result=&dollarformat($result,$target); }
830: elsif ($commamode) { $result=&commaformat($result,$target); }
1.46 albertel 831: }
1.73 albertel 832: return $result;
1.48 albertel 833: }
834:
1.80 albertel 835: sub commaformat {
1.73 albertel 836: my ($number,$target) = @_;
837: if ($number =~ /\./) {
1.102 albertel 838: while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
839: $number = $1.$2.','.$3.$4;
1.73 albertel 840: }
841: } else {
1.102 albertel 842: while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
843: $number = $1.$2.','.$3.$4;
1.73 albertel 844: }
845: }
1.80 albertel 846: return $number;
847: }
848:
849: sub dollarformat {
850: my ($number,$target) = @_;
851: if (!$target) { $target = $external::target; }
852: $number=&commaformat($number,$target);
1.73 albertel 853: if ($target eq 'tex') {
854: $number='\$'.$number; #' stupid emacs
855: } else {
856: $number='$'.$number; #' stupid emacs
857: }
858: return $number;
1.2 albertel 859: }
1.5 albertel 860:
1.97 albertel 861: # format of form ns or nS where n is an integer
862: sub format_significant_figures {
863: my ($number,$format) = @_;
864: return '0' if ($number == 0);
865: # extract number of significant figures needed
866: my ($sig) = ($format =~ /(\d+)s/i);
867: # arbitrary choice - suggestions ?? or throw error message?
868: $sig = 3 if ($sig eq '');
869: # save the minus sign
870: my $sign = ($number < 0) ? '-' : '';
871: $number = abs($number);
872: # needed to correct for a number greater than 1 (or
873: my $power = ($number < 1) ? 0 : 1;
874: # could round up. Take the integer part of log10.
875: my $x10 = int(log($number)/log(10));
876: # find number with values left of decimal pt = # of sign figs.
877: my $xsig = $number*10**($sig-$x10-$power);
878: # get just digits left of decimal pt - also rounds off correctly
879: my $xint = sprintf('%.0f',$xsig);
880: # save any trailing zero's
881: my ($zeros) = ($xint =~ /(0+)$/);
882: # return number to original magnitude
883: my $numSig = $xint*10**($x10-$sig+$power);
884: # insert trailing zero's if have decimal point
885: $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
1.98 albertel 886: # put a decimal pt for number ending with 0 and length = # of sig fig
887: $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
888: if (length($numSig) < $sig) {
889: $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
890: }
1.97 albertel 891: # return number with sign
892: return $sign.$numSig;
893:
894: }
895:
1.5 albertel 896: sub map {
1.27 ng 897: my ($phrase,$dest,$source)=@_;
1.51 albertel 898: my @oldseed=&random_get_seed();
1.27 ng 899: my @seed = &random_seed_from_phrase($phrase);
900: &random_set_seed(@seed);
901: my $destct = scalar(@$dest);
1.28 ng 902: if (!$source) {
903: my @output;
904: my @idx = &math_random_permuted_index($destct);
905: my $ctr = 0;
906: while ($ctr < $destct) {
907: $output[$ctr] = $$dest[$idx[$ctr]];
1.27 ng 908: $ctr++;
1.28 ng 909: }
1.51 albertel 910: &random_set_seed(@oldseed);
1.28 ng 911: return @output;
1.27 ng 912: } else {
1.28 ng 913: my $num = scalar(@$source);
914: my @idx = &math_random_permuted_index($num);
915: my $ctr = 0;
916: my $tot = $num;
917: $tot = $destct if $destct < $num;
918: if (ref($$dest[0])) {
919: while ($ctr < $tot) {
920: ${$$dest[$ctr]} = $$source[$idx[$ctr]];
921: $ctr++;
922: }
923: } else {
924: while ($ctr < $tot) {
925: $$dest[$ctr] = $$source[$idx[$ctr]];
926: $ctr++;
927: }
928: }
1.27 ng 929: }
1.56 albertel 930: &random_set_seed(@oldseed);
1.51 albertel 931: return '';
1.27 ng 932: }
933:
934: sub rmap {
935: my ($phrase,$dest,$source)=@_;
1.51 albertel 936: my @oldseed=&random_get_seed();
1.27 ng 937: my @seed = &random_seed_from_phrase($phrase);
938: &random_set_seed(@seed);
939: my $destct = scalar(@$dest);
1.28 ng 940: if (!$source) {
941: my @idx = &math_random_permuted_index($destct);
942: my $ctr = 0;
943: my @r_idx;
944: while ($ctr < $destct) {
945: $r_idx[$idx[$ctr]] = $ctr;
946: $ctr++;
947: }
948: my @output;
949: $ctr = 0;
950: while ($ctr < $destct) {
951: $output[$ctr] = $$dest[$r_idx[$ctr]];
1.27 ng 952: $ctr++;
1.28 ng 953: }
1.51 albertel 954: &random_set_seed(@oldseed);
1.28 ng 955: return @output;
1.27 ng 956: } else {
1.28 ng 957: my $num = scalar(@$source);
958: my @idx = &math_random_permuted_index($num);
959: my $ctr = 0;
960: my $tot = $num;
961: $tot = $destct if $destct < $num;
962: my @r_idx;
1.27 ng 963: while ($ctr < $tot) {
1.28 ng 964: $r_idx[$idx[$ctr]] = $ctr;
1.27 ng 965: $ctr++;
1.28 ng 966: }
967: $ctr = 0;
968: if (ref($$dest[0])) {
969: while ($ctr < $tot) {
970: ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
971: $ctr++;
972: }
973: } else {
974: while ($ctr < $tot) {
975: $$dest[$ctr] = $$source[$r_idx[$ctr]];
976: $ctr++;
977: }
978: }
1.6 albertel 979: }
1.51 albertel 980: &random_set_seed(@oldseed);
981: return '';
1.5 albertel 982: }
1.22 ng 983:
1.23 ng 984: sub capa_id { return }
985:
986: sub problem { return }
987:
1.22 ng 988: sub name{
1.73 albertel 989: my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
990: $fullname = "" if $fullname eq ", ";
991: $fullname =~ s/\%2d/-/g;
992: return $fullname;
1.22 ng 993: }
994:
995: sub student_number {
1.73 albertel 996: my $id = &EXT('environment.id');
997: $id = '' if $id eq "";
998: return $id;
1.22 ng 999: }
1000:
1001: sub class {
1.73 albertel 1002: my $course = &EXT('course.description');
1003: $course = '' if $course eq "";
1004: return $course;
1.22 ng 1005: }
1006:
1.112 www 1007: sub firstname {
1008: my $firstname = &EXT('environment.firstname');
1009: $firstname = '' if $firstname eq "";
1010: return $firstname;
1011: }
1012:
1013: sub lastname {
1014: my $lastname = &EXT('environment.lastname');
1015: $lastname = '' if $lastname eq "";
1016: return $lastname;
1017: }
1018:
1.22 ng 1019: sub sec {
1.73 albertel 1020: my $sec = &EXT('request.course.sec');
1021: $sec = '' if $sec eq "";
1022: return $sec;
1.22 ng 1023: }
1024:
1.23 ng 1025: sub open_date {
1.73 albertel 1026: my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
1027: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
1028: my @hm = split(/:/,$dc[3]);
1029: my $ampm = " am";
1030: if ($hm[0] > 12) {
1031: $hm[0]-=12;
1032: $ampm = " pm";
1033: }
1034: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.23 ng 1035: }
1036:
1037: sub due_date {
1.73 albertel 1038: my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
1039: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
1040: my @hm = split(/:/,$dc[3]);
1041: my $ampm = " am";
1042: if ($hm[0] > 12) {
1043: $hm[0]-=12;
1044: $ampm = " pm";
1045: }
1046: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.23 ng 1047: }
1048:
1049: sub answer_date {
1.73 albertel 1050: my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
1051: return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
1052: my @hm = split(/:/,$dc[3]);
1053: my $ampm = " am";
1054: if ($hm[0] > 12) {
1055: $hm[0]-=12;
1056: $ampm = " pm";
1057: }
1058: return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
1.24 ng 1059: }
1060:
1061: sub array_moments {
1.73 albertel 1062: my @input=@_;
1063: my (@output,$N);
1064: $N=scalar (@input);
1065: $output[0]=$N;
1066: if ($N <= 1) {
1067: $output[1]=$input[0];
1068: $output[1]="Input array not defined" if ($N == 0);
1069: $output[2]="variance undefined for N<=1";
1070: $output[3]="skewness undefined for N<=1";
1071: $output[4]="kurtosis undefined for N<=1";
1072: return @output;
1073: }
1074: my $sum=0;
1075: foreach my $line (@input) {
1076: $sum+=$line;
1077: }
1078: $output[1] = $sum/$N;
1079: my ($x,$sdev,$var,$skew,$kurt) = 0;
1080: foreach my $line (@input) {
1081: $x=$line-$output[1];
1082: $var+=$x**2;
1083: $skew+=$x**3;
1084: $kurt+=$x**4;
1085: }
1086: $output[2]=$var/($N-1);
1087: $sdev=CORE::sqrt($output[2]);
1088: if ($sdev == 0) {
1089: $output[3]="inf-variance=0";
1090: $output[4]="inf-variance=0";
1091: return @output;
1092: }
1093: $output[3]=$skew/($sdev**3*$N);
1094: $output[4]=$kurt/($sdev**4*$N)-3;
1.24 ng 1095: return @output;
1096: }
1.5 albertel 1097:
1098: sub choose {
1.73 albertel 1099: my $num = $_[0];
1100: return $_[$num];
1.5 albertel 1101: }
1.23 ng 1102:
1.101 albertel 1103: #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
1104: #sub sum1 {
1105: # my ($start,$end,$sub)=@_;
1106: # my $sum=0;
1107: # for (my $i=$start;$i<=$end;$i++) {
1108: # $sum+=&$sub($i);
1109: # }
1110: # return $sum
1111: #}
1112:
1113: #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
1114: #sub sum2 {
1115: # my ($varname,$start,$end,$line)=@_;
1116: # my $sum=0;
1117: # for (my $i=$start;$i<=$end;$i++) {
1118: # my $func=sub {
1119: # eval("\$".$varname."=$i");
1120: # eval($line);
1121: # };
1122: # $sum+=&$func($i);
1123: # }
1124: # return $sum
1125: #}
1126:
1.49 albertel 1127: # expiremental idea
1128: sub proper_path {
1.73 albertel 1129: my ($path)=@_;
1130: if ( $external::target eq "tex" ) {
1131: return '/home/httpd/html'.$path;
1132: } else {
1133: return $path;
1134: }
1.49 albertel 1135: }
1.23 ng 1136:
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