PHP-kode til beregning af e
1 <?
2
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3
4 define ('LENGTH', 12);
5 define ('ZEROS', '00000000000000000000');
6 define ('MAX', 1000000000000); 7 define ('MAXLIMIT', 30000);
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8
9
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10
11 function set_value (&$var,&$val,$def=1) {
12 if (isset($val))
13 $var=$val;
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14 else
15 $var=$def;
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16 }
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17
18 function zerofill ($block) {
19 $extra=LENGTH-strlen($block);
20 return substr(ZEROS,0,$extra).$block;
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21 }
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22
23 function long_divide ($number,$n) {
24 $rest=0;
25 foreach ($number as $nr => $block) {
26 $tal=$block+$rest*MAX;
27 $number[$nr]=floor($tal/$n);
28 $rest=$tal%$n;
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29 }
30 return $number;
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31 }
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32
33 function long_add ($number,$addend) {
34 $blocks=count($number);
35 $mente=0;
36 for ($nr=$blocks-1; $nr>=0; --$nr) {
37 $sum=$number[$nr]+$addend[$nr]+$mente;
38 $number[$nr]=$sum%MAX;
39 $mente=$sum/MAX;
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40 }
41 $number[0]+=$mente;
42 return $number;
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43 }
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44
45 function display ($e) {
46 GLOBAL $decimals;
47 $first_digit=floor(array_shift($e));
48 echo "<table>\n";
49 echo "<tr><td>e = $first_digit,</td></tr>\n";
50 $buffer="";
51 $echoed=10;
52 $units=0;
53 echo "<tr>";
54 foreach ($e as $block) {
55 $buffer.=zerofill($block);
56 while (strlen($buffer)>9 && $echoed<$decimals) {
57 $echoed+=10;
58 echo "<td>".substr($buffer,0,10)."</td>";
59 $buffer=substr($buffer,10);
60 if (++$units%5==0)
61 echo "</tr>\n<tr>";
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62 }
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63 }
64 $rest=$decimals-$echoed+10;
65 echo "<td>".substr($buffer,0,$rest)."</td></tr>";
66 echo "</table>\n";
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67 }
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68
69
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70
71 if (isset($_GET['show']))
72 show_source('beregn_e.inc.php');
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73 exit();
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74
75 echo "<pre> 1 1 1<br>";
76 echo " e = 1 + --- + --- + --- ...<br>";
77 echo " 1! 2! 3!</pre>\n";
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78
79 set_value($decimals,$_POST['digits'],5);
80 $blocks=floor($decimals/LENGTH);
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81
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82 echo "
83 <p>Her kan man beregne konstanten e, grundtal for den naturlige logaritme.
84 På grund af tidsbegrænsninger på serveren er der sat en maksimum på 30'000
85 decimaler, men metoden i sig selv er kun begrænset af computerens
86 tilgængelige arbejdslager.</p>
87 <p>Der er ikke noget sindsoprivende nyt i beregningerne, og på nogle
88 hjemmesider kan man få programmer der er mange gange hurtigere, men
89 <a href='?page=matematik/beregningsmetode'>metoden</a>
90 er enkel og kan implementeres i stort set alle programmeringssprog.</p>
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91
92 <form action='#' method='post'>
93 <p>Hvor mange decimaler? <input type='text' size='6' name='digits' value='$decimals'>
94 <input type='submit' name='send' value='OK'></p>
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95 </form>
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96 ";
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97
98 if (isset($_POST['send']) && $decimals<=MAXLIMIT) {
99 $blocks=floor($decimals/LENGTH);
100 while ($blocks*LENGTH<$decimals)
101 ++$blocks;
102 ++$blocks;
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103
104 $e=array_fill(0,$blocks,0);
105 $e[0]=1;
106 $rec_fact=$e;
107 $old_e=[0];
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108
109
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110
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111 $n=0;
112 $compare=0;
113 $start = microtime(1);
114 while ($compare<=$blocks) {
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115 ++$n;
116 $old_e=$e;
117 $rec_fact=long_divide($rec_fact,$n);
118 $e=long_add($e,$rec_fact);
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119
120 if (!isset($e[$compare]))
121 break;
122 if ($e[$compare]==$old_e[$compare])
123 ++$compare;
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124 }
125 echo " Beregningstid i sekunder: "
126 .number_format(microtime(1)-$start,6,',',"'")."<br>"
127 ." Sidste fakultetstal: $n";
128 display($e);
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129 }
130 ?>