1 files changed, 114 insertions, 0 deletions
diff --git a/engine.php b/engine.php
new file mode 100644
index 0000000..674353a
--- /dev/null
+++ b/engine.php
@@ -0,0 +1,114 @@
+<?php
+
+function vptable($n) {
+	$table = array();
+
+	$v0 = 10;
+	$x = 15 * sqrt($n);
+	$xCeil = ceil($x);
+	//$R = pow((sqrt(5)-1)/2, 3);
+	$R = 0.236068;
+
+	for($imp=0;$imp<=$xCeil;$imp++) {
+		$vPrec = $v0 + $v0*( (1-pow($R,$imp/$x))/(1-$R) );
+		$v = round(100*$vPrec)/100;
+		$v = min($v,2*$v0);
+		$table[$imp] = $v;
+	}
+	
+	$ddv = dd($table);
+	$testViol = testViol($ddv);
+	while($testViol) {
+		$m = minViol($ddv);
+		if($m > 0) {
+			$table[$m-1] = $table[$m-1] + 0.01;
+			$ddv = dd($table);
+		}
+		$testViol = testViol($ddv);
+	}
+	
+	return $table;
+}
+
+function vptable_discrete($n) {
+	$table = array();
+	$v0 = 10;
+
+	for($v=$v0+0.5;$v<=2*$v0-0.5;$v++) {
+		$i = floor(imap($v,$n));
+		$table[floor($v)] = $i;
+	}
+	
+	$i = array(-$table[10]-1);
+	foreach($table as $imp) $i[] = $imp;
+	$ddi = diff(diff($i));
+	$testViol = testViolNegative($ddi);
+	while($testViol) {
+		$m = minViolNegative($ddi);
+		$i[$m+1] = $i[$m+1] - 1;
+		$ddi = diff(diff($i));
+		$testViol = testViolNegative($ddi);
+	}
+	for($j=1;$j<=10;$j++) {
+		$table[9+$j] = $i[$j];
+	}
+	
+	return $table;
+}
+
+// help functions
+
+function imap($v,$n) {
+	$v0 = 10;
+	$x = 15 * sqrt($n);
+	$R = 0.236068;
+	$logR = log($R);
+	return $x * (log( 1 - (1-$R)*($v/$v0 - 1) )/$logR);
+}
+
+
+function dd($v) {
+	$v = diff($v);
+	foreach($v as $k=>$e) {
+		$v[$k] = round($e*100);
+	}
+	$v = diff($v);
+	array_unshift($v,0,0);
+	return $v;
+}
+
+function diff($v) {
+	$diff = array();
+	for($i=0;$i<count($v)-1;$i++) {
+		$diff[$i] = $v[$i+1]-$v[$i];
+	}
+	return $diff;
+}
+
+function testViol($v) {
+	$sum = 0;
+	foreach($v as $e) {
+		if($e>0) $sum++;
+	}
+	return $sum>0;
+}
+function testViolNegative($v) {
+	$sum = 0;
+	foreach($v as $k=>$e) {
+		if($e<0) $sum++;
+	}
+	return $sum>0;
+}
+
+function minViol($v) {
+	foreach($v as $k=>$e) {
+		if($e>0) return $k;
+	}
+	return -1;
+}
+function minViolNegative($v) {
+	foreach($v as $k=>$e) {
+		if($e<0) return $k;
+	}
+	return -1;
+}