Class: Math_Fibonacci

Examples:

 include_once 'Math/Fibonacci.php';

 $idx = 20;
 echo "Calculate F($idx), fast equation = ";
 $fib =& Math_Fibonacci::term($idx);
 echo $fib->toString()."\n";
 // Calculate F(20), fast equation = 6765

 $idx = 55;
 echo "Calculate F($idx), lookup table = ";
 $fib =& Math_Fibonacci::term($idx);
 echo $fib->toString()."\n";
 // Calculate F(55), lookup table = 139583862445

 $idx = 502;
 echo "Calculate F($idx), addition loop = ";
 $fib = Math_Fibonacci::term($idx);
 echo $fib->toString()."\n";
 // Calculate F(502), addition loop = 365014740723634211012237077906479355996081581501455497852747829366800199361550174096573645929019489792751

 echo "\nSeries from F(0) to F(10):\n";
 $series = Math_Fibonacci::series(10);
 foreach ($series as $n=>$fib) {
     echo "n = $n, F(n) = ".$fib->toString()."\n";
 }
 // Series from F(0) to F(10):
 // n = 0, F(n) = 0
 // n = 1, F(n) = 1
 // n = 2, F(n) = 1
 // n = 3, F(n) = 2
 // n = 4, F(n) = 3
 // n = 5, F(n) = 5
 // n = 6, F(n) = 8
 // n = 7, F(n) = 13
 // n = 8, F(n) = 21
 // n = 9, F(n) = 34
 // n = 10, F(n) = 55

 echo "\nand now from F(11) to F(19):\n";
 $series = Math_Fibonacci::series(11, 19);
 foreach ($series as $n=>$fib) {
     echo "n = $n, F(n) = ".$fib->toString()."\n";
 }
 // and now from F(11) to F(19):
 // n = 11, F(n) = 89
 // n = 12, F(n) = 144
 // n = 13, F(n) = 233
 // n = 14, F(n) = 377
 // n = 15, F(n) = 610
 // n = 16, F(n) = 987
 // n = 17, F(n) = 1597
 // n = 18, F(n) = 2584
 // n = 19, F(n) = 4181

 echo "\nChecking if 26 and 4181 are Fibonacci numbers\n";
 $verb = Math_Fibonacci::isFibonacci(new Math_Integer(26)) ? 'is' : 'is not';
 echo "26 $verb a Fibonacci number\n";
 // 26 is not a Fibonacci number
 $verb = Math_Fibonacci::isFibonacci(new Math_Integer(4181)) ? 'is' : 'is not';
 echo "4181 $verb a Fibonacci number\n";
 // 4181 is a Fibonacci number

 echo "\nDecompose 34512\n";
 $decarr = Math_Fibonacci::decompose(new Math_Integer(34512));
 foreach ($decarr as $fib) {
     $index = Math_Fibonacci::getIndexOf($fib);
     echo "F(".$index->toString().") = ".$fib->toString()."\n";
 }
 // Decompose 34512
 // F(23) = 28657
 // F(19) = 4181
 // F(17) = 1597
 // F(10) = 55
 // F(8) = 21
 // F(2) = 1

 echo "\nF(n) closest to 314156 is: ";
 $fib = Math_Fibonacci::closestTo(new Math_Integer(314156));
 echo $fib->toString()."\n\n";
 // F(n) closest to 314156 is: 317811

 echo 'The index for 1597 is : ';
 $idx = Math_Fibonacci::getIndexOf(new Math_Integer(1597));
 echo $idx->toString()."\n\n";
 // The index for 1597 is : 17

 $bigint = '3141579834521345220291';
 echo "Finding the Fibonacci numbers that add up to $bigint\n";
 $series = Math_Fibonacci::decompose(new Math_Integer($bigint));
 foreach ($series as $fib) {
     $index = Math_Fibonacci::getIndexOf($fib);
     echo "F(".$index->toString().") = ".$fib->toString()."\n";
 }
 // Finding the Fibonacci numbers that add up to 3141579834521345220291
 // F(104) = 2427893228399975082453
 // F(101) = 573147844013817084101
 // F(98) = 135301852344706746049
 // F(91) = 4660046610375530309
 // F(86) = 420196140727489673
 // F(83) = 99194853094755497
 // F(81) = 37889062373143906
 // F(79) = 14472334024676221
 // F(76) = 3416454622906707
 // F(74) = 1304969544928657
 // F(71) = 308061521170129
 // F(68) = 72723460248141
 // F(63) = 6557470319842
 // F(60) = 1548008755920
 // F(57) = 365435296162
 // F(53) = 53316291173
 // F(51) = 20365011074
 // F(49) = 7778742049
 // F(44) = 701408733
 // F(37) = 24157817
 // F(31) = 1346269
 // F(26) = 121393
 // F(20) = 6765
 // F(16) = 987
 // F(13) = 233
 // F(8) = 21
 // F(6) = 8
 // F(3) = 2

 

closestTo   [line 353]

decompose   [line 320]

getIndexOf   [line 387]

isFibonacci   [line 303]

series   [line 270]

term   [line 209]