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POFibonacci LFSRs calculation optimisation
 

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    <p><a href="http://en.wikipedia.org/wiki/Linear_feedback_shift_register" rel="nofollow">Fibonacci LFSR</a> is described on wiki, it's pretty simple. <br />I'd like to calucate the period of some Fibonacci's LFSR and use generated sequence for ciphering later. <br /> Let's take and example from wiki:</p> <blockquote> <p>x<sup>16</sup> + x<sup>14</sup> + x<sup>13</sup> + x<sup>11</sup> + 1;</p> </blockquote> <pre><code>//code from wiki: include &lt;stdint.h&gt; uint16_t lfsr = 0xACE1u; unsigned bit; unsigned period = 0; do { /* taps: 16 14 13 11; characteristic polynomial: x^16 + x^14 + x^13 + x^11 + 1 */ bit = ((lfsr &gt;&gt; 0) ^ (lfsr &gt;&gt; 2) ^ (lfsr &gt;&gt; 3) ^ (lfsr &gt;&gt; 5) ) &amp; 1; lfsr = (lfsr &gt;&gt; 1) | (bit &lt;&lt; 15); ++period; } while(lfsr != 0xACE1u); </code></pre> <p>My weakly try so far in php:</p> <pre><code>function getPeriod(){ $polynoms = array(16, 14, 13, 11); $input = $polynoms[0] - 1; $n = sizeof($polynoms); for ($i = 1; $i &lt; $n; $i++) $polynoms[$i] = $polynoms[0] - $polynoms[$i]; $polynoms[0] = 0; //reversed polynoms == array(0, 2, 3, 5); $lfsr = 0x1; //begining state $period = 0; //gmp -- php library for long numbers; $lfsr = gmp_init($lfsr, 16); do { $bit = $lfsr; //bit = x^16 &gt;&gt; 0; for($i = 1; $i &lt; $n; $i++) { //bit ^= lfsr &gt;&gt; 2 ^ lfst &gt;&gt; 3 ^ lfst &gt;&gt; 5; $bit = gmp_xor($bit, ( gmp_div_q($lfsr, gmp_pow(2, $polynoms[$i])) )); } //bit &amp;= 1; $bit = gmp_and($bit, 1); //lfsr = $lfsr &gt;&gt; 1 | $lsfr &lt;&lt; (16 - 1); $lfsr = gmp_or( (gmp_div_q($lfsr, 2)), (gmp_mul($bit, gmp_pow(2, $input))) ); $period++; } while (gmp_cmp($lfsr, 0x1) != 0); echo '&lt;br /&gt;period = '.$period; //period == 65535 == 2^16 - 1; -- and that's correct; // I hope, at least; return $period; } </code></pre> <p><br/> <b>Problem:</b> <br />If i try to modulate work of i.e.</p> <blockquote> <p>x<sup>321</sup> + x<sup>14</sup> + x<sup>13</sup> + x<sup>11</sup> + 1;</p> </blockquote> <p>i got an error:"<strong>Fatal error: Maximum execution time of 30 seconds exceeded in /var/www/Dx02/test.php</strong>"; <br /> <br /> Can i somehow optimize (accelerate :) ) the calculation? <br /> <br />Any help is appreciated. Thank you and excuse me for my English.</p>
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    1. COLooks like you are reading it incorrectly. There should be no multiplication, no power. It's all done using bitwise operators. You shouldn't need any special library. the ^ means xor in C. Same in PHP. If you do this using bit manipulation it will go very fast.
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    2. COthere's one big problem using bit manipulation: 32bit (x86) OS. This means if i try to do `1 << 31` i'll get below 0 result (`-2147483648`, exatcly) but not `2147483648` and `1 << 32` will return `1`, if i'm not mistaken. That's why i used gmp library and not bitwise shift.
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    3. COhmm yea, have you tried the more efficient algorithm? Galois LFSR. Looks easier to implement as well. I don't know how fast that hack is you have for shifting, but it seems like it's the only way.
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