- **Factoring**
(*https://www.mersenneforum.org/forumdisplay.php?f=19*)

- - **Distribution of relations over the sieving interval in SIQS**
(*https://www.mersenneforum.org/showthread.php?t=19375*)

Distribution of relations over the sieving interval in SIQS1 Attachment(s)
I was wondering whether anyone might know why the distribution, over the sieving interval, of relations found by SIQS seems to have 2 narrow spikes round about 0.7M either side of 0 (though not quite symmetrical, presumably due to asymmetrical parabolas?) See attachment. The peaks are around 3 times the general level. This is true of full relations, 1-partials and 2-partials.
Is this a well-known phenomena? Could it be used in any way to tune the QS algorithms? Cheers, Mick. |

[QUOTE=mickfrancis;373864]I was wondering whether anyone might know why the distribution, over the sieving interval, of relations found by SIQS seems to have 2 narrow spikes round about 0.7M either side of 0 (though not quite symmetrical, presumably due to asymmetrical parabolas?) See attachment. The peaks are around 3 times the general level. This is true of full relations, 1-partials and 2-partials.
Is this a well-known phenomena? Could it be used in any way to tune the QS algorithms? Cheers, Mick.[/QUOTE]Hint: how many real roots does a quadratic have? The term "chicken feet" is also relevant, though it may not appear so at first! |

[QUOTE=mickfrancis;373864]I was wondering whether anyone might know why the distribution, over the sieving interval, of relations found by SIQS seems to have 2 narrow spikes round about 0.7M either side of 0 (though not quite symmetrical, presumably due to asymmetrical parabolas?) See attachment. The peaks are around 3 times the general level. This is true of full relations, 1-partials and 2-partials.
Is this a well-known phenomena? Could it be used in any way to tune the QS algorithms? Cheers, Mick.[/QUOTE] It is well known and has a simple origin as Xilman points out. Klechibar talks about it in "The Quadratic Sieve - introduction to theory with regard to implementation issues". Early versions of YAFU tried to take advantage of it, but I don't believe the improvement (if any) amounted to much. It is too expensive to check every 'x' to see if you are close to a root or not. As a compromise I think I put a little more effort into all sieve hits within the block containing the root, but the gain at the root offsets the loss away from the root within the block... |

Thanks for the replies, guys - interesting.
Mick. |

All times are UTC. The time now is 23:02. |

Powered by vBulletin® Version 3.8.11

Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.