[libmath-prime-util-perl] 20/43: AKS comments
Partha P. Mukherjee
ppm-guest at moszumanska.debian.org
Thu May 21 18:53:07 UTC 2015
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ppm-guest pushed a commit to annotated tag v0.40
in repository libmath-prime-util-perl.
commit c81f07527775779b331d7d7c5e4a6766a4ec75a7
Author: Dana Jacobsen <dana at acm.org>
Date: Fri Mar 28 07:02:15 2014 -0700
AKS comments
---
aks.c | 21 ++++++++++++++-------
1 file changed, 14 insertions(+), 7 deletions(-)
diff --git a/aks.c b/aks.c
index 8e0dd20..81d9d06 100644
--- a/aks.c
+++ b/aks.c
@@ -4,14 +4,21 @@
#include <math.h>
#include <float.h>
-/*
- * The AKS v6 algorithm, for native integers. Based on the AKS v6 paper.
- * As with most AKS implementations, it's really slow.
+/* The AKS primality algorithm for native integers.
+ *
+ * There are two versions here. The v6 algorithm from the latest AKS paper,
+ * as well as one with improvements from Bernstein and Voloch and better r/s
+ * selection derived from Folkmar Bornemann's 2002 Pari implementation.
+ *
+ * Note that AKS is very, very slow compared to other methods. It is, however,
+ * polynomial in log(N), and log-log performance graphs show nice straight
+ * lines for both implementations. However APR-CL and ECPP both start out
+ * much faster and the slope will be less for any sizes of N that we're
+ * interested in.
+ *
+ * For native 64-bit integers this is purely a coding exercise, as BPSW is
+ * a million times faster and gives proven results.
*
- * If we know there is a lgamma function (C99), then this uses the
- * improvements from Folkmar Bornemann's 2002 Pari implementation. This
- * includes Bernstein and Voloch's much, much better r/s selection. The
- * performance difference is huge.
*
* When n < 2^(wordbits/2)-1, we can do a straightforward intermediate:
* r = (r + a * b) % n
--
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