[libmath-prime-util-perl] 04/05: 10-15% speedup for ranged totient internals

[Partha P. Mukherjee]

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ppm-guest pushed a commit to annotated tag v0.31
in repository libmath-prime-util-perl.

commit a7281dcb418ab5accc00e44396f354f98534b076
Author: Dana Jacobsen <dana at acm.org>
Date:   Tue Aug 6 17:13:09 2013 -0700

    10-15% speedup for ranged totient internals
---
 Changes |  2 ++
 TODO    |  4 +++-
 util.c  | 26 +++++++++++++++-----------
 3 files changed, 20 insertions(+), 12 deletions(-)

diff --git a/Changes b/Changes
index 0446afb..3f6ab5e 100644
--- a/Changes
+++ b/Changes
@@ -7,6 +7,8 @@ Revision history for Perl module Math::Prime::Util
     - Some platforms were using __int128 when it wasn't supported.  Only
       x86_64 and Power64 use it now.
 
+    - Small speedup for ranged totient internals.
+
 0.30  2013-08-06
 
     [API Changes]
diff --git a/TODO b/TODO
index dc0f142..146dc4c 100644
--- a/TODO
+++ b/TODO
@@ -26,7 +26,9 @@
 
 - More efficient Mertens.  The current version has poor growth.
 
-- More efficient totient segment.  Do we really need primes to n/2?
+- It may be possible to have a more efficient ranged totient.  We're using
+  the sieve up to n/2, which is better than most people seem to use, but I'm
+  not completely convinced we can't do better.
 
 - Implement S2 calculation for LMO prime count.
 
diff --git a/util.c b/util.c
index f0742f4..523ce65 100644
--- a/util.c
+++ b/util.c
@@ -837,22 +837,26 @@ signed char* _moebius_range(UV lo, UV hi)
 
 UV* _totient_range(UV lo, UV hi) {
   UV* totients;
-  UV i, sievehi;
+  UV i, hidiv2;
   if (hi < lo) croak("_totient_range error hi %lu < lo %lu\n", hi, lo);
   New(0, totients, hi-lo+1, UV);
   if (totients == 0)
     croak("Could not get memory for %"UVuf" totients\n", hi);
-  for (i = lo; i <= hi; i++)
-    totients[i-lo] = i;
-  sievehi = hi/2;
-  for (i=P2GTLO(2*2,2,lo); i <= hi; i += 2) totients[i-lo] -= totients[i-lo]/2;
-  START_DO_FOR_EACH_PRIME(3, sievehi) {
-    for (i = P2GTLO(2*p,p,lo); i <= hi; i += p)
-      totients[i-lo] -= totients[i-lo]/p;
+  for (i = lo; i <= hi; i++) {
+    UV v = i;
+    if (i % 2 == 0)  v -= v/2;
+    if (i % 3 == 0)  v -= v/3;
+    if (i % 5 == 0)  v -= v/5;
+    totients[i-lo] = v;
+  }
+  hidiv2 = hi/2;
+  START_DO_FOR_EACH_PRIME(2, hi) {
+    if (p >= lo)
+      totients[p-lo] = p-1;
+    if (p >= 7 && p <= hidiv2)
+      for (i = P2GTLO(2*p,p,lo); i <= hi; i += p)
+        totients[i-lo] -= totients[i-lo]/p;
   } END_DO_FOR_EACH_PRIME
-  for (i = lo; i <= hi; i++)
-    if (totients[i-lo] == i)
-      totients[i-lo] = i-1;
   return totients;
 }
 

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