[libmath-prime-util-perl] 21/35: Use Lehmer for small prime counts (below 8000 million), LMO for large

[Partha P. Mukherjee]

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ppm-guest pushed a commit to annotated tag v0.33
in repository libmath-prime-util-perl.

commit 126995b7335475361dc3cde621a6ed67e32cc211
Author: Dana Jacobsen <dana at acm.org>
Date:   Thu Nov 7 14:58:15 2013 -0800

    Use Lehmer for small prime counts (below 8000 million), LMO for large
---
 Changes                | 3 +++
 XS.xs                  | 3 +++
 lib/Math/Prime/Util.pm | 6 ++++--
 3 files changed, 10 insertions(+), 2 deletions(-)

diff --git a/Changes b/Changes
index 8c2726c..9cbb680 100644
--- a/Changes
+++ b/Changes
@@ -23,6 +23,9 @@ Revision history for Perl module Math::Prime::Util
 
     - Fixed Pure Perl 33- to 64-bit is_pseudoprime.
 
+    - prime_count uses Lehmer below a threshold (8000M), LMO above.
+      This keeps good performance while still using low memory.
+
     - Perl RiemannZeta changes:
 
       - Borwein Zeta calculations done in BigInt instead of BigFloat (speed).
diff --git a/XS.xs b/XS.xs
index f5b5f16..de47b4e 100644
--- a/XS.xs
+++ b/XS.xs
@@ -222,6 +222,9 @@ _XS_nth_prime(IN UV n)
 UV
 _XS_divisor_sum(IN UV n, IN UV k)
 
+UV
+_XS_legendre_phi(IN UV x, IN UV a)
+
 
 UV
 _get_prime_cache_size()
diff --git a/lib/Math/Prime/Util.pm b/lib/Math/Prime/Util.pm
index fc1603d..544af84 100644
--- a/lib/Math/Prime/Util.pm
+++ b/lib/Math/Prime/Util.pm
@@ -1910,8 +1910,10 @@ sub prime_count {
       #if ($est_lehmer < $est_segment) {
       if ( ($high / ($high-$low+1)) < 100 ) {
         my $count;
-        $count  = _XS_LMO_pi($high);
-        $count -= _XS_LMO_pi($low-1) if $low > 2;
+        $count  =   ($high > 8_000_000_000) ? _XS_LMO_pi($high)  : _XS_lehmer_pi($high);
+        if ($low > 2) {
+          $count -= ($low  > 8_000_000_000) ? _XS_LMO_pi($low-1) : _XS_lehmer_pi($low-1);
+        }
         return $count;
       }
     }

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