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ppm-guest pushed a commit to annotated tag v0.40
in repository libmath-prime-util-perl.
commit 2caa6e5709c03674694305a465d7e2104593cac7
Author: Dana Jacobsen <d...@acm.org>
Date: Fri Mar 28 12:43:41 2014 -0700
Small nth_twin_prime speedup. xt test for twin_prime_count
---
MANIFEST | 1 +
util.c | 14 +++++-----
xt/twin_prime_count.t | 76 +++++++++++++++++++++++++++++++++++++++++++++++++++
3 files changed, 84 insertions(+), 7 deletions(-)
diff --git a/MANIFEST b/MANIFEST
index 554f354..31a067d 100644
--- a/MANIFEST
+++ b/MANIFEST
@@ -145,4 +145,5 @@ xt/test-primes-script2.pl
xt/test-factor-yafu.pl
xt/test-nextprime-yafu.pl
xt/test-ispower.pl
+xt/twin_prime_count.t
.travis.yml
diff --git a/util.c b/util.c
index 771c52a..6a46b47 100644
--- a/util.c
+++ b/util.c
@@ -966,14 +966,14 @@ UV nth_twin_prime(UV n)
void* ctx = start_segment_primes(beg, end, &segment);
while (next_segment_primes(ctx, &seg_base, &seg_low, &seg_high)) {
UV p, bytes = (seg_high-seg_low+29)/30;
+ UV s = ((UV)segment[0]) << 8;
for (p = 0; p < bytes; p++) {
- UV s = segment[p];
- int twin1 = !(s & 0x0C);
- int twin2 = !(s & 0x30);
- int twin3 = !(s & 0x80) && ((p+1 < bytes) ? !(segment[p+1] & 0x01) :
_XS_is_prime(seg_high+2));
- if (twin1 && !--n) { nth=seg_base+p*30+11; break; }
- if (twin2 && !--n) { nth=seg_base+p*30+17; break; }
- if (twin3 && !--n) { nth=seg_base+p*30+29; break; }
+ s >>= 8;
+ if (p+1 < bytes) s |= (((UV)segment[p+1]) << 8);
+ else if (!_XS_is_prime(seg_high+2)) s |= 0xFF00;
+ if (!(s & 0x000C) && !--n) { nth=seg_base+p*30+11; break; }
+ if (!(s & 0x0030) && !--n) { nth=seg_base+p*30+17; break; }
+ if (!(s & 0x0180) && !--n) { nth=seg_base+p*30+29; break; }
}
if (n == 0) break;
}
diff --git a/xt/twin_prime_count.t b/xt/twin_prime_count.t
new file mode 100644
index 0000000..a7898a3
--- /dev/null
+++ b/xt/twin_prime_count.t
@@ -0,0 +1,76 @@
+#!/usr/bin/env perl
+use strict;
+use warnings;
+
+use Test::More;
+use Math::Prime::Util qw/twin_prime_count/;
+
+# 2^n using primesieve (fast), double checked with Pari 2.7.0 (slow):
+# a(n)=my(s, p=2); forprime(q=3, 2^n, if(q-p==2, s++); p=q); s
+# for (i=1,35,print(2^i," ", a(i)))
+# 10^n from tables
+my %tpcvals = (
+ 1 => 0,
+ 2 => 0,
+ 4 => 1,
+ 8 => 2,
+ 16 => 3,
+ 32 => 5,
+ 64 => 7,
+ 128 => 10,
+ 256 => 17,
+ 512 => 24,
+ 1024 => 36,
+ 2048 => 62,
+ 4096 => 107,
+ 8192 => 177,
+ 16384 => 290,
+ 32768 => 505,
+ 65536 => 860,
+ 131072 => 1526,
+ 262144 => 2679,
+ 524288 => 4750,
+ 1048576 => 8535,
+ 2097152 => 15500,
+ 4194304 => 27995,
+ 8388608 => 50638,
+ 16777216 => 92246,
+ 33554432 => 168617,
+ 67108864 => 309561,
+ 134217728 => 571313,
+ 268435456 => 1056281,
+ 536870912 => 1961080,
+ 1073741824 => 3650557,
+ 2147483648 => 6810670,
+ 4294967296 => 12739574,
+ 8589934592 => 23878645,
+ 17179869184 => 44849427,
+ 34359738368 => 84384508,
+ 68719476736 => 159082253,
+# 137438953472 => 300424743,
+ 10 => 2,
+ 100 => 8,
+ 1000 => 35,
+ 10000 => 205,
+ 100000 => 1224,
+ 1000000 => 8169,
+ 10000000 => 58980,
+ 100000000 => 440312,
+ 1000000000 => 3424506,
+ 10000000000 => 27412679,
+ 100000000000 => 224376048,
+ 1000000000000 => 1870585220,
+ 10000000000000 => 15834664872,
+ 100000000000000 => 135780321665,
+ 1000000000000000 => 1177209242304,
+ 10000000000000000 => 10304195697298,
+ 100000000000000000 => 90948839353159,
+ 1000000000000000000 => 808675888577436,
+);
+
+plan tests => scalar(keys %tpcvals);
+
+foreach my $n (sort {$a <=> $b} keys %tpcvals) {
+ my $tpc = $tpcvals{$n};
+ is( twin_prime_count($n), $tpc, "Pi_2($n) = $tpc" );
+}
--
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