- Added the RangeNumber .each_squarefree_almost_prime(k, {...}) met…

…hod. Iterates over the squarefree k-almost primes in the self range a..b. Example: # iterate over squarefree semiprimes in the range 1..100 1..100 -> each_squarefree_almost_prime(2, { .say }) # iterate over squarefree 3-almost primes in the range 50..100 50..100 -> each_squarefree_almost_prime(3, { .say }) - Adjusted the stepping value when iterating over k-almost primes and squarefree k-almost primes for better performance.
trizen · Mar 9, 2021 · 14cd46e · 14cd46e
1 parent 0a48608
commit 14cd46e
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diff --git a/lib/Sidef/Types/Number/Number.pm b/lib/Sidef/Types/Number/Number.pm
@@ -994,7 +994,7 @@ package Sidef::Types::Number::Number {
                     $upto = $to;
                 }
 
-                ## say ":: Sieving ($from, $upto) with step = $step";
+                #~ say ":: Sieving ($from, $upto) with step = $step";
                 @buffer = @{$buffer_callback->($from, $upto)};
                 $from   = $upto + 1;
                 @buffer || next;
@@ -9933,6 +9933,18 @@ package Sidef::Types::Number::Number {
         CORE::int($n * (CORE::log($n) + CORE::log(CORE::log($n)) - 1));
     }
 
+    sub _nth_almost_prime_lower {
+        my ($n, $k) = @_;
+
+        my $factorial_km1 = 1;
+
+        for my $j (2 .. $k - 1) {
+            $factorial_km1 *= $j;
+        }
+
+        CORE::int(($n * CORE::log($n)) / ((CORE::log(CORE::log($n))**($k - 1)) / $factorial_km1));
+    }
+
     sub _prime_count_range {
         my ($x, $y) = @_;
 
@@ -15657,11 +15669,25 @@ package Sidef::Types::Number::Number {
 
         $k = _any2ui($$k) // return ZERO;
 
-        if (Math::GMPz::Rmpz_sgn($from) <= 0) {
-            $from = $ONE;
+        if (Math::GMPz::Rmpz_cmp_ui($from, $k) <= 0 and $k > 0) {
+            $from = Math::GMPz::Rmpz_init_set_ui(0);
+            Math::GMPz::Rmpz_setbit($from, $k);    # from = 2**k
         }
 
-        _generic_each($from, $to, $block, sub { 5e6 }, sub { _sieve_almost_primes($_[0], $_[1], $k) });
+#<<<
+        _generic_each($from, $to, $block, sub {
+                my ($from) = @_;
+
+                my $t    = Math::GMPz::Rmpz_get_d($from);
+                my $step = ($k > 0) ? (_nth_almost_prime_lower($t + CORE::log($t) * 2e4, $k) - _nth_almost_prime_lower($t, $k)) : 0;
+
+                if ($step <= 0 or $step > 1e9) {
+                    $step = 100_000_000 * $k;
+                }
+
+                $step;
+            }, sub { _sieve_almost_primes($_[0], $_[1], $k) });
+#>>>
     }
 
     *each_almost_prime = \&almost_primes_each;
@@ -15722,7 +15748,13 @@ package Sidef::Types::Number::Number {
             $from = $ONE;
         }
 
-        _generic_each($from, $to, $block, sub { 1e7 }, sub { _sieve_almost_primes($_[0], $_[1], $k, squarefree => 1) });
+        my $step = ($k > 8) ? Math::Prime::Util::GMP::pn_primorial($k) : 1e7;
+
+        if ($step > ULONG_MAX) {
+            $step = Math::GMPz::Rmpz_init_set_str($step, 10);
+        }
+
+        _generic_each($from, $to, $block, sub { $step }, sub { _sieve_almost_primes($_[0], $_[1], $k, squarefree => 1) });
     }
 
     *each_squarefree_almost_prime = \&squarefree_almost_primes_each;

diff --git a/lib/Sidef/Types/Range/RangeNumber.pm b/lib/Sidef/Types/Range/RangeNumber.pm
@@ -443,6 +443,25 @@ package Sidef::Types::Range::RangeNumber {
         return $self;
     }
 
+    sub each_squarefree_almost_prime {
+        my ($self, $k, $block) = @_;
+
+        $k = Sidef::Types::Number::Number->new($k);
+
+        if ($self->{step}->is_one) {
+
+            my $left  = Sidef::Types::Number::Number->new($self->{from});
+            my $right = Sidef::Types::Number::Number->new($self->{to});
+
+            Sidef::Types::Number::Number::each_squarefree_almost_prime($k, $left, $right, $block);
+            return $self;
+        }
+
+        $self->lazy->grep(Sidef::Types::Block::Block->new(code => sub { $_[0]->is_squarefree && $_[0]->is_almost_prime($k) }))
+          ->each($block);
+        return $self;
+    }
+
     sub dump {
         my ($self) = @_;
         Sidef::Types::String::String->new("$self");

diff --git a/lib/Sidef/Types/Range/RangeNumber.pod b/lib/Sidef/Types/Range/RangeNumber.pod
@@ -123,6 +123,14 @@ Return the
 
 =cut
 
+=head2 each_squarefree_almost_prime
+
+RangeNumber.each_squarefree_almost_prime() -> I<Obj>
+
+Return the
+
+=cut
+
 =head2 gcd
 
 RangeNumber.gcd() -> I<Obj>

diff --git a/scripts/Tests/number_methods.sf b/scripts/Tests/number_methods.sf
@@ -168,16 +168,31 @@ assert_eq(
     2.almost_primes(10, 100)
 )
 
+assert_eq(
+    gather { 10..100 -> each_squarefree_almost_prime(2, {|k| take(k) }) },
+    2.squarefree_almost_primes(10, 100)
+)
+
 assert_eq(
     gather { 10..100 -> each_almost_prime(3, {|k| take(k) }) },
     3.almost_primes(10, 100)
 )
 
+assert_eq(
+    gather { 10..100 -> each_squarefree_almost_prime(3, {|k| take(k) }) },
+    3.squarefree_almost_primes(10, 100)
+)
+
 assert_eq(
     gather { 10..100 `by` 3 -> each_almost_prime(3, {|k| take(k) }) },
     10..100 `by` 3 -> grep { .is_almost_prime(3) }
 )
 
+assert_eq(
+    gather { 10..200 `by` 3 -> each_squarefree_almost_prime(3, {|k| take(k) }) },
+    10..200 `by` 3 -> grep { .is_almost_prime(3) && .is_squarefree }
+)
+
 assert_eq(
     gather { 10..100 `by` 3 -> each_almost_prime(2, {|k| take(k) }) },
     10..100 `by` 3 -> grep { .is_almost_prime(2) }