From d52bb1ffee5b64206a26323f7475c5aaf4a5046d Mon Sep 17 00:00:00 2001
From: trizen <trizen@protonmail.com>
Date: Thu, 7 Jan 2021 17:30:08 +0200
Subject: [PATCH] - Added the Number `flt_factor(n, tries=1e4)` method.

Tries to find a factor of `n`, using a new factorization method, inspired by Fermat's Little Theorem (FLT).

The method is particularily effective for numbers that have factors closed to each other, or have a factor `k` for which `znorder(2,k)` is small.

Example:

	say flt_factor(1759590140239532167230871849749630652332178307219845847129)	#=> [12072684186515582507, 145749703467343411357142937615495959947]
	say flt_factor(28168370236334094367936640078057043313881469151722840306493)	#=> [30426633744568826749, 925780041026134419587821276142742168257]

...taking 0.007s in total.
---
 lib/Sidef/Types/Number/Number.pm  | 50 +++++++++++++++++++++++++++++++
 lib/Sidef/Types/Number/Number.pod |  8 +++++
 2 files changed, 58 insertions(+)

diff --git a/lib/Sidef/Types/Number/Number.pm b/lib/Sidef/Types/Number/Number.pm
index 9ebd35f8a..1ac97eed6 100644
--- a/lib/Sidef/Types/Number/Number.pm
+++ b/lib/Sidef/Types/Number/Number.pm
@@ -12975,6 +12975,56 @@ package Sidef::Types::Number::Number {
         Sidef::Types::Array::Array->new([bless(\$n)]);
     }
 
+    # "Fermat's Little Theorem" factorization method
+    sub flt_factor {
+        my ($n, $k) = @_;
+        _valid(\$k) if defined($k);
+
+        $n = _any2mpz($$n) // return Sidef::Types::Array::Array->new();
+
+        if (defined($k)) {
+            $k = _any2ui($$k) // 1e4;
+        }
+        else {
+            $k = 1e4;
+        }
+
+        state $z = Math::GMPz::Rmpz_init_nobless();
+        state $t = Math::GMPz::Rmpz_init_nobless();
+
+        Math::GMPz::Rmpz_powm($z, $TWO, $n, $n);
+
+        # Cannot factor Fermat pseudoprimes
+        if (Math::GMPz::Rmpz_cmp_ui($z, 2) == 0) {
+            return Sidef::Types::Array::Array->new([bless \$n]);
+        }
+
+        for (my $j = 1 ; $j <= $k ; $j += 2) {
+
+            Math::GMPz::Rmpz_powm_ui($t, $TWO, $j, $n);
+            Math::GMPz::Rmpz_sub($t, $z, $t);
+            Math::GMPz::Rmpz_gcd($t, $t, $n);
+
+            if (Math::GMPz::Rmpz_cmp_ui($t, 1) > 0) {
+
+                if (Math::GMPz::Rmpz_cmp($t, $n) == 0) {
+                    return Sidef::Types::Array::Array->new([bless \$n]);
+                }
+
+                my $x = Math::GMPz::Rmpz_init();
+                my $y = Math::GMPz::Rmpz_init();
+
+                Math::GMPz::Rmpz_set($y, $t);
+                Math::GMPz::Rmpz_divexact($x, $n, $t);
+
+                my @f = map { bless \$_ } sort { Math::GMPz::Rmpz_cmp($a, $b) } ($x, $y);
+                return Sidef::Types::Array::Array->new(\@f);
+            }
+        }
+
+        Sidef::Types::Array::Array->new([bless(\$n)]);
+    }
+
     sub squfof_factor {
         my ($n, $k) = @_;
         _valid(\$k) if defined($k);
diff --git a/lib/Sidef/Types/Number/Number.pod b/lib/Sidef/Types/Number/Number.pod
index 76b425efd..4b1cfc0df 100644
--- a/lib/Sidef/Types/Number/Number.pod
+++ b/lib/Sidef/Types/Number/Number.pod
@@ -1902,6 +1902,14 @@ Return the
 
 =cut
 
+=head2 flt_factor
+
+Number.flt_factor() -> I<Obj>
+
+Return the
+
+=cut
+
 =head2 gcd
 
 Number.gcd() -> I<Obj>