- Added the Number quadratic_nonresidue(n) method.

Returns the least quadratic non-residue of n. Also aliased as `qnr(n)`.

Example:

	say qnr(17676352761153241)	#=> 37
	say qnr(172138573277896681)	#=> 41

MANIFEST

@@ -903,6 +903,7 @@ scripts/Tests/prefix_methods.sf
 scripts/Tests/prefix_unary_operators.sf
 scripts/Tests/problem_of_apollonius.sf
 scripts/Tests/pythagorean_means.sf
+scripts/Tests/quadratic_nonresidue.sf
 scripts/Tests/quicksort.sf
 scripts/Tests/quoted_strings.sf
 scripts/Tests/rand_pick.sf

README.md

@@ -32,9 +32,9 @@ Sidef is a modern, high-level, general-purpose programming language, inspired by
 
 ### WWW
 
-* Gitbook: [https://trizen.gitbooks.io/sidef-lang](https://trizen.gitbooks.io/sidef-lang)
-* Tutorial: [https://github.com/trizen/sidef/wiki](https://github.com/trizen/sidef/wiki)
-* RosettaCode: [https://rosettacode.org/wiki/Sidef](https://rosettacode.org/wiki/Sidef)
+* Gitbook: https://trizen.gitbook.io/sidef-lang/ ([legacy](https://trizen.gitbooks.io/sidef-lang))
+* Tutorial: https://github.com/trizen/sidef/wiki
+* RosettaCode: https://rosettacode.org/wiki/Sidef
 
 ## EXAMPLES
 

lib/Sidef/Types/Number/Number.pm

@@ -6867,6 +6867,57 @@ package Sidef::Types::Number::Number {
         bless \$r;
     }
 
+    sub quadratic_nonresidue {
+        my ($n) = @_;
+
+        # Least quadratic non-residue of n. (OEIS: A020649)
+        # Inspired by Dana Jacobsen's code from Math::Prime::Util::PP.
+
+        $n = _any2mpz($$n) // goto &nan;
+
+        if (Math::GMPz::Rmpz_cmp_ui($n, 2) <= 0) {
+            return bless \$n;
+        }
+
+        if (Math::GMPz::Rmpz_ui_kronecker(2, $n) == -1) {
+            return TWO;
+        }
+
+        if (_primality_pretest($n) && Math::Prime::Util::GMP::is_prob_prime($n)) {
+            for (my $k = 3 ; ; $k = Math::Prime::Util::GMP::next_prime($k)) {
+                if (Math::GMPz::Rmpz_ui_kronecker($k, $n) == -1) {
+                    return __PACKAGE__->_set_uint($k);
+                }
+            }
+        }
+
+        if (Math::GMPz::Rmpz_even_p($n)) {
+            return TWO if Math::GMPz::Rmpz_scan1($n, 0) >= 2;
+        }
+
+        foreach my $k (3, 5, 11, 13, 19) {
+            if (Math::GMPz::Rmpz_divisible_ui_p($n, $k)) {
+                return TWO;
+            }
+        }
+
+        my %f;
+        ++$f{$_} for Math::Prime::Util::GMP::factor($n);
+
+        my @factors =
+          map { ($_ < ULONG_MAX) ? Math::GMPz::Rmpz_init_set_ui($_) : Math::GMPz::Rmpz_init_set_str($_, 10) } keys %f;
+
+        for (my $k = 2 ; ; $k = Math::Prime::Util::GMP::next_prime($k)) {
+            foreach my $p (@factors) {
+                if (Math::GMPz::Rmpz_cmp_ui($p, $k) > 0 and Math::GMPz::Rmpz_ui_kronecker($k, $p) == -1) {
+                    return __PACKAGE__->_set_uint($k);
+                }
+            }
+        }
+    }
+
+    *qnr = \&quadratic_nonresidue;
+
     sub sqrtmod {
         my ($x, $y) = @_;
         _valid(\$y);

scripts/Tests/quadratic_nonresidue.sf

@@ -0,0 +1,14 @@
+#!/usr/bin/ruby
+
+# Tests for the least quadratic non-residue of n.
+
+var a = %n[3277, 3281, 121463, 491209, 11530801, 512330281, 15656266201, 139309114031, 7947339136801, 72054898434289, 334152420730129, 17676352761153241, 172138573277896681]
+var b = %n[3, 7, 23, 71, 311, 479, 1559, 5711, 10559, 18191, 31391, 422231, 701399, 366791, 3818929, 9257329, 22000801, 36415991, 48473881, 175244281, 120293879, 427733329, 131486759, 3389934071, 2929911599, 7979490791, 36504256799, 23616331489, 89206899239, 121560956039]
+
+assert_eq(a.map { .qnr }, a.len.pn_primes)
+assert_eq(b.map { .qnr }, b.len.pn_primes)
+
+assert_eq(1..100 -> map { .prime.qnr }, %n[2, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 2, 2, 2, 7, 5, 3, 2, 3, 5, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 2, 7, 5, 2, 3, 2, 3, 2, 2, 3, 7, 7, 2, 3, 5, 2, 3, 2, 3, 2, 2, 2, 11, 5, 2, 2, 5, 2, 2, 3, 7, 3, 2, 2, 5, 2, 2, 3, 7, 2, 2, 7, 5, 3, 2, 3, 5, 2, 3, 2, 13, 3, 2, 2, 5, 2, 3, 2, 2])
+assert_eq(3..110 -> map { .qnr },       %n[2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 5, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 5, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 5, 2, 2, 5, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2])
+
+say "** Test passed!"