Version 23.03

MANIFEST

@@ -195,7 +195,9 @@ scripts/extend_your_language.sf
 'scripts/Extended tests/chebyshev_factorization_method.sf'
 'scripts/Extended tests/digits2num.pl'
 'scripts/Extended tests/fermat_pseudoprimes.sf'
+'scripts/Extended tests/fermat_pseudoprimes_to_base_n.sf'
 'scripts/Extended tests/fermat_with_n_factors.sf'
+'scripts/Extended tests/fermat_with_n_factors_to_base_n.sf'
 'scripts/Extended tests/inverse_of_multiplicative_functions.sf'
 'scripts/Extended tests/inverse_sigma.sf'
 'scripts/Extended tests/is_almost_prime.sf'
@@ -218,7 +220,9 @@ scripts/extend_your_language.sf
 'scripts/Extended tests/range_sum.sf'
 'scripts/Extended tests/sqrtmod.pl'
 'scripts/Extended tests/squarefree_pseudoprimes.sf'
+'scripts/Extended tests/strong_fermat_pseudoprimes_to_base_n.sf'
 'scripts/Extended tests/strong_fermat_with_n_factors.sf'
+'scripts/Extended tests/strong_fermat_with_n_factors_to_base_n.sf'
 'scripts/Extended tests/sumdigits.pl'
 scripts/fast_fourier_transform.sf
 scripts/faulhaber_s_formula.sf

bin/sidef

@@ -897,7 +897,7 @@ Outputs:
 The interactive mode (a.k.a. REPL) is available by simply executing the C<sidef> command, or by specifying the C<-i> command-line switch:
 
     $ sidef -i
-    Sidef 22.12, running on Linux, using Perl v5.36.0.
+    Sidef 23.03, running on Linux, using Perl v5.36.0.
     Type "help", "copyright" or "license" for more information.
     > n = 41
     #1 = 41

lib/Sidef.pm

@@ -3,7 +3,7 @@ package Sidef {
     use utf8;
     use 5.016;
 
-    our $VERSION = '22.12';
+    our $VERSION = '23.03';
 
     our $SPACES      = 0;    # the current number of indentation spaces
     our $SPACES_INCR = 4;    # the number of indentation spaces

scripts/Extended tests/fermat_pseudoprimes_to_base_n.sf

@@ -0,0 +1,45 @@
+#!/usr/bin/ruby
+
+# Tests for the Number "fermat_psp" method.
+
+# Timings:
+#   04 March 2023: 2.813s (with MPU)
+#   04 March 2023: 3.690s (without MPU)
+
+func T(n,k) {       # OEIS: A271873
+    if (n < 2) {
+        return []
+    }
+
+    var x = 1
+    var y = 2*x
+
+    loop {
+        var v = k.fermat_psp(n,x,y)
+        v.len >= 1 && return v[0]
+        x = y+1
+        y = 2*x
+    }
+}
+
+assert_eq(
+    {|x| {|y| T(x,y) }.map(2..6) }.map(2..6),
+    [
+        %n[341  561 11305   825265  45593065]
+        %n[ 91  286 41041   825265 130027051]
+        %n[ 15  435 11305   418285  30534805]
+        %n[124  561 41041  2203201  68800501]
+        %n[ 35 1105 25585   682465  12306385]
+    ]
+)
+
+assert_eq(
+    {|k|
+        {|n|
+            T(n, k - n + 2)
+        }.map(2..k)
+    }.map(2..14).flat,
+    %n[341, 561, 91, 11305, 286, 15, 825265, 41041, 435, 124, 45593065, 825265, 11305, 561, 35, 370851481, 130027051, 418285, 41041, 1105, 6, 38504389105, 2531091745, 30534805, 2203201, 25585, 561, 21, 7550611589521, 38504389105, 370851481, 68800501, 682465, 62745, 105, 28, 277960972890601, 5342216661145, 38504389105, 979865601, 12306385, 902785, 1365, 286, 33, 32918038719446881, 929845918823185, 7550611589521, 232250619601, 305246305, 87570145, 121485, 2926, 561, 10, 1730865304568301265, 36116918534792305, 277960972890601, 9746347772161, 16648653385, 9073150801, 2103465, 421876, 41041, 70, 65, 606395069520916762801, 6748244949134115505, 32918038719446881, 1237707914764321, 1387198666945, 211215631705, 96537441, 5533066, 1242241, 1330, 385, 6, 59989606772480422038001, 144331068898382107105, 1730865304568301265, 21083752607078161, 75749848475665, 24465723528961, 3958035081, 85851766, 68800501, 668865, 5005, 105, 15]
+)
+
+say ":: Test passed!"

scripts/Extended tests/fermat_with_n_factors_to_base_n.sf

@@ -0,0 +1,38 @@
+#!/usr/bin/ruby
+
+# Smallest base-n Fermat pseudoprime with n distinct prime factors.
+# https://oeis.org/A271874
+
+# Timings:
+#   04 march 2023: 3.305s (with MPU)
+#   04 march 2023: 3.637s (without MPU)
+
+func a(n) {
+    return nil if (n < 2)
+
+    var x = 1
+    var y = 2*x
+
+    loop {
+        #say "Sieving range: #{[x,y]}"
+        var arr = n.fermat_psp(n,x,y)
+
+        if (arr.len >= 1) {
+            return arr[0]
+        }
+
+        x = y+1
+        y = 2*x
+    }
+}
+
+var arr = gather {
+    for n in (2..16) {
+        say "a(#{n}) = #{take(a(n))}"
+    }
+}
+
+assert_eq(
+    arr,
+    %n[341, 286, 11305, 2203201, 12306385, 9073150801, 3958035081, 2539184851126, 152064312120721, 10963650080564545, 378958695265110961, 1035551157050957605345, 57044715596229144811105, 6149883077429715389052001, 426634466310819456228926101]
+)

scripts/Extended tests/pseudoprimes.sf

@@ -2,6 +2,10 @@
 
 # Extended tests for some pseudoprime-related functions.
 
+# Timings:
+#   5 Mar 2023: 5.869s (with MPU)
+#   5 Mar 2023: 8.218s (without MPU)
+
 assert_eq(
     13.lucas_carmichael(2*409810997884396741919),
     %n[409810997884396741919, 527999053751911334879, 752983545644288511839, 760276539527430038399, 761686421126390272799, 777695624868402683135]

scripts/Extended tests/strong_fermat_pseudoprimes_to_base_n.sf

@@ -0,0 +1,45 @@
+#!/usr/bin/ruby
+
+# Tests for the Number "strong_fermat_psp" method.
+
+# Timings:
+#   05 March 2023: 1.617s (with MPU)
+#   05 March 2023: 2.512s (without MPU)
+
+func T(n,k) {       # OEIS: A271873
+    if (n < 2) {
+        return []
+    }
+
+    var x = 1
+    var y = 2*x
+
+    loop {
+        var v = k.strong_fermat_psp(n,x,y)
+        v.len >= 1 && return v[0]
+        x = y+1
+        y = 2*x
+    }
+}
+
+assert_eq(
+    {|x| {|y| T(x,y) }.map(2..6) }.map(2..6),
+    [
+        %n[2047, 15841,  800605, 293609485,  10761055201]
+        %n[ 703,  8911,  152551,  41341321,  12283706701]
+        %n[ 341,  4371,  129921,   9224391,   2592053871]
+        %n[ 781, 24211, 4382191, 381347461,   9075517561]
+        %n[ 217, 29341, 3405961, 557795161, 333515107081]
+    ]
+)
+
+assert_eq(
+    {|k|
+        {|n|
+            T(n, k - n + 2)
+        }.map(2..k)
+    }.map(2..10).flat,
+    %n[2047, 15841, 703, 800605, 8911, 341, 293609485, 152551, 4371, 781, 10761055201, 41341321, 129921, 24211, 217, 5478598723585, 12283706701, 9224391, 4382191, 29341, 325, 713808066913201, 1064404682551, 2592053871, 381347461, 3405961, 58825, 65, 90614118359482705, 19142275066201, 201068525791, 9075517561, 557795161, 1611805, 15841, 91, 5993318051893040401, 31475449738947061, 15804698567581, 2459465259031, 333515107081, 299048101, 205465, 1729, 91]
+)
+
+say ":: Test passed!"

scripts/Extended tests/strong_fermat_with_n_factors_to_base_n.sf

@@ -0,0 +1,37 @@
+#!/usr/bin/ruby
+
+# Smallest base-n strong Fermat pseudoprime with n distinct prime factors.
+
+# Timings:
+#   04 march 2023: 1.308s (with MPU)
+#   04 march 2023: 1.929s (without MPU)
+
+func a(n) {
+    return nil if (n < 2)
+
+    var x = 1
+    var y = 2*x
+
+    loop {
+        #say "Sieving range: #{[x,y]}"
+        var arr = n.strong_fermat_psp(n,x,y)
+
+        if (arr.len >= 1) {
+            return arr[0]
+        }
+
+        x = y+1
+        y = 2*x
+    }
+}
+
+var arr = gather {
+    for n in (2..9) {
+        say "a(#{n}) = #{take(a(n))}"
+    }
+}
+
+assert_eq(
+    arr,
+    %n[2047, 8911, 129921, 381347461, 333515107081, 37388680793101, 713808066913201, 665242007427361]
+)