#include this file into another for subclass testing my $version = ${"$class\::VERSION"}; use strict; ############################################################################## # for testing inheritance of _swap package Math::Foo; use Math::BigInt lib => $main::CL; use vars qw/@ISA/; @ISA = (qw/Math::BigInt/); use overload # customized overload for sub, since original does not use swap there '-' => sub { my @a = ref($_[0])->_swap(@_); $a[0]->bsub($a[1])}; sub _swap { # a fake _swap, which reverses the params my $self = shift; # for override in subclass if ($_[2]) { my $c = ref ($_[0] ) || 'Math::Foo'; return ( $_[0]->copy(), $_[1] ); } else { return ( Math::Foo->new($_[1]), $_[0] ); } } ############################################################################## package main; my $CALC = $class->config()->{lib}; ok ($CALC,$CL); my ($f,$z,$a,$exp,@a,$m,$e,$round_mode,$expected_class); while () { chomp; next if /^#/; # skip comments if (s/^&//) { $f = $_; next; } elsif (/^\$/) { $round_mode = $_; $round_mode =~ s/^\$/$class\->/; next; } @args = split(/:/,$_,99); $ans = pop(@args); $expected_class = $class; if ($ans =~ /(.*?)=(.*)/) { $expected_class = $2; $ans = $1; } $try = "\$x = $class->new(\"$args[0]\");"; if ($f eq "bnorm") { $try = "\$x = $class->bnorm(\"$args[0]\");"; # some is_xxx tests } elsif ($f =~ /^is_(zero|one|odd|even|negative|positive|nan|int)$/) { $try .= "\$x->$f() || 0;"; } elsif ($f eq "is_inf") { $try .= "\$x->is_inf('$args[1]');"; } elsif ($f eq "binf") { $try .= "\$x->binf('$args[1]');"; } elsif ($f eq "bone") { $try .= "\$x->bone('$args[1]');"; # some unary ops } elsif ($f =~ /^b(nan|floor|ceil|sstr|neg|abs|inc|dec|not|sqrt|fac)$/) { $try .= "\$x->$f();"; } elsif ($f =~ /^(numify|length|stringify|as_hex|as_bin)$/) { $try .= "\$x->$f();"; } elsif ($f eq "exponent"){ # ->bstr() to see if an object is returned $try .= '$x = $x->exponent()->bstr();'; } elsif ($f eq "mantissa"){ # ->bstr() to see if an object is returned $try .= '$x = $x->mantissa()->bstr();'; } elsif ($f eq "parts"){ $try .= '($m,$e) = $x->parts();'; # ->bstr() to see if an object is returned $try .= '$m = $m->bstr(); $m = "NaN" if !defined $m;'; $try .= '$e = $e->bstr(); $e = "NaN" if !defined $e;'; $try .= '"$m,$e";'; }elsif ($f eq "bexp"){ $try .= "\$x->bexp();"; } else { # binary ops $try .= "\$y = $class->new('$args[1]');"; if ($f eq "bcmp") { $try .= '$x->bcmp($y);'; } elsif ($f eq "bround") { $try .= "$round_mode; \$x->bround(\$y);"; } elsif ($f eq "bacmp"){ $try .= '$x->bacmp($y);'; } elsif ($f eq "badd"){ $try .= '$x + $y;'; } elsif ($f eq "bsub"){ $try .= '$x - $y;'; } elsif ($f eq "bmul"){ $try .= '$x * $y;'; } elsif ($f eq "bdiv"){ $try .= '$x / $y;'; } elsif ($f eq "bdiv-list"){ $try .= 'join (",",$x->bdiv($y));'; # overload via x= } elsif ($f =~ /^.=$/){ $try .= "\$x $f \$y;"; # overload via x } elsif ($f =~ /^.$/){ $try .= "\$x $f \$y;"; } elsif ($f eq "bmod"){ $try .= '$x % $y;'; } elsif ($f eq "bgcd") { if (defined $args[2]) { $try .= " \$z = $class->new('$args[2]'); "; } $try .= "$class\::bgcd(\$x, \$y"; $try .= ", \$z" if (defined $args[2]); $try .= " );"; } elsif ($f eq "blcm") { if (defined $args[2]) { $try .= " \$z = $class->new('$args[2]'); "; } $try .= "$class\::blcm(\$x, \$y"; $try .= ", \$z" if (defined $args[2]); $try .= " );"; }elsif ($f eq "blsft"){ if (defined $args[2]) { $try .= "\$x->blsft(\$y,$args[2]);"; } else { $try .= "\$x << \$y;"; } }elsif ($f eq "brsft"){ if (defined $args[2]) { $try .= "\$x->brsft(\$y,$args[2]);"; } else { $try .= "\$x >> \$y;"; } }elsif ($f eq "bnok"){ $try .= "\$x->bnok(\$y);"; }elsif ($f eq "broot"){ $try .= "\$x->broot(\$y);"; }elsif ($f eq "blog"){ $try .= "\$x->blog(\$y);"; }elsif ($f eq "band"){ $try .= "\$x & \$y;"; }elsif ($f eq "bior"){ $try .= "\$x | \$y;"; }elsif ($f eq "bxor"){ $try .= "\$x ^ \$y;"; }elsif ($f eq "bpow"){ $try .= "\$x ** \$y;"; } elsif( $f eq "bmodinv") { $try .= "\$x->bmodinv(\$y);"; }elsif ($f eq "digit"){ $try .= "\$x->digit(\$y);"; } else { $try .= "\$z = $class->new(\"$args[2]\");"; # Functions with three arguments if( $f eq "bmodpow") { $try .= "\$x->bmodpow(\$y,\$z);"; } else { warn "Unknown op '$f'"; } } } # end else all other ops $ans1 = eval $try; # convert hex/binary targets to decimal if ($ans =~ /^(0x0x|0b0b)/) { $ans =~ s/^0[xb]//; $ans = Math::BigInt->new($ans)->bstr(); } if ($ans eq "") { ok_undef ($ans1); } else { # print "try: $try ans: $ans1 $ans\n"; print "# Tried: '$try'\n" if !ok ($ans1, $ans); ok (ref($ans),$expected_class) if $expected_class ne $class; } # check internal state of number objects is_valid($ans1,$f) if ref $ans1; } # endwhile data tests close DATA; # test some more @a = (); for (my $i = 1; $i < 10; $i++) { push @a, $i; } ok "@a", "1 2 3 4 5 6 7 8 9"; # test whether self-multiplication works correctly (result is 2**64) $try = "\$x = $class->new('4294967296');"; $try .= '$a = $x->bmul($x);'; $ans1 = eval $try; print "# Tried: '$try'\n" if !ok ($ans1, $class->new(2) ** 64); # test self-pow $try = "\$x = $class->new(10);"; $try .= '$a = $x->bpow($x);'; $ans1 = eval $try; print "# Tried: '$try'\n" if !ok ($ans1, $class->new(10) ** 10); ############################################################################### # test whether op destroys args or not (should better not) $x = $class->new(3); $y = $class->new(4); $z = $x & $y; ok ($x,3); ok ($y,4); ok ($z,0); $z = $x | $y; ok ($x,3); ok ($y,4); ok ($z,7); $x = $class->new(1); $y = $class->new(2); $z = $x | $y; ok ($x,1); ok ($y,2); ok ($z,3); $x = $class->new(5); $y = $class->new(4); $z = $x ^ $y; ok ($x,5); ok ($y,4); ok ($z,1); $x = $class->new(-5); $y = -$x; ok ($x, -5); $x = $class->new(-5); $y = abs($x); ok ($x, -5); $x = $class->new(8); $y = $class->new(-1); $z = $class->new(5033); my $u = $x->copy()->bmodpow($y,$z); ok ($u,4404); ok ($y,-1); ok ($z,5033); $x = $class->new(-5); $y = -$x; ok ($x,-5); ok ($y,5); $x = $class->new(-5); $y = $x->copy()->bneg(); ok ($x,-5); ok ($y,5); $x = $class->new(-5); $y = $class->new(3); $x->bmul($y); ok ($x,-15); ok ($y,3); $x = $class->new(-5); $y = $class->new(3); $x->badd($y); ok ($x,-2); ok ($y,3); $x = $class->new(-5); $y = $class->new(3); $x->bsub($y); ok ($x,-8); ok ($y,3); $x = $class->new(-15); $y = $class->new(3); $x->bdiv($y); ok ($x,-5); ok ($y,3); $x = $class->new(-5); $y = $class->new(3); $x->bmod($y); ok ($x,1); ok ($y,3); $x = $class->new(5); $y = $class->new(3); $x->bmul($y); ok ($x,15); ok ($y,3); $x = $class->new(5); $y = $class->new(3); $x->badd($y); ok ($x,8); ok ($y,3); $x = $class->new(5); $y = $class->new(3); $x->bsub($y); ok ($x,2); ok ($y,3); $x = $class->new(15); $y = $class->new(3); $x->bdiv($y); ok ($x,5); ok ($y,3); $x = $class->new(5); $y = $class->new(3); $x->bmod($y); ok ($x,2); ok ($y,3); $x = $class->new(5); $y = $class->new(-3); $x->bmul($y); ok ($x,-15); ok($y,-3); $x = $class->new(5); $y = $class->new(-3); $x->badd($y); ok ($x,2); ok($y,-3); $x = $class->new(5); $y = $class->new(-3); $x->bsub($y); ok ($x,8); ok($y,-3); $x = $class->new(15); $y = $class->new(-3); $x->bdiv($y); ok ($x,-5); ok($y,-3); $x = $class->new(5); $y = $class->new(-3); $x->bmod($y); ok ($x,-1); ok($y,-3); ############################################################################### # check whether overloading cmp works $try = "\$x = $class->new(0);"; $try .= "\$y = 10;"; $try .= "'false' if \$x ne \$y;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "false" ); # we cant test for working cmpt with other objects here, we would need a dummy # object with stringify overload for this. see Math::String tests as example ############################################################################### # check reversed order of arguments $try = "\$x = $class->new(10); \$x = 2 ** \$x;"; $try .= "'ok' if \$x == 1024;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); $try = "\$x = $class->new(10); \$x = 2 * \$x;"; $try .= "'ok' if \$x == 20;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); $try = "\$x = $class->new(10); \$x = 2 + \$x;"; $try .= "'ok' if \$x == 12;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); $try = "\$x = $class\->new(10); \$x = 2 - \$x;"; $try .= "'ok' if \$x == -8;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); $try = "\$x = $class\->new(10); \$x = 20 / \$x;"; $try .= "'ok' if \$x == 2;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); $try = "\$x = $class\->new(3); \$x = 20 % \$x;"; $try .= "'ok' if \$x == 2;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); $try = "\$x = $class\->new(7); \$x = 20 & \$x;"; $try .= "'ok' if \$x == 4;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); $try = "\$x = $class\->new(7); \$x = 0x20 | \$x;"; $try .= "'ok' if \$x == 0x27;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); $try = "\$x = $class\->new(7); \$x = 0x20 ^ \$x;"; $try .= "'ok' if \$x == 0x27;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); ############################################################################### # check badd(4,5) form $try = "\$x = $class\->badd(4,5);"; $try .= "'ok' if \$x == 9;"; $ans = eval $try; print "# For '$try'\n" if (!ok "$ans" , "ok" ); ############################################################################### # check undefs: NOT DONE YET ############################################################################### # bool $x = $class->new(1); if ($x) { ok (1,1); } else { ok($x,'to be true') } $x = $class->new(0); if (!$x) { ok (1,1); } else { ok($x,'to be false') } ############################################################################### # objectify() @args = Math::BigInt::objectify(2,4,5); ok (scalar @args,3); # $class, 4, 5 ok ($args[0] =~ /^Math::BigInt/); ok ($args[1],4); ok ($args[2],5); @args = Math::BigInt::objectify(0,4,5); ok (scalar @args,3); # $class, 4, 5 ok ($args[0] =~ /^Math::BigInt/); ok ($args[1],4); ok ($args[2],5); @args = Math::BigInt::objectify(2,4,5); ok (scalar @args,3); # $class, 4, 5 ok ($args[0] =~ /^Math::BigInt/); ok ($args[1],4); ok ($args[2],5); @args = Math::BigInt::objectify(2,4,5,6,7); ok (scalar @args,5); # $class, 4, 5, 6, 7 ok ($args[0] =~ /^Math::BigInt/); ok ($args[1],4); ok (ref($args[1]),$args[0]); ok ($args[2],5); ok (ref($args[2]),$args[0]); ok ($args[3],6); ok (ref($args[3]),''); ok ($args[4],7); ok (ref($args[4]),''); @args = Math::BigInt::objectify(2,$class,4,5,6,7); ok (scalar @args,5); # $class, 4, 5, 6, 7 ok ($args[0],$class); ok ($args[1],4); ok (ref($args[1]),$args[0]); ok ($args[2],5); ok (ref($args[2]),$args[0]); ok ($args[3],6); ok (ref($args[3]),''); ok ($args[4],7); ok (ref($args[4]),''); ############################################################################### # test whether an opp calls objectify properly or not (or at least does what # it should do given non-objects, w/ or w/o objectify()) ok ($class->new(123)->badd(123),246); ok ($class->badd(123,321),444); ok ($class->badd(123,$class->new(321)),444); ok ($class->new(123)->bsub(122),1); ok ($class->bsub(321,123),198); ok ($class->bsub(321,$class->new(123)),198); ok ($class->new(123)->bmul(123),15129); ok ($class->bmul(123,123),15129); ok ($class->bmul(123,$class->new(123)),15129); ok ($class->new(15129)->bdiv(123),123); ok ($class->bdiv(15129,123),123); ok ($class->bdiv(15129,$class->new(123)),123); ok ($class->new(15131)->bmod(123),2); ok ($class->bmod(15131,123),2); ok ($class->bmod(15131,$class->new(123)),2); ok ($class->new(2)->bpow(16),65536); ok ($class->bpow(2,16),65536); ok ($class->bpow(2,$class->new(16)),65536); ok ($class->new(2**15)->brsft(1),2**14); ok ($class->brsft(2**15,1),2**14); ok ($class->brsft(2**15,$class->new(1)),2**14); ok ($class->new(2**13)->blsft(1),2**14); ok ($class->blsft(2**13,1),2**14); ok ($class->blsft(2**13,$class->new(1)),2**14); ############################################################################### # test for floating-point input (other tests in bnorm() below) $z = 1050000000000000; # may be int on systems with 64bit? $x = $class->new($z); ok ($x->bsstr(),'105e+13'); # not 1.05e+15 $z = 1e+129; # definitely a float (may fail on UTS) # don't compare to $z, since some Perl versions stringify $z into something # like '1.e+129' or something equally ugly $x = $class->new($z); ok ($x->bsstr(),'1e+129'); ############################################################################### # test for whitespace inlcuding newlines to be handled correctly # ok ($Math::BigInt::strict,1); # the default foreach my $c ( qw/1 12 123 1234 12345 123456 1234567 12345678 123456789 1234567890/) { my $m = $class->new($c); ok ($class->new("$c"),$m); ok ($class->new(" $c"),$m); ok ($class->new("$c "),$m); ok ($class->new(" $c "),$m); ok ($class->new("\n$c"),$m); ok ($class->new("$c\n"),$m); ok ($class->new("\n$c\n"),$m); ok ($class->new(" \n$c\n"),$m); ok ($class->new(" \n$c \n"),$m); ok ($class->new(" \n$c\n "),$m); ok ($class->new(" \n$c\n1"),'NaN'); ok ($class->new("1 \n$c\n1"),'NaN'); } ############################################################################### # prime number tests, also test for **= and length() # found on: http://www.utm.edu/research/primes/notes/by_year.html # ((2^148)-1)/17 $x = $class->new(2); $x **= 148; $x++; $x = $x / 17; ok ($x,"20988936657440586486151264256610222593863921"); ok ($x->length(),length "20988936657440586486151264256610222593863921"); # MM7 = 2^127-1 $x = $class->new(2); $x **= 127; $x--; ok ($x,"170141183460469231731687303715884105727"); $x = $class->new('215960156869840440586892398248'); ($x,$y) = $x->length(); ok ($x,30); ok ($y,0); $x = $class->new('1_000_000_000_000'); ($x,$y) = $x->length(); ok ($x,13); ok ($y,0); # test <<=, >>= $x = $class->new('2'); my $y = $class->new('18'); ok ($x <<= $y, 2 << 18); ok ($x, 2 << 18); ok ($x >>= $y, 2); ok ($x, 2); # I am afraid the following is not yet possible due to slowness # Also, testing for 2 meg output is a bit hard ;) #$x = $class->new(2); $x **= 6972593; $x--; # 593573509*2^332162+1 has exactly 1,000,000 digits # takes about 24 mins on 300 Mhz, so cannot be done yet ;) #$x = $class->new(2); $x **= 332162; $x *= "593573509"; $x++; #ok ($x->length(),1_000_000); ############################################################################### # inheritance and overriding of _swap $x = Math::Foo->new(5); $x = $x - 8; # 8 - 5 instead of 5-8 ok ($x,3); ok (ref($x),'Math::Foo'); $x = Math::Foo->new(5); $x = 8 - $x; # 5 - 8 instead of 8 - 5 ok ($x,-3); ok (ref($x),'Math::Foo'); ############################################################################### # Test whether +inf eq inf # This tried to test whether BigInt inf equals Perl inf. Unfortunately, Perl # hasn't (before 5.7.3 at least) a consistent way to say inf, and some things # like 1e100000 crash on some platforms. So simple test for the string 'inf' $x = $class->new('+inf'); ok ($x,'inf'); ############################################################################### ############################################################################### # the followin tests only make sense with Math::BigInt::Calc or BareCalc or # FastCalc exit if $CALC !~ /^Math::BigInt::(|Bare|Fast)Calc$/; # for Pari et al. ############################################################################### # check proper length of internal arrays my $bl = $CL->_base_len(); my $BASE = '9' x $bl; my $MAX = $BASE; $BASE++; $x = $class->new($MAX); is_valid($x); # f.i. 9999 $x += 1; ok ($x,$BASE); is_valid($x); # 10000 $x -= 1; ok ($x,$MAX); is_valid($x); # 9999 again ############################################################################### # check numify $x = $class->new($BASE-1); ok ($x->numify(),$BASE-1); $x = $class->new(-($BASE-1)); ok ($x->numify(),-($BASE-1)); # +0 is to protect from 1e15 vs 100000000 (stupid to_string aaaarglburblll...) $x = $class->new($BASE); ok ($x->numify()+0,$BASE+0); $x = $class->new(-$BASE); ok ($x->numify(),-$BASE); $x = $class->new( -($BASE*$BASE*1+$BASE*1+1) ); ok($x->numify(),-($BASE*$BASE*1+$BASE*1+1)); ############################################################################### # test bug in _digits with length($c[-1]) where $c[-1] was "00001" instead of 1 $x = $class->new($BASE-2); $x++; $x++; $x++; $x++; if ($x > $BASE) { ok (1,1) } else { ok ("$x < $BASE","$x > $BASE"); } $x = $class->new($BASE+3); $x++; if ($x > $BASE) { ok (1,1) } else { ok ("$x > $BASE","$x < $BASE"); } # test for +0 instead of int(): $x = $class->new($MAX); ok ($x->length(), length($MAX)); ############################################################################### # test bug that $class->digit($string) did not work ok ($class->digit(123,2),1); ############################################################################### # bug in sub where number with at least 6 trailing zeros after any op failed $x = $class->new(123456); $z = $class->new(10000); $z *= 10; $x -= $z; ok ($z, 100000); ok ($x, 23456); ############################################################################### # bug in shortcut in mul() # construct a number with a zero-hole of BASE_LEN_SMALL { my @bl = $CL->_base_len(); my $bl = $bl[4]; $x = '1' x $bl . '0' x $bl . '1' x $bl . '0' x $bl; $y = '1' x (2*$bl); $x = $class->new($x)->bmul($y); # result is 123..$bl . $bl x (3*bl-1) . $bl...321 . '0' x $bl $y = ''; my $d = ''; for (my $i = 1; $i <= $bl; $i++) { $y .= $i; $d = $i.$d; } $y .= $bl x (3*$bl-1) . $d . '0' x $bl; ok ($x,$y); ############################################################################# # see if mul shortcut for small numbers works $x = '9' x $bl; $x = $class->new($x); # 999 * 999 => 998 . 001, 9999*9999 => 9998 . 0001 ok ($x*$x, '9' x ($bl-1) . '8' . '0' x ($bl-1) . '1'); } ############################################################################### # bug with rest "-0" in div, causing further div()s to fail $x = $class->new('-322056000'); ($x,$y) = $x->bdiv('-12882240'); ok ($y,'0'); is_valid($y); # $y not '-0' ############################################################################### # bug in $x->bmod($y) # if $x < 0 and $y > 0 $x = $class->new('-629'); ok ($x->bmod(5033),4404); ############################################################################### # bone/binf etc as plain calls (Lite failed them) ok ($class->bzero(),0); ok ($class->bone(),1); ok ($class->bone('+'),1); ok ($class->bone('-'),-1); ok ($class->bnan(),'NaN'); ok ($class->binf(),'inf'); ok ($class->binf('+'),'inf'); ok ($class->binf('-'),'-inf'); ok ($class->binf('-inf'),'-inf'); ############################################################################### # is_one('-') ok ($class->new(1)->is_one('-'),0); ok ($class->new(-1)->is_one('-'),1); ok ($class->new(1)->is_one(),1); ok ($class->new(-1)->is_one(),0); ############################################################################### # [perl #30609] bug with $x -= $x not beeing 0, but 2*$x $x = $class->new(3); $x -= $x; ok ($x, 0); $x = $class->new(-3); $x -= $x; ok ($x, 0); $x = $class->new('NaN'); $x -= $x; ok ($x->is_nan(), 1); $x = $class->new('inf'); $x -= $x; ok ($x->is_nan(), 1); $x = $class->new('-inf'); $x -= $x; ok ($x->is_nan(), 1); $x = $class->new('NaN'); $x += $x; ok ($x->is_nan(), 1); $x = $class->new('inf'); $x += $x; ok ($x->is_inf(), 1); $x = $class->new('-inf'); $x += $x; ok ($x->is_inf('-'), 1); $x = $class->new(3); $x += $x; ok ($x, 6); $x = $class->new(-3); $x += $x; ok ($x, -6); $x = $class->new(3); $x *= $x; ok ($x, 9); $x = $class->new(-3); $x *= $x; ok ($x, 9); $x = $class->new(3); $x /= $x; ok ($x, 1); $x = $class->new(-3); $x /= $x; ok ($x, 1); $x = $class->new(3); $x %= $x; ok ($x, 0); $x = $class->new(-3); $x %= $x; ok ($x, 0); ############################################################################### # all tests done 1; ############################################################################### ############################################################################### # Perl 5.005 does not like ok ($x,undef) sub ok_undef { my $x = shift; ok (1,1) and return if !defined $x; ok ($x,'undef'); } ############################################################################### # sub to check validity of a BigInt internally, to ensure that no op leaves a # number object in an invalid state (f.i. "-0") sub is_valid { my ($x,$f) = @_; my $e = 0; # error? # allow the check to pass for all Lite, and all MBI and subclasses # ok as reference? $e = 'Not a reference to Math::BigInt' if ref($x) !~ /^Math::BigInt/; if (ref($x) ne 'Math::BigInt::Lite') { # has ok sign? $e = "Illegal sign $x->{sign} (expected: '+', '-', '-inf', '+inf' or 'NaN'" if $e eq '0' && $x->{sign} !~ /^(\+|-|\+inf|-inf|NaN)$/; $e = "-0 is invalid!" if $e ne '0' && $x->{sign} eq '-' && $x == 0; $e = $CALC->_check($x->{value}) if $e eq '0'; } # test done, see if error did crop up ok (1,1), return if ($e eq '0'); ok (1,$e." after op '$f'"); } __DATA__ &.= 1234:-345:1234-345 &+= 1:2:3 -1:-2:-3 &-= 1:2:-1 -1:-2:1 &*= 2:3:6 -1:5:-5 &%= 100:3:1 8:9:8 -629:5033:4404 &/= 100:3:33 -8:2:-4 &|= 2:1:3 &&= 5:7:5 &^= 5:7:2 &blog NaNlog:2:NaN 122:NaNlog:NaN NaNlog1:NaNlog:NaN 122:inf:NaN inf:122:NaN 122:-inf:NaN -inf:122:NaN -inf:-inf:NaN inf:inf:NaN 0:4:NaN -21:4:NaN 21:-21:NaN # normal results 1024:2:10 81:3:4 # 3.01.. truncate 82:3:4 # 3.9... truncate 80:3:3 15625:5:6 15626:5:6 15624:5:5 1000:10:3 10000:10:4 100000:10:5 1000000:10:6 10000000:10:7 100000000:10:8 4096:2:12 # these tests do not work since BigInt can't deal with Lite objects #100000000:10:8 #8916100448256:12:12 #8916100448257:12:12 #8916100448255:12:11 #2251799813685248:8:17 #72057594037927936:2:56 #144115188075855872:2:57 #288230376151711744:2:58 #576460752303423488:2:59 #1329227995784915872903807060280344576:2:120 # $x == $base => result 1 3:3:1 # $x < $base => result 0 ($base ** 0 <= $x) 3:4:0 # $x == 1 => result 0 1:5:0 &is_negative 0:0 -1:1 1:0 +inf:0 -inf:1 NaNneg:0 &is_positive 0:0 -1:0 1:1 +inf:1 -inf:0 NaNneg:0 &is_int -inf:0 +inf:0 NaNis_int:0 1:1 0:1 123e12:1 &is_odd abc:0 0:0 1:1 3:1 -1:1 -3:1 10000001:1 10000002:0 2:0 120:0 121:1 &is_even abc:0 0:1 1:0 3:0 -1:0 -3:0 10000001:0 10000002:1 2:1 120:1 121:0 &bacmp +0:-0:0 +0:+1:-1 -1:+1:0 +1:-1:0 -1:+2:-1 +2:-1:1 -123456789:+987654321:-1 +123456789:-987654321:-1 +987654321:+123456789:1 -987654321:+123456789:1 -123:+4567889:-1 # NaNs acmpNaN:123: 123:acmpNaN: acmpNaN:acmpNaN: # infinity +inf:+inf:0 -inf:-inf:0 +inf:-inf:0 -inf:+inf:0 +inf:123:1 -inf:123:1 +inf:-123:1 -inf:-123:1 123:-inf:-1 -123:inf:-1 -123:-inf:-1 123:inf:-1 # return undef +inf:NaN: NaN:inf: -inf:NaN: NaN:-inf: &bnorm 0e999:0 0e-999:0 -0e999:0 -0e-999:0 123:123 # binary input 0babc:NaN 0b123:NaN 0b0:0 -0b0:0 -0b1:-1 0b0001:1 0b001:1 0b011:3 0b101:5 0b1001:9 0b10001:17 0b100001:33 0b1000001:65 0b10000001:129 0b100000001:257 0b1000000001:513 0b10000000001:1025 0b100000000001:2049 0b1000000000001:4097 0b10000000000001:8193 0b100000000000001:16385 0b1000000000000001:32769 0b10000000000000001:65537 0b100000000000000001:131073 0b1000000000000000001:262145 0b10000000000000000001:524289 0b100000000000000000001:1048577 0b1000000000000000000001:2097153 0b10000000000000000000001:4194305 0b100000000000000000000001:8388609 0b1000000000000000000000001:16777217 0b10000000000000000000000001:33554433 0b100000000000000000000000001:67108865 0b1000000000000000000000000001:134217729 0b10000000000000000000000000001:268435457 0b100000000000000000000000000001:536870913 0b1000000000000000000000000000001:1073741825 0b10000000000000000000000000000001:2147483649 0b100000000000000000000000000000001:4294967297 0b1000000000000000000000000000000001:8589934593 0b10000000000000000000000000000000001:17179869185 0b_101:NaN 0b1_0_1:5 0b0_0_0_1:1 # hex input -0x0:0 0xabcdefgh:NaN 0x1234:4660 0xabcdef:11259375 -0xABCDEF:-11259375 -0x1234:-4660 0x12345678:305419896 0x1_2_3_4_56_78:305419896 0xa_b_c_d_e_f:11259375 0x_123:NaN 0x9:9 0x11:17 0x21:33 0x41:65 0x81:129 0x101:257 0x201:513 0x401:1025 0x801:2049 0x1001:4097 0x2001:8193 0x4001:16385 0x8001:32769 0x10001:65537 0x20001:131073 0x40001:262145 0x80001:524289 0x100001:1048577 0x200001:2097153 0x400001:4194305 0x800001:8388609 0x1000001:16777217 0x2000001:33554433 0x4000001:67108865 0x8000001:134217729 0x10000001:268435457 0x20000001:536870913 0x40000001:1073741825 0x80000001:2147483649 0x100000001:4294967297 0x200000001:8589934593 0x400000001:17179869185 0x800000001:34359738369 # bug found by Mark Lakata in Calc.pm creating too big one-element numbers in _from_hex() 0x2dd59e18a125dbed30a6ab1d93e9c855569f44f75806f0645dc9a2e98b808c3:1295719234436071846486578237372801883390756472611551858964079371952886122691 # inf input inf:inf +inf:inf -inf:-inf 0inf:NaN # abnormal input :NaN abc:NaN 1 a:NaN 1bcd2:NaN 11111b:NaN +1z:NaN -1z:NaN # only one underscore between two digits _123:NaN _123_:NaN 123_:NaN 1__23:NaN 1E1__2:NaN 1_E12:NaN 1E_12:NaN 1_E_12:NaN +_1E12:NaN +0_1E2:100 +0_0_1E2:100 -0_0_1E2:-100 -0_0_1E+0_0_2:-100 E1:NaN E23:NaN 1.23E1:NaN 1.23E-1:NaN # bug with two E's in number beeing valid 1e2e3:NaN 1e2r:NaN 1e2.0:NaN # bug with two '.' in number beeing valid 1.2.2:NaN 1.2.3e1:NaN -1.2.3:NaN -1.2.3e-4:NaN 1.2e3.4:NaN 1.2e-3.4:NaN 1.2.3.4:NaN 1.2.t:NaN 1..2:NaN 1..2e1:NaN 1..2e1..1:NaN 12e1..1:NaN ..2:NaN .-2:NaN # leading zeros 012:12 0123:123 01234:1234 012345:12345 0123456:123456 01234567:1234567 012345678:12345678 0123456789:123456789 01234567891:1234567891 012345678912:12345678912 0123456789123:123456789123 01234567891234:1234567891234 # some inputs that result in zero 0e0:0 +0e0:0 +0e+0:0 -0e+0:0 0e-0:0 -0e-0:0 +0e-0:0 000:0 00e2:0 00e02:0 000e002:0 000e1230:0 00e-3:0 00e+3:0 00e-03:0 00e+03:0 -000:0 -00e2:0 -00e02:0 -000e002:0 -000e1230:0 -00e-3:0 -00e+3:0 -00e-03:0 -00e+03:0 # normal input 0:0 +0:0 +00:0 +000:0 000000000000000000:0 -0:0 -0000:0 +1:1 +01:1 +001:1 +00000100000:100000 123456789:123456789 -1:-1 -01:-1 -001:-1 -123456789:-123456789 -00000100000:-100000 1_2_3:123 10000000000E-1_0:1 1E2:100 1E1:10 1E0:1 1.23E2:123 100E-1:10 # floating point input # .2e2:20 1.E3:1000 1.01E2:101 1010E-1:101 -1010E0:-1010 -1010E1:-10100 1234.00:1234 # non-integer numbers -1010E-2:NaN -1.01E+1:NaN -1.01E-1:NaN &bnan 1:NaN 2:NaN abc:NaN &bone 2:+:1 2:-:-1 boneNaN:-:-1 boneNaN:+:1 2:abc:1 3::1 &binf 1:+:inf 2:-:-inf 3:abc:inf &is_nan 123:0 abc:1 NaN:1 -123:0 &is_inf +inf::1 -inf::1 abc::0 1::0 NaN::0 -1::0 +inf:-:0 +inf:+:1 -inf:-:1 -inf:+:0 -inf:-inf:1 -inf:+inf:0 +inf:-inf:0 +inf:+inf:1 # it must be exactly /^[+-]inf$/ +infinity::0 -infinity::0 &blsft abc:abc:NaN +2:+2:8 +1:+32:4294967296 +1:+48:281474976710656 +8:-2:NaN # excercise base 10 +12345:4:10:123450000 -1234:0:10:-1234 +1234:0:10:1234 +2:2:10:200 +12:2:10:1200 +1234:-3:10:NaN 1234567890123:12:10:1234567890123000000000000 -3:1:2:-6 -5:1:2:-10 -2:1:2:-4 -102533203:1:2:-205066406 &brsft abc:abc:NaN +8:+2:2 +4294967296:+32:1 +281474976710656:+48:1 +2:-2:NaN # excercise base 10 -1234:0:10:-1234 +1234:0:10:1234 +200:2:10:2 +1234:3:10:1 +1234:2:10:12 +1234:-3:10:NaN 310000:4:10:31 12300000:5:10:123 1230000000000:10:10:123 09876123456789067890:12:10:9876123 1234561234567890123:13:10:123456 820265627:1:2:410132813 # test shifting negative numbers in base 2 -15:1:2:-8 -14:1:2:-7 -13:1:2:-7 -12:1:2:-6 -11:1:2:-6 -10:1:2:-5 -9:1:2:-5 -8:1:2:-4 -7:1:2:-4 -6:1:2:-3 -5:1:2:-3 -4:1:2:-2 -3:1:2:-2 -2:1:2:-1 -1:1:2:-1 -1640531254:2:2:-410132814 -1640531254:1:2:-820265627 -820265627:1:2:-410132814 -205066405:1:2:-102533203 &bsstr +inf:inf -inf:-inf 1e+34:1e+34 123.456E3:123456e+0 100:1e+2 bsstrabc:NaN -5:-5e+0 -100:-1e+2 &numify numifyabc:NaN +inf:inf -inf:-inf 5:5 -5:-5 100:100 -100:-100 &bneg bnegNaN:NaN +inf:-inf -inf:inf abd:NaN 0:0 1:-1 -1:1 +123456789:-123456789 -123456789:123456789 &babs babsNaN:NaN +inf:inf -inf:inf 0:0 1:1 -1:1 +123456789:123456789 -123456789:123456789 &bcmp bcmpNaN:bcmpNaN: bcmpNaN:0: 0:bcmpNaN: 0:0:0 -1:0:-1 0:-1:1 1:0:1 0:1:-1 -1:1:-1 1:-1:1 -1:-1:0 1:1:0 123:123:0 123:12:1 12:123:-1 -123:-123:0 -123:-12:-1 -12:-123:1 123:124:-1 124:123:1 -123:-124:1 -124:-123:-1 100:5:1 -123456789:987654321:-1 +123456789:-987654321:1 -987654321:123456789:-1 -inf:5432112345:-1 +inf:5432112345:1 -inf:-5432112345:-1 +inf:-5432112345:1 +inf:+inf:0 -inf:-inf:0 +inf:-inf:1 -inf:+inf:-1 5:inf:-1 5:inf:-1 -5:-inf:1 -5:-inf:1 # return undef +inf:NaN: NaN:inf: -inf:NaN: NaN:-inf: &binc abc:NaN +inf:inf -inf:-inf +0:1 +1:2 -1:0 &bdec abc:NaN +inf:inf -inf:-inf +0:-1 +1:0 -1:-2 &badd abc:abc:NaN abc:0:NaN +0:abc:NaN +inf:-inf:NaN -inf:+inf:NaN +inf:+inf:inf -inf:-inf:-inf baddNaN:+inf:NaN baddNaN:+inf:NaN +inf:baddNaN:NaN -inf:baddNaN:NaN 0:0:0 1:0:1 0:1:1 1:1:2 -1:0:-1 0:-1:-1 -1:-1:-2 -1:+1:0 +1:-1:0 +9:+1:10 +99:+1:100 +999:+1:1000 +9999:+1:10000 +99999:+1:100000 +999999:+1:1000000 +9999999:+1:10000000 +99999999:+1:100000000 +999999999:+1:1000000000 +9999999999:+1:10000000000 +99999999999:+1:100000000000 +10:-1:9 +100:-1:99 +1000:-1:999 +10000:-1:9999 +100000:-1:99999 +1000000:-1:999999 +10000000:-1:9999999 +100000000:-1:99999999 +1000000000:-1:999999999 +10000000000:-1:9999999999 +123456789:987654321:1111111110 -123456789:987654321:864197532 -123456789:-987654321:-1111111110 +123456789:-987654321:-864197532 -1:10001:10000 -1:100001:100000 -1:1000001:1000000 -1:10000001:10000000 -1:100000001:100000000 -1:1000000001:1000000000 -1:10000000001:10000000000 -1:100000000001:100000000000 -1:1000000000001:1000000000000 -1:10000000000001:10000000000000 -1:-10001:-10002 -1:-100001:-100002 -1:-1000001:-1000002 -1:-10000001:-10000002 -1:-100000001:-100000002 -1:-1000000001:-1000000002 -1:-10000000001:-10000000002 -1:-100000000001:-100000000002 -1:-1000000000001:-1000000000002 -1:-10000000000001:-10000000000002 &bsub abc:abc:NaN abc:+0:NaN +0:abc:NaN +inf:-inf:inf -inf:+inf:-inf +inf:+inf:NaN -inf:-inf:NaN +0:+0:0 +1:+0:1 +0:+1:-1 +1:+1:0 -1:+0:-1 +0:-1:1 -1:-1:0 -1:+1:-2 +1:-1:2 +9:+1:8 +99:+1:98 +999:+1:998 +9999:+1:9998 +99999:+1:99998 +999999:+1:999998 +9999999:+1:9999998 +99999999:+1:99999998 +999999999:+1:999999998 +9999999999:+1:9999999998 +99999999999:+1:99999999998 +10:-1:11 +100:-1:101 +1000:-1:1001 +10000:-1:10001 +100000:-1:100001 +1000000:-1:1000001 +10000000:-1:10000001 +100000000:-1:100000001 +1000000000:-1:1000000001 +10000000000:-1:10000000001 +123456789:+987654321:-864197532 -123456789:+987654321:-1111111110 -123456789:-987654321:864197532 +123456789:-987654321:1111111110 10001:1:10000 100001:1:100000 1000001:1:1000000 10000001:1:10000000 100000001:1:100000000 1000000001:1:1000000000 10000000001:1:10000000000 100000000001:1:100000000000 1000000000001:1:1000000000000 10000000000001:1:10000000000000 10001:-1:10002 100001:-1:100002 1000001:-1:1000002 10000001:-1:10000002 100000001:-1:100000002 1000000001:-1:1000000002 10000000001:-1:10000000002 100000000001:-1:100000000002 1000000000001:-1:1000000000002 10000000000001:-1:10000000000002 &bmul abc:abc:NaN abc:+0:NaN +0:abc:NaN NaNmul:+inf:NaN NaNmul:-inf:NaN -inf:NaNmul:NaN +inf:NaNmul:NaN +inf:+inf:inf +inf:-inf:-inf -inf:+inf:-inf -inf:-inf:inf +0:+0:0 +0:+1:0 +1:+0:0 +0:-1:0 -1:+0:0 123456789123456789:0:0 0:123456789123456789:0 -1:-1:1 -1:+1:-1 +1:-1:-1 +1:+1:1 +2:+3:6 -2:+3:-6 +2:-3:-6 -2:-3:6 111:111:12321 10101:10101:102030201 1001001:1001001:1002003002001 100010001:100010001:10002000300020001 10000100001:10000100001:100002000030000200001 11111111111:9:99999999999 22222222222:9:199999999998 33333333333:9:299999999997 44444444444:9:399999999996 55555555555:9:499999999995 66666666666:9:599999999994 77777777777:9:699999999993 88888888888:9:799999999992 99999999999:9:899999999991 +25:+25:625 +12345:+12345:152399025 +99999:+11111:1111088889 9999:10000:99990000 99999:100000:9999900000 999999:1000000:999999000000 9999999:10000000:99999990000000 99999999:100000000:9999999900000000 999999999:1000000000:999999999000000000 9999999999:10000000000:99999999990000000000 99999999999:100000000000:9999999999900000000000 999999999999:1000000000000:999999999999000000000000 9999999999999:10000000000000:99999999999990000000000000 99999999999999:100000000000000:9999999999999900000000000000 999999999999999:1000000000000000:999999999999999000000000000000 9999999999999999:10000000000000000:99999999999999990000000000000000 99999999999999999:100000000000000000:9999999999999999900000000000000000 999999999999999999:1000000000000000000:999999999999999999000000000000000000 9999999999999999999:10000000000000000000:99999999999999999990000000000000000000 &bdiv-list 100:20:5,0 4095:4095:1,0 -4095:-4095:1,0 4095:-4095:-1,0 -4095:4095:-1,0 123:2:61,1 9:5:1,4 9:4:2,1 # inf handling and general remainder 5:8:0,5 0:8:0,0 11:2:5,1 11:-2:-5,-1 -11:2:-5,1 # see table in documentation in MBI 0:inf:0,0 0:-inf:0,0 5:inf:0,5 5:-inf:0,5 -5:inf:0,-5 -5:-inf:0,-5 inf:5:inf,0 -inf:5:-inf,0 inf:-5:-inf,0 -inf:-5:inf,0 5:5:1,0 -5:-5:1,0 inf:inf:NaN,NaN -inf:-inf:NaN,NaN -inf:inf:NaN,NaN inf:-inf:NaN,NaN 8:0:inf,8 inf:0:inf,inf # exceptions to reminder rule -8:0:-inf,-8 -inf:0:-inf,-inf 0:0:NaN,NaN # test the shortcut in Calc if @$x == @$yorg 1234567812345678:123456712345678:10,688888898 12345671234567:1234561234567:10,58888897 123456123456:12345123456:10,4888896 1234512345:123412345:10,388895 1234567890999999999:1234567890:1000000000,999999999 1234567890000000000:1234567890:1000000000,0 1234567890999999999:9876543210:124999998,9503086419 1234567890000000000:9876543210:124999998,8503086420 96969696969696969696969696969678787878626262626262626262626262:484848484848484848484848486666666666666689898989898989898989:199,484848484848484848484848123012121211954972727272727272727451 # bug in v1.76 1267650600228229401496703205375:1267650600228229401496703205376:0,1267650600228229401496703205375 # excercise shortcut for numbers of the same length in div 999999999999999999999999999999999:999999999999999999999999999999999:1,0 999999999999999999999999999999999:888888888888888888888888888888888:1,111111111111111111111111111111111 999999999999999999999999999999999:777777777777777777777777777777777:1,222222222222222222222222222222222 999999999999999999999999999999999:666666666666666666666666666666666:1,333333333333333333333333333333333 999999999999999999999999999999999:555555555555555555555555555555555:1,444444444444444444444444444444444 999999999999999999999999999999999:444444444444444444444444444444444:2,111111111111111111111111111111111 999999999999999999999999999999999:333333333333333333333333333333333:3,0 999999999999999999999999999999999:222222222222222222222222222222222:4,111111111111111111111111111111111 999999999999999999999999999999999:111111111111111111111111111111111:9,0 9999999_9999999_9999999_9999999:3333333_3333333_3333333_3333333:3,0 9999999_9999999_9999999_9999999:3333333_0000000_0000000_0000000:3,999999999999999999999 9999999_9999999_9999999_9999999:3000000_0000000_0000000_0000000:3,999999999999999999999999999 9999999_9999999_9999999_9999999:2000000_0000000_0000000_0000000:4,1999999999999999999999999999 9999999_9999999_9999999_9999999:1000000_0000000_0000000_0000000:9,999999999999999999999999999 9999999_9999999_9999999_9999999:100000_0000000_0000000_0000000:99,99999999999999999999999999 9999999_9999999_9999999_9999999:10000_0000000_0000000_0000000:999,9999999999999999999999999 9999999_9999999_9999999_9999999:1000_0000000_0000000_0000000:9999,999999999999999999999999 9999999_9999999_9999999_9999999:100_0000000_0000000_0000000:99999,99999999999999999999999 9999999_9999999_9999999_9999999:10_0000000_0000000_0000000:999999,9999999999999999999999 9999999_9999999_9999999_9999999:1_0000000_0000000_0000000:9999999,999999999999999999999 &bdiv abc:abc:NaN abc:1:NaN 1:abc:NaN 0:0:NaN # inf handling (see table in doc) 0:inf:0 0:-inf:0 5:inf:0 5:-inf:0 -5:inf:0 -5:-inf:0 inf:5:inf -inf:5:-inf inf:-5:-inf -inf:-5:inf 5:5:1 -5:-5:1 inf:inf:NaN -inf:-inf:NaN -inf:inf:NaN inf:-inf:NaN 8:0:inf inf:0:inf -8:0:-inf -inf:0:-inf 0:0:NaN 11:2:5 -11:-2:5 -11:2:-5 11:-2:-5 0:1:0 0:-1:0 1:1:1 -1:-1:1 1:-1:-1 -1:1:-1 1:2:0 2:1:2 1:26:0 1000000000:9:111111111 2000000000:9:222222222 3000000000:9:333333333 4000000000:9:444444444 5000000000:9:555555555 6000000000:9:666666666 7000000000:9:777777777 8000000000:9:888888888 9000000000:9:1000000000 35500000:113:314159 71000000:226:314159 106500000:339:314159 1000000000:3:333333333 +10:+5:2 +100:+4:25 +1000:+8:125 +10000:+16:625 999999999999:9:111111111111 999999999999:99:10101010101 999999999999:999:1001001001 999999999999:9999:100010001 999999999999999:99999:10000100001 +1111088889:99999:11111 -5:-3:1 -5:3:-1 4:3:1 4:-3:-1 1:3:0 1:-3:0 -2:-3:0 -2:3:0 8:3:2 -8:3:-2 14:-3:-4 -14:3:-4 -14:-3:4 14:3:4 # bug in Calc with '99999' vs $BASE-1 10000000000000000000000000000000000000000000000000000000000000000000000000000000000:10000000375084540248994272022843165711074:999999962491547381984643365663244474111576 # test the shortcut in Calc if @$x == @$yorg 1234567812345678:123456712345678:10 12345671234567:1234561234567:10 123456123456:12345123456:10 1234512345:123412345:10 1234567890999999999:1234567890:1000000000 1234567890000000000:1234567890:1000000000 1234567890999999999:9876543210:124999998 1234567890000000000:9876543210:124999998 96969696969696969696969696969678787878626262626262626262626262:484848484848484848484848486666666666666689898989898989898989:199 # bug up to v0.35 in Calc (--$q one too many) 84696969696969696956565656566184292929292929292847474747436308080808080808086765396464646464646465:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999999 84696969696969696943434343434871161616161616161452525252486813131313131313143230042929292929292930:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999998 84696969696969696969696969697497424242424242424242424242385803030303030303030300750000000000000000:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6450000000000000000 84696969696969696930303030303558030303030303030057575757537318181818181818199694689393939393939395:13131313131313131313131313131394949494949494949494949494943535353535353535353535:6449999999999999997 # excercise shortcut for numbers of the same length in div 999999999999999999999999999999999:999999999999999999999999999999999:1 999999999999999999999999999999999:888888888888888888888888888888888:1 999999999999999999999999999999999:777777777777777777777777777777777:1 999999999999999999999999999999999:666666666666666666666666666666666:1 999999999999999999999999999999999:555555555555555555555555555555555:1 999999999999999999999999999999999:444444444444444444444444444444444:2 999999999999999999999999999999999:333333333333333333333333333333333:3 999999999999999999999999999999999:222222222222222222222222222222222:4 999999999999999999999999999999999:111111111111111111111111111111111:9 9999999_9999999_9999999_9999999:3333333_3333333_3333333_3333333:3 9999999_9999999_9999999_9999999:3333333_0000000_0000000_0000000:3 9999999_9999999_9999999_9999999:3000000_0000000_0000000_0000000:3 9999999_9999999_9999999_9999999:2000000_0000000_0000000_0000000:4 9999999_9999999_9999999_9999999:1000000_0000000_0000000_0000000:9 9999999_9999999_9999999_9999999:100000_0000000_0000000_0000000:99 9999999_9999999_9999999_9999999:10000_0000000_0000000_0000000:999 9999999_9999999_9999999_9999999:1000_0000000_0000000_0000000:9999 9999999_9999999_9999999_9999999:100_0000000_0000000_0000000:99999 9999999_9999999_9999999_9999999:10_0000000_0000000_0000000:999999 9999999_9999999_9999999_9999999:1_0000000_0000000_0000000:9999999 # bug with shortcut in Calc 0.44 949418181818187070707070707070707070:181818181853535353535353535353535353:5 &bmodinv # format: number:modulus:result # bmodinv Data errors abc:abc:NaN abc:5:NaN 5:abc:NaN # bmodinv Expected Results from normal use 1:5:1 3:5:2 -2:5:2 8:5033:4404 1234567891:13:6 -1234567891:13:7 324958749843759385732954874325984357439658735983745:2348249874968739:1741662881064902 ## bmodinv Error cases / useless use of function 3:-5:NaN inf:5:NaN 5:inf:NaN -inf:5:NaN 5:-inf:NaN &bmodpow # format: number:exponent:modulus:result # bmodpow Data errors abc:abc:abc:NaN 5:abc:abc:NaN abc:5:abc:NaN abc:abc:5:NaN 5:5:abc:NaN 5:abc:5:NaN abc:5:5:NaN # bmodpow Expected results 0:0:2:1 1:0:2:1 0:0:1:0 8:7:5032:3840 8:-1:5033:4404 98436739867439843769485798542749827593285729587325:43698764986460981048259837659386739857456983759328457:6943857329857295827698367:3104744730915914415259518 # bmodpow Error cases 8:8:-5:NaN 8:-1:16:NaN inf:5:13:NaN 5:inf:13:NaN &bmod # inf handling, see table in doc 0:inf:0 0:-inf:0 5:inf:5 5:-inf:5 -5:inf:-5 -5:-inf:-5 inf:5:0 -inf:5:0 inf:-5:0 -inf:-5:0 5:5:0 -5:-5:0 inf:inf:NaN -inf:-inf:NaN -inf:inf:NaN inf:-inf:NaN 8:0:8 inf:0:inf # exceptions to reminder rule -inf:0:-inf -8:0:-8 0:0:NaN abc:abc:NaN abc:1:abc:NaN 1:abc:NaN 0:0:NaN 0:1:0 1:0:1 0:-1:0 -1:0:-1 1:1:0 -1:-1:0 1:-1:0 -1:1:0 1:2:1 2:1:0 1000000000:9:1 2000000000:9:2 3000000000:9:3 4000000000:9:4 5000000000:9:5 6000000000:9:6 7000000000:9:7 8000000000:9:8 9000000000:9:0 35500000:113:33 71000000:226:66 106500000:339:99 1000000000:3:1 10:5:0 100:4:0 1000:8:0 10000:16:0 999999999999:9:0 999999999999:99:0 999999999999:999:0 999999999999:9999:0 999999999999999:99999:0 -9:+5:1 +9:-5:-1 -9:-5:-4 -5:3:1 -2:3:1 4:3:1 1:3:1 -5:-3:-2 -2:-3:-2 4:-3:-2 1:-3:-2 4095:4095:0 100041000510123:3:0 152403346:12345:4321 9:5:4 # test shortcuts in Calc # 1ex % 9 is always == 1, 1ex % 113 is != 1 for x = (4..9), 1ex % 10 = 0 1234:9:1 123456:9:3 12345678:9:0 1234567891:9:1 123456789123:9:6 12345678912345:9:6 1234567891234567:9:1 123456789123456789:9:0 1234:10:4 123456:10:6 12345678:10:8 1234567891:10:1 123456789123:10:3 12345678912345:10:5 1234567891234567:10:7 123456789123456789:10:9 1234:113:104 123456:113:60 12345678:113:89 1234567891:113:64 123456789123:113:95 12345678912345:113:53 1234567891234567:113:56 123456789123456789:113:39 # bug in bmod() not modifying the variable in place -629:5033:4404 # bug in bmod() in Calc in the _div_use_div() shortcut code path, # when X == X and X was big 111111111111111111111111111111:111111111111111111111111111111:0 12345678901234567890:12345678901234567890:0 &bgcd inf:12:NaN -inf:12:NaN 12:inf:NaN 12:-inf:NaN inf:inf:NaN inf:-inf:NaN -inf:-inf:NaN abc:abc:NaN abc:+0:NaN +0:abc:NaN +0:+0:0 +0:+1:1 +1:+0:1 +1:+1:1 +2:+3:1 +3:+2:1 -3:+2:1 -3:-2:1 -144:-60:12 144:-60:12 144:60:12 100:625:25 4096:81:1 1034:804:2 27:90:56:1 27:90:54:9 &blcm abc:abc:NaN abc:+0:NaN +0:abc:NaN +0:+0:NaN +1:+0:0 +0:+1:0 +27:+90:270 +1034:+804:415668 &band abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:0 3:2:2 +8:+2:0 +281474976710656:0:0 +281474976710656:1:0 +281474976710656:+281474976710656:281474976710656 281474976710656:-1:281474976710656 -2:-3:-4 -1:-1:-1 -6:-6:-6 -7:-4:-8 -7:4:0 -4:7:4 # negative argument is bitwise shorter than positive [perl #26559] 30:-3:28 123:-1:123 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0x0xFFFF 0xFFFFFF:0xFFFFFF:0x0xFFFFFF 0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF 0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0x0xF0F0 0x0F0F:0x0F0F:0x0x0F0F 0xF0F0F0:0xF0F0F0:0x0xF0F0F0 0x0F0F0F:0x0F0F0F:0x0x0F0F0F 0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0 0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F 0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0 0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F 0x1F0F0F0F0F0F:0x3F0F0F0F0F0F:0x0x1F0F0F0F0F0F &bior abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:3 +8:+2:10 +281474976710656:0:281474976710656 +281474976710656:1:281474976710657 +281474976710656:281474976710656:281474976710656 -2:-3:-1 -1:-1:-1 -6:-6:-6 -7:4:-3 -4:7:-1 +281474976710656:-1:-1 30:-3:-1 30:-4:-2 300:-76:-68 -76:300:-68 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0x0xFFFF 0xFFFFFF:0xFFFFFF:0x0xFFFFFF 0xFFFFFFFF:0xFFFFFFFF:0x0xFFFFFFFF 0xFFFFFFFFFF:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0:0xFFFF:0x0xFFFF 0:0xFFFFFF:0x0xFFFFFF 0:0xFFFFFFFF:0x0xFFFFFFFF 0:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xFFFF:0:0x0xFFFF 0xFFFFFF:0:0x0xFFFFFF 0xFFFFFFFF:0:0x0xFFFFFFFF 0xFFFFFFFFFF:0:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0x0xF0F0 0x0F0F:0x0F0F:0x0x0F0F 0xF0F0:0x0F0F:0x0xFFFF 0xF0F0F0:0xF0F0F0:0x0xF0F0F0 0x0F0F0F:0x0F0F0F:0x0x0F0F0F 0x0F0F0F:0xF0F0F0:0x0xFFFFFF 0xF0F0F0F0:0xF0F0F0F0:0x0xF0F0F0F0 0x0F0F0F0F:0x0F0F0F0F:0x0x0F0F0F0F 0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF 0xF0F0F0F0F0:0xF0F0F0F0F0:0x0xF0F0F0F0F0 0x0F0F0F0F0F:0x0F0F0F0F0F:0x0x0F0F0F0F0F 0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0x0xF0F0F0F0F0F0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0x0x0F0F0F0F0F0F 0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF 0x1F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF &bxor abc:abc:NaN abc:0:NaN 0:abc:NaN 1:2:3 +8:+2:10 +281474976710656:0:281474976710656 +281474976710656:1:281474976710657 +281474976710656:281474976710656:0 -2:-3:3 -1:-1:0 -6:-6:0 -7:4:-3 -4:7:-5 4:-7:-3 -4:-7:5 30:-3:-29 30:-4:-30 300:-76:-360 -76:300:-360 # equal arguments are treated special, so also do some test with unequal ones 0xFFFF:0xFFFF:0 0xFFFFFF:0xFFFFFF:0 0xFFFFFFFF:0xFFFFFFFF:0 0xFFFFFFFFFF:0xFFFFFFFFFF:0 0xFFFFFFFFFFFF:0xFFFFFFFFFFFF:0 0:0xFFFF:0x0xFFFF 0:0xFFFFFF:0x0xFFFFFF 0:0xFFFFFFFF:0x0xFFFFFFFF 0:0xFFFFFFFFFF:0x0xFFFFFFFFFF 0:0xFFFFFFFFFFFF:0x0xFFFFFFFFFFFF 0xFFFF:0:0x0xFFFF 0xFFFFFF:0:0x0xFFFFFF 0xFFFFFFFF:0:0x0xFFFFFFFF 0xFFFFFFFFFF:0:0x0xFFFFFFFFFF 0xFFFFFFFFFFFF:0:0x0xFFFFFFFFFFFF 0xF0F0:0xF0F0:0 0x0F0F:0x0F0F:0 0xF0F0:0x0F0F:0x0xFFFF 0xF0F0F0:0xF0F0F0:0 0x0F0F0F:0x0F0F0F:0 0x0F0F0F:0xF0F0F0:0x0xFFFFFF 0xF0F0F0F0:0xF0F0F0F0:0 0x0F0F0F0F:0x0F0F0F0F:0 0x0F0F0F0F:0xF0F0F0F0:0x0xFFFFFFFF 0xF0F0F0F0F0:0xF0F0F0F0F0:0 0x0F0F0F0F0F:0x0F0F0F0F0F:0 0x0F0F0F0F0F:0xF0F0F0F0F0:0x0xFFFFFFFFFF 0xF0F0F0F0F0F0:0xF0F0F0F0F0F0:0 0x0F0F0F0F0F0F:0x0F0F0F0F0F0F:0 0x0F0F0F0F0F0F:0xF0F0F0F0F0F0:0x0xFFFFFFFFFFFF &bnot abc:NaN +0:-1 +8:-9 +281474976710656:-281474976710657 -1:0 -2:1 -12:11 &digit 0:0:0 12:0:2 12:1:1 123:0:3 123:1:2 123:2:1 123:-1:1 123:-2:2 123:-3:3 123456:0:6 123456:1:5 123456:2:4 123456:3:3 123456:4:2 123456:5:1 123456:-1:1 123456:-2:2 123456:-3:3 100000:-3:0 100000:0:0 100000:1:0 &mantissa abc:NaN 1e4:1 2e0:2 123:123 -1:-1 -2:-2 +inf:inf -inf:-inf &exponent abc:NaN 1e4:4 2e0:0 123:0 -1:0 -2:0 0:1 +inf:inf -inf:inf &parts abc:NaN,NaN 1e4:1,4 2e0:2,0 123:123,0 -1:-1,0 -2:-2,0 0:0,1 +inf:inf,inf -inf:-inf,inf &bfac -1:NaN NaNfac:NaN +inf:inf -inf:NaN 0:1 1:1 2:2 3:6 4:24 5:120 6:720 7:5040 8:40320 9:362880 10:3628800 11:39916800 12:479001600 20:2432902008176640000 22:1124000727777607680000 69:171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000 &bpow abc:12:NaN 12:abc:NaN 0:0:1 0:1:0 0:2:0 0:-1:inf 0:-2:inf 1:0:1 1:1:1 1:2:1 1:3:1 1:-1:1 1:-2:1 1:-3:1 2:0:1 2:1:2 2:2:4 2:3:8 3:3:27 -2:2:4 -2:3:-8 -2:4:16 -2:5:-32 2:-1:NaN -2:-1:NaN 2:-2:NaN -2:-2:NaN # inf tests +inf:1234500012:inf -inf:1234500012:inf -inf:1234500013:-inf +inf:-12345000123:inf -inf:-12345000123:-inf # -inf * -inf = inf -inf:2:inf -inf:0:NaN -inf:-1:0 -inf:inf:NaN 2:inf:inf 2:-inf:0 0:inf:0 0:-inf:inf -1:-inf:NaN -1:inf:NaN -2:inf:NaN -2:-inf:0 NaN:inf:NaN NaN:-inf:NaN -inf:NaN:NaN inf:NaN:NaN inf:-inf:NaN 1:inf:1 1:-inf:1 # 1 ** -x => 1 / (1 ** x) -1:0:1 -2:0:1 -1:1:-1 -1:2:1 -1:3:-1 -1:4:1 -1:5:-1 -1:-1:-1 -1:-2:1 -1:-3:-1 -1:-4:1 10:2:100 10:3:1000 10:4:10000 10:5:100000 10:6:1000000 10:7:10000000 10:8:100000000 10:9:1000000000 10:20:100000000000000000000 123456:2:15241383936 -2:2:4 -2:3:-8 -2:4:16 -2:5:-32 -3:2:9 -3:3:-27 -3:4:81 -3:5:-243 &length 100:3 10:2 1:1 0:1 12345:5 10000000000000000:17 -123:3 215960156869840440586892398248:30 &broot # sqrt() +0:2:0 +1:2:1 -1:2:NaN # -$x ** (1/2) => -$y, but not in froot() -123:2:NaN +inf:2:inf -inf:2:NaN 2:2:1 -2:2:NaN 4:2:2 9:2:3 16:2:4 100:2:10 123:2:11 15241:2:123 144:2:12 12:2:3 0.49:2:0 0.0049:2:0 # invalid ones 1:NaN:NaN -1:NaN:NaN 0:NaN:NaN -inf:NaN:NaN +inf:NaN:NaN NaN:0:NaN NaN:2:NaN NaN:inf:NaN NaN:inf:NaN 12:-inf:NaN 12:inf:NaN +0:0:NaN +1:0:NaN -1:0:NaN -2:0:NaN -123.45:0:NaN +inf:0:NaN 12:1:12 -12:1:NaN 8:-1:NaN -8:-1:NaN # cubic root 8:3:2 -8:3:NaN # fourths root 16:4:2 81:4:3 # 2 ** 64 18446744073709551616:4:65536 18446744073709551616:8:256 18446744073709551616:16:16 18446744073709551616:32:4 18446744073709551616:64:2 18446744073709551616:128:1 # 213 ** 15 84274086103068221283760416414557757:15:213 # see t/bigroot.t for more tests &bsqrt 145:12 144:12 143:11 16:4 170:13 169:13 168:12 4:2 3:1 2:1 9:3 12:3 256:16 100000000:10000 4000000000000:2000000 152399026:12345 152399025:12345 152399024:12344 # 2 ** 64 => 2 ** 32 18446744073709551616:4294967296 84274086103068221283760416414557757:290299993288095377 1:1 0:0 -2:NaN -123:NaN Nan:NaN +inf:inf -inf:NaN # see t/biglog.t for more tests &bexp NaN:NaN inf:inf 1:2 2:7 # see t/bignok.t for more tests &bnok +inf:10:inf NaN:NaN:NaN NaN:1:NaN 1:NaN:NaN 1:1:1 # k > n 1:2:0 2:3:0 # k < 0 1:-2:0 # 7 over 3 = 35 7:3:35 7:6:7 100:90:17310309456440 100:95:75287520 2:0:1 7:0:1 2:1:2 &bround $round_mode('trunc') 0:12:0 NaNbround:12:NaN +inf:12:inf -inf:12:-inf 1234:0:1234 1234:2:1200 123456:4:123400 123456:5:123450 123456:6:123456 +10123456789:5:10123000000 -10123456789:5:-10123000000 +10123456789:9:10123456700 -10123456789:9:-10123456700 +101234500:6:101234000 -101234500:6:-101234000 #+101234500:-4:101234000 #-101234500:-4:-101234000 $round_mode('zero') +20123456789:5:20123000000 -20123456789:5:-20123000000 +20123456789:9:20123456800 -20123456789:9:-20123456800 +201234500:6:201234000 -201234500:6:-201234000 #+201234500:-4:201234000 #-201234500:-4:-201234000 +12345000:4:12340000 -12345000:4:-12340000 $round_mode('+inf') +30123456789:5:30123000000 -30123456789:5:-30123000000 +30123456789:9:30123456800 -30123456789:9:-30123456800 +301234500:6:301235000 -301234500:6:-301234000 #+301234500:-4:301235000 #-301234500:-4:-301234000 +12345000:4:12350000 -12345000:4:-12340000 $round_mode('-inf') +40123456789:5:40123000000 -40123456789:5:-40123000000 +40123456789:9:40123456800 -40123456789:9:-40123456800 +401234500:6:401234000 +401234500:6:401234000 #-401234500:-4:-401235000 #-401234500:-4:-401235000 +12345000:4:12340000 -12345000:4:-12350000 $round_mode('odd') +50123456789:5:50123000000 -50123456789:5:-50123000000 +50123456789:9:50123456800 -50123456789:9:-50123456800 +501234500:6:501235000 -501234500:6:-501235000 #+501234500:-4:501235000 #-501234500:-4:-501235000 +12345000:4:12350000 -12345000:4:-12350000 $round_mode('even') +60123456789:5:60123000000 -60123456789:5:-60123000000 +60123456789:9:60123456800 -60123456789:9:-60123456800 +601234500:6:601234000 -601234500:6:-601234000 #+601234500:-4:601234000 #-601234500:-4:-601234000 #-601234500:-9:0 #-501234500:-9:0 #-601234500:-8:0 #-501234500:-8:0 +1234567:7:1234567 +1234567:6:1234570 +12345000:4:12340000 -12345000:4:-12340000 $round_mode('common') +60123456789:5:60123000000 +60123199999:5:60123000000 +60123299999:5:60123000000 +60123399999:5:60123000000 +60123499999:5:60123000000 +60123500000:5:60124000000 +60123600000:5:60124000000 +60123700000:5:60124000000 +60123800000:5:60124000000 +60123900000:5:60124000000 -60123456789:5:-60123000000 -60123199999:5:-60123000000 -60123299999:5:-60123000000 -60123399999:5:-60123000000 -60123499999:5:-60123000000 -60123500000:5:-60124000000 -60123600000:5:-60124000000 -60123700000:5:-60124000000 -60123800000:5:-60124000000 -60123900000:5:-60124000000 &is_zero 0:1 NaNzero:0 +inf:0 -inf:0 123:0 -1:0 1:0 &is_one 0:0 NaNone:0 +inf:0 -inf:0 1:1 2:0 -1:0 -2:0 # floor and ceil tests are pretty pointless in integer space...but play safe &bfloor 0:0 NaNfloor:NaN +inf:inf -inf:-inf -1:-1 -2:-2 2:2 3:3 abc:NaN &bceil NaNceil:NaN +inf:inf -inf:-inf 0:0 -1:-1 -2:-2 2:2 3:3 abc:NaN &as_hex 128:0x80 -128:-0x80 0:0x0 -0:0x0 1:0x1 0x123456789123456789:0x123456789123456789 +inf:inf -inf:-inf NaNas_hex:NaN &as_bin 128:0b10000000 -128:-0b10000000 0:0b0 -0:0b0 1:0b1 0b1010111101010101010110110110110110101:0b1010111101010101010110110110110110101 0x123456789123456789:0b100100011010001010110011110001001000100100011010001010110011110001001 +inf:inf -inf:-inf NaNas_bin:NaN