# include this file into another for subclass testing # This file is nearly identical to bigintpm.t, except that certain results # are _requird_ to be different due to "upgrading" or "promoting" to BigFloat. # The reverse is not true, any unmarked results can be either BigInt or # BigFloat, depending on how good the internal optimization is (e.g. it # is usually desirable to have 2 ** 2 return a BigInt, not a BigFloat). # Results that are required to be BigFloat are marked with C<^> at the end. # Please note that the testcount goes up by two for each extra result marked # with ^, since then we test whether it has the proper class and that it left # the upgrade variable alone. my $version = ${"$class\::VERSION"}; ############################################################################## # 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 = $class->config()->{lib}; is ($CALC,$CL); my ($f,$z,$a,$exp,@a,$m,$e,$round_mode,$expected_class); while () { $_ =~ s/[\n\r]//g; # remove newlines 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 = $ECL; $ans =~ s/\^$//; } $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();"; } elsif ($f eq "as_hex") { $try .= '$x->as_hex();'; } elsif ($f eq "as_bin") { $try .= '$x->as_bin();'; } 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 eq "length") { $try .= '$x->length();'; } 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,$e";'; } else { if ($args[1] !~ /\./) { $try .= "\$y = $class->new(\"$args[1]\");"; # BigInt } else { $try .= "\$y = $ECL->new(\"$args[1]\");"; # BigFloat } if ($f eq "bcmp") { $try .= '$x->bcmp($y);'; } elsif ($f eq "bround") { $try .= "$round_mode; \$x->bround(\$y);"; } elsif ($f eq "broot") { $try .= "\$x->broot(\$y);"; } elsif ($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 "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 "digit"){ $try = "\$x = $class->new('$args[0]'); \$x->digit($args[1]);"; } else { warn "Unknown op '$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 ($ans eq "") { is ($ans1, undef); } else { # print "try: $try ans: $ans1 $ans\n"; print "# Tried: '$try'\n" if !is ($ans1, $ans); if ($expected_class ne $class) { is (ref($ans1),$expected_class); # also checks that it really is ref! is ($Math::BigInt::upgrade,'Math::BigFloat'); # still okay? } } # check internal state of number objects is_valid($ans1,$f) if ref $ans1; } # endwhile data tests close DATA; my $warn = ''; $SIG{__WARN__} = sub { $warn = shift; }; # these should not warn $warn = ''; eval "\$z = 3.17 <= \$y"; is ($z, 1); is ($warn, ''); $warn = ''; eval "\$z = \$y >= 3.17"; is ($z, 1); is ($warn, ''); # all tests done 1; ############################################################################### # sub to check validity of a BigInt internally, to ensure that no op leaves a # number object in an invalid state (f.i. "-0") sub is_valid { my ($x,$f,$c) = @_; # The checks here are loosened a bit to allow BigInt or BigFloats to pass my $e = 0; # error? # ok as reference? # $e = "Not a reference to $c" if (ref($x) || '') ne $c; # 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 $e eq '0'; # test done, see if error did crop up is (1,1), return if ($e eq '0'); is (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 &/= 100:3:33.33333333333333333333333333333333333333 -8:2:-4 &|= 2:1:3 &&= 5:7:5 &^= 5:7:2 &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_odd abc:0 0:0 1:1 3:1 -1:1 -3:1 10000001:1 10000002:0 2:0 120:0 121:1 &is_int NaN:0 inf:0 -inf:0 1:1 12:1 123e12:1 &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 # return undef +inf:NaN: NaN:inf: -inf:NaN: NaN:-inf: &bnorm 123:123 12.3:12.3^ # 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 # 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 1.23E1:12.3^ 1.23E-1:0.123^ # bug with two E's in number being valid 1e2e3:NaN 1e2r:NaN 1e2.0: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 # 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:-10.1^ -1.01E+1:-10.1^ -1.01E-1:-0.101^ &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 # 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 &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 &bsstr 1e+34:1e+34 123.456E3:123456e+0 100:1e+2 abc:NaN &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 2:2.5:4.5^ -123:-1.5:-124.5^ -1.2:1:-0.2^ &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 &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 3:3.5:10.5^ 3.5:3:10.5^ &bdiv-list 100:20:5,0 4095:4095:1,0 -4095:-4095:1,0 4095:-4095:-1,0 -4095:4095:-1,0 123:2:61.5,1 9:5:1.8,4 9:4:2.25,1 # inf handling and general remainder 5:8:0.625,5 0:8:0,0 11:2:5.5,1 11:-2:-5.5,-1 -11:2:-5.5,1 # 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 &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 11:2:5.5^ -11:-2:5.5^ -11:2:-5.5^ 11:-2:-5.5^ 0:1:0 0:-1:0 1:1:1 -1:-1:1 1:-1:-1 -1:1:-1 1:2:0.5^ 2:1:2 1000000000:9:111111111.1111111111111111111111111111111^ 2000000000:9:222222222.2222222222222222222222222222222^ 3000000000:9:333333333.3333333333333333333333333333333^ 4000000000:9:444444444.4444444444444444444444444444444^ 5000000000:9:555555555.5555555555555555555555555555556^ 6000000000:9:666666666.6666666666666666666666666666667^ 7000000000:9:777777777.7777777777777777777777777777778^ 8000000000:9:888888888.8888888888888888888888888888889^ 9000000000:9:1000000000 35500000:113:314159.2920353982300884955752212389380531^ 71000000:226:314159.2920353982300884955752212389380531^ 106500000:339:314159.2920353982300884955752212389380531^ 1000000000:3:333333333.3333333333333333333333333333333^ +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:-3:1.666666666666666666666666666666666666667^ -5:3:-1.666666666666666666666666666666666666667^ 4:3:1.333333333333333333333333333333333333333^ 4:-3:-1.333333333333333333333333333333333333333^ 1:3:0.3333333333333333333333333333333333333333^ 1:-3:-0.3333333333333333333333333333333333333333^ -2:-3:0.6666666666666666666666666666666666666667^ -2:3:-0.6666666666666666666666666666666666666667^ 8:5:1.6^ -8:5:-1.6^ 14:-3:-4.666666666666666666666666666666666666667^ -14:3:-4.666666666666666666666666666666666666667^ -14:-3:4.666666666666666666666666666666666666667^ 14:3:4.666666666666666666666666666666666666667^ # bug in Calc with '99999' vs $BASE-1 #10000000000000000000000000000000000000000000000000000000000000000000000000000000000:10000000375084540248994272022843165711074:999999962491547381984643365663244474111576 12:24:0.5^ &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 &bgcd 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:+2:1 100:625:25 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 -2:-3:-4 -1:-1:-1 -6:-6:-6 -7:-4:-8 -7:4:0 -4:7:4 # 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 # 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 # 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 10:3628800 11:39916800 12:479001600 &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:-1:0.5^ -2:-1:-0.5^ 2:-2:0.25^ # Y is even => result positive -2:-2:0.25^ # Y is odd => result negative -2:-3:-0.125^ +inf:1234500012:inf -inf:1234500012:inf -inf:1234500013:-inf +inf:-12345000123:inf -inf:-12345000123:-inf # 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 -2:2:4 -2:3:-8 -2:4:16 -2:5:-32 -3:2:9 -3:3:-27 -3:4:81 -3:5:-243 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 #2:0.5:1.41^ &length 100:3 10:2 1:1 0:1 12345:5 10000000000000000:17 -123:3 215960156869840440586892398248:30 # broot always upgrades &broot 144:2:12^ 123:2:11.09053650640941716205160010260993291846^ # bsqrt always upgrades &bsqrt 145:12.04159457879229548012824103037860805243^ 144:12^ 143:11.95826074310139802112984075619561661399^ 16:4 170:13.03840481040529742916594311485836883306^ 169:13 168:12.96148139681572046193193487217599331541^ 4:2 3:1.732050807568877293527446341505872366943^ 2:1.41421356237309504880168872420969807857^ 9:3 12:3.464101615137754587054892683011744733886^ 256:16 100000000:10000 4000000000000:2000000 152399026:12345.00004050222755607815159966235881398^ 152399025:12345 152399024:12344.99995949777231103967404745303741942^ 1:1 0:0 -2:NaN -123:NaN Nan:NaN +inf:inf -inf:NaN &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 &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 +inf:inf -inf:-inf NaNas_bin:NaN