[p5sagit/p5-mst-13.2.git] / lib / Math / BigInt / t / bigintpm.inc

#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 (<DATA>) 
  {
  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";';
   } else {
    # binary ops
    $try .= "\$y = $class->new('$args[1]');";
    if ($f eq "bcmp")
      {
      $try .= '$x <=> $y;';
      } elsif ($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 "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);

# 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);

###############################################################################
# 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
8916100448256:12:12
8916100448257:12:12
8916100448255:12:11
2251799813685248:8:17
72057594037927936:2:56
144115188075855872:2:57
288230376151711744:2:58
576460752303423488:2:59
4096:2:12
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
0:1
-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
# 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
# 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
# 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
&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
&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
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
7:5040
8:40320
9:362880
10:3628800
11:39916800
12:479001600
&bpow
abc:12:NaN
12:abc:NaN
0:0:1
0:1:0
0:2:0
0:-1:NaN
0:-2:NaN
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:NaN
-2:-1:NaN
2:-2:NaN
-2:-2:NaN
+inf:1234500012:inf
-inf:1234500012:-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
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
&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 ** 32
18446744073709551616:4:65536
18446744073709551616:8:256
18446744073709551616:16:16
18446744073709551616:32:4
18446744073709551616:64:2
18446744073709551616:128:1
&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
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
0x123456789123456789:0b100100011010001010110011110001001000100100011010001010110011110001001
+inf:inf
-inf:-inf
NaNas_bin:NaN