BigInt v1.68 - pre-release

Message-Id: <200312230106.27661@bloodgate.com>

p4raw-id: //depot/perl@21956

12 files changed, 1055 insertions, 649 deletions

diff --git a/lib/Math/BigFloat.pm b/lib/Math/BigFloat.pm
index 3b8d5a6e04..9071648b51 100644
--- a/lib/Math/BigFloat.pm
+++ b/lib/Math/BigFloat.pm
@@ -12,16 +12,15 @@ package Math::BigFloat;
 #   _p: precision
 #   _f: flags, used to signal MBI not to touch our private parts
 
-$VERSION = '1.41';
+$VERSION = '1.42';
 require 5.005;
 use Exporter;
 @ISA =       qw(Exporter Math::BigInt);
 
 use strict;
-use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode/;
-use vars qw/$upgrade $downgrade/;
-# the following are internal and should never be accessed from the outside
-use vars qw/$_trap_nan $_trap_inf/;
+# $_trap_inf and $_trap_nan are internal and should never be accessed from the outside
+use vars qw/$AUTOLOAD $accuracy $precision $div_scale $round_mode $rnd_mode
+	    $upgrade $downgrade $_trap_nan $_trap_inf/;
 my $class = "Math::BigFloat";
 
 use overload
@@ -50,7 +49,7 @@ my $MBI = 'Math::BigInt'; # the package we are using for our private parts
 
 # the following are private and not to be used from the outside:
 
-use constant MB_NEVER_ROUND => 0x0001;
+sub MB_NEVER_ROUND () { 0x0001; }
 
 # are NaNs ok? (otherwise it dies when encountering an NaN) set w/ config()
 $_trap_nan = 0;
@@ -151,6 +150,7 @@ sub new
     return $self->bnorm();
     }
   #print "new string '$wanted'\n";
+
   my ($mis,$miv,$mfv,$es,$ev) = Math::BigInt::_split(\$wanted);
   if (!ref $mis)
     {
@@ -172,10 +172,33 @@ sub new
     # undef,undef to signal MBI that we don't need no bloody rounding
     $self->{_e} = $MBI->new("$$es$$ev",undef,undef);	# exponent
     $self->{_m} = $MBI->new("$$miv$$mfv",undef,undef); 	# create mant.
-    # print  $self->{_e}, " ", $self->{_m},"\n";
+
+    # this is to prevent automatically rounding when MBI's globals are set
+    $self->{_m}->{_f} = MB_NEVER_ROUND;
+    $self->{_e}->{_f} = MB_NEVER_ROUND;
+
     # 3.123E0 = 3123E-3, and 3.123E-2 => 3123E-5
-    $self->{_e} -= CORE::length($$mfv) if CORE::length($$mfv) != 0;
+    $self->{_e}->bsub( $MBI->new(CORE::length($$mfv),undef,undef))
+      if CORE::length($$mfv) != 0;
     $self->{sign} = $$mis;
+    
+    #print "$$miv$$mfv $$es$$ev\n";
+
+    # we can only have trailing zeros on the mantissa of $$mfv eq ''
+    if (CORE::length($$mfv) == 0)
+      {
+      my $zeros = $self->{_m}->_trailing_zeros(); # correct for trailing zeros 
+      if ($zeros != 0)
+        {
+        $self->{_m}->brsft($zeros,10); $self->{_e}->badd($MBI->new($zeros));
+        }
+      }
+#    else
+#      {
+      # for something like 0Ey, set y to 1, and -0 => +0
+      $self->{sign} = '+', $self->{_e}->bone() if $self->{_m}->is_zero();
+#      }
+    return $self->round(@r) if !$downgrade;
     }
   # if downgrade, inf, NaN or integers go down
 
@@ -352,8 +375,8 @@ sub bsstr
 sub numify 
   {
   # Make a number from a BigFloat object
-  # simple return string and let Perl's atoi()/atof() handle the rest
-  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+  # simple return a string and let Perl's atoi()/atof() handle the rest
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
   $x->bsstr(); 
   }
 
@@ -361,7 +384,7 @@ sub numify
 # public stuff (usually prefixed with "b")
 
 # tels 2001-08-04 
-# todo: this must be overwritten and return NaN for non-integer values
+# XXX TODO this must be overwritten and return NaN for non-integer values
 # band(), bior(), bxor(), too
 #sub bnot
 #  {
@@ -371,7 +394,6 @@ sub numify
 sub bcmp 
   {
   # Compares 2 values.  Returns one of undef, <0, =0, >0. (suitable for sort)
-  # (BFLOAT or num_str, BFLOAT or num_str) return cond_code
 
   # set up parameters
   my ($self,$x,$y) = (ref($_[0]),@_);
@@ -437,7 +459,6 @@ sub bacmp
   {
   # Compares 2 values, ignoring their signs. 
   # Returns one of undef, <0, =0, >0. (suitable for sort)
-  # (BFLOAT or num_str, BFLOAT or num_str) return cond_code
   
   # set up parameters
   my ($self,$x,$y) = (ref($_[0]),@_);
@@ -573,7 +594,6 @@ sub bsub
     ($self,$x,$y,$a,$p,$r) = objectify(2,@_);
     }
 
-  # XXX TODO: remove?
   if ($y->is_zero())		# still round for not adding zero
     {
     return $x->round($a,$p,$r);
@@ -589,42 +609,45 @@ sub bsub
 sub binc
   {
   # increment arg by one
-  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
 
   if ($x->{_e}->sign() eq '-')
     {
-    return $x->badd($self->bone(),$a,$p,$r);	#  digits after dot
+    return $x->badd($self->bone(),@r);	#  digits after dot
     }
 
-  if (!$x->{_e}->is_zero())
+  if (!$x->{_e}->is_zero())			# _e == 0 for NaN, inf, -inf
     {
+    # 1e2 => 100, so after the shift below _m has a '0' as last digit
     $x->{_m}->blsft($x->{_e},10);		# 1e2 => 100
-    $x->{_e}->bzero();
+    $x->{_e}->bzero();				# normalize
+    # we know that the last digit of $x will be '1' or '9', depending on the
+    # sign
     }
   # now $x->{_e} == 0
   if ($x->{sign} eq '+')
     {
     $x->{_m}->binc();
-    return $x->bnorm()->bround($a,$p,$r);
+    return $x->bnorm()->bround(@r);
     }
   elsif ($x->{sign} eq '-')
     {
     $x->{_m}->bdec();
     $x->{sign} = '+' if $x->{_m}->is_zero(); # -1 +1 => -0 => +0
-    return $x->bnorm()->bround($a,$p,$r);
+    return $x->bnorm()->bround(@r);
     }
   # inf, nan handling etc
-  $x->badd($self->bone(),$a,$p,$r);		# does round 
+  $x->badd($self->bone(),@r);			# badd() does round 
   }
 
 sub bdec
   {
   # decrement arg by one
-  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
 
   if ($x->{_e}->sign() eq '-')
     {
-    return $x->badd($self->bone('-'),$a,$p,$r);	#  digits after dot
+    return $x->badd($self->bone('-'),@r);	#  digits after dot
     }
 
   if (!$x->{_e}->is_zero())
@@ -640,16 +663,16 @@ sub bdec
     $x->{_m}->binc();
     $x->{sign} = '-' if $zero;			# 0 => 1 => -1
     $x->{sign} = '+' if $x->{_m}->is_zero();	# -1 +1 => -0 => +0
-    return $x->bnorm()->round($a,$p,$r);
+    return $x->bnorm()->round(@r);
     }
   # > 0
   elsif ($x->{sign} eq '+')
     {
     $x->{_m}->bdec();
-    return $x->bnorm()->round($a,$p,$r);
+    return $x->bnorm()->round(@r);
     }
   # inf, nan handling etc
-  $x->badd($self->bone('-'),$a,$p,$r);		# does round 
+  $x->badd($self->bone('-'),@r);		# does round 
   } 
 
 sub DEBUG () { 0; }
@@ -718,15 +741,40 @@ sub blog
     $x = Math::BigFloat->new($x);
     $self = ref($x);
     }
-  # first calculate the log to base e (using reduction by 10 (and probably 2))
-  $self->_log_10($x,$scale);
- 
-  # and if a different base was requested, convert it
-  if (defined $base)
+  
+  my $done = 0;
+
+  # If the base is defined and an integer, try to calculate integer result
+  # first. This is very fast, and in case the real result was found, we can
+  # stop right here.
+  if (defined $base && $base->is_int() && $x->is_int())
+    {
+    my $int = $x->{_m}->copy();
+    $int->blsft($x->{_e},10) unless $x->{_e}->is_zero();
+    $int->blog($base->as_number());
+    # if ($exact)
+    if ($base->copy()->bpow($int) == $x)
+      {
+      # found result, return it
+      $x->{_m} = $int;
+      $x->{_e} = $MBI->bzero();
+      $x->bnorm();
+      $done = 1;
+      }
+    }
+
+  if ($done == 0)
     {
-    $base = Math::BigFloat->new($base) unless $base->isa('Math::BigFloat');
-    # not ln, but some other base (don't modify $base)
-    $x->bdiv( $base->copy()->blog(undef,$scale), $scale );
+    # first calculate the log to base e (using reduction by 10 (and probably 2))
+    $self->_log_10($x,$scale);
+ 
+    # and if a different base was requested, convert it
+    if (defined $base)
+      {
+      $base = Math::BigFloat->new($base) unless $base->isa('Math::BigFloat');
+      # not ln, but some other base (don't modify $base)
+      $x->bdiv( $base->copy()->blog(undef,$scale), $scale );
+      }
     }
  
   # shortcut to not run through _find_round_parameters again
@@ -1541,20 +1589,23 @@ sub bfac
   {
   # (BFLOAT or num_str, BFLOAT or num_str) return BFLOAT
   # compute factorial number, modifies first argument
-  my ($self,$x,@r) = objectify(1,@_);
 
+  # set up parameters
+  my ($self,$x,@r) = (ref($_[0]),@_);
+  # objectify is costly, so avoid it
+  ($self,$x,@r) = objectify(1,@_) if !ref($x);
+
+ return $x if $x->{sign} eq '+inf';	# inf => inf
   return $x->bnan() 
     if (($x->{sign} ne '+') ||		# inf, NaN, <0 etc => NaN
      ($x->{_e}->{sign} ne '+'));	# digits after dot?
 
   # use BigInt's bfac() for faster calc
-  if (! _is_zero_or_one($x->{_e}))	
+  if (! $x->{_e}->is_zero())
     {
-    $x->{_m}->blsft($x->{_e},10);	# unnorm
-    $x->{_e}->bzero();			# norm again
+    $x->{_m}->blsft($x->{_e},10);	# change 12e1 to 120e0
+    $x->{_e}->bzero();
     }
-  $x->{_m}->blsft($x->{_e},10);		# un-norm m
-  $x->{_e}->bzero();						# norm again
   $x->{_m}->bfac();			# calculate factorial
   $x->bnorm()->round(@r); 		# norm again and round result
   }
@@ -1948,7 +1999,7 @@ sub blsft
 
 sub DESTROY
   {
-  # going through AUTOLOAD for every DESTROY is costly, so avoid it by empty sub
+  # going through AUTOLOAD for every DESTROY is costly, avoid it by empty sub
   }
 
 sub AUTOLOAD
@@ -2123,16 +2174,19 @@ sub bnorm
 
   return $x if $x->{sign} !~ /^[+-]$/;		# inf, nan etc
 
-#  if (!$x->{_m}->is_odd())
-#    {
-    my $zeros = $x->{_m}->_trailing_zeros();	# correct for trailing zeros 
-    if ($zeros != 0)
-      {
-      $x->{_m}->brsft($zeros,10); $x->{_e}->badd($zeros);
-      }
-    # for something like 0Ey, set y to 1, and -0 => +0
+  my $zeros = $x->{_m}->_trailing_zeros();	# correct for trailing zeros 
+  if ($zeros != 0)
+    {
+    my $z = $MBI->new($zeros,undef,undef);
+    $x->{_m}->brsft($z,10); $x->{_e}->badd($z);
+    }
+  else
+    {
+    # $x can only be 0Ey if there are no trailing zeros ('0' has 0 trailing
+    # zeros). So, for something like 0Ey, set y to 1, and -0 => +0
     $x->{sign} = '+', $x->{_e}->bone() if $x->{_m}->is_zero();
-#    }
+    }
+
   # this is to prevent automatically rounding when MBI's globals are set
   $x->{_m}->{_f} = MB_NEVER_ROUND;
   $x->{_e}->{_f} = MB_NEVER_ROUND;
diff --git a/lib/Math/BigInt.pm b/lib/Math/BigInt.pm
index 1b166004a2..aeee0e281f 100644
--- a/lib/Math/BigInt.pm
+++ b/lib/Math/BigInt.pm
@@ -18,14 +18,14 @@ package Math::BigInt;
 my $class = "Math::BigInt";
 require 5.005;
 
-$VERSION = '1.67';
+$VERSION = '1.68';
 use Exporter;
 @ISA =       qw( Exporter );
 @EXPORT_OK = qw( objectify bgcd blcm); 
-use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode/;
-use vars qw/$upgrade $downgrade/;
-# the following are internal and should never be accessed from the outside
-use vars qw/$_trap_nan $_trap_inf/;
+# _trap_inf and _trap_nan are internal and should never be accessed from the
+# outside
+use vars qw/$round_mode $accuracy $precision $div_scale $rnd_mode 
+	    $upgrade $downgrade $_trap_nan $_trap_inf/;
 use strict;
 
 # Inside overload, the first arg is always an object. If the original code had
@@ -66,11 +66,6 @@ use overload
                "$_[1]" cmp $_[0]->bstr() :
                $_[0]->bstr() cmp "$_[1]" },
 
-#'cos' => sub {
-#  require Math::Big; 
-#  return Math::Big::cos($_[0], ref($_[0])->accuracy());
-#  },
-
 # make cos()/sin()/exp() "work" with BigInt's or subclasses
 'cos'	=>	sub { cos($_[0]->numify()) }, 
 'sin'	=>	sub { sin($_[0]->numify()) }, 
@@ -152,7 +147,7 @@ $downgrade = undef;			# default is no downgrade
 
 # these are internally, and not to be used from the outside
 
-use constant MB_NEVER_ROUND => 0x0001;
+sub MB_NEVER_ROUND () { 0x0001; }
 
 $_trap_nan = 0;				# are NaNs ok? set w/ config()
 $_trap_inf = 0;				# are infs ok? set w/ config()
@@ -164,6 +159,9 @@ my %CAN;				# cache for $CALC->can(...)
 my $IMPORT = 0;				# was import() called yet?
 					# used to make require work
 
+my $EMU_LIB = 'Math/BigInt/CalcEmu.pm';	# emulate low-level math
+my $EMU = 'Math::BigInt::CalcEmu';	# emulate low-level math
+
 ##############################################################################
 # the old code had $rnd_mode, so we need to support it, too
 
@@ -172,7 +170,16 @@ sub TIESCALAR  { my ($class) = @_; bless \$round_mode, $class; }
 sub FETCH      { return $round_mode; }
 sub STORE      { $rnd_mode = $_[0]->round_mode($_[1]); }
 
-BEGIN { tie $rnd_mode, 'Math::BigInt'; }
+BEGIN
+  { 
+  # tie to enable $rnd_mode to work transparently
+  tie $rnd_mode, 'Math::BigInt'; 
+
+  # set up some handy alias names
+  *as_int = \&as_number;
+  *is_pos = \&is_positive;
+  *is_neg = \&is_negative;
+  }
 
 ############################################################################## 
 
@@ -798,8 +805,9 @@ sub bsstr
     return 'inf';					# +inf
     }
   my ($m,$e) = $x->parts();
-  my $sign = 'e+'; # e can only be positive
-  return $m->bstr().$sign.$e->bstr();
+  #$m->bstr() . 'e+' . $e->bstr(); 	# e can only be positive in BigInt
+  # 'e+' because E can only be positive in BigInt
+  $m->bstr() . 'e+' . ${$CALC->_str($e->{value})}; 
   }
 
 sub bstr 
@@ -814,7 +822,7 @@ sub bstr
     return 'inf';					# +inf
     }
   my $es = ''; $es = $x->{sign} if $x->{sign} eq '-';
-  return $es.${$CALC->_str($x->{value})};
+  $es.${$CALC->_str($x->{value})};
   }
 
 sub numify 
@@ -834,7 +842,7 @@ sub numify
 sub sign
   {
   # return the sign of the number: +/-/-inf/+inf/NaN
-  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_); 
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_); 
   
   $x->{sign};
   }
@@ -960,7 +968,7 @@ sub round
   $r = ${"$c\::round_mode"} unless defined $r;
   if ($r !~ /^(even|odd|\+inf|\-inf|zero|trunc)$/)
     {
-   
+    require Carp; Carp::croak ("Unknown round mode '$r'");
     }
 
   # now round, by calling either fround or ffround:
@@ -979,7 +987,7 @@ sub bnorm
   { 
   # (numstr or BINT) return BINT
   # Normalize number -- no-op here
-  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
   $x;
   }
 
@@ -1050,7 +1058,7 @@ sub bcmp
     }
 
   # $x && $y both < 0
-  $CALC->_acmp($y->{value},$x->{value});	# swaped (lib returns 0,1,-1)
+  $CALC->_acmp($y->{value},$x->{value});	# swaped acmp (lib returns 0,1,-1)
   }
 
 sub bacmp 
@@ -1116,12 +1124,11 @@ sub badd
     return $x;
     }
     
-  my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); # get signs
+  my ($sx, $sy) = ( $x->{sign}, $y->{sign} ); 		# get signs
 
   if ($sx eq $sy)  
     {
     $x->{value} = $CALC->_add($x->{value},$y->{value});	# same sign, abs add
-    $x->{sign} = $sx;
     }
   else 
     {
@@ -1140,7 +1147,6 @@ sub badd
     else # a < 0
       {
       $x->{value} = $CALC->_sub($x->{value}, $y->{value}); # abs sub
-      $x->{sign} = $sx;
       }
     }
   $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
@@ -1204,29 +1210,32 @@ sub binc
 sub bdec
   {
   # decrement arg by one
-  my ($self,$x,$a,$p,$r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
+  my ($self,$x,@r) = ref($_[0]) ? (ref($_[0]),@_) : objectify(1,@_);
   return $x if $x->modify('bdec');
   
-  my $zero = $CALC->_is_zero($x->{value}) && $x->{sign} eq '+';
-  # <= 0
-  if (($x->{sign} eq '-') || $zero) 
+  if ($x->{sign} eq '-')
     {
+    # < 0
     $x->{value} = $CALC->_inc($x->{value});
-    $x->{sign} = '-' if $zero;			# 0 => 1 => -1
-    $x->{sign} = '+' if $CALC->_is_zero($x->{value}); # -1 +1 => -0 => +0
-    $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
-    return $x;
-    }
-  # > 0
-  elsif ($x->{sign} eq '+')
+    } 
+  else
     {
-    $x->{value} = $CALC->_dec($x->{value});
-    $x->round($a,$p,$r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
-    return $x;
+    return $x->badd($self->bone('-'),@r) unless $x->{sign} eq '+'; # inf/NaN
+    # >= 0
+    if ($CALC->_is_zero($x->{value}))
+      {
+      # == 0
+      $x->{value} = $CALC->_one(); $x->{sign} = '-';		# 0 => -1
+      }
+    else
+      {
+      # > 0
+      $x->{value} = $CALC->_dec($x->{value});
+      }
     }
-  # inf, nan handling etc
-  $x->badd($self->bone('-'),$a,$p,$r);			# badd does round
-  } 
+  $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+  $x;
+  }
 
 sub blog
   {
@@ -1238,7 +1247,7 @@ sub blog
   # objectify is costly, so avoid it
   if ((!ref($_[0])) || (ref($_[0]) ne ref($_[1])))
     {
-    ($self,$x,$base,@r) = objectify(2,@_);
+    ($self,$x,$base,@r) = objectify(2,$class,@_);
     }
 
   # inf, -inf, NaN, <0 => NaN
@@ -1256,26 +1265,8 @@ sub blog
     return $x->round(@r);
     }
 
-  return $x->bnan() if $x->is_zero() || $base->is_zero() || $base->is_one();
-
-  my $acmp = $x->bacmp($base);
-  return $x->bone('+',@r) if $acmp == 0;
-  return $x->bzero(@r) if $acmp < 0 || $x->is_one();
- 
-  # blog($x,$base) ** $base + $y = $x 
-
-  # this trial multiplication is very fast, even for large counts (like for
-  # 2 ** 1024, since this still requires only 1024 very fast steps
-  # (multiplication of a large number by a very small number is very fast))
-  # See Calc for an even faster algorightmn
-  my $x_org = $x->copy();		# preserve orgx 
-  $x->bzero();				# keep ref to $x
-  my $trial = $base->copy();
-  while ($trial->bacmp($x_org) <= 0)
-    {
-    $trial->bmul($base); $x->binc();
-    }
-  $x->round(@r);
+  require $EMU_LIB;
+  __emu_blog($self,$x,$base,@r);
   }
 
 sub blcm 
@@ -1661,53 +1652,15 @@ sub bmodinv
     {
     my $sign;
     ($x->{value},$sign) = $CALC->_modinv($x->{value},$y->{value});
-    $x->bnan() if !defined $x->{value};                 # in case no GCD found
-    return $x if !defined $sign;                        # already real result
-    $x->{sign} = $sign;                                 # flip/flop see below
-    $x->bmod($y);                                       # calc real result
+    return $x->bnan() if !defined $x->{value};		# in case no GCD found
+    return $x if !defined $sign;			# already real result
+    $x->{sign} = $sign;					# flip/flop see below
+    $x->bmod($y);					# calc real result
     return $x;
     }
-  my ($u, $u1) = ($self->bzero(), $self->bone());
-  my ($a, $b) = ($y->copy(), $x->copy());
-
-  # first step need always be done since $num (and thus $b) is never 0
-  # Note that the loop is aligned so that the check occurs between #2 and #1
-  # thus saving us one step #2 at the loop end. Typical loop count is 1. Even
-  # a case with 28 loops still gains about 3% with this layout.
-  my $q;
-  ($a, $q, $b) = ($b, $a->bdiv($b));                    # step #1
-  # Euclid's Algorithm (calculate GCD of ($a,$b) in $a and also calculate
-  # two values in $u and $u1, we use only $u1 afterwards)
-  my $sign = 1;                                         # flip-flop
-  while (!$b->is_zero())                                # found GCD if $b == 0
-    {
-    # the original algorithm had:
-    # ($u, $u1) = ($u1, $u->bsub($u1->copy()->bmul($q))); # step #2
-    # The following creates exact the same sequence of numbers in $u1,
-    # except for the sign ($u1 is now always positive). Since formerly
-    # the sign of $u1 was alternating between '-' and '+', the $sign
-    # flip-flop will take care of that, so that at the end of the loop
-    # we have the real sign of $u1. Keeping numbers positive gains us
-    # speed since badd() is faster than bsub() and makes it possible
-    # to have the algorithmn in Calc for even more speed.
-
-    ($u, $u1) = ($u1, $u->badd($u1->copy()->bmul($q))); # step #2
-    $sign = - $sign;                                    # flip sign
-
-    ($a, $q, $b) = ($b, $a->bdiv($b));                  # step #1 again
-    }
 
-  # If the gcd is not 1, then return NaN! It would be pointless to
-  # have called bgcd to check this first, because we would then be
-  # performing the same Euclidean Algorithm *twice*.
-  return $x->bnan() unless $a->is_one();
-
-  $u1->bneg() if $sign != 1;                            # need to flip?
-
-  $u1->bmod($y);                                        # calc result
-  $x->{value} = $u1->{value};                           # and copy over to $x
-  $x->{sign} = $u1->{sign};                             # to modify in place
-  $x;
+  require $EMU_LIB;
+  __emu_bmodinv($self,$x,$y,@r);
   }
 
 sub bmodpow
@@ -1742,24 +1695,8 @@ sub bmodpow
     return $num;
     }
 
-  # in the trivial case,
-  return $num->bzero(@r) if $mod->is_one();
-  return $num->bone('+',@r) if $num->is_zero() or $num->is_one();
-
-  # $num->bmod($mod);           # if $x is large, make it smaller first
-  my $acc = $num->copy();	# but this is not really faster...
-
-  $num->bone(); # keep ref to $num
-
-  my $expbin = $exp->as_bin(); $expbin =~ s/^[-]?0b//; # ignore sign and prefix
-  my $len = CORE::length($expbin);
-  while (--$len >= 0)
-    {
-    $num->bmul($acc)->bmod($mod) if substr($expbin,$len,1) eq '1';
-    $acc->bmul($acc)->bmod($mod);
-    }
-
-  $num;
+  require $EMU_LIB;
+  __emu_bmodpow($self,$num,$exp,$mod,@r);
   }
 
 ###############################################################################
@@ -1772,7 +1709,8 @@ sub bfac
 
   return $x if $x->modify('bfac');
  
-  return $x->bnan() if $x->{sign} ne '+';	# inf, NnN, <0 etc => NaN
+  return $x if $x->{sign} eq '+inf';		# inf => inf
+  return $x->bnan() if $x->{sign} ne '+';	# NaN, <0 etc => NaN
 
   if ($CAN{fac})
     {
@@ -1780,17 +1718,8 @@ sub bfac
     return $x->round(@r);
     }
 
-  return $x->bone('+',@r) if $x->is_zero() || $x->is_one();	# 0 or 1 => 1
-
-  my $n = $x->copy();
-  $x->bone();
-  # seems we need not to temp. clear A/P of $x since the result is the same
-  my $f = $self->new(2);
-  while ($f->bacmp($n) < 0)
-    {
-    $x->bmul($f); $f->binc();
-    }
-  $x->bmul($f,@r);			# last step and also round
+  require $EMU_LIB;
+  __emu_bfac($self,$x,@r);
   }
  
 sub bpow 
@@ -1815,8 +1744,9 @@ sub bpow
   $r[3] = $y;					# no push!
   return $x if $x->{sign} =~ /^[+-]inf$/;	# -inf/+inf ** x
   return $x->bnan() if $x->{sign} eq $nan || $y->{sign} eq $nan;
-  return $x->bone('+',@r) if $y->is_zero();
-  return $x->round(@r) if $x->is_one() || $y->is_one();
+
+  # cases 0 ** Y, X ** 0, X ** 1, 1 ** Y are handled by Calc or Emu
+
   if ($x->{sign} eq '-' && $CALC->_is_one($x->{value}))
     {
     # if $x == -1 and odd/even y => +1/-1
@@ -1825,44 +1755,18 @@ sub bpow
     }
   # 1 ** -y => 1 / (1 ** |y|)
   # so do test for negative $y after above's clause
-  return $x->bnan() if $y->{sign} eq '-';
-  return $x->round(@r) if $x->is_zero();  # 0**y => 0 (if not y <= 0)
+  return $x->bnan() if $y->{sign} eq '-' && !$x->is_one();
 
   if ($CAN{pow})
     {
     $x->{value} = $CALC->_pow($x->{value},$y->{value});
+    $x->{sign} = '+' if $CALC->_is_zero($y->{value});
     $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
     return $x;
     }
 
-# based on the assumption that shifting in base 10 is fast, and that mul
-# works faster if numbers are small: we count trailing zeros (this step is
-# O(1)..O(N), but in case of O(N) we save much more time due to this),
-# stripping them out of the multiplication, and add $count * $y zeros
-# afterwards like this:
-# 300 ** 3 == 300*300*300 == 3*3*3 . '0' x 2 * 3 == 27 . '0' x 6
-# creates deep recursion since brsft/blsft use bpow sometimes.
-#  my $zeros = $x->_trailing_zeros();
-#  if ($zeros > 0)
-#    {
-#    $x->brsft($zeros,10);	# remove zeros
-#    $x->bpow($y);		# recursion (will not branch into here again)
-#    $zeros = $y * $zeros; 	# real number of zeros to add
-#    $x->blsft($zeros,10);
-#    return $x->round(@r);
-#    }
-
-  my $pow2 = $self->bone();
-  my $y_bin = $y->as_bin(); $y_bin =~ s/^0b//;
-  my $len = CORE::length($y_bin);
-  while (--$len > 0)
-    {
-    $pow2->bmul($x) if substr($y_bin,$len,1) eq '1';	# is odd?
-    $x->bmul($x);
-    }
-  $x->bmul($pow2);
-  $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
-  $x;
+  require $EMU_LIB;
+  __emu_bpow($self,$x,$y,@r);
   }
 
 sub blsft 
@@ -1890,7 +1794,7 @@ sub blsft
     $x->{value} = $t; return $x->round(@r);
     }
   # fallback
-  return $x->bmul( $self->bpow($n, $y, @r), @r );
+  $x->bmul( $self->bpow($n, $y, @r), @r );
   }
 
 sub brsft 
@@ -1946,6 +1850,7 @@ sub brsft
       $x->{value} = $res->{value};	# take over value
       return $x->round(@r);		# we are done now, magic, isn't?
       }
+    # x < 0, n == 2, y == 1
     $x->bdec();				# n == 2, but $y == 1: this fixes it
     }
 
@@ -1976,12 +1881,11 @@ sub band
   return $x if $x->modify('band');
 
   $r[3] = $y;				# no push!
-  local $Math::BigInt::upgrade = undef;
 
   return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
 
-  my $sx = 1; $sx = -1 if $x->{sign} eq '-';
-  my $sy = 1; $sy = -1 if $y->{sign} eq '-';
+  my $sx = $x->{sign} eq '+' ? 1 : -1;
+  my $sy = $y->{sign} eq '+' ? 1 : -1;
   
   if ($CAN{and} && $sx == 1 && $sy == 1)
     {
@@ -1994,92 +1898,9 @@ sub band
     $x->{value} = $CALC->_signed_and($x->{value},$y->{value},$sx,$sy);
     return $x->round(@r);
     }
-  
-  return $x->bzero(@r) if $y->is_zero() || $x->is_zero();
-  
-  my $sign = 0;					# sign of result
-  $sign = 1 if ($x->{sign} eq '-') && ($y->{sign} eq '-');
-
-  my ($bx,$by);
-
-  if ($sx == -1)				# if x is negative
-    {
-    # two's complement: inc and flip all "bits" in $bx
-    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
-    $bx =~ s/-?0x//; 
-    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  else
-    {
-    $bx = $x->as_hex();				# get binary representation
-    $bx =~ s/-?0x//;
-    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  if ($sy == -1)				# if y is negative
-    {
-    # two's complement: inc and flip all "bits" in $by
-    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
-    $by =~ s/-?0x//; 
-    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  else
-    {
-    $by = $y->as_hex();				# get binary representation
-    $by =~ s/-?0x//;
-    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  # now we have bit-strings from X and Y, reverse them for padding
-  $bx = reverse $bx;
-  $by = reverse $by;
-
-  # cut the longer string to the length of the shorter one (the result would
-  # be 0 due to AND anyway)
-  my $diff = CORE::length($bx) - CORE::length($by);
-  if ($diff > 0)
-    {
-    $bx = substr($bx,0,CORE::length($by));
-    }
-  elsif ($diff < 0)
-    {
-    $by = substr($by,0,CORE::length($bx));
-    }
-
-  # and the strings together
-  my $r = $bx & $by;
-
-  # and reverse the result again
-  $bx = reverse $r;
-
-  # one of $x or $y was negative, so need to flip bits in the result
-  # in both cases (one or two of them negative, or both positive) we need
-  # to get the characters back.
-  if ($sign == 1)
-    {
-    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
-    }
-  else
-    {
-    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
-    }
-
-  $bx = '0x' . $bx;
-  if ($CAN{from_hex})
-    {
-    $x->{value} = $CALC->_from_hex( \$bx );
-    }
-  else
-    {
-    $r = $self->new($bx);
-    $x->{value} = $r->{value};
-    }
-  
-  # calculate sign of result 
-  $x->{sign} = '+';
-  $x->{sign} = '-' if $sx == $sy && $sx == -1 && !$x->is_zero();
-
-  $x->bdec() if $sign == 1;
-
-  $x->round(@r);
+ 
+  require $EMU_LIB;
+  __emu_band($self,$x,$y,$sx,$sy,@r);
   }
 
 sub bior 
@@ -2102,8 +1923,8 @@ sub bior
 
   return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
 
-  my $sx = 1; $sx = -1 if $x->{sign} eq '-';
-  my $sy = 1; $sy = -1 if $y->{sign} eq '-';
+  my $sx = $x->{sign} eq '+' ? 1 : -1;
+  my $sy = $y->{sign} eq '+' ? 1 : -1;
 
   # the sign of X follows the sign of X, e.g. sign of Y irrelevant for bior()
   
@@ -2114,96 +1935,15 @@ sub bior
     return $x->round(@r);
     }
 
-  # if lib can do negatvie values, so use it
+  # if lib can do negative values, let it handle this
   if ($CAN{signed_or})
     {
     $x->{value} = $CALC->_signed_or($x->{value},$y->{value},$sx,$sy);
     return $x->round(@r);
     }
 
-  return $x->round(@r) if $y->is_zero();
-
-  my $sign = 0;					# sign of result
-  $sign = 1 if ($x->{sign} eq '-') || ($y->{sign} eq '-');
-
-  my ($bx,$by);
-
-  if ($sx == -1)				# if x is negative
-    {
-    # two's complement: inc and flip all "bits" in $bx
-    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
-    $bx =~ s/-?0x//; 
-    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  else
-    {
-    $bx = $x->as_hex();				# get binary representation
-    $bx =~ s/-?0x//;
-    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  if ($sy == -1)				# if y is negative
-    {
-    # two's complement: inc and flip all "bits" in $by
-    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
-    $by =~ s/-?0x//; 
-    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  else
-    {
-    $by = $y->as_hex();				# get binary representation
-    $by =~ s/-?0x//;
-    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  # now we have bit-strings from X and Y, reverse them for padding
-  $bx = reverse $bx;
-  $by = reverse $by;
-
-  # padd the shorter string
-  my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
-  my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
-  my $diff = CORE::length($bx) - CORE::length($by);
-  if ($diff > 0)
-    {
-    $by .= $yy x $diff;
-    }
-  elsif ($diff < 0)
-    {
-    $bx .= $xx x abs($diff);
-    }
-
-  # or the strings together
-  my $r = $bx | $by;
-
-  # and reverse the result again
-  $bx = reverse $r;
-
-  # one of $x or $y was negative, so need to flip bits in the result
-  # in both cases (one or two of them negative, or both positive) we need
-  # to get the characters back.
-  if ($sign == 1)
-    {
-    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
-    }
-  else
-    {
-    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
-    }
-
-  $bx = '0x' . $bx;
-  if ($CAN{from_hex})
-    {
-    $x->{value} = $CALC->_from_hex( \$bx );
-    }
-  else
-    {
-    $r = $self->new($bx);
-    $x->{value} = $r->{value};
-    }
-
-  # if one of X or Y was negative, we need to decrement result
-  $x->bdec() if $sign == 1;
-
-  $x->round(@r);
+  require $EMU_LIB;
+  __emu_bior($self,$x,$y,$sx,$sy,@r);
   }
 
 sub bxor 
@@ -2222,12 +1962,10 @@ sub bxor
   return $x if $x->modify('bxor');
   $r[3] = $y;				# no push!
 
-  local $Math::BigInt::upgrade = undef;
-
   return $x->bnan() if ($x->{sign} !~ /^[+-]$/ || $y->{sign} !~ /^[+-]$/);
   
-  my $sx = 1; $sx = -1 if $x->{sign} eq '-';
-  my $sy = 1; $sy = -1 if $y->{sign} eq '-';
+  my $sx = $x->{sign} eq '+' ? 1 : -1;
+  my $sy = $y->{sign} eq '+' ? 1 : -1;
 
   # don't use lib for negative values
   if ($CAN{xor} && $sx == 1 && $sy == 1)
@@ -2236,104 +1974,20 @@ sub bxor
     return $x->round(@r);
     }
   
-  # if lib can do negatvie values, so use it
+  # if lib can do negative values, let it handle this
   if ($CAN{signed_xor})
     {
     $x->{value} = $CALC->_signed_xor($x->{value},$y->{value},$sx,$sy);
     return $x->round(@r);
     }
 
-  return $x->round(@r) if $y->is_zero();
-
-  my $sign = 0;					# sign of result
-  $sign = 1 if $x->{sign} ne $y->{sign};
-
-  my ($bx,$by);
-  
-  if ($sx == -1)				# if x is negative
-    {
-    # two's complement: inc and flip all "bits" in $bx
-    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
-    $bx =~ s/-?0x//; 
-    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  else
-    {
-    $bx = $x->as_hex();				# get binary representation
-    $bx =~ s/-?0x//;
-    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  if ($sy == -1)				# if y is negative
-    {
-    # two's complement: inc and flip all "bits" in $by
-    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
-    $by =~ s/-?0x//; 
-    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  else
-    {
-    $by = $y->as_hex();				# get binary representation
-    $by =~ s/-?0x//;
-    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
-    }
-  # now we have bit-strings from X and Y, reverse them for padding
-  $bx = reverse $bx;
-  $by = reverse $by;
-
-  # padd the shorter string
-  my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
-  my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
-  my $diff = CORE::length($bx) - CORE::length($by);
-  if ($diff > 0)
-    {
-    $by .= $yy x $diff;
-    }
-  elsif ($diff < 0)
-    {
-    $bx .= $xx x abs($diff);
-    }
-
-  # xor the strings together
-  my $r = $bx ^ $by;
-
-  # and reverse the result again
-  $bx = reverse $r;
-
-  # one of $x or $y was negative, so need to flip bits in the result
-  # in both cases (one or two of them negative, or both positive) we need
-  # to get the characters back.
-  if ($sign == 1)
-    {
-    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
-    }
-  else
-    {
-    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
-    }
-
-  $bx = '0x' . $bx;
-  if ($CAN{from_hex})
-    {
-    $x->{value} = $CALC->_from_hex( \$bx );
-    }
-  else
-    {
-    $r = $self->new($bx);
-    $x->{value} = $r->{value};
-    }
-
-  # calculate sign of result 
-  $x->{sign} = '+';
-  $x->{sign} = '-' if $sx != $sy && !$x->is_zero();
-
-  $x->bdec() if $sign == 1;
-
-  $x->round(@r);
+  require $EMU_LIB;
+  __emu_bxor($self,$x,$y,$sx,$sy,@r);
   }
 
 sub length
   {
-  my ($self,$x) = ref($_[0]) ? (ref($_[0]),$_[0]) : objectify(1,@_);
+  my ($self,$x) = ref($_[0]) ? (undef,$_[0]) : objectify(1,@_);
 
   my $e = $CALC->_len($x->{value}); 
   wantarray ? ($e,0) : $e;
@@ -2349,7 +2003,7 @@ sub digit
 
 sub _trailing_zeros
   {
-  # return the amount of trailing zeros in $x
+  # return the amount of trailing zeros in $x (as scalar)
   my $x = shift;
   $x = $class->new($x) unless ref $x;
 
@@ -2381,28 +2035,8 @@ sub bsqrt
     return $x->round(@r);
     }
 
-  # this is slow:
-  return $x->round(@r) if $x->is_zero();		# 0,1 => 0,1
-
-  return $x->bone('+',@r) if $x < 4;			# 1,2,3 => 1
-  my $y = $x->copy();
-  my $l = int($x->length()/2);
-  
-  $x->bone();					# keep ref($x), but modify it
-  $x->blsft($l,10) if $l != 0;			# first guess: 1.('0' x (l/2))
-
-  my $last = $self->bzero();
-  my $two = $self->new(2);
-  my $lastlast = $self->bzero();
-  #my $lastlast = $x+$two;
-  while ($last != $x && $lastlast != $x)
-    {
-    $lastlast = $last; $last = $x->copy(); 
-    $x->badd($y / $x); 
-    $x->bdiv($two);
-    }
-  $x->bdec() if $x * $x > $y;				# overshot?
-  $x->round(@r);
+  require $EMU_LIB;
+  __emu_bsqrt($self,$x,@r);
   }
 
 sub broot
@@ -2437,48 +2071,8 @@ sub broot
     return $x->round(@r);
     }
 
-  return $x->bsqrt() if $y->bacmp(2) == 0;	# 2 => square root
-
-  # since we take at least a cubic root, and only 8 ** 1/3 >= 2 (==2):
-  return $x->bone('+',@r) if $x < 8;		# $x=2..7 => 1
-
-  my $num = $x->numify();
-
-  if ($num <= 1000000)
-    {
-    $x = $self->new( int($num ** (1 / $y->numify()) ));
-    return $x->round(@r);
-    }
-
-  # if $n is a power of two, we can repeatedly take sqrt($X) and find the
-  # proper result, because sqrt(sqrt($x)) == root($x,4)
-  # See Calc.pm for more details
-  my $b = $y->as_bin();
-  if ($b =~ /0b1(0+)/)
-    {
-    my $count = CORE::length($1);	# 0b100 => len('00') => 2
-    my $cnt = $count;			# counter for loop
-    my $shift = $self->new(6);
-    $x->blsft($shift);			# add some zeros (even amount)
-    while ($cnt-- > 0)
-      {
-      # 'inflate' $X by adding more zeros
-      $x->blsft($shift);
-      # calculate sqrt($x), $x is now a bit too big, again. In the next
-      # round we make even bigger, again.
-      $x->bsqrt($x);
-      }
-    # $x is still to big, so truncate result
-    $x->brsft($shift);
-    }
-  else
-    {
-    # Should compute a guess of the result (by rule of thumb), then improve it
-    # via Newton's method or something similiar.
-    # XXX TODO
-    warn ('broot() not fully implemented in BigInt.');
-    }
-  return $x->round(@r);
+  require $EMU_LIB;
+  __emu_broot($self,$x,$y,@r);
   }
 
 sub exponent
@@ -2488,13 +2082,12 @@ sub exponent
  
   if ($x->{sign} !~ /^[+-]$/)
     {
-    my $s = $x->{sign}; $s =~ s/^[+-]//;
-    return $self->new($s); 		# -inf,+inf => inf
+    my $s = $x->{sign}; $s =~ s/^[+-]//;  # NaN, -inf,+inf => NaN or inf
+    return $self->new($s);
     }
-  my $e = $class->bzero();
-  return $e->binc() if $x->is_zero();
-  $e += $x->_trailing_zeros();
-  $e;
+  return $self->bone() if $x->is_zero();
+
+  $self->new($x->_trailing_zeros());
   }
 
 sub mantissa
@@ -2504,10 +2097,11 @@ sub mantissa
 
   if ($x->{sign} !~ /^[+-]$/)
     {
-    return $self->new($x->{sign}); 		# keep + or - sign
+    # for NaN, +inf, -inf: keep the sign
+    return $self->new($x->{sign});
     }
-  my $m = $x->copy();
-  # that's inefficient
+  my $m = $x->copy(); delete $m->{_p}; delete $m->{_a};
+  # that's a bit inefficient:
   my $zeros = $m->_trailing_zeros();
   $m->brsft($zeros,10) if $zeros != 0;
   $m;
@@ -2529,18 +2123,14 @@ sub bfround
   # precision: round to the $Nth digit left (+$n) or right (-$n) from the '.'
   # $n == 0 || $n == 1 => round to integer
   my $x = shift; $x = $class->new($x) unless ref $x;
+
   my ($scale,$mode) = $x->_scale_p($x->precision(),$x->round_mode(),@_);
-  return $x if !defined $scale;		# no-op
-  return $x if $x->modify('bfround');
+
+  return $x if !defined $scale || $x->modify('bfround');	# no-op
 
   # no-op for BigInts if $n <= 0
-  if ($scale <= 0)
-    {
-    $x->{_a} = undef;				# clear an eventual set A
-    $x->{_p} = $scale; return $x;
-    }
+  $x->bround( $x->length()-$scale, $mode) if $scale > 0;
 
-  $x->bround( $x->length()-$scale, $mode);
   $x->{_a} = undef;				# bround sets {_a}
   $x->{_p} = $scale;				# so correct it
   $x;
@@ -2549,9 +2139,7 @@ sub bfround
 sub _scan_for_nonzero
   {
   # internal, used by bround()
-  my $x = shift;
-  my $pad = shift;
-  my $xs = shift;
+  my ($x,$pad,$xs) = @_;
  
   my $len = $x->length();
   return 0 if $len == 1;		# '5' is trailed by invisible zeros
@@ -2708,35 +2296,15 @@ sub as_hex
 
   return $x->bstr() if $x->{sign} !~ /^[+-]$/;	# inf, nan etc
 
-  my $es = ''; my $s = '';
+  my $s = '';
   $s = $x->{sign} if $x->{sign} eq '-';
   if ($CAN{as_hex})
     {
-    $es = ${$CALC->_as_hex($x->{value})};
+    return $s . ${$CALC->_as_hex($x->{value})};
     }
-  else
-    {
-    return '0x0' if $x->is_zero();
 
-    my $x1 = $x->copy()->babs(); my ($xr,$x10000,$h);
-    if ($] >= 5.006)
-      {
-      $x10000 = Math::BigInt->new (0x10000); $h = 'h4';
-      }
-    else
-      {
-      $x10000 = Math::BigInt->new (0x1000); $h = 'h3';
-      }
-    while (!$x1->is_zero())
-      {
-      ($x1, $xr) = bdiv($x1,$x10000);
-      $es .= unpack($h,pack('v',$xr->numify()));
-      }
-    $es = reverse $es;
-    $es =~ s/^[0]+//; 	# strip leading zeros
-    $s .= '0x';
-    }
-  $s . $es;
+  require $EMU_LIB;
+  __emu_as_hex(ref($x),$x,$s);
   }
 
 sub as_bin
@@ -2746,34 +2314,15 @@ sub as_bin
 
   return $x->bstr() if $x->{sign} !~ /^[+-]$/;	# inf, nan etc
 
-  my $es = ''; my $s = '';
-  $s = $x->{sign} if $x->{sign} eq '-';
+  my $s = ''; $s = $x->{sign} if $x->{sign} eq '-';
   if ($CAN{as_bin})
     {
-    $es = ${$CALC->_as_bin($x->{value})};
-    }
-  else
-    {
-    return '0b0' if $x->is_zero();
-    my $x1 = $x->copy()->babs(); my ($xr,$x10000,$b);
-    if ($] >= 5.006)
-      {
-      $x10000 = Math::BigInt->new (0x10000); $b = 'b16';
-      }
-    else
-      {
-      $x10000 = Math::BigInt->new (0x1000); $b = 'b12';
-      }
-    while (!$x1->is_zero())
-      {
-      ($x1, $xr) = bdiv($x1,$x10000);
-      $es .= unpack($b,pack('v',$xr->numify()));
-      }
-    $es = reverse $es; 
-    $es =~ s/^[0]+//; 	# strip leading zeros
-    $s .= '0b';
+    return $s . ${$CALC->_as_bin($x->{value})};
     }
-  $s . $es;
+
+  require $EMU_LIB;
+  __emu_as_bin(ref($x),$x,$s);
+
   }
 
 ##############################################################################
@@ -2977,17 +2526,17 @@ sub __from_hex
   my $sign = '+'; $sign = '-' if ($$hs =~ /^-/);
 
   $$hs =~ s/^[+-]//;			# strip sign
-  if ($CAN{'_from_hex'})
+  if ($CAN{'from_hex'})
     {
     $x->{value} = $CALC->_from_hex($hs);
     }
   else
     {
     # fallback to pure perl
-    my $mul = Math::BigInt->bzero(); $mul++;
+    my $mul = Math::BigInt->bone();
     my $x65536 = Math::BigInt->new(65536);
-    my $len = CORE::length($$hs)-2;
-    $len = int($len/4);			# 4-digit parts, w/o '0x'
+    my $len = CORE::length($$hs)-2;		# minus 2 for 0x
+    $len = int($len/4);				# 4-digit parts, w/o '0x'
     my $val; my $i = -4;
     while ($len >= 0)
       {
@@ -3016,15 +2565,15 @@ sub __from_bin
 
   my $sign = '+'; $sign = '-' if ($$bs =~ /^\-/);
   $$bs =~ s/^[+-]//;				# strip sign
-  if ($CAN{'_from_bin'})
+  if ($CAN{'from_bin'})
     {
     $x->{value} = $CALC->_from_bin($bs);
     }
   else
     {
-    my $mul = Math::BigInt->bzero(); $mul++;
+    my $mul = Math::BigInt->bone();
     my $x256 = Math::BigInt->new(256);
-    my $len = CORE::length($$bs)-2;
+    my $len = CORE::length($$bs)-2;		# minus 2 for 0b
     $len = int($len/8);				# 8-digit parts, w/o '0b'
     my $val; my $i = -8;
     while ($len >= 0)
@@ -3142,7 +2691,7 @@ sub __gcd
 
 ###############################################################################
 # this method return 0 if the object can be modified, or 1 for not
-# We use a fast use constant statement here, to avoid costly calls. Subclasses
+# We use a fast constant sub() here, to avoid costly calls. Subclasses
 # may override it with special code (f.i. Math::BigInt::Constant does so)
 
 sub modify () { 0; }
@@ -3182,8 +2731,8 @@ Math::BigInt - Arbitrary size integer math package
   $x->is_one('-');	# if $x is -1
   $x->is_odd();		# if $x is odd
   $x->is_even();	# if $x is even
-  $x->is_positive();	# if $x >= 0
-  $x->is_negative();	# if $x <  0
+  $x->is_pos();		# if $x >= 0
+  $x->is_neg();		# if $x <  0
   $x->is_inf(sign);	# if $x is +inf, or -inf (sign is default '+')
   $x->is_int();		# if $x is an integer (not a float)
 
@@ -3260,14 +2809,15 @@ Math::BigInt - Arbitrary size integer math package
   $x->mantissa();	   # return (signed) mantissa as BigInt
   $x->parts();		   # return (mantissa,exponent) as BigInt
   $x->copy();		   # make a true copy of $x (unlike $y = $x;)
-  $x->as_number();	   # return as BigInt (in BigInt: same as copy())
+  $x->as_int();		   # return as BigInt (in BigInt: same as copy())
+  $x->numify();		   # return as scalar (might overflow!)
   
   # conversation to string (do not modify their argument)
   $x->bstr();		   # normalized string
   $x->bsstr();		   # normalized string in scientific notation
   $x->as_hex();		   # as signed hexadecimal string with prefixed 0x
   $x->as_bin();		   # as signed binary string with prefixed 0b
-  
+
 
   # precision and accuracy (see section about rounding for more)
   $x->precision();	   # return P of $x (or global, if P of $x undef)
@@ -3546,10 +3096,10 @@ like:
 
 	if ($x == 0)
 
-=head2 is_positive()/is_negative()
+=head2 is_pos()/is_neg()
 	
-	$x->is_positive();		# true if >= 0
-	$x->is_negative();		# true if <  0
+	$x->is_pos();			# true if >= 0
+	$x->is_neg();			# true if <  0
 
 The methods return true if the argument is positive or negative, respectively.
 C<NaN> is neither positive nor negative, while C<+inf> counts as positive, and
@@ -3557,6 +3107,11 @@ C<-inf> is negative. A C<zero> is positive.
 
 These methods are only testing the sign, and not the value.
 
+C<is_positive()> and C<is_negative()> are aliase to C<is_pos()> and
+C<is_neg()>, respectively. C<is_positive()> and C<is_negative()> were
+introduced in v1.36, while C<is_pos()> and C<is_neg()> were only introduced
+in v1.68.
+
 =head2 is_odd()/is_even()/is_int()
 
 	$x->is_odd();			# true if odd, false for even
@@ -3785,13 +3340,21 @@ Return the signed mantissa of $x as BigInt.
 
 	$x->copy();		# make a true copy of $x (unlike $y = $x;)
 
-=head2 as_number
+=head2 as_int
 
-	$x->as_number();	# return as BigInt (in BigInt: same as copy())
+	$x->as_int();	
+
+Returns $x as a BigInt (truncated towards zero). In BigInt this is the same as
+C<copy()>. 
+
+C<as_number()> is an alias to this method. C<as_number> was introduced in
+v1.22, while C<as_int()> was only introduced in v1.68.
   
-=head2 bsrt
+=head2 bstr
+
+	$x->bstr();
 
-	$x->bstr();		# return normalized string
+Returns a normalized string represantation of C<$x>.
 
 =head2 bsstr
 
diff --git a/lib/Math/BigInt/Calc.pm b/lib/Math/BigInt/Calc.pm
index 02770e22e1..e1cae77867 100644
--- a/lib/Math/BigInt/Calc.pm
+++ b/lib/Math/BigInt/Calc.pm
@@ -4,11 +4,9 @@ use 5.005;
 use strict;
 # use warnings;	# dont use warnings for older Perls
 
-require Exporter;
-use vars qw/@ISA $VERSION/;
-@ISA = qw(Exporter);
+use vars qw/$VERSION/;
 
-$VERSION = '0.37';
+$VERSION = '0.38';
 
 # Package to store unsigned big integers in decimal and do math with them
 
@@ -194,6 +192,10 @@ sub _new
   # 1ex format. Assumes normalized value as input.
   my $d = $_[1];
   my $il = length($$d)-1;
+
+  # < BASE_LEN due len-1 above
+  return [ int($$d) ] if $il < $BASE_LEN;	# shortcut for short numbers
+
   # this leaves '00000' instead of int 0 and will be corrected after any op
   [ reverse(unpack("a" . ($il % $BASE_LEN+1) 
     . ("a$BASE_LEN" x ($il / $BASE_LEN)), $$d)) ];
@@ -1240,6 +1242,22 @@ sub _pow
   # ref to array, ref to array, return ref to array
   my ($c,$cx,$cy) = @_;
 
+  if (scalar @$cy == 1 && $cy->[0] == 0)
+    {
+    splice (@$cx,1); $cx->[0] = 1;		# y == 0 => x => 1
+    return $cx;
+    }
+  if ((scalar @$cx == 1 && $cx->[0] == 1) ||	#    x == 1
+      (scalar @$cy == 1 && $cy->[0] == 1))	# or y == 1
+    {
+    return $cx;
+    }
+  if (scalar @$cx == 1 && $cx->[0] == 0)
+    {
+    splice (@$cx,1); $cx->[0] = 0;		# 0 ** y => 0 (if not y <= 0)
+    return $cx;
+    }
+
   my $pow2 = _one();
 
   my $y_bin = ${_as_bin($c,$cy)}; $y_bin =~ s/^0b//;
@@ -1346,8 +1364,7 @@ sub _log_int
   return if (scalar @$x == 1 && $x->[0] == 0);
   # BASE 0 or 1 => NaN
   return if (scalar @$base == 1 && $base->[0] < 2);
-  my $cmp = _acmp($c,$x,$base);
-  # X == BASE => 1
+  my $cmp = _acmp($c,$x,$base); # X == BASE => 1
   if ($cmp == 0)
     {
     splice (@$x,1); $x->[0] = 1;
@@ -1366,11 +1383,43 @@ sub _log_int
   my $x_org = _copy($c,$x);		# preserve x
   splice(@$x,1); $x->[0] = 1;		# keep ref to $x
 
+  my $trial = _copy($c,$base);
+
+  # XXX TODO this only works if $base has only one element
+  if (scalar @$base == 1)
+    {
+    # compute int ( length_in_base_10(X) / ( log(base) / log(10) ) )
+    my $len = _len($c,$x_org);
+    my $res = int($len / (log($base->[0]) / log(10))) || 1; # avoid $res == 0
+
+    $x->[0] = $res;
+    $trial = _pow ($c, _copy($c, $base), $x);
+    my $a = _acmp($x,$trial,$x_org);
+    return ($x,1) if $a == 0;
+    # we now that $res is too small
+    if ($res < 0)
+      {
+      _mul($c,$trial,$base); _add($c, $x, [1]);
+      }
+    else
+      {
+      # or too big
+      _div($c,$trial,$base); _sub($c, $x, [1]);
+      }
+    # did we now get the right result?
+    $a = _acmp($x,$trial,$x_org);
+    return ($x,1) if $a == 0;		# yes, exactly
+    # still too big
+    if ($a > 0)
+      {
+      _div($c,$trial,$base); _sub($c, $x, [1]);
+      }
+    } 
+  
   # simple loop that increments $x by two in each step, possible overstepping
   # the real result by one
 
-  # use a loop that keeps $x as scalar as long as possible (this is faster)
-  my $trial = _copy($c,$base); my $a;
+  my $a;
   my $base_mul = _mul($c, _copy($c,$base), $base);
 
   while (($a = _acmp($x,$trial,$x_org)) < 0)
@@ -1981,6 +2030,7 @@ slow) fallback routines to emulate these:
 	_root(obj)	return the n'th (n >= 3) root of obj (truncated to int)
 	_fac(obj)	return factorial of object 1 (1*2*3*4..)
 	_pow(obj,obj)	return object 1 to the power of object 2
+			return undef for NaN
 	_gcd(obj,obj)	return Greatest Common Divisor of two objects
 	
 	_zeros(obj)	return number of trailing decimal zeros
diff --git a/lib/Math/BigInt/CalcEmu.pm b/lib/Math/BigInt/CalcEmu.pm
new file mode 100644
index 0000000000..4ec244edb5
--- /dev/null
+++ b/lib/Math/BigInt/CalcEmu.pm
@@ -0,0 +1,594 @@
+package Math::BigInt;
+
+use 5.005;
+use strict;
+# use warnings;	# dont use warnings for older Perls
+
+use vars qw/$VERSION/;
+
+$VERSION = '0.01';
+
+# See SYNOPSIS below.
+
+my $CALC_EMU;
+
+BEGIN
+  {
+  $CALC_EMU = Math::BigInt->config()->{'lib'};
+  }
+
+sub __emu_blog
+  {
+  my ($self,$x,$base,@r) = @_;
+
+  return $x->bnan() if $x->is_zero() || $base->is_zero() || $base->is_one();
+
+  my $acmp = $x->bacmp($base);
+  return $x->bone('+',@r) if $acmp == 0;
+  return $x->bzero(@r) if $acmp < 0 || $x->is_one();
+
+  # blog($x,$base) ** $base + $y = $x
+
+  # this trial multiplication is very fast, even for large counts (like for
+  # 2 ** 1024, since this still requires only 1024 very fast steps
+  # (multiplication of a large number by a very small number is very fast))
+  # See Calc for an even faster algorightmn
+  my $x_org = $x->copy();		# preserve orgx
+  $x->bzero();				# keep ref to $x
+  my $trial = $base->copy();
+  while ($trial->bacmp($x_org) <= 0)
+    {
+    $trial->bmul($base); $x->binc();
+    }
+  $x->round(@r);
+  }
+
+sub __emu_bmodinv
+  {
+  my ($self,$x,$y,@r) = @_;
+
+  my ($u, $u1) = ($self->bzero(), $self->bone());
+  my ($a, $b) = ($y->copy(), $x->copy());
+
+  # first step need always be done since $num (and thus $b) is never 0
+  # Note that the loop is aligned so that the check occurs between #2 and #1
+  # thus saving us one step #2 at the loop end. Typical loop count is 1. Even
+  # a case with 28 loops still gains about 3% with this layout.
+  my $q;
+  ($a, $q, $b) = ($b, $a->bdiv($b));			# step #1
+  # Euclid's Algorithm (calculate GCD of ($a,$b) in $a and also calculate
+  # two values in $u and $u1, we use only $u1 afterwards)
+  my $sign = 1;						# flip-flop
+  while (!$b->is_zero())				# found GCD if $b == 0
+    {
+    # the original algorithm had:
+    # ($u, $u1) = ($u1, $u->bsub($u1->copy()->bmul($q))); # step #2
+    # The following creates exact the same sequence of numbers in $u1,
+    # except for the sign ($u1 is now always positive). Since formerly
+    # the sign of $u1 was alternating between '-' and '+', the $sign
+    # flip-flop will take care of that, so that at the end of the loop
+    # we have the real sign of $u1. Keeping numbers positive gains us
+    # speed since badd() is faster than bsub() and makes it possible
+    # to have the algorithmn in Calc for even more speed.
+
+    ($u, $u1) = ($u1, $u->badd($u1->copy()->bmul($q)));	# step #2
+    $sign = - $sign;					# flip sign
+
+    ($a, $q, $b) = ($b, $a->bdiv($b));			# step #1 again
+    }
+
+  # If the gcd is not 1, then return NaN! It would be pointless to have
+  # called bgcd to check this first, because we would then be performing
+  # the same Euclidean Algorithm *twice* in case the gcd is 1.
+  return $x->bnan() unless $a->is_one();
+
+  $u1->bneg() if $sign != 1;				# need to flip?
+
+  $u1->bmod($y);					# calc result
+  $x->{value} = $u1->{value};				# and copy over to $x
+  $x->{sign} = $u1->{sign};				# to modify in place
+  $x->round(@r);
+  }
+
+sub __emu_bmodpow
+  {
+  my ($self,$num,$exp,$mod,@r) = @_;
+
+  # in the trivial case,
+  return $num->bzero(@r) if $mod->is_one();
+  return $num->bone('+',@r) if $num->is_zero() or $num->is_one();
+
+  # $num->bmod($mod);           # if $x is large, make it smaller first
+  my $acc = $num->copy();       # but this is not really faster...
+
+  $num->bone(); # keep ref to $num
+
+  my $expbin = $exp->as_bin(); $expbin =~ s/^[-]?0b//; # ignore sign and prefix
+  my $len = CORE::length($expbin);
+  while (--$len >= 0)
+    {
+    $num->bmul($acc)->bmod($mod) if substr($expbin,$len,1) eq '1';
+    $acc->bmul($acc)->bmod($mod);
+    }
+
+  $num->round(@r);
+  }
+
+sub __emu_bfac
+  {
+  my ($self,$x,@r) = @_;
+
+  return $x->bone('+',@r) if $x->is_zero() || $x->is_one();     # 0 or 1 => 1
+
+  my $n = $x->copy();
+  $x->bone();
+  # seems we need not to temp. clear A/P of $x since the result is the same
+  my $f = $self->new(2);
+  while ($f->bacmp($n) < 0)
+    {
+    $x->bmul($f); $f->binc();
+    }
+  $x->bmul($f,@r);			# last step and also round result
+  }
+
+sub __emu_bpow
+  {
+  my ($self,$x,$y,@r) = @_;
+
+  return $x->bone('+',@r) if $y->is_zero();
+  return $x->round(@r) if $x->is_one() || $y->is_one();
+  return $x->round(@r) if $x->is_zero();  # 0**y => 0 (if not y <= 0)
+
+  my $pow2 = $self->bone();
+  my $y_bin = $y->as_bin(); $y_bin =~ s/^0b//;
+  my $len = CORE::length($y_bin);
+  while (--$len > 0)
+    {
+    $pow2->bmul($x) if substr($y_bin,$len,1) eq '1';    # is odd?
+    $x->bmul($x);
+    }
+  $x->bmul($pow2);
+  $x->round(@r) if !exists $x->{_f} || $x->{_f} & MB_NEVER_ROUND == 0;
+  $x;
+  }
+
+sub __emu_band
+  {
+  my ($self,$x,$y,$sx,$sy,@r) = @_;
+
+  return $x->bzero(@r) if $y->is_zero() || $x->is_zero();
+  
+  my $sign = 0;					# sign of result
+  $sign = 1 if $sx == -1 && $sy == -1;
+
+  my ($bx,$by);
+
+  if ($sx == -1)				# if x is negative
+    {
+    # two's complement: inc and flip all "bits" in $bx
+    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
+    $bx =~ s/-?0x//;
+    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $bx = $x->as_hex();				# get binary representation
+    $bx =~ s/-?0x//;
+    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  if ($sy == -1)				# if y is negative
+    {
+    # two's complement: inc and flip all "bits" in $by
+    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
+    $by =~ s/-?0x//;
+    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $by = $y->as_hex();				# get binary representation
+    $by =~ s/-?0x//;
+    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  # now we have bit-strings from X and Y, reverse them for padding
+  $bx = reverse $bx;
+  $by = reverse $by;
+
+  # cut the longer string to the length of the shorter one (the result would
+  # be 0 due to AND anyway)
+  my $diff = CORE::length($bx) - CORE::length($by);
+  if ($diff > 0)
+    {
+    $bx = substr($bx,0,CORE::length($by));
+    }
+  elsif ($diff < 0)
+    {
+    $by = substr($by,0,CORE::length($bx));
+    }
+
+  # and the strings together
+  my $r = $bx & $by;
+
+  # and reverse the result again
+  $bx = reverse $r;
+
+  # one of $x or $y was negative, so need to flip bits in the result
+  # in both cases (one or two of them negative, or both positive) we need
+  # to get the characters back.
+  if ($sign == 1)
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
+    }
+  else
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
+    }
+
+  $bx = '0x' . $bx;
+  if ($CALC_EMU->can('_from_hex'))
+    {
+    $x->{value} = $CALC_EMU->_from_hex( \$bx );
+    }
+  else
+    {
+    $r = $self->new($bx);
+    $x->{value} = $r->{value};
+    }
+
+  # calculate sign of result
+  $x->{sign} = '+';
+  #$x->{sign} = '-' if $sx == $sy && $sx == -1 && !$x->is_zero();
+  $x->{sign} = '-' if $sign == 1 && !$x->is_zero();
+
+  $x->bdec() if $sign == 1;
+
+  $x->round(@r);
+  }
+
+sub __emu_bior
+  {
+  my ($self,$x,$y,$sx,$sy,@r) = @_;
+
+  return $x->round(@r) if $y->is_zero();
+
+  my $sign = 0;					# sign of result
+  $sign = 1 if ($sx == -1) || ($sy == -1);
+
+  my ($bx,$by);
+
+  if ($sx == -1)				# if x is negative
+    {
+    # two's complement: inc and flip all "bits" in $bx
+    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
+    $bx =~ s/-?0x//;
+    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $bx = $x->as_hex();				# get binary representation
+    $bx =~ s/-?0x//;
+    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  if ($sy == -1)				# if y is negative
+    {
+    # two's complement: inc and flip all "bits" in $by
+    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
+    $by =~ s/-?0x//;
+    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $by = $y->as_hex();				# get binary representation
+    $by =~ s/-?0x//;
+    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  # now we have bit-strings from X and Y, reverse them for padding
+  $bx = reverse $bx;
+  $by = reverse $by;
+
+  # padd the shorter string
+  my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
+  my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
+  my $diff = CORE::length($bx) - CORE::length($by);
+  if ($diff > 0)
+    {
+    $by .= $yy x $diff;
+    }
+  elsif ($diff < 0)
+    {
+    $bx .= $xx x abs($diff);
+    }
+
+  # or the strings together
+  my $r = $bx | $by;
+
+  # and reverse the result again
+  $bx = reverse $r;
+
+  # one of $x or $y was negative, so need to flip bits in the result
+  # in both cases (one or two of them negative, or both positive) we need
+  # to get the characters back.
+  if ($sign == 1)
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
+    }
+  else
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
+    }
+
+  $bx = '0x' . $bx;
+  if ($CALC_EMU->can('_from_hex'))
+    {
+    $x->{value} = $CALC_EMU->_from_hex( \$bx );
+    }
+  else
+    {
+    $r = $self->new($bx);
+    $x->{value} = $r->{value};
+    }
+
+  # if one of X or Y was negative, we need to decrement result
+  $x->bdec() if $sign == 1;
+
+  $x->round(@r);
+  }
+
+sub __emu_bxor
+  {
+  my ($self,$x,$y,$sx,$sy,@r) = @_;
+
+  return $x->round(@r) if $y->is_zero();
+
+  my $sign = 0;					# sign of result
+  $sign = 1 if $x->{sign} ne $y->{sign};
+
+  my ($bx,$by);
+
+  if ($sx == -1)				# if x is negative
+    {
+    # two's complement: inc and flip all "bits" in $bx
+    $bx = $x->binc()->as_hex();			# -1 => 0, -2 => 1, -3 => 2 etc
+    $bx =~ s/-?0x//;
+    $bx =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $bx = $x->as_hex();				# get binary representation
+    $bx =~ s/-?0x//;
+    $bx =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  if ($sy == -1)				# if y is negative
+    {
+    # two's complement: inc and flip all "bits" in $by
+    $by = $y->copy()->binc()->as_hex();		# -1 => 0, -2 => 1, -3 => 2 etc
+    $by =~ s/-?0x//;
+    $by =~ tr/0123456789abcdef/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  else
+    {
+    $by = $y->as_hex();				# get binary representation
+    $by =~ s/-?0x//;
+    $by =~ tr/fedcba9876543210/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/;
+    }
+  # now we have bit-strings from X and Y, reverse them for padding
+  $bx = reverse $bx;
+  $by = reverse $by;
+
+  # padd the shorter string
+  my $xx = "\x00"; $xx = "\x0f" if $sx == -1;
+  my $yy = "\x00"; $yy = "\x0f" if $sy == -1;
+  my $diff = CORE::length($bx) - CORE::length($by);
+  if ($diff > 0)
+    {
+    $by .= $yy x $diff;
+    }
+  elsif ($diff < 0)
+    {
+    $bx .= $xx x abs($diff);
+    }
+
+  # xor the strings together
+  my $r = $bx ^ $by;
+
+  # and reverse the result again
+  $bx = reverse $r;
+
+  # one of $x or $y was negative, so need to flip bits in the result
+  # in both cases (one or two of them negative, or both positive) we need
+  # to get the characters back.
+  if ($sign == 1)
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/0123456789abcdef/;
+    }
+  else
+    {
+    $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
+    }
+
+  $bx = '0x' . $bx;
+  if ($CALC_EMU->can('_from_hex'))
+    {
+    $x->{value} = $CALC_EMU->_from_hex( \$bx );
+    }
+  else
+    {
+    $r = $self->new($bx);
+    $x->{value} = $r->{value};
+    }
+
+  # calculate sign of result
+  $x->{sign} = '+';
+  $x->{sign} = '-' if $sx != $sy && !$x->is_zero();
+
+  $x->bdec() if $sign == 1;
+
+  $x->round(@r);
+  }
+
+sub __emu_bsqrt
+  {
+  my ($self,$x,@r) = @_;
+
+  # this is slow:
+  return $x->round(@r) if $x->is_zero();	# 0,1 => 0,1
+
+  return $x->bone('+',@r) if $x < 4;		# 1,2,3 => 1
+  my $y = $x->copy();
+  my $l = int($x->length()/2);
+
+  $x->bone();					# keep ref($x), but modify it
+  $x->blsft($l,10) if $l != 0;			# first guess: 1.('0' x (l/2))
+
+  my $last = $self->bzero();
+  my $two = $self->new(2);
+  my $lastlast = $self->bzero();
+  #my $lastlast = $x+$two;
+  while ($last != $x && $lastlast != $x)
+    {
+    $lastlast = $last; $last = $x->copy();
+    $x->badd($y / $x);
+    $x->bdiv($two);
+    }
+  $x->bdec() if $x * $x > $y;			# overshot?
+  $x->round(@r);
+  }
+
+sub __emu_broot
+  {
+  my ($self,$x,$y,@r) = @_;
+
+  return $x->bsqrt() if $y->bacmp(2) == 0;	# 2 => square root
+
+  # since we take at least a cubic root, and only 8 ** 1/3 >= 2 (==2):
+  return $x->bone('+',@r) if $x < 8;		# $x=2..7 => 1
+
+  my $num = $x->numify();
+
+  if ($num <= 1000000)
+    {
+    $x = $self->new( int ( sprintf ("%.8f", $num ** (1 / $y->numify() ))));
+    return $x->round(@r);
+    }
+
+  # if $n is a power of two, we can repeatedly take sqrt($X) and find the
+  # proper result, because sqrt(sqrt($x)) == root($x,4)
+  # See Calc.pm for more details
+  my $b = $y->as_bin();
+  if ($b =~ /0b1(0+)/)
+    {
+    my $count = CORE::length($1);		# 0b100 => len('00') => 2
+    my $cnt = $count;				# counter for loop
+    my $shift = $self->new(6);
+    $x->blsft($shift);				# add some zeros (even amount)
+    while ($cnt-- > 0)
+      {
+      # 'inflate' $X by adding more zeros
+      $x->blsft($shift);
+      # calculate sqrt($x), $x is now a bit too big, again. In the next
+      # round we make even bigger, again.
+      $x->bsqrt($x);
+      }
+    # $x is still to big, so truncate result
+    $x->brsft($shift);
+    }
+  else
+    {
+    # Should compute a guess of the result (by rule of thumb), then improve it
+    # via Newton's method or something similiar.
+    # XXX TODO
+    warn ('broot() not fully implemented in BigInt.');
+    }
+  $x->round(@r);
+  }
+
+sub __emu_as_hex
+  {
+  my ($self,$x,$s) = @_;
+
+  return '0x0' if $x->is_zero();
+
+  my $x1 = $x->copy()->babs(); my ($xr,$x10000,$h,$es);
+  if ($] >= 5.006)
+    {
+    $x10000 = $self->new (0x10000); $h = 'h4';
+    }
+  else
+    {
+    $x10000 = $self->new (0x1000); $h = 'h3';
+    }
+  while (!$x1->is_zero())
+    {
+    ($x1, $xr) = bdiv($x1,$x10000);
+    $es .= unpack($h,pack('v',$xr->numify()));
+    }
+  $es = reverse $es;
+  $es =~ s/^[0]+//;		# strip leading zeros
+  $s . '0x' . $es;
+  }
+
+sub __emu_as_bin
+  {
+  my ($self,$x,$s) = @_;
+
+  return '0b0' if $x->is_zero();
+
+  my $x1 = $x->copy()->babs(); my ($xr,$x10000,$b,$es);
+  if ($] >= 5.006)
+    {
+    $x10000 = $self->new (0x10000); $b = 'b16';
+    }
+  else
+    {
+    $x10000 = $self->new (0x1000); $b = 'b12';
+    }
+  while (!$x1->is_zero())
+    {
+    ($x1, $xr) = bdiv($x1,$x10000);
+    $es .= unpack($b,pack('v',$xr->numify()));
+    }
+  $es = reverse $es;
+  $es =~ s/^[0]+//;   # strip leading zeros
+  $s . '0b' . $es;
+  }
+
+##############################################################################
+##############################################################################
+
+1;
+__END__
+
+=head1 NAME
+
+Math::BigInt::CalcEmu - Emulate low-level math with BigInt code
+
+=head1 SYNOPSIS
+
+Contains routines that emulate low-level math functions in BigInt, e.g.
+optional routines the low-level math package does not provide on it's own.
+
+Will be loaded on demand and automatically by BigInt.
+
+Stuff here is really low-priority to optimize,
+since it is far better to implement the operation in the low-level math
+libary directly, possible even using a call to the native lib.
+
+=head1 DESCRIPTION
+
+=head1 METHODS
+
+=head1 LICENSE
+ 
+This program is free software; you may redistribute it and/or modify it under
+the same terms as Perl itself. 
+
+=head1 AUTHORS
+
+(c) Tels http://bloodgate.com 2003 - based on BigInt code by
+Tels from 2001-2003.
+
+=head1 SEE ALSO
+
+L<Math::BigInt>, L<Math::BigFloat>, L<Math::BigInt::BitVect>,
+L<Math::BigInt::GMP> and L<Math::BigInt::Pari>.
+
+=cut
diff --git a/lib/Math/BigInt/t/alias.inc b/lib/Math/BigInt/t/alias.inc
new file mode 100644
index 0000000000..84310fcbf3
--- /dev/null
+++ b/lib/Math/BigInt/t/alias.inc
@@ -0,0 +1,12 @@
+
+# alias subroutine testing, included by sub_ali.t and mbi_ali.t
+
+my $x = $CL->new(123);
+
+is ($x->is_pos(), 1, '123 is positive');
+is ($x->is_neg(), 0, '123 is not negative');
+is ($x->as_int(), 123, '123 is 123 as int');
+is (ref($x->as_int()), $CL, '123 is scalar as int');
+$x->bneg();
+is ($x->is_pos(), 0, '-123 is not positive');
+is ($x->is_neg(), 1, '-123 is negative');
diff --git a/lib/Math/BigInt/t/bigfltpm.inc b/lib/Math/BigInt/t/bigfltpm.inc
index 60a8f08e3f..1a05a6655b 100644
--- a/lib/Math/BigInt/t/bigfltpm.inc
+++ b/lib/Math/BigInt/t/bigfltpm.inc
@@ -1201,7 +1201,7 @@ abc:1:abc:NaN
 &ffac
 Nanfac:NaN
 -1:NaN
-+inf:NaN
++inf:inf
 -inf:NaN
 0:1
 1:1
diff --git a/lib/Math/BigInt/t/bigintc.t b/lib/Math/BigInt/t/bigintc.t
index 8d352eb731..1f0804cf9c 100644
--- a/lib/Math/BigInt/t/bigintc.t
+++ b/lib/Math/BigInt/t/bigintc.t
@@ -14,7 +14,7 @@ use Math::BigInt::Calc;
 
 BEGIN
   {
-  plan tests => 296;
+  plan tests => 300;
   }
 
 my ($BASE_LEN, $AND_BITS, $XOR_BITS, $OR_BITS, $BASE_LEN_SMALL, $MAX_VAL) =
@@ -224,6 +224,15 @@ $x = $C->_new(\"81"); $n = $C->_new(\"4"); 	# 3*3*3*3 == 81
 ok (${$C->_str($C->_root($x,$n))},'3');
 
 # _pow (and _root)
+$x = $C->_new(\"0"); $n = $C->_new(\"3"); 	# 0 ** y => 0
+ok (${$C->_str($C->_pow($x,$n))}, 0);
+$x = $C->_new(\"3"); $n = $C->_new(\"0"); 	# x ** 0 => 1
+ok (${$C->_str($C->_pow($x,$n))}, 1);
+$x = $C->_new(\"1"); $n = $C->_new(\"3"); 	# 1 ** y => 1
+ok (${$C->_str($C->_pow($x,$n))}, 1);
+$x = $C->_new(\"5"); $n = $C->_new(\"1"); 	# x ** 1 => x
+ok (${$C->_str($C->_pow($x,$n))}, 5);
+
 $x = $C->_new(\"81"); $n = $C->_new(\"3"); 	# 81 ** 3 == 531441 
 ok (${$C->_str($C->_pow($x,$n))},81 ** 3);
 
diff --git a/lib/Math/BigInt/t/bigintpm.inc b/lib/Math/BigInt/t/bigintpm.inc
index db52553c92..3cbb993c67 100644
--- a/lib/Math/BigInt/t/bigintpm.inc
+++ b/lib/Math/BigInt/t/bigintpm.inc
@@ -1891,7 +1891,7 @@ abc:NaN,NaN
 &bfac
 -1:NaN
 NaNfac:NaN
-+inf:NaN
++inf:inf
 -inf:NaN
 0:1
 1:1
diff --git a/lib/Math/BigInt/t/mbf_ali.t b/lib/Math/BigInt/t/mbf_ali.t
new file mode 100644
index 0000000000..1ca43157e3
--- /dev/null
+++ b/lib/Math/BigInt/t/mbf_ali.t
@@ -0,0 +1,42 @@
+#!/usr/bin/perl -w
+
+# test that the new alias names work
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/mbf_ali.t//i;
+  if ($ENV{PERL_CORE})
+    {
+    # testing with the core distribution
+    @INC = qw(../t/lib);
+    }
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 6;
+  }
+
+use Math::BigFloat;
+
+use vars qw/$x $CL/;
+
+$CL = 'Math::BigFloat';
+
+require 'alias.inc';
+
+
diff --git a/lib/Math/BigInt/t/mbi_ali.t b/lib/Math/BigInt/t/mbi_ali.t
new file mode 100644
index 0000000000..402801733b
--- /dev/null
+++ b/lib/Math/BigInt/t/mbi_ali.t
@@ -0,0 +1,42 @@
+#!/usr/bin/perl -w
+
+# test that the new alias names work
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/mbi_ali.t//i;
+  if ($ENV{PERL_CORE})
+    {
+    # testing with the core distribution
+    @INC = qw(../t/lib);
+    }
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 6;
+  }
+
+use Math::BigInt;
+
+use vars qw/$x $CL/;
+
+$CL = 'Math::BigInt';
+
+require 'alias.inc';
+
+
diff --git a/lib/Math/BigInt/t/sub_ali.t b/lib/Math/BigInt/t/sub_ali.t
new file mode 100644
index 0000000000..93620a9d82
--- /dev/null
+++ b/lib/Math/BigInt/t/sub_ali.t
@@ -0,0 +1,40 @@
+#!/usr/bin/perl -w
+
+# test that the new alias names work
+
+use Test::More;
+use strict;
+
+BEGIN
+  {
+  $| = 1;
+  # to locate the testing files
+  my $location = $0; $location =~ s/sub_ali.t//i;
+  if ($ENV{PERL_CORE})
+    {
+    # testing with the core distribution
+    @INC = qw(../t/lib);
+    }
+  unshift @INC, qw(../lib);
+  if (-d 't')
+    {
+    chdir 't';
+    require File::Spec;
+    unshift @INC, File::Spec->catdir(File::Spec->updir, $location);
+    }
+  else
+    {
+    unshift @INC, $location;
+    }
+  print "# INC = @INC\n";
+
+  plan tests => 6;
+  }
+
+use Math::BigInt::Subclass;
+
+use vars qw/$CL $x/;
+$CL = 'Math::BigInt::Subclass';
+
+require 'alias.inc';
+
diff --git a/lib/Math/BigInt/t/upgrade.inc b/lib/Math/BigInt/t/upgrade.inc
index 0b66640649..49dbf91823 100644
--- a/lib/Math/BigInt/t/upgrade.inc
+++ b/lib/Math/BigInt/t/upgrade.inc
@@ -1245,7 +1245,7 @@ abc:NaN,NaN
 &bfac
 -1:NaN
 NaNfac:NaN
-+inf:NaN
++inf:inf
 -inf:NaN
 0:1
 1:1