X-Git-Url: http://git.shadowcat.co.uk/gitweb/gitweb.cgi?a=blobdiff_plain;f=lib%2FMath%2FBigInt%2FCalcEmu.pm;h=9f7fd16434a22870a946d47430139d8cac0cc8ed;hb=29489e7c741791873ea464cb7e13d2b5a19577a7;hp=d5d1734b220ffe6df0644023c3fe7313f495c5be;hpb=3a427a117ca05296a5c3d5d88415dc040792253b;p=p5sagit%2Fp5-mst-13.2.git

diff --git a/lib/Math/BigInt/CalcEmu.pm b/lib/Math/BigInt/CalcEmu.pm
index d5d1734..9f7fd16 100644
--- a/lib/Math/BigInt/CalcEmu.pm
+++ b/lib/Math/BigInt/CalcEmu.pm
@@ -1,12 +1,13 @@
-package Math::BigInt;
+package Math::BigInt::CalcEmu;
 
 use 5.005;
 use strict;
 # use warnings;	# dont use warnings for older Perls
-
 use vars qw/$VERSION/;
 
-$VERSION = '0.02';
+$VERSION = '0.04';
+
+package Math::BigInt;
 
 # See SYNOPSIS below.
 
@@ -17,141 +18,6 @@ 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) = @_;
@@ -193,26 +59,29 @@ sub __emu_band
   $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)
+  # 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)
     {
-    $bx = substr($bx,0,CORE::length($by));
+    # if $yy eq "\x00", we can cut $bx, otherwise we need to padd $by
+    $by .= $yy x $diff;
     }
   elsif ($diff < 0)
     {
-    $by = substr($by,0,CORE::length($bx));
+    # if $xx eq "\x00", we can cut $by, otherwise we need to padd $bx
+    $bx .= $xx x abs($diff);
     }
-
+  
   # 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
+  # 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)
     {
@@ -223,20 +92,12 @@ sub __emu_band
     $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
     }
 
+  # leading zeros will be stripped by _from_hex()
   $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};
-    }
+  $x->{value} = $CALC_EMU->_from_hex( $bx );
 
   # 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;
@@ -316,16 +177,13 @@ sub __emu_bior
     $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
     }
 
+  # leading zeros will be stripped by _from_hex()
   $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};
-    }
+  $x->{value} = $CALC_EMU->_from_hex( $bx );
+
+  # calculate sign of result
+  $x->{sign} = '+';
+  $x->{sign} = '-' if $sign == 1 && !$x->is_zero();
 
   # if one of X or Y was negative, we need to decrement result
   $x->bdec() if $sign == 1;
@@ -405,16 +263,9 @@ sub __emu_bxor
     $bx =~ tr/\x0f\x0e\x0d\x0c\x0b\x0a\x09\x08\x07\x06\x05\x04\x03\x02\x01\x00/fedcba9876543210/;
     }
 
+  # leading zeros will be stripped by _from_hex()
   $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};
-    }
+  $x->{value} = $CALC_EMU->_from_hex( $bx );
 
   # calculate sign of result
   $x->{sign} = '+';
@@ -425,170 +276,6 @@ sub __emu_bxor
   $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
-    {
-    # trial computation by starting with 2,4,6,8,10 etc until we overstep
-    my $step;
-    my $trial = $self->new(2);
-    my $two = $self->new(2);
-    my $s_128 = $self->new(128);
-
-    local undef $Math::BigInt::accuracy;
-    local undef $Math::BigInt::precision;
-
-    # while still to do more than X steps
-    do
-      {
-      $step = $self->new(2);
-      while ( $trial->copy->bpow($y)->bacmp($x) < 0)
-        {
-        $step->bmul($two);
-        $trial->badd($step);
-        }
-
-      # hit exactly?
-      if ( $trial->copy->bpow($y)->bacmp($x) == 0)
-        {
-        $x->{value} = $trial->{value};	# make copy while preserving ref to $x
-        return $x->round(@r);
-        }
-      # overstepped, so go back on step
-      $trial->bsub($step);
-      } while ($step > $s_128);
-
-    $step = $two->copy();
-    while ( $trial->copy->bpow($y)->bacmp($x) < 0)
-      {
-      $trial->badd($step);
-      }
-
-    # not hit exactly?
-    if ( $x->bacmp( $trial->copy()->bpow($y) ) < 0)
-      {
-      $trial->bdec();
-      }
-    # copy result into $x (preserve ref)
-    $x->{value} = $trial->{value};
-    }
-  $x->round(@r);
-  }
-
-sub __emu_as_hex
-  {
-  my ($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;
-  }
-
 ##############################################################################
 ##############################################################################
 
@@ -621,7 +308,7 @@ the same terms as Perl itself.
 
 =head1 AUTHORS
 
-(c) Tels http://bloodgate.com 2003 - based on BigInt code by
+(c) Tels http://bloodgate.com 2003, 2004 - based on BigInt code by
 Tels from 2001-2003.
 
 =head1 SEE ALSO