calc.pm

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       {
       $xv->[0] = $xv->[0] - ($xv->[1] = int($xv->[0] * $RBASE)) * $MBASE;
       };
    return $xv;
    }
  # shortcut for result == 0
  if ( ((@$xv == 1) && ($xv->[0] == 0)) ||
       ((@$yv == 1) && ($yv->[0] == 0)) )
    {
    @$xv = (0);
    return $xv;
    }

  # since multiplying $x with $x fails, make copy in this case
  $yv = [@$xv] if $xv == $yv;	# same references?

  if ($LEN_CONVERT != 0)
    {
    $c->_to_small($xv); $c->_to_small($yv);
    }

  my @prod = (); my ($prod,$car,$cty,$xi,$yi);

  for $xi (@$xv)
    {
    $car = 0; $cty = 0;

    # slow variant
#    for $yi (@$yv)
#      {
#      $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
#      $prod[$cty++] =
#       $prod - ($car = int($prod * RBASE)) * $MBASE;  # see USE_MUL
#      }
#    $prod[$cty] += $car if $car; # need really to check for 0?
#    $xi = shift @prod;

    # faster variant
    # looping through this if $xi == 0 is silly - so optimize it away!
    $xi = (shift @prod || 0), next if $xi == 0;
    for $yi (@$yv)
      {
      $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
##     this is actually a tad slower
##        $prod = $prod[$cty]; $prod += ($car + $xi * $yi);	# no ||0 here
      $prod[$cty++] =
       $prod - ($car = int($prod * $RBASE)) * $MBASE;  # see USE_MUL
      }
    $prod[$cty] += $car if $car; # need really to check for 0?
    $xi = shift @prod || 0;	# || 0 makes v5.005_3 happy
    }
  push @$xv, @prod;
  if ($LEN_CONVERT != 0)
    {
    $c->_to_large($yv);
    $c->_to_large($xv);
    }
  else
    {
    __strip_zeros($xv);
    }
  $xv;
  }                                                                             

sub _mul_use_div
  {
  # (ref to int_num_array, ref to int_num_array)
  # multiply two numbers in internal representation
  # modifies first arg, second need not be different from first
  my ($c,$xv,$yv) = @_;
 
  # shortcut for two very short numbers (improved by Nathan Zook)
  # works also if xv and yv are the same reference
  if ((@$xv == 1) && (@$yv == 1))
    {
    if (($xv->[0] *= $yv->[0]) >= $MBASE)
        {
        $xv->[0] =
            $xv->[0] - ($xv->[1] = int($xv->[0] / $MBASE)) * $MBASE;
        };
    return $xv;
    }
  # shortcut for result == 0
  if ( ((@$xv == 1) && ($xv->[0] == 0)) ||
       ((@$yv == 1) && ($yv->[0] == 0)) )
    {
    @$xv = (0);
    return $xv;
    }

 
  # since multiplying $x with $x fails, make copy in this case
  $yv = [@$xv] if $xv == $yv;	# same references?

  if ($LEN_CONVERT != 0)
    {
    $c->_to_small($xv); $c->_to_small($yv);
    }
  
  my @prod = (); my ($prod,$car,$cty,$xi,$yi);
  for $xi (@$xv)
    {
    $car = 0; $cty = 0;
    # looping through this if $xi == 0 is silly - so optimize it away!
    $xi = (shift @prod || 0), next if $xi == 0;
    for $yi (@$yv)
      {
      $prod = $xi * $yi + ($prod[$cty] || 0) + $car;
      $prod[$cty++] =
       $prod - ($car = int($prod / $MBASE)) * $MBASE;
      }
    $prod[$cty] += $car if $car; # need really to check for 0?
    $xi = shift @prod || 0;	# || 0 makes v5.005_3 happy
    }
  push @$xv, @prod;
  if ($LEN_CONVERT != 0)
    {
    $c->_to_large($yv);
    $c->_to_large($xv);
    }
  else
    {
    __strip_zeros($xv);
    }
  $xv;
  }                                                                             

sub _div_use_mul
  {
  # ref to array, ref to array, modify first array and return remainder if 
  # in list context
  my ($c,$x,$yorg) = @_;

  if (@$x == 1 && @$yorg == 1)
    {
    # shortcut, $yorg and $x are two small numbers
    if (wantarray)
      {
      my $r = [ $x->[0] % $yorg->[0] ];
      $x->[0] = int($x->[0] / $yorg->[0]);
      return ($x,$r); 
      }
    else
      {
      $x->[0] = int($x->[0] / $yorg->[0]);
      return $x; 
      }
    }
  if (@$yorg == 1)
    {
    my $rem;
    $rem = _mod($c,[ @$x ],$yorg) if wantarray;

    # shortcut, $y is < $BASE
    my $j = scalar @$x; my $r = 0; 
    my $y = $yorg->[0]; my $b;
    while ($j-- > 0)
      {
      $b = $r * $MBASE + $x->[$j];
      $x->[$j] = int($b/$y);
      $r = $b % $y;
      }
    pop @$x if @$x > 1 && $x->[-1] == 0;	# splice up a leading zero 
    return ($x,$rem) if wantarray;
    return $x;
    }

  my $y = [ @$yorg ];				# always make copy to preserve
  if ($LEN_CONVERT != 0)
    {
    $c->_to_small($x); $c->_to_small($y);
    }

  my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1,@d,$tmp,$q,$u2,$u1,$u0);

  $car = $bar = $prd = 0;
  if (($dd = int($MBASE/($y->[-1]+1))) != 1) 
    {
    for $xi (@$x) 
      {
      $xi = $xi * $dd + $car;
      $xi -= ($car = int($xi * $RBASE)) * $MBASE;	# see USE_MUL
      }
    push(@$x, $car); $car = 0;
    for $yi (@$y) 
      {
      $yi = $yi * $dd + $car;
      $yi -= ($car = int($yi * $RBASE)) * $MBASE;	# see USE_MUL
      }
    }
  else 
    {
    push(@$x, 0);
    }
  @q = (); ($v2,$v1) = @$y[-2,-1];
  $v2 = 0 unless $v2;
  while ($#$x > $#$y) 
    {
    ($u2,$u1,$u0) = @$x[-3..-1];
    $u2 = 0 unless $u2;
    #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n"
    # if $v1 == 0;
     $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$MBASE+$u1)/$v1));
    --$q while ($v2*$q > ($u0*$MBASE+$u1-$q*$v1)*$MBASE+$u2);
    if ($q)
      {
      ($car, $bar) = (0,0);
      for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
        {
        $prd = $q * $y->[$yi] + $car;
        $prd -= ($car = int($prd * $RBASE)) * $MBASE;	# see USE_MUL
	$x->[$xi] += $MBASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0));
	}
      if ($x->[-1] < $car + $bar) 
        {
        $car = 0; --$q;
	for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
          {
	  $x->[$xi] -= $MBASE
	   if ($car = (($x->[$xi] += $y->[$yi] + $car) > $MBASE));
	  }
	}   
      }
      pop(@$x); unshift(@q, $q);
    }
  if (wantarray) 
    {
    @d = ();
    if ($dd != 1)  
      {
      $car = 0; 
      for $xi (reverse @$x) 
        {
        $prd = $car * $MBASE + $xi;
        $car = $prd - ($tmp = int($prd / $dd)) * $dd; # see USE_MUL
        unshift(@d, $tmp);
        }
      }
    else 
      {
      @d = @$x;
      }
    @$x = @q;
    my $d = \@d; 
    if ($LEN_CONVERT != 0)
      {
      $c->_to_large($x); $c->_to_large($d);
      }
    else
      {
      __strip_zeros($x);
      __strip_zeros($d);
      }
    return ($x,$d);
    }
  @$x = @q;
  if ($LEN_CONVERT != 0)
    {
    $c->_to_large($x);
    }
  else
    {
    __strip_zeros($x);
    }
  $x;
  }

sub _div_use_div
  {
  # ref to array, ref to array, modify first array and return remainder if 
  # in list context
  my ($c,$x,$yorg) = @_;

  if (@$x == 1 && @$yorg == 1)
    {
    # shortcut, $yorg and $x are two small numbers
    if (wantarray)
      {
      my $r = [ $x->[0] % $yorg->[0] ];
      $x->[0] = int($x->[0] / $yorg->[0]);
      return ($x,$r); 
      }
    else
      {
      $x->[0] = int($x->[0] / $yorg->[0]);
      return $x; 
      }
    }
  if (@$yorg == 1)
    {
    my $rem;
    $rem = _mod($c,[ @$x ],$yorg) if wantarray;

    # shortcut, $y is < $BASE
    my $j = scalar @$x; my $r = 0; 
    my $y = $yorg->[0]; my $b;
    while ($j-- > 0)
      {
      $b = $r * $MBASE + $x->[$j];
      $x->[$j] = int($b/$y);
      $r = $b % $y;
      }
    pop @$x if @$x > 1 && $x->[-1] == 0;	# splice up a leading zero 
    return ($x,$rem) if wantarray;
    return $x;
    }

  my $y = [ @$yorg ];				# always make copy to preserve
  if ($LEN_CONVERT != 0)
    {
    $c->_to_small($x); $c->_to_small($y);
    }
 
  my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1,@d,$tmp,$q,$u2,$u1,$u0);

  $car = $bar = $prd = 0;
  if (($dd = int($MBASE/($y->[-1]+1))) != 1) 
    {
    for $xi (@$x) 
      {
      $xi = $xi * $dd + $car;
      $xi -= ($car = int($xi / $MBASE)) * $MBASE;
      }
    push(@$x, $car); $car = 0;
    for $yi (@$y) 
      {
      $yi = $yi * $dd + $car;
      $yi -= ($car = int($yi / $MBASE)) * $MBASE;
      }
    }
  else 
    {
    push(@$x, 0);
    }
  @q = (); ($v2,$v1) = @$y[-2,-1];
  $v2 = 0 unless $v2;
  while ($#$x > $#$y) 
    {
    ($u2,$u1,$u0) = @$x[-3..-1];
    $u2 = 0 unless $u2;
    #warn "oups v1 is 0, u0: $u0 $y->[-2] $y->[-1] l ",scalar @$y,"\n"
    # if $v1 == 0;
     $q = (($u0 == $v1) ? $MAX_VAL : int(($u0*$MBASE+$u1)/$v1));
    --$q while ($v2*$q > ($u0*$MBASE+$u1-$q*$v1)*$MBASE+$u2);
    if ($q)
      {
      ($car, $bar) = (0,0);
      for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
        {
        $prd = $q * $y->[$yi] + $car;
        $prd -= ($car = int($prd / $MBASE)) * $MBASE;
	$x->[$xi] += $MBASE if ($bar = (($x->[$xi] -= $prd + $bar) < 0));
	}
      if ($x->[-1] < $car + $bar) 
        {
        $car = 0; --$q;
	for ($yi = 0, $xi = $#$x-$#$y-1; $yi <= $#$y; ++$yi,++$xi) 
          {
	  $x->[$xi] -= $MBASE
	   if ($car = (($x->[$xi] += $y->[$yi] + $car) > $MBASE));
	  }
	}   
      }
    pop(@$x); unshift(@q, $q);
    }
  if (wantarray) 
    {
    @d = ();
    if ($dd != 1)  
      {
      $car = 0; 
      for $xi (reverse @$x) 
        {
        $prd = $car * $MBASE + $xi;
        $car = $prd - ($tmp = int($prd / $dd)) * $dd;
        unshift(@d, $tmp);
        }
      }
    else 
      {
      @d = @$x;
      }
    @$x = @q;
    my $d = \@d; 
    if ($LEN_CONVERT != 0)
      {
      $c->_to_large($x); $c->_to_large($d);
      }
    else
      {
      __strip_zeros($x);
      __strip_zeros($d);
      }
    return ($x,$d);
    }
  @$x = @q;
  if ($LEN_CONVERT != 0)
    {
    $c->_to_large($x);
    }
  else
    {
    __strip_zeros($x);
    }
  $x;
  }

##############################################################################
# testing

sub _acmp
  {
  # internal absolute post-normalized compare (ignore signs)
  # ref to array, ref to array, return <0, 0, >0
  # arrays must have at least one entry; this is not checked for

  my ($c,$cx,$cy) = @_;

  # fast comp based on number of array elements (aka pseudo-length)
  my $lxy = scalar @$cx - scalar @$cy;
  return -1 if $lxy < 0;				# already differs, ret
  return 1 if $lxy > 0;					# ditto

  # now calculate length based on digits, not parts
  # we need only the length of the last element, since both array have the
  # same number of parts
  $lxy = length(int($cx->[-1])) - length(int($cy->[-1]));
  return -1 if $lxy < 0;
  return 1 if $lxy > 0;

  # hm, same lengths,  but same contents? So we need to check all parts:
  my $a; my $j = scalar @$cx - 1;
  # manual way (abort if unequal, good for early ne)
  while ($j >= 0)
    {
    last if ($a = $cx->[$j] - $cy->[$j]); $j--;
    }
  return 1 if $a > 0;
  return -1 if $a < 0;
  0;						# numbers are equal
  }

sub _len
  {