calc.pm

source of perl for linux application,

      }
    else 
      {
      @d = @$x;
      }
    @$x = @q;
    my $d = \@d; 
    __strip_zeros($x);
    __strip_zeros($d);
    return ($x,$d);
    }
  @$x = @q;
  __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) = @_;

  # the general div algorithmn here is about O(N*N) and thus quite slow, so
  # we first check for some special cases and use shortcuts to handle them.

  # This works, because we store the numbers in a chunked format where each
  # element contains 5..7 digits (depending on system).

  # if both numbers have only one element:
  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 $x; 
      }
    }
  # if x has more than one, but y has only one element:
  if (@$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 * $BASE + $x->[$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;
    }
  # now x and y have more than one element

  # check whether y has more elements than x, if yet, the result will be 0
  if (@$yorg > @$x)
    {
    my $rem;
    $rem = [@$x] if wantarray;			# make copy
    splice (@$x,1);				# keep ref to original array
    $x->[0] = 0;				# set to 0
    return ($x,$rem) if wantarray;		# including remainder?
    return $x;					# only x, which is [0] now
    }
  # check whether the numbers have the same number of elements, in that case
  # the result will fit into one element and can be computed efficiently
  if (@$yorg == @$x)
    {
    my $rem;
    # if $yorg has more digits than $x (it's leading element is longer than
    # the one from $x), the result will also be 0:
    if (length(int($yorg->[-1])) > length(int($x->[-1])))
      {
      $rem = [@$x] if wantarray;		# make copy
      splice (@$x,1);				# keep ref to org array
      $x->[0] = 0;				# set to 0
      return ($x,$rem) if wantarray;		# including remainder?
      return $x;
      }
    # now calculate $x / $yorg

    if (length(int($yorg->[-1])) == length(int($x->[-1])))
      {
      # same length, so make full compare

      my $a = 0; my $j = scalar @$x - 1;
      # manual way (abort if unequal, good for early ne)
      while ($j >= 0)
        {
        last if ($a = $x->[$j] - $yorg->[$j]); $j--;
        }
      # $a contains the result of the compare between X and Y
      # a < 0: x < y, a == 0: x == y, a > 0: x > y
      if ($a <= 0)
        {
        $rem = [ 0 ];			# a = 0 => x == y => rem 0
        $rem = [@$x] if $a != 0;	# a < 0 => x < y => rem = x
        splice(@$x,1);			# keep single element
        $x->[0] = 0;			# if $a < 0
        $x->[0] = 1 if $a == 0; 	# $x == $y
        return ($x,$rem) if wantarray;	# including remainder?
        return $x;
        }
      # $x >= $y, so proceed normally

      }
    }

  # all other cases:

  my $y = [ @$yorg ];				# always make copy to preserve
 
  my ($car,$bar,$prd,$dd,$xi,$yi,@q,$v2,$v1,@d,$tmp,$q,$u2,$u1,$u0);

  $car = $bar = $prd = 0;
  if (($dd = int($BASE/($y->[-1]+1))) != 1) 
    {
    for $xi (@$x) 
      {
      $xi = $xi * $dd + $car;
      $xi -= ($car = int($xi / $BASE)) * $BASE;
      }
    push(@$x, $car); $car = 0;
    for $yi (@$y) 
      {
      $yi = $yi * $dd + $car;
      $yi -= ($car = int($yi / $BASE)) * $BASE;
      }
    }
  else 
    {
    push(@$x, 0);
    }

  # @q will accumulate the final result, $q contains the current computed
  # part of the final result

  @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*$BASE+$u1)/$v1));
    --$q while ($v2*$q > ($u0*$BASE+$u1-$q*$v1)*$BASE+$u2);
    if ($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 / $BASE)) * $BASE;
	$x->[$xi] += $BASE if ($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] -= $BASE
	   if ($car = (($x->[$xi] += $y->[$yi] + $car) >= $BASE));
	  }
	}   
      }
    pop(@$x); unshift(@q, $q);
    }
  if (wantarray) 
    {
    @d = ();
    if ($dd != 1)  
      {
      $car = 0; 
      for $xi (reverse @$x) 
        {
        $prd = $car * $BASE + $xi;
        $car = $prd - ($tmp = int($prd / $dd)) * $dd;
        unshift(@d, $tmp);
        }
      }
    else 
      {
      @d = @$x;
      }
    @$x = @q;
    my $d = \@d; 
    __strip_zeros($x);
    __strip_zeros($d);
    return ($x,$d);
    }
  @$x = @q;
  __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) = @_;
 
  # shortcut for short numbers 
  return (($cx->[0] <=> $cy->[0]) <=> 0) 
   if scalar @$cx == scalar @$cy && scalar @$cx == 1;

  # fast comp based on number of array elements (aka pseudo-length)
  my $lxy = (scalar @$cx - scalar @$cy)
  # or length of first element if same number of elements (aka difference 0)
    ||
  # need int() here because sometimes the last element is '00018' vs '18'
   (length(int($cx->[-1])) - length(int($cy->[-1])));
  return -1 if $lxy < 0;				# already differs, ret
  return 1 if $lxy > 0;					# ditto

  # manual way (abort if unequal, good for early ne)
  my $a; my $j = scalar @$cx;
  while (--$j >= 0)
    {
    last if ($a = $cx->[$j] - $cy->[$j]);
    }
  $a <=> 0;
  }

sub _len
  {
  # compute number of digits in base 10

  # int() because add/sub sometimes leaves strings (like '00005') instead of
  # '5' in this place, thus causing length() to report wrong length
  my $cx = $_[1];

  (@$cx-1)*$BASE_LEN+length(int($cx->[-1]));
  }

sub _digit
  {
  # return the nth digit, negative values count backward
  # zero is rightmost, so _digit(123,0) will give 3
  my ($c,$x,$n) = @_;

  my $len = _len('',$x);

  $n = $len+$n if $n < 0;		# -1 last, -2 second-to-last
  $n = abs($n);				# if negative was too big
  $len--; $n = $len if $n > $len;	# n to big?
  
  my $elem = int($n / $BASE_LEN);	# which array element
  my $digit = $n % $BASE_LEN;		# which digit in this element
  $elem = '0' x $BASE_LEN . @$x[$elem];	# get element padded with 0's
  substr($elem,-$digit-1,1);
  }

sub _zeros
  {
  # return amount of trailing zeros in decimal
  # check each array elem in _m for having 0 at end as long as elem == 0
  # Upon finding a elem != 0, stop
  my $x = $_[1];

  return 0 if scalar @$x == 1 && $x->[0] == 0;

  my $zeros = 0; my $elem;
  foreach my $e (@$x)
    {
    if ($e != 0)
      {
      $elem = "$e";				# preserve x
      $elem =~ s/.*?(0*$)/$1/;			# strip anything not zero
      $zeros *= $BASE_LEN;			# elems * 5
      $zeros += length($elem);			# count trailing zeros
      last;					# early out
      }
    $zeros ++;					# real else branch: 50% slower!
    }
  $zeros;
  }

##############################################################################
# _is_* routines

sub _is_zero
  {
  # return true if arg is zero 
  (((scalar @{$_[1]} == 1) && ($_[1]->[0] == 0))) <=> 0;
  }

sub _is_even
  {
  # return true if arg is even
  (!($_[1]->[0] & 1)) <=> 0; 
  }

sub _is_odd
  {
  # return true if arg is even
  (($_[1]->[0] & 1)) <=> 0; 
  }

sub _is_one
  {
  # return true if arg is one
  (scalar @{$_[1]} == 1) && ($_[1]->[0] == 1) <=> 0; 
  }

sub _is_two
  {
  # return true if arg is two 
  (scalar @{$_[1]} == 1) && ($_[1]->[0] == 2) <=> 0; 
  }

sub _is_ten
  {
  # return true if arg is ten 
  (scalar @{$_[1]} == 1) && ($_[1]->[0] == 10) <=> 0; 
  }

sub __strip_zeros
  {
  # internal normalization function that strips leading zeros from the array
  # args: ref to array
  my $s = shift;
 
  my $cnt = scalar @$s; # get count of parts
  my $i = $cnt-1;
  push @$s,0 if $i < 0;		# div might return empty results, so fix it

  return $s if @$s == 1;		# early out

  #print "strip: cnt $cnt i $i\n";
  # '0', '3', '4', '0', '0',
  #  0    1    2    3    4
  # cnt = 5, i = 4
  # i = 4
  # i = 3
  # => fcnt = cnt - i (5-2 => 3, cnt => 5-1 = 4, throw away from 4th pos)
  # >= 1: skip first part (this can be zero)
  while ($i > 0) { last if $s->[$i] != 0; $i--; }
  $i++; splice @$s,$i if ($i < $cnt); # $i cant be 0
  $s;                                                                    
  }                                                                             

###############################################################################
# check routine to test internal state for corruptions

sub _check
  {
  # used by the test suite
  my $x = $_[1];

  return "$x is not a reference" if !ref($x);

  # are all parts are valid?
  my $i = 0; my $j = scalar @$x; my ($e,$try);
  while ($i < $j)
    {
    $e = $x->[$i]; $e = 'undef' unless defined $e;
    $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e)";
    last if $e !~ /^[+]?[0-9]+$/;
    $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (stringify)";
    last if "$e" !~ /^[+]?[0-9]+$/;
    $try = '=~ /^[\+]?[0-9]+\$/; '."($x, $e) (cat-stringify)";
    last if '' . "$e" !~ /^[+]?[0-9]+$/;
    $try = ' < 0 || >= $BASE; '."($x, $e)";
    last if $e <0 || $e >= $BASE;
    # this test is disabled, since new/bnorm and certain ops (like early out
    # in add/sub) are allowed/expected to leave '00000' in some elements
    #$try = '=~ /^00+/; '."($x, $e)";
    #last if $e =~ /^00+/;
    $i++;
    }
  return "Illegal part '$e' at pos $i (tested: $try)" if $i < $j;
  0;
  }


###############################################################################

sub _mod
  {
  # if possible, use mod shortcut
  my ($c,$x,$yo) = @_;

  # slow way since $y to big
  if (scalar @$yo > 1)
    {
    my ($xo,$rem) = _div($c,$x,$yo);
    return $rem;
    }

  my $y = $yo->[0];
  # both are single element arrays
  if (scalar @$x == 1)
    {
    $x->[0] %= $y;
    return $x;
    }

  # @y is a single element, but @x has more than one element
  my $b = $BASE % $y;
  if ($b == 0)
    {
    # when BASE % Y == 0 then (B * BASE) % Y == 0
    # (B * BASE) % $y + A % Y => A % Y
    # so need to consider only last element: O(1)
    $x->[0] %= $y;
    }
  elsif ($b == 1)
    {
    # else need to go through all elements: O(N), but loop is a bit simplified
    my $r = 0;
    foreach (@$x)
      {
      $r = ($r + $_) % $y;		# not much faster, but heh...
      #$r += $_ % $y; $r %= $y;
      }
    $r = 0 if $r == $y;
    $x->[0] = $r;
    }
  else
    {
    # else need to go through all elements: O(N)
    my $r = 0; my $bm = 1;
    foreach (@$x)
      {
      $r = ($_ * $bm + $r) % $y;
      $bm = ($bm * $b) % $y;

      #$r += ($_ % $y) * $bm;
      #$bm *= $b;
      #$bm %= $y;
      #$r %= $y;
      }
    $r = 0 if $r == $y;
    $x->[0] = $r;
    }
  splice (@$x,1);		# keep one element of $x
  $x;
  }

##############################################################################
# shifts

sub _rsft
  {
  my ($c,$x,$y,$n) = @_;

  if ($n != 10)
    {
    $n = _new($c,$n); return _div($c,$x, _pow($c,$n,$y));
    }

  # shortcut (faster) for shifting by 10)
  # multiples of $BASE_LEN
  my $dst = 0;				# destination
  my $src = _num($c,$y);		# as normal int
  my $xlen = (@$x-1)*$BASE_LEN+length(int($x->[-1]));  # len of x in digits
  if ($src >= $xlen or ($src == $xlen and ! defined $x->[1]))
    {
    # 12345 67890 shifted right by more than 10 digits => 0
    splice (@$x,1);                    # leave only one element
    $x->[0] = 0;                       # set to zero
    return $x;