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lib/Math/NumSeq/RadixWithoutDigit.pm  view on Meta::CPAN

#                = (9^len - 1)/8 - 1
#                = (9^len - 1 - 8)/8
#                = (9^len - 9)/8
#     8*i + 1 = 9^level
#
#     add sentinel 1*9^len, so
#     from = i - (9^len - 9)/8 + 9^len
#          = i + (- 9^len + 9)/8 + 9^len
#          = i + (- 9^len + 9 + 8*9^len)/8
#          = i + (7*9^len + 9) / 8
#
#     and which is then a high digit 2*9^len too big
#
sub ith {
  my ($self, $i) = @_;
  ### RadixWithoutDigit ith(): $i

  $i -= $self->i_start;    # i_start=0 or i_start=1 both begin at value=0

  if (_is_infinite($i)) {
    return $i;  # don't loop forever if $i is +infinity
  }

  my $radix = $self->{'radix'};
  my $digit = $self->{'digit'};

  if ($radix == 2) {
    if ($digit == 0) {
      my $base = ($i < 30 ? 2 : Math::NumSeq::_to_bigint(2));
      return ($base ** ($i+1)) - 1;
    } else {
      ### radix 2 without 1 no values ...
      return undef;
    }
  }

  if ($digit == -1) {
    $digit = $radix-1;
  }

  my $r1 = $radix - 1;
  # if ($i < $r1) {
  #   return $i + ($i >= $digit);
  # }
  my $r2 = $radix - 2;
  ### $radix
  ### $r1
  ### $r2

  my $value = 0;
  if ($digit == 0) {
    my $len = 1;
    while (($r1**$len - $r1) / $r2 <= $i) {
      $len++;
    }
    $len--;
    ### $len
    ### base: ($r1**$len - $r1) / $r2
    ### sentinel: $r1**$len
    ### adj add: $r1**$len - ($r1**$len - $r1) / $r2
    ### adj formula: (($r2-1)*$r1**$len + $r1) / $r2

    ### assert: $i >= ($r1 ** $len - $r1) / $r2
    ### assert: $i < ($r1 ** $len - $r1) / $r2 + $r1 ** $len

    $i += (($r2-1)*$r1**$len + $r1) / $r2;
    $value = -2 * $radix**$len;
    ### i remainder: $i
    ### $value

    ### assert: $i >= $r1 ** $len
    ### assert: $i < 2 * $r1 ** $len
  }

  # $i converted to radix-1 digits, built back up as radix
  my $power = 1;
  while ($i > 0) {
    my $d = $i % $r1;
    $i = int($i/$r1);
    ### $value
    ### $d
    ### $power
    if ($d >= $digit) {
      $d++;
      ### inc to d: $d
    }
    $value += $power * $d;
    $power *= $radix;
  }
  ### stop at i: $i
  $value += $power * $i;

  ### $value
  return $value;

  # my $digit = 1;
  # my $x = $i;
  # while ($x) {
  #   ### x mod $radix: $x%$radix
  #   if (($x % $radix) == $digit) {
  #     ### add: $digit
  #     $i += $digit;
  #     $x++;
  #   }
  #   $x = int($x/$radix);
  #   $digit *= $radix;
  # }
  # return (($self->{'i'} = $i),
  #         1);
}

sub pred {
  my ($self, $value) = @_;

  my $radix = $self->{'radix'};
  my $digit = $self->{'digit'};
  if ($digit == -1) {
    $digit = $radix-1;
  }

  if ($value < 0