path: root/Master/texmf-dist/tex/latex/longdivision/longdivision.sty

%% Package: longdivision.sty version 1.0
%% Author: Hood Chatham
%% Email: hood@mit.edu
%% Date: 2/5/2017
%% License: Latex Project Public License


\ProvidesPackage{longdivision}
\RequirePackage{xparse}

\ExplSyntaxOn


% Core registers
\bool_new:N \l__longdiv_mathmode_bool
\bool_new:N \l_longdiv_repeating_decimal_bool
\bool_new:N \l__longdiv_added_point_bool
\bool_new:N \l__longdiv_seen_point_bool
\bool_new:N \l__longdiv_seen_digit_bool
\bool_new:N \l__longdiv_stopped_early_stage_bool
\int_new:N  \l__longdiv_quotient_int
\int_new:N  \l__longdiv_position_int
\int_new:N  \l__longdiv_point_digit_int
\int_new:N  \l__longdiv_repeat_digit_int

\dim_new:N \g__longdiv_temp_dim % For measuring the distance to the right side of digits

% These are used to make sure division doesn't run off the page.
\int_new:N  \l__longdiv_extra_digits_int
\int_new:N  \l__longdiv_max_extra_digits_int
\int_set:Nn \l__longdiv_max_extra_digits_int { 100 } % Infinite (just needs to be greater than max_total_digits_int and max_display_divisions_int)
\int_new:N  \l__longdiv_digits_requested_int
\int_set:Nn \l__longdiv_digits_requested_int { 100 } % Infinite (just needs to be greater than max_total_digits_int and max_display_divisions_int)

\int_const:Nn \c__longdiv_max_total_digits_int { 60 }
\int_const:Nn \c__longdiv_max_display_divisions_int { 20 }
\int_new:N \l__longdiv_display_divisions_int

% Key-value arguments
\cs_new:Npn \longdivisionkeys #1 { \keys_set:nn { longdivision } { #1 } }

\keys_define:nn { longdivision }
{
    stage .int_set:N = \l__longdiv_digits_requested_int,
    max~extra~digits .int_set:N = \l__longdiv_max_extra_digits_int,
    unknown .code:n = {
        %\def\temp{#1}\show\temp
        \int_set:Nn \l__longdiv_max_extra_digits_int { \l_keys_key_tl }
    }
}

\cs_new:Nn \longdiv_register_repeating_decimal_style_choices:n {
    \keys_define:nn { longdivision } {
        repeating~decimal~style .choices:nn =
        { #1 }
        {
            \cs_set_eq:Nc \longdiv_linkedlist_indicate_repeating_decimal:n { longdiv_linkedlist_indicate_repeating_decimal_##1:n }
        }
    }
}

\cs_new:Nn \longdiv_register_style_choices:n {
    \keys_define:nn { longdivision } {
        style .choices:nn =
            { #1 }
            {
                \cs_set_eq:Nc \longdiv_typeset_main: { longdiv_typeset_main_##1: }
            }
    }
}

\longdiv_register_style_choices:n { default, standard, tikz, german }
\longdiv_register_repeating_decimal_style_choices:n { overline, dots, dots~all, parentheses, none }

\cs_new:Nn \longdiv_define_style:nn {
    \cs_new:cpn { longdiv_typeset_main_ #1 :} { #2 }
    \longdiv_register_style_choices:n { #1 }
}
\let \longdivdefinestyle \longdiv_define_style:nn

%%
%% The linked list
%%

% This token list just stores a reference to the first entry in the linked list
\tl_new:N \l__longdiv_linkedlist_tl
\tl_set:Nn\l__longdiv_linkedlist_tl { \longdiv_linkedlist_next:n { 0 } }
\int_new:N \l__longdiv_linkedlist_length_int

% Set the next entry to be a no-op so that when expanded the last "null pointer" just disappears
\cs_new:Nn \longdiv_linkedlist_set_next_do_nothing: {
    \cs_set_eq:cN { longdiv_linkedlist ~ \int_use:N \l__longdiv_linkedlist_length_int } \prg_do_nothing:
}
\longdiv_linkedlist_set_next_do_nothing:

% "pointer" to next element (argument is the element's id)
\cs_new:Nn \longdiv_linkedlist_next:n { \use:c { longdiv_linkedlist ~ #1 } }

\cs_new:Nn \longdiv_linkedlist_add:n {
    \cs_set:cpx { longdiv_linkedlist ~ \int_use:N \l__longdiv_linkedlist_length_int}{
        \exp_not:n{ \longdiv_linkedlist_element:n { #1 } } \exp_not:N \longdiv_linkedlist_next:n { \int_eval:n { \l__longdiv_linkedlist_length_int + 1} }
    }
    \int_incr:N \l__longdiv_linkedlist_length_int
    \longdiv_linkedlist_set_next_do_nothing:
}
\cs_new_eq:NN \longdiv_linkedlist_element:n \use:n
\cs_generate_variant:Nn \longdiv_linkedlist_add:n { f }

% The easy implementation of remove_tail and the \longdiv_linkedlist_indicate_repeating_decimal commands is why I chose the "linked list" format.
% Delete last element of list.
\cs_new:Nn \longdiv_linkedlist_remove_tail: {
    \int_decr:N \l__longdiv_linkedlist_length_int
    \longdiv_linkedlist_set_next_do_nothing:
}

%%
%% Entry points
%%

% \tl_rescan to ignore spaces in input.
\NewDocumentCommand \longdivision { omm } {
    \group_begin:
    \IfNoValueF { #1 } {
        \keys_set:nn { longdivision } { #1 }
    }
    \tl_rescan:nn { \ExplSyntaxOn } { \longdiv_start:xx { #2 } { #3 } }
    \group_end:
}

% Same as \longdiv[0]{#1}{#2}.
\NewDocumentCommand \intlongdivision { omm } {
    \group_begin:
    \IfNoValueF { #1 } {
        \keys_set:nn { longdivision } { #1 }
    }
    \int_set:Nn \l__longdiv_max_extra_digits_int { 0 }
    \tl_rescan:nn { \ExplSyntaxOn } { \longdiv_start:xx { #2 } { #3 } }
    \group_end:
}

% Check input is valid then enter main loop.
% We use \int_eval:w to ensure that the dividend has no unnecessary leading zeroes and doesn't begin with a decimal point.
% Note that \int_eval:n wouldn't work here because it inserts a "\relax" token that would not get eaten by \numexpr if
% #1 contains a decimal point. This "\relax" causes trouble for the division main loop.
\cs_new:Nn \longdiv_start:nn {
    \longdiv_check_dividend:n { #1 }
    \longdiv_check_divisor:n { #2 }
    % Second copy of #1 is eaten by \longdiv_typeset:nnn to print the dividend
    \exp_args:Nnnff \longdiv_get_new_digit:nnn { } { #2 } { \int_eval:w 0#1 } { \int_eval:w 0#1  }
    \longdiv_break_point: { #1 } { #2 }
}
\cs_generate_variant:Nn \longdiv_start:nn { xx }

\cs_new_eq:NN \longdiv_break_point: \use_none:nn

%%
%% Input checkers
%%

% Parse through the dividend token by token
% Check that every token is a digit with the exception of at most one .
\cs_new:Nn \longdiv_check_dividend:n {
    \longdiv_check_dividend_before_point:N #1 \q_stop
}

\cs_new:Nn \longdiv_check_dividend_before_point:N {
    \token_if_eq_meaning:NNF #1 \q_stop {
        \token_if_eq_meaning:NNTF #1 . {
            \longdiv_check_dividend_seen_point:N
        }{
            \longdiv_check_dividend_isdigit:N #1
            \longdiv_check_dividend_before_point:N
        }
    }
}

\cs_new:Nn \longdiv_check_dividend_seen_point:N {
    \token_if_eq_meaning:NNF #1 \q_stop {
        \longdiv_check_dividend_isdigit:N #1
        \longdiv_check_dividend_seen_point:N
    }
}

\cs_new:Nn \longdiv_check_dividend_isdigit:N {
    \bool_if:nF { \token_if_eq_meaning_p:NN #1 0
      || \token_if_eq_meaning_p:NN #1 1 || \token_if_eq_meaning_p:NN #1 2 || \token_if_eq_meaning_p:NN #1 3
      || \token_if_eq_meaning_p:NN #1 4 || \token_if_eq_meaning_p:NN #1 5 || \token_if_eq_meaning_p:NN #1 6
      || \token_if_eq_meaning_p:NN #1 7 || \token_if_eq_meaning_p:NN #1 8 || \token_if_eq_meaning_p:NN #1 9
    }{
        \longdiv_error:nwnn { dividend_invalid }
    }
}

% Check that there is no ., that it is at most 8 digits, and that the entire argument can get assigned to a count variable
% There's no way to do this last check in expl3, so I use plaintex \newcount, \afterassignment, and \l__longdiv_temp_int =.
\newcount \l__longdiv_temp_int
\cs_new:Nn \longdiv_check_divisor:n {
    \tl_if_in:nnT { #1 } { . } {
        \longdiv_error:nwnn { divisor_not_int }
    }
    % We have to do the length check before the "validity" check because the "validity" check makes an assignment
    % which throws a low level error if the number to be assigned is too large.
    \int_compare:nNnF { \tl_count:n { #1 } } < \c_nine {
        \longdiv_error:nwnn { divisor_too_large }
    }
    % Idea here: if #1 is a valid number, \l__longdiv_temp_int = 0#1 will absorb all of it.
    % So if there's any left, throw an error. Leading zero ensures that it fails on -1 and
    % that if #1 starts with some other nondigit character that it won't cause
    % "Missing number, treated as zero."
    \afterassignment \longdiv_check_divisor_aux:w
    \l__longdiv_temp_int = 0 #1 \scan_stop:
}

\cs_new:Npn \longdiv_check_divisor_aux:w #1 \scan_stop: {
    \tl_if_empty:nF { #1 } {
        \longdiv_error:nwnn { divisor_invalid }
    }
    \int_compare:nNnT \l__longdiv_temp_int = \c_zero {
        \longdiv_error:nwnn { divisor_zero }
    }
}

% Absorb up to break_point to gracefully quit out of the macro
\cs_new:Npn \longdiv_error:nwnn #1 #2 \longdiv_break_point: {
    \msg_error:nnnn { longdivision } { #1 }
}

% Errors:
\msg_new:nnn { longdivision } { dividend_invalid } { Dividend ~ '#1' ~ is ~ invalid ~ (\msg_line_context:).}
\msg_new:nnn { longdivision } { divisor_too_large }
    { Divisor ~ '#2' ~ is ~ too ~ large ~ (\msg_line_context:). ~ It ~ has ~ \tl_count:n { #2 } ~ digits, ~ but ~ divisors ~ can ~ be ~ at ~ most ~ 9 ~ digits ~ long. }
\msg_new:nnn { longdivision } { divisor_not_int } { Divisor ~ '#2' ~ is ~ not ~ an ~ integer ~ (\msg_line_context:). }
\msg_new:nnn { longdivision } { divisor_invalid } { Divisor ~ '#2' ~ is ~ invalid ~ (\msg_line_context:). }

% Warnings:
\msg_new:nnn { longdivision } { work_stopped_early } { The ~ work ~ display ~ stopped ~ early ~ to ~ avoid ~ running ~ off ~ the ~ page ~ (\msg_line_context:). }
\msg_new:nnn { longdivision } { division_stopped_early } { The ~ division ~ stopped ~ early ~ to ~ avoid ~ running ~ off ~ the ~ page ~ (\msg_line_context:).}
\msg_new:nnn { longdivision } { no_division_occurred }
    { Either ~ the ~ dividend ~ was ~ zero ~ or ~ you ~ used ~ \token_to_str:N \intlongdiv \space and ~ the ~ dividend ~ was ~less ~ than ~ the ~ divisor. ~
      This ~ isn't ~ a ~ big ~ deal, ~ but ~ the ~ result ~ probably ~ looks ~ silly. }
\msg_new:nnn { longdivision } { no_tikz } { You ~ requested ~ "style~=~tikz" ~ but ~ tikz ~ has ~ not ~ been ~ loaded. ~ Falling ~ back ~ to ~ "style~=~standard". }


%%
%% Division
%%

% #1 -- remainder
% #2 -- divisor
% #3 -- rest of digits of dividend
\cs_new:Nn \longdiv_get_new_digit:nnn {
    \tl_if_empty:nTF { #3 } { % Are we out of digits?
        % If we haven't hit the decimal point add it to the quotient and dividend
        % Set seen_digit false so that we can remove the decimal point later if it divided evenly or we used \intlongdiv
        \bool_if:NF \l__longdiv_seen_point_bool {
            \longdiv_add_point: %
            \bool_set_false:N \l__longdiv_seen_digit_bool
            \bool_set_true:N \l__longdiv_added_point_bool
        }
        \longdiv_divide_no_more_digits:nn { #1 } { #2 }
    }{
        \longdiv_get_new_digit_aux:nnw { #1 } { #2 } #3;
    }
}
\cs_generate_variant:Nn \longdiv_get_new_digit:nnn {xnn}

\cs_new:Npn \longdiv_get_new_digit_aux:nnw #1 #2 #3 #4;{
    \token_if_eq_meaning:NNTF #3 . {
        \longdiv_add_point:
        \bool_set_true:N \l__longdiv_seen_digit_bool % Prevent this decimal point from being removed later
        \bool_set_false:N \l__longdiv_added_point_bool
        \longdiv_get_new_digit:nnn { #1 } { #2 } { #4 }
    }{
        \longdiv_divide:nn { #1 #3 } { #2 } { #4 }
    }
}

% Adds a decimal point, with a leading 0 if necessary, and records the current position in \l__longdiv_point_digit_int
\cs_new:Nn \longdiv_add_point: {
    \bool_set_true:N \l__longdiv_seen_point_bool
    \bool_if:NTF \l__longdiv_seen_digit_bool {
        \longdiv_linkedlist_add:n { . }
    }{
        \longdiv_linkedlist_add:n { 0. } % Add a leading zero

    }
    \int_set_eq:NN \l__longdiv_point_digit_int \l__longdiv_position_int % Record the position of the point
}

% Divide when we still have more digits.
% #1 -- thing to divide
% #2 -- divisor
% Finds the quotient, adds it to the linked list and to the work token list then recurses.
\cs_new:Nn \longdiv_divide:nn {
    \int_compare:nNnTF \l__longdiv_position_int = \l__longdiv_digits_requested_int {
        \longdiv_divide_end_early:nnn { #1 } { #2 }
    }{
        \int_set:Nn \l__longdiv_quotient_int { \int_div_truncate:nn { #1 } { #2 } }
        \bool_if:nTF {
            \int_compare_p:nNn \l__longdiv_quotient_int = \c_zero % If the quotient was zero, we might not have to print it
            && !\l__longdiv_seen_digit_bool % If no other digits have been printed
            && !\l__longdiv_seen_point_bool % And we are before the decimal point
        }{
            \int_incr:N \l__longdiv_digits_requested_int % Get an extra digit, this one doesn't count.
        }{ % Otherwise print it and record that we've seen a digit (all further 0's must be printed)
            \bool_set_true:N \l__longdiv_seen_digit_bool
            \longdiv_linkedlist_add:f { \int_use:N \l__longdiv_quotient_int }
        }
        \int_incr:N \l__longdiv_position_int
        \longdiv_divide_record:nn{ #1 }{ #2 }
        \longdiv_get_new_digit:xnn { \longdiv_remainder:nn { #1 } { #2 } } { #2 }
    }
}

\cs_generate_variant:Nn \tl_reverse:n {f}

% Called if we stop early due to \l__longdiv_digits_requested_int.
% #1 -- thing to divide
% #2 -- divisor
% #3 -- rest of digits of dividend
% If we stop early, we have to pad the quotient with the extra length of the dividend
% because the top bar of the division symbol uses the length of the quotient to determine
% the length of the bar, but we need it to always be at least as long as the dividend.
% Also, we need to delete the extra digit that has been carried down
\cs_new:Nn \longdiv_divide_end_early:nnn {
    % For some reason we need to shift the typeset work over by half a digit if we quit early due to "stage" option
    % so we need to set a flag so that the work typesetter can know to do this.
    \bool_set_true:N \l__longdiv_stopped_early_stage_bool
   % \int_set:Nn \l_tmpa_int { \use:c { longdiv_linkedlist ~ \int_eval:n { \l__longdiv_linkedlist_length_int - 1 } } }
    \longdiv_linkedlist_add:n { \phantom { #3 0 } }
    \exp_args:Nx \longdiv_typeset:nnn { \longdiv_delete_last:n { #1 } } { #2 }
}

% Deletes the last digit of number.
\cs_new:Nn \longdiv_delete_last:n {  \tl_reverse:f { \tl_tail:f { \tl_reverse:f { #1 } } } }

% Divide when we are out of digits.
% #1 -- remainder from last time (we will add a zero to the end)
% #2 -- divisor
% This case is more complicated because we have to check for repeated remainders, and whether to stop
% though we are certainly after the decimal point so we don't need to check whether we need to print 0's.
\cs_new:Nn \longdiv_divide_no_more_digits:nn {
    % If we've seen this remainder before, we're done. Use the appropriate command
    % to insert the overline, and then typeset everything
    \cs_if_exist_use:cTF { longdiv_remainders ~ \int_eval:n { #1 } }{ % \int_eval:n to remove leading zero
        \longdiv_typeset:nnn { #1 } { #2 }
    }{
        \bool_if:nTF {
              \int_compare_p:nNn \l__longdiv_extra_digits_int = \l__longdiv_max_extra_digits_int
            ||\int_compare_p:nNn \l__longdiv_position_int = \c__longdiv_max_total_digits_int
            ||\int_compare_p:nNn \l__longdiv_position_int = \l__longdiv_digits_requested_int
        }{
            \int_compare:nNnT \l__longdiv_position_int = \c__longdiv_max_total_digits_int {
                \msg_warning:nn { longdivision } { division_stopped_early }
            }
            \longdiv_typeset:nnn { #1 } { #2 }
        }{
            % Otherwise, record that we've seen this remainder and the position we're in
            % In case this is the first digit of the repeated part
            \cs_set:cpx { longdiv_remainders ~ \int_eval:n { #1 } }{ % \int_eval:n to remove leading zero
                \int_set:Nn \l__longdiv_repeat_digit_int { \int_use:N \l__longdiv_linkedlist_length_int }
                \exp_not:N \longdiv_linkedlist_indicate_repeating_decimal:n { \int_use:N \l__longdiv_linkedlist_length_int }
            }
            % Now we have to use #1 0 everywhere
            \int_set:Nn \l__longdiv_quotient_int { \int_div_truncate:nn { #1 0 } { #2 } }
            \longdiv_linkedlist_add:f { \int_use:N \l__longdiv_quotient_int }
            \bool_set_true:N \l__longdiv_seen_digit_bool % We've seen a digit after the decimal point, don't need to remove it
            \int_incr:N \l__longdiv_position_int
            \int_incr:N \l__longdiv_extra_digits_int
            \longdiv_divide_record:nn { #1 0 } { #2 }
            \longdiv_divide_no_more_digits:xn { \longdiv_remainder:nn { #1 0 } { #2 } } { #2 }
        }
    }
}
\cs_generate_variant:Nn \longdiv_divide_no_more_digits:nn { xn }

% Whenever we see the remainder 0, we're done, and we don't have to put an overline.
\cs_new:cpn { longdiv_remainders ~ 0 }{}

% This command checks if the quotient was zero, and if so preserves the leading zero by avoiding \int_eval:n
% This is so that e.g, \longdiv{14.1}{7} doesn't screw up
\cs_new:Nn \longdiv_remainder:nn {
    \int_compare:nNnTF \l__longdiv_quotient_int = \c_zero
        { #1 }
        { \int_eval:n { #1 - \l__longdiv_quotient_int * #2 } }
}


% We're going to store the "work" for the long division in this tl as a series of triples:
% #1 -- number of digits we've processed so far (for positioning subtractions and determining if point should be added)
% #2 -- old remainder (thing to subtract from)
% #3 -- quotient * divisor (thing to subtract)
\tl_new:N \l__longdiv_work_tl
\cs_new:Nn \longdiv_divide_record:nn {
    \int_compare:nNnTF \l__longdiv_display_divisions_int < \c__longdiv_max_display_divisions_int {
        \int_compare:nNnF \l__longdiv_quotient_int = \c_zero { % If the quotient was zero, nothing needs to be typeset
            \tl_set:Nx \l__longdiv_work_tl {
                \l__longdiv_work_tl
                    { \int_use:N \l__longdiv_position_int } { #1 } { \int_eval:n { \l__longdiv_quotient_int * #2 } }
            }
            \int_incr:N \l__longdiv_display_divisions_int
        }
    }{
        \int_compare:nNnT \l__longdiv_display_divisions_int = \c__longdiv_max_display_divisions_int {
            \int_compare:nNnF \l__longdiv_quotient_int = \c_zero {
                \tl_set:Nx \l__longdiv_work_tl {
                    \l__longdiv_work_tl
                        { \int_use:N \l__longdiv_position_int } { #1 } { \int_eval:n { \l__longdiv_quotient_int * #2 } }
                        \exp_not:N \longdiv_typeset_work_last:nn { \int_use:N \l__longdiv_position_int } { \int_eval:n { #1 - \l__longdiv_quotient_int * #2 } }
                }
                \int_incr:N \l__longdiv_display_divisions_int
                \msg_warning:nn { longdivision } { work_stopped_early }
            }
        }
    }
}

%%
%% Typesetting
%%


%% Indicate repeating decimals
% These are all different implementations of \longdiv_linkedlist_indicate_repeating_decimal:n
% They take one input which is the index of the start of the repeating decimal in the linked list

% Chosen using "repeating decimal style", default is "dots all"
% possible values: "overline", "dots", "dots all", "parentheses"

% Put an \overline over the repeated digits. \overline only works in math mode, so we have to use \ensuremath. Then we put an \hbox
% to take ourselves
\cs_new:Nn \longdiv_linkedlist_indicate_repeating_decimal_overline:n {
    \cs_set:cpx { longdiv_linkedlist ~ #1 }{
        \ensuremath{ \overline { \bool_if:NF \l__longdiv_mathmode_bool \hbox {  \exp_not:f { \use:c { longdiv_linkedlist ~ #1 } } } } }
    }
}

\cs_new:cn { longdiv_linkedlist_indicate_repeating_decimal_dots~all:n } {
    \cs_set:cpx { longdiv_linkedlist ~ #1 }{
        \exp_not:n {
            \cs_set:Npn \longdiv_linkedlist_element:n ##1 { \dot ##1 }
        }
        \ensuremath { \noexpand \dot \exp_not:f { \use:c { longdiv_linkedlist ~ #1 } } }
    }
}

\cs_new:Nn \longdiv_linkedlist_indicate_repeating_decimal_dots:n {
    \cs_set:cpx { longdiv_linkedlist ~ \int_eval:n { \l__longdiv_linkedlist_length_int - 1 } }{
        \noexpand\dot \use:c { longdiv_linkedlist ~ \int_eval:n { \l__longdiv_linkedlist_length_int - 1 } }
    }
    \cs_set:cpx { longdiv_linkedlist ~ #1 }{
        \ensuremath { \noexpand \dot \exp_not:f { \use:c { longdiv_linkedlist ~ #1 } } }
    }
}

\bool_new:N \l__longdiv_repeating_decimal_parentheses_bool
\cs_new:Nn \longdiv_linkedlist_indicate_repeating_decimal_parentheses:n {
    \cs_set:cpx { longdiv_linkedlist ~ #1 }{
        ( \exp_not:f { \use:c { longdiv_linkedlist ~ #1 } } )
    }
    % Don't insert extra space for parenthesis in german typesetting because the quotient isn't directly above dividend and work.
    \cs_if_eq:NNF \longdiv_typeset_main: \longdiv_typeset_main_german:{
        \bool_set_true:N \l__longdiv_repeating_decimal_parentheses_bool
        \cs_set:Nn \longdiv_typeset_extra_zeroes: {
            \bool_if:NT \l__longdiv_added_point_bool { . }
            \prg_replicate:nn { #1 - \l__longdiv_linkedlist_length_int + \l__longdiv_extra_digits_int } { 0 } \hphantom (
            \prg_replicate:nn { \l__longdiv_position_int - #1 } { 0 } \hphantom{ ) }
        }
    }
}

% Do nothing, don't indicate repeating digits at all.
\cs_new:Nn \longdiv_linkedlist_indicate_repeating_decimal_none:n {

}

\cs_new_eq:NN \longdiv_linkedlist_indicate_repeating_decimal:n \longdiv_linkedlist_indicate_repeating_decimal_overline:n


% \l__longdiv_linkedlist_tl -- quotient
% #1 -- remainder
% #2 -- divisor
% #3 -- dividend
\cs_new:Nn \longdiv_typeset:nnn {
    \mode_if_math:TF { \bool_set_true:N \l__longdiv_mathmode_bool } { \bool_set_false:N \l__longdiv_mathmode_bool }
    \cs_set:Npn \longdiv_typeset_dividend: {
        \longdiv_typeset_number:n {
            #3
            \bool_if:NT \l__longdiv_seen_digit_bool { % we don't want to add a trailing decimal point to the dividend if it divided evenly
                \longdiv_typeset_extra_zeroes:
            }
        }
    }
    \cs_set:Npn \longdiv_typeset_work: { \longdiv_typeset_work:n { #1 } }
    \cs_set:Npn \longdiv_typeset_divisor: { \longdiv_typeset_number:n { #2 } }
    \cs_set:Npn \longdiv_typeset_remainder: { \longdiv_typeset_number:n { #1 } } % This isn't used in current typesetting code, just could be nice to have
    \bool_set:Nn \l_longdiv_repeating_decimal_bool { \int_compare_p:nNn \l__longdiv_repeat_digit_int > 0 } % This isn't used in current typesetting code, just could be nice to have
    \let\longdivdividend\longdiv_typeset_dividend:
    \let\longdivdivisor\longdiv_typeset_divisor:
    \let\longdivquotient\longdiv_typeset_quotient:
    \let\longdivwork\longdiv_typeset_work:
    \bool_if:NF \l__longdiv_seen_digit_bool { \longdiv_linkedlist_remove_tail: } % If we haven't seen any new digits since adding a terminal decimal point, delete it.
    \longdiv_typeset_main:
}


\cs_new:Nn \longdiv_typeset_extra_zeroes: {
    \bool_if:NT \l__longdiv_added_point_bool { . }
    \prg_replicate:nn { \l__longdiv_extra_digits_int } { 0 }
}

\cs_new:Nn \longdiv_typeset_main_default: {
    \bool_if:NTF \l__longdiv_is_tikz_loaded_bool {
        \longdiv_typeset_main_tikz:
    } {
        \longdiv_typeset_main_standard:
    }
}
\cs_new_eq:NN \longdiv_typeset_main: \longdiv_typeset_main_default:


\longdiv_define_style:nn { standard } {
    \hskip4pt
    \rule{0pt}{22pt} \longdiv_typeset_divisor: \, \begin{tabular}[b]{@{}r@{}}
        \longdiv_typeset_quotient:\,
        \\\hline

    \smash{\big)}\begin{tabular}[t]{@{}l@{}}
    \longdiv_typeset_dividend: \\
    \longdiv_typeset_work:\\[3pt]
    \end{tabular}\,
    \end{tabular}
    \hskip5.3pt
}

\bool_new:N \l__longdiv_is_tikz_loaded_bool
\AtBeginDocument{ \@ifpackageloaded { tikz }{ \bool_gset_true:N \l__longdiv_is_tikz_loaded_bool } { } }

\longdiv_define_style:nn { german } {
    \begin{tabular}[t]{@{}l@{}}
    \longdiv_typeset_dividend: \hskip1pt : \hskip1pt \longdiv_typeset_divisor: \hskip4pt = \hskip4pt \longdiv_typeset_quotient: \\
    \longdiv_typeset_work:
    \end{tabular}
}


\newlength{\longdiv@dividendlength}
\newlength{\longdiv@dividendheight}
\newlength{\longdiv@divisorheight}
\newlength{\longdiv@maxheight}

\let\longdiv@ifl@aded\@ifl@aded
\let\longdiv@pkgextension\@pkgextension
\def\longdiv@ifpackageloaded{\@ifl@aded\@pkgextension}

\longdiv_define_style:nn { tikz }{
    \let\@ifl@aded\longdiv@ifl@aded
    \let\@pkgextension \longdiv@pkgextension
    \bool_if:NTF \l__longdiv_is_tikz_loaded_bool {
        \longdiv@typeset@tikz@rest
    } {
        \msg_warning:nn { longdivision } { no_tikz }
        \longdiv_typeset_main_standard:
    }
}


\def\longdiv@typeset@tikz@rest{
    \let\longdiv@typeset@dividend\longdiv_typeset_dividend:
    \let\longdiv@typeset@divisor\longdiv_typeset_divisor:
    \let\longdiv@typeset@quotient\longdiv_typeset_quotient:
    \let\longdiv@typeset@work\longdiv_typeset_work:
    \settowidth{\longdiv@dividendlength}{1.\longdiv_typeset_dividend:}
    \settoheight{\longdiv@dividendheight}{\longdiv_typeset_dividend:}
    \settoheight{\longdiv@maxheight}{\longdiv_typeset_dividend:\longdiv_typeset_divisor:}
    \settoheight{\longdiv@divisorheight}{\longdiv_typeset_divisor:}
    \l__longdiv_rulethickness_dim = 0.2mm
    \longdiv@typeset@main@tikz@helper
}

\ExplSyntaxOff
\def\longdiv@typeset@main@tikz@helper{
    \begin{tikzpicture} [baseline=.5pt]
        \draw (1pt,.5*\longdiv@divisorheight)  node [left] {\longdiv@typeset@divisor};
        \draw (\longdiv@dividendlength,.5*\longdiv@dividendheight) node [left]  {\longdiv@typeset@dividend};
        \draw [line width=0.2mm]  (0pt,-.22*\longdiv@dividendheight) arc (-70:60:\longdiv@maxheight*.41 and \longdiv@maxheight*.88) -- ++(\longdiv@dividendlength-2pt,0pt);
        \draw (\longdiv@dividendlength,\longdiv@divisorheight+\longdiv@maxheight*.3) node[above left] {
            \longdiv@typeset@quotient
        };
        \draw (0,0) node[below right] {
            \begin{tabular}[t]{@{}l@{}}
            \longdiv@typeset@work
            \end{tabular}
        };
    \end{tikzpicture}
}
\ExplSyntaxOn


\cs_new:Nn \longdiv_typeset_quotient: {
    \int_compare:nNnTF \l__longdiv_linkedlist_length_int = \c_zero
        {
            \bool_if:NTF \l__longdiv_stopped_early_stage_bool
                { }
                { \longdiv_typeset_number:n { 0 } }
        }
        { \longdiv_typeset_number:n { \l__longdiv_linkedlist_tl } }
}


\cs_new:Nn \longdiv_typeset_number:n {
    \bool_if:NTF \l__longdiv_mathmode_bool { \ensuremath{#1} } { #1 }
}


% Iterate through the division "work" and typeset it
\cs_new:Nn \longdiv_typeset_work:n {
    \tl_if_empty:NTF \l__longdiv_work_tl {
        \msg_warning:nn { longdivision } { no_division_occurred }
    }{
        \exp_after:wN \longdiv_typeset_work_first:nnn \l__longdiv_work_tl
        \int_compare:nNnT \l__longdiv_display_divisions_int < \c__longdiv_max_display_divisions_int {
            \exp_args:No \longdiv_typeset_work_last:nn { \int_use:N \l__longdiv_position_int } { #1 }
        }
    }
}

% #1 -- digits in to the right side of the numbers we are writing
% #2 -- remainder from last time with new digits added to the right
% #3 -- quotient * divisor
% _first only typesets quotient * divisor and the line
% _rest typesets result from last time, quotient * divisor and the line
% _last only typesets the remainder from last time
\cs_new:Nn \longdiv_typeset_work_first:nnn {
    \longdiv_typeset_setwidth:n { #1 }
    \hspace{\g__longdiv_temp_dim}
    \llap { \longdiv_insert_point_ifneeded:nn { #1 } { #3 } }
    \\\longdiv_rule:nn{#1}{#3}
    \peek_meaning:NT \bgroup {
        \longdiv_typeset_work_rest:nnn
    }
}

\cs_new:Nn \longdiv_typeset_work_rest:nnn {
    \longdiv_typeset_setwidth:n { #1 }
    \hspace{\g__longdiv_temp_dim}
    \llap { \longdiv_insert_point_ifneeded:nn { #1 } { #2 } }
    \\
    \hspace{\g__longdiv_temp_dim}
    \llap { \longdiv_insert_point_ifneeded:nn { #1 } { #3 } }
    \\\longdiv_rule:nn{#1}{#3}
    \peek_meaning:NT \bgroup {
        \longdiv_typeset_work_rest:nnn
    }
}

% #1 -- digits in to the right side of the numbers we are writing
% #2 -- remainder from last time with new digits added to the right
\cs_new:Nn \longdiv_typeset_work_last:nn {
    \longdiv_typeset_setwidth:n { #1 }
    \hspace{\g__longdiv_temp_dim}
    \llap { \longdiv_insert_point_ifneeded:nn { #1 } { #2 } }
}

% #1 -- the start position of the substring
% #2 -- the substring
% #3 -- the position we are checking for
\prg_new_conditional:Nnn \longdiv_if_contains_position:nnn { TF,T,F } {
    \bool_if:nTF {
           \int_compare_p:nNn { #1  }                      > #3
        && \int_compare_p:nNn { #1  - \tl_count:n { #2 } } < #3
    }{
        \prg_return_true:
    }{
        \prg_return_false:
    }
}

% Set \g__longdiv_temp_dim equal to digitwidth * number of digits
% If we are past the decimal point, add  \c__longdiv_pointwidth_dim
\cs_new:Nn \longdiv_typeset_setwidth:n {
    \dim_gset:Nn \g__longdiv_temp_dim { #1\c__longdiv_digitwidth_dim }
    % For some reason we need to shift everything over by half a digit if we quit early due to "stage" option
    \bool_if:NT \l__longdiv_stopped_early_stage_bool { \dim_gadd:Nn \g__longdiv_temp_dim { -0.5\c__longdiv_digitwidth_dim } }
    \int_compare:nNnT \l__longdiv_point_digit_int < { #1 } {
        \dim_gadd:Nn \g__longdiv_temp_dim \c__longdiv_pointwidth_dim
    }
    \bool_if:NT \l__longdiv_repeating_decimal_parentheses_bool {
        \int_compare:nNnT \l__longdiv_repeat_digit_int < { #1  } {
            \dim_gadd:Nn \g__longdiv_temp_dim \c__longdiv_parenwidth_dim
        }
    }
}

% If the number ends after the decimal point ( #1 > \l__longdiv_point_digit_int )
% and start before it ( #1 - length(#2) < \l__longdiv_point_digit_int) insert a
% decimal point in the appropriate position of #2. Otherwise just return #2
\cs_new:Nn \longdiv_insert_point_ifneeded:nn {
    \tl_set:Nn \l_tmpa_tl { #2 }
    \bool_if:NT \l__longdiv_repeating_decimal_parentheses_bool {
        \longdiv_if_contains_position:nnnT { #1 } { #2 } { \l__longdiv_repeat_digit_int } {
            \tl_set:Nx \l_tmpa_tl {
                \exp_not:N \longdiv_insert:nff { \hskip \c__longdiv_parenwidth_dim } %)
                                               { \int_eval:n{\l__longdiv_repeat_digit_int - #1 + \tl_count:n { #2 }} }
                                               { \tl_use:N \l_tmpa_tl }
            }
        }
    }
    \longdiv_if_contains_position:nnnT { #1 } { #2 } { \l__longdiv_point_digit_int } {
        \tl_set:Nx \l_tmpa_tl { \longdiv_insert:nff . {\int_eval:n{\l__longdiv_point_digit_int - #1 + \tl_count:n { #2 }}} { \tl_use:N \l_tmpa_tl } }
    }
    \longdiv_typeset_number:n { \tl_use:N \l_tmpa_tl }
}

% Walk #2 digits across #3 and then insert #1
\cs_new:Nn \longdiv_insert:nnn {
    \longdiv_insert_aux:onN { #2 } { #1 } #3
}
\cs_generate_variant:Nn \longdiv_insert:nnn { nff }

\cs_new:Nn \longdiv_insert_aux:nnN {
    \int_compare:nNnTF { #1 } = \c_zero {
        #2#3
    }{
        #3 \longdiv_insert_aux:onN { \int_eval:n { #1 - 1 } } { #2 }
    }
}
\cs_generate_variant:Nn \longdiv_insert_aux:nnN {onN}


% Okay, this is another section where we are adulterated with plaintex stuff.
% It would be easy to reimplement \settowidth, but \hrule and \noalign have no
% expl3 name anyways. Since I only use these dim variables with \settowidth, I declare
% them with \newdimen rather than \dim_new:N
\newdimen   \c__longdiv_digitwidth_dim
\settowidth \c__longdiv_digitwidth_dim { 0 }
\newdimen   \c__longdiv_pointwidth_dim
\settowidth \c__longdiv_pointwidth_dim { . }
\newdimen   \c__longdiv_parenwidth_dim
\settowidth \c__longdiv_parenwidth_dim { ( }
\newdimen   \l__longdiv_tempwidth_dim
\newdimen \l__longdiv_rulethickness_dim
\l__longdiv_rulethickness_dim = 0.2mm

\cs_new:Nn \longdiv_rule:nn {
    \noalign {
        \settowidth \l__longdiv_tempwidth_dim { #2 }
        % Check whether the decimal point occurred in the middle of the current number
        % because if so, it's longer by pointwidth.
        \longdiv_if_contains_position:nnnT { #1 } { #2 } { \l__longdiv_point_digit_int } {
            \dim_add:Nn \l__longdiv_tempwidth_dim \c__longdiv_pointwidth_dim
        }
        % If we use parens to denote the repeating part of the quotient, they take up space too. Test if a paren occurs.
        \bool_if:NT \l__longdiv_repeating_decimal_parentheses_bool {
            \longdiv_if_contains_position:nnnT { #1 } { #2 } { \l__longdiv_point_digit_int } {
                \dim_add:Nn \l__longdiv_tempwidth_dim \c__longdiv_parenwidth_dim
            }
        }
        \box_move_right:nn { \g__longdiv_temp_dim - \l__longdiv_tempwidth_dim } {
            \vbox:n { \hrule width \l__longdiv_tempwidth_dim height \l__longdiv_rulethickness_dim }
        }
    }
}

\ExplSyntaxOff