%% 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