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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/longdivision/longdivision.sty |
Initial commit
Diffstat (limited to 'macros/latex/contrib/longdivision/longdivision.sty')
-rw-r--r-- | macros/latex/contrib/longdivision/longdivision.sty | 765 |
1 files changed, 765 insertions, 0 deletions
diff --git a/macros/latex/contrib/longdivision/longdivision.sty b/macros/latex/contrib/longdivision/longdivision.sty new file mode 100644 index 0000000000..98349704fe --- /dev/null +++ b/macros/latex/contrib/longdivision/longdivision.sty @@ -0,0 +1,765 @@ +%% 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 |