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author | Karl Berry <karl@freefriends.org> | 2017-02-06 23:37:59 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2017-02-06 23:37:59 +0000 |
commit | eb1b06cb07745cb30557b035fa78e1bd90c5df9a (patch) | |
tree | f0a02b3460ecca0eefc41756ef5a5b6eeb294fee /Master/texmf-dist/tex/latex/longdivision/longdivision.sty | |
parent | 3b82837a4c3eea1141abcab4c26823c64a671fe1 (diff) |
longdivision (6feb17)
git-svn-id: svn://tug.org/texlive/trunk@43159 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/latex/longdivision/longdivision.sty')
-rw-r--r-- | Master/texmf-dist/tex/latex/longdivision/longdivision.sty | 485 |
1 files changed, 485 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/latex/longdivision/longdivision.sty b/Master/texmf-dist/tex/latex/longdivision/longdivision.sty new file mode 100644 index 00000000000..e25d7671b8b --- /dev/null +++ b/Master/texmf-dist/tex/latex/longdivision/longdivision.sty @@ -0,0 +1,485 @@ +%% 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 + +%% +%% 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{#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_generate_variant:Nn \longdiv_linkedlist_add:n {f} + +% The easy implementation of these next two 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: +} + +% #1 -- pointer to an element of the list +% Puts an overline over the rest of the list starting at a certain position. For "repeating decimals". +\cs_new:Nn \longdiv_linkedlist_put_overline:n { + \cs_set:cpx { longdiv_linkedlist ~ #1 }{ + $\overline { \exp_not:f { \use:c { longdiv_linkedlist ~ #1 } } }$ + } +} + + +%% +%% Entry points +%% + +% \tl_rescan to ignore spaces in input. +\NewDocumentCommand \longdivision { omm } { + \group_begin: + \IfNoValueF { #1 } { + \int_set:Nn \l__longdiv_max_extra_digits_int { #1 } + } + \tl_rescan:nn { \ExplSyntaxOn } { \longdiv_start:nn { #2 } { #3 } } + \group_end: +} + +% Same as \longdiv[0]{#1}{#2}. +\NewDocumentCommand \intlongdivision { mm } { + \group_begin: + \int_set:Nn \l__longdiv_max_extra_digits_int { 0 } + \tl_rescan:nn { \ExplSyntaxOn } { \longdiv_start:nn { #1 } { #2 } } + \group_end: +} + +% Check input is valid then enter main loop. +% We use etex \numexpr 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 } { \the\numexpr 0#1 } { \the\numexpr 0#1 } + \longdiv_break_point: { #1 } { #2 } +} + +\cs_set_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. } + + + +%% +%% Division +%% + +% Core registers +\bool_new:N \l__longdiv_seen_point_bool +\bool_new:N \l__longdiv_seen_digit_bool +\int_new:N \l__longdiv_quotient_int +\int_new:N \l__longdiv_position_int +\int_new:N \l__longdiv_point_digit_int + +\tl_new:N \l__longdiv_extra_places_tl % This is for storing extra zeroes appended to the dividend +\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_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 + +% #1 -- remainder +% #2 -- divisor +% #3 -- rest of divits +\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: % + \tl_set:Nn \l__longdiv_extra_places_tl { . } + \bool_set_false:N \l__longdiv_seen_digit_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 + \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 { + %\tl_show:n{#1} + \int_set:Nn \l__longdiv_quotient_int { \int_div_truncate:nn { #1 } { #2 } } + \bool_if:nF { + \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 + }{ % 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 } +} + + +% 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: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 + \exp_not:N \longdiv_linkedlist_put_overline:n { \int_use:N \l__longdiv_linkedlist_length_int } + } + % Now we have to use #10 everywhere + \int_set:Nn \l__longdiv_quotient_int { \int_div_truncate:nn { #10 } { #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 + \tl_set:Nx \l__longdiv_extra_places_tl { \l__longdiv_extra_places_tl 0 } % Store an extra 0 appended to the dividend + \longdiv_divide_record:nn{#10}{#2} + \longdiv_divide_no_more_digits:xn { \longdiv_remainder:nn { #10 } { #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_set: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 +%% + + +% \l__longdiv_linkedlist_tl -- quotient +% #1 -- remainder +% #2 -- divisor +% #3 -- dividend +\cs_new:Nn \longdiv_typeset:nnn { + % If we haven't seen any new digits since adding a terminal decimal point, delete it. + \bool_if:NF \l__longdiv_seen_digit_bool { \longdiv_linkedlist_remove_tail: } + + #2\,\begin{tabular}[b]{@{}r@{}} + \int_compare:nNnTF \l__longdiv_linkedlist_length_int = \c_zero + { 0 } + { \l__longdiv_linkedlist_tl } + \\\hline + \big)\begin{tabular}[t]{@{}l@{}} + % Likewise we don't want to add a trailing decimal point to the dividend if it divided evenly + #3 \bool_if:NT \l__longdiv_seen_digit_bool { \l__longdiv_extra_places_tl } \\ + \longdiv_typeset_work:n { #1 } + \end{tabular} + \end{tabular} +} + +% 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:Npn \longdiv_typeset_work_last:nn #1 #2 { + \longdiv_typeset_setwidth:n { #1 } + \hspace{\g__longdiv_temp_dim} + \llap { \longdiv_insert_point_ifneeded:nn { #1 } { #2 } } +} + +% 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 } + \int_compare:nNnT \l__longdiv_point_digit_int < {#1} { + \dim_gadd:Nn \g__longdiv_temp_dim \c__longdiv_pointwidth_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 { + \bool_if:nTF { + \int_compare_p:nNn { #1 } > \l__longdiv_point_digit_int + && \int_compare_p:nNn { #1 - \tl_count:n { #2 } } < \l__longdiv_point_digit_int + }{ + \longdiv_insert_point:nn {\int_eval:n{\l__longdiv_point_digit_int - #1 + \tl_count:n { #2 }}} { #2 } + }{ + #2 + } +} + +% Walk #1 digits across #2 and then insert a decimal point. +\cs_new:Nn \longdiv_insert_point:nn { + \longdiv_insert_point_aux:oN { #1 } #2 +} + +\cs_new:Nn \longdiv_insert_point_aux:nN { + \int_compare:nNnTF { #1 } = \c_zero { + .#2 + }{ + #2 \longdiv_insert_point_aux:oN { \int_eval:n { #1 - 1 } } + } +} +\cs_generate_variant:Nn \longdiv_insert_point_aux:nN {oN} + + +% 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 \l__longdiv_tempwidth_dim + +\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. + \bool_if:nT { + \int_compare_p:nNn { #1 } > \l__longdiv_point_digit_int + && \int_compare_p:nNn { #1 - \tl_count:n { #2 } } < \l__longdiv_point_digit_int + }{ + \dim_add:Nn \l__longdiv_tempwidth_dim \c__longdiv_pointwidth_dim + } + \box_move_right:nn { \g__longdiv_temp_dim - \l__longdiv_tempwidth_dim } { + \vbox:n { \hrule width \l__longdiv_tempwidth_dim } + } + } +} + +\ExplSyntaxOff |