diff options
Diffstat (limited to 'Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx')
| -rw-r--r-- | Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx | 123 |
1 files changed, 122 insertions, 1 deletions
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx index 1827c24b804..c4d2decc1df 100644 --- a/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx +++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx @@ -40,7 +40,7 @@ % {latex-team@latex-project.org}^^A % }^^A % } -% \date{Released 2019-02-15} +% \date{Released 2019-03-05} % % \maketitle % @@ -64,6 +64,7 @@ % { % \@@_parse_word_exp:N , % \@@_parse_word_ln:N , +% \@@_parse_word_fact:N, % } % Unary functions. % \begin{macrocode} @@ -71,6 +72,8 @@ { \@@_parse_unary_function:NNN \@@_exp_o:w ? } \cs_new:Npn \@@_parse_word_ln:N { \@@_parse_unary_function:NNN \@@_ln_o:w ? } +\cs_new:Npn \@@_parse_word_fact:N + { \@@_parse_unary_function:NNN \@@_fact_o:w ? } % \end{macrocode} % \end{macro} % @@ -1247,6 +1250,124 @@ % \end{macrocode} % \end{macro} % +% \subsection{Factorial} +% +% \begin{variable}{\c_@@_fact_max_arg_int} +% The maximum integer whose factorial fits in the exponent range is +% $3248$, as $3249!\sim 10^{10000.8}$ +% \begin{macrocode} +\int_const:Nn \c_@@_fact_max_arg_int { 3248 } +% \end{macrocode} +% \end{variable} +% +% \begin{macro}[EXP]{\@@_fact_o:w} +% First detect $\pm 0$ and $+\infty$ and \texttt{nan}. Then note that +% factorial of anything with a negative sign (except $-0$) is +% undefined. Then call \cs{@@_small_int:wTF} to get an integer as the +% argument, and start a loop. This is not the most efficient way of +% computing the factorial, but it works all right. Of course we work +% with $24$ digits instead of~$16$. It is easy to check that +% computing factorials with this precision is enough. +% \begin{macrocode} +\cs_new:Npn \@@_fact_o:w #1 \s_@@ \@@_chk:w #2#3#4; @ + { + \if_case:w #2 \exp_stop_f: + \@@_case_return_o:Nw \c_one_fp + \or: + \or: + \if_meaning:w 0 #3 + \exp_after:wN \@@_case_return_same_o:w + \fi: + \or: + \@@_case_return_same_o:w + \fi: + \if_meaning:w 2 #3 + \@@_case_use:nw { \@@_invalid_operation_o:fw { fact } } + \fi: + \@@_fact_pos_o:w + \s_@@ \@@_chk:w #2 #3 #4 ; + } +% \end{macrocode} +% \end{macro} +% +% \begin{macro}[EXP]{\@@_fact_pos_o:w, \@@_fact_int_o:w} +% Then check the input is an integer, and call +% \cs{@@_facorial_int_o:n} with that \texttt{int} as an argument. If +% it's too big the factorial overflows. Otherwise call +% \cs{@@_sanitize:Nw} with a positive sign marker~|0| and an integer +% expression that will mop up any exponent in the calculation. +% \begin{macrocode} +\cs_new:Npn \@@_fact_pos_o:w #1; + { + \@@_small_int:wTF #1; + { \@@_fact_int_o:n } + { \@@_invalid_operation_o:fw { fact } #1; } + } +\cs_new:Npn \@@_fact_int_o:n #1 + { + \if_int_compare:w #1 > \c_@@_fact_max_arg_int + \@@_case_return:nw + { + \exp_after:wN \exp_after:wN \exp_after:wN \@@_overflow:w + \exp_after:wN \c_inf_fp + } + \fi: + \exp_after:wN \@@_sanitize:Nw + \exp_after:wN 0 + \int_value:w \@@_int_eval:w + \@@_fact_loop_o:w #1 . 4 , { 1 } { } { } { } { } { } ; + } +% \end{macrocode} +% \end{macro} +% +% \begin{macro}[EXP]{\@@_fact_loop_o:w} +% The loop receives an integer |#1| whose factorial we want to +% compute, which we progressively decrement, and the result so far as +% an extended-precision number |#2| in the form +% \meta{exponent}|,|\meta{mantissa}|;|. The loop goes in steps of two +% because we compute |#1*#1-1| as an integer expression (it must fit +% since |#1| is at most $3248$), then multiply with the result so far. +% We don't need to fill in most of the mantissa with zeros because +% \cs{@@_ep_mul:wwwwn} first normalizes the extended precision number +% to avoid loss of precision. When reaching a small enough number +% simply use a table of factorials less than $10^8$. This limit is +% chosen because the normalization step cannot deal with larger +% integers. +% \begin{macrocode} +\cs_new:Npn \@@_fact_loop_o:w #1 . #2 ; + { + \if_int_compare:w #1 < 12 \exp_stop_f: + \@@_fact_small_o:w #1 + \fi: + \exp_after:wN \@@_ep_mul:wwwwn + \exp_after:wN 4 \exp_after:wN , + \exp_after:wN { \int_value:w \@@_int_eval:w #1 * (#1 - 1) } + { } { } { } { } { } ; + #2 ; + { + \exp_after:wN \@@_fact_loop_o:w + \int_value:w \@@_int_eval:w #1 - 2 . + } + } +\cs_new:Npn \@@_fact_small_o:w #1 \fi: #2 ; #3 ; #4 + { + \fi: + \exp_after:wN \@@_ep_mul:wwwwn + \exp_after:wN 4 \exp_after:wN , + \exp_after:wN + { + \int_value:w + \if_case:w #1 \exp_stop_f: + 1 \or: 1 \or: 2 \or: 6 \or: 24 \or: 120 \or: 720 \or: 5040 + \or: 40320 \or: 362880 \or: 3628800 \or: 39916800 + \fi: + } { } { } { } { } { } ; + #3 ; + \@@_ep_to_float_o:wwN 0 + } +% \end{macrocode} +% \end{macro} +% % \begin{macrocode} %</initex|package> % \end{macrocode} |