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authorKarl Berry <karl@freefriends.org>2019-03-05 22:35:14 +0000
committerKarl Berry <karl@freefriends.org>2019-03-05 22:35:14 +0000
commit68872ff6a2a91fa0e84763fc9316493d82075c95 (patch)
tree0546ec4c414553802e31a423aec44f74d252f645 /Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx
parent541c4ddf7c5b402b9cfe8af5ef4e49ffa15d3e83 (diff)
l3 (5mar19)
git-svn-id: svn://tug.org/texlive/trunk@50246 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx')
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx123
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}