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authorKarl Berry <karl@freefriends.org>2010-12-19 00:30:41 +0000
committerKarl Berry <karl@freefriends.org>2010-12-19 00:30:41 +0000
commita3486a2d404fca82e9fc0db0a72c7d61efe4824b (patch)
tree967c74ad591a3d41a4bc66c41f9a0d582b65a704 /Master
parent64fe2e9d7165882dc60a0c1fb71883e0b4ec2b15 (diff)
expl3 2103 (18dec10)
git-svn-id: svn://tug.org/texlive/trunk@20793 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master')
-rw-r--r--Master/texmf-dist/doc/latex/expl3/expl3.pdfbin512728 -> 512728 bytes
-rw-r--r--Master/texmf-dist/doc/latex/expl3/l3calc.pdfbin377232 -> 377232 bytes
-rw-r--r--Master/texmf-dist/doc/latex/expl3/source3.pdfbin1525597 -> 1566978 bytes
-rw-r--r--Master/texmf-dist/source/latex/expl3/l3fp.dtx2210
-rw-r--r--Master/texmf-dist/source/latex/expl3/l3tl.dtx4
-rw-r--r--Master/texmf-dist/tex/latex/expl3/l3fp.sty1485
-rw-r--r--Master/texmf-dist/tex/latex/expl3/l3tl.sty4
7 files changed, 3284 insertions, 419 deletions
diff --git a/Master/texmf-dist/doc/latex/expl3/expl3.pdf b/Master/texmf-dist/doc/latex/expl3/expl3.pdf
index 495ba14c90b..4d7031157c1 100644
--- a/Master/texmf-dist/doc/latex/expl3/expl3.pdf
+++ b/Master/texmf-dist/doc/latex/expl3/expl3.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/expl3/l3calc.pdf b/Master/texmf-dist/doc/latex/expl3/l3calc.pdf
index b7f84e689ea..72c3a8a8c21 100644
--- a/Master/texmf-dist/doc/latex/expl3/l3calc.pdf
+++ b/Master/texmf-dist/doc/latex/expl3/l3calc.pdf
Binary files differ
diff --git a/Master/texmf-dist/doc/latex/expl3/source3.pdf b/Master/texmf-dist/doc/latex/expl3/source3.pdf
index 274b62d1bfc..7d0fc94fb96 100644
--- a/Master/texmf-dist/doc/latex/expl3/source3.pdf
+++ b/Master/texmf-dist/doc/latex/expl3/source3.pdf
Binary files differ
diff --git a/Master/texmf-dist/source/latex/expl3/l3fp.dtx b/Master/texmf-dist/source/latex/expl3/l3fp.dtx
index f5b1d427096..8eb2530143c 100644
--- a/Master/texmf-dist/source/latex/expl3/l3fp.dtx
+++ b/Master/texmf-dist/source/latex/expl3/l3fp.dtx
@@ -35,7 +35,7 @@
\RequirePackage{l3names}
%</driver|package>
%\fi
-\GetIdInfo$Id: l3fp.dtx 2092 2010-11-25 20:44:04Z joseph $
+\GetIdInfo$Id: l3fp.dtx 2104 2010-12-18 09:29:34Z joseph $
{L3 Experimental floating-point operations}
%\iffalse
%<*driver>
@@ -65,8 +65,8 @@
% A floating point number is one which is stored as a mantissa and
% a separate exponent. This module implements arithmetic using radix
% \( 10 \) floating point numbers. This means that the mantissa should
-% be a real number in the range \( 1 \le \string| x \string| < 10 \),
-% with the
+% be a real number in the range \( 1 \le \expandafter\mathopen\string|
+% x \expandafter\mathclose\string| < 10 \), with the
% exponent given as an integer between \( -99 \) and \( 99 \). In the
% input, the exponent part is represented starting with an \texttt{e}.
% As this is a low-level module, error-checking is minimal. Numbers
@@ -100,11 +100,19 @@
%
%\subsection{Constants}
%
+%\begin{variable}{ \c_e_fp }
+% The value of the base of natural numbers, \( \mathrm{e} \).
+%\end{variable}
+%
%\begin{variable}{ \c_one_fp }
% A floating point variable with permanent value \( 1 \): used for
% speeding up some comparisons.
%\end{variable}
%
+%\begin{variable}{ \c_pi_fp }
+% The value of \( \pi \).
+%\end{variable}
+%
%\begin{variable}{ \c_undefined_fp }
% A special marker floating point variable representing the result of
% an operation which does not give a defined result (such as division
@@ -131,6 +139,19 @@
%\end{function}
%
%\begin{function}{
+% \fp_const:Nn |
+% \fp_const:cn |
+%}
+% \begin{syntax}
+% \cs{fp_const:Nn} \meta{floating point variable} \Arg{value}
+% \end{syntax}
+% Creates a new constant \meta{floating point variable} or raises an
+% error if the name is already taken. The value of the
+% \meta{floating point variable} will be set globally to the
+% \meta{value}.
+%\end{function}
+%
+%\begin{function}{
% \fp_set_eq:NN |
% \fp_set_eq:cN |
% \fp_set_eq:Nc |
@@ -413,22 +434,25 @@
% input stream by the predicate version.
%\end{function}
%
-%\begin{function}{
-% \fp_compare:nNn / (TF) |
-% \fp_compare:NNN / (TF) |
-%}
+%\begin{function}{ \fp_compare:nNn / (TF) }
% \begin{syntax}
-% \cs{fp_compare:nNnTF} \Arg{value1} \meta{relation} \Arg{value2}
-% ~~\Arg{true code} \Arg{false code}
-% \cs{fp_compare:NNNTF} \Arg{fp1} \meta{relation} \Arg{fp2}
+% \cs{fp_compare:nNnTF}
+% ~~\Arg{floating point1} \meta{relation} \Arg{floating point2}
% ~~\Arg{true code} \Arg{false code}
% \end{syntax}
-% Compares the two \meta{values} or \meta{floating points} based on the
-% \meta{relation} (\texttt{=}, \verb"<" or \verb">"), and leaves
-% either the \meta{true code} or \meta{false code} in the input stream,
-% as appropriate to the truth of the test and the variant of the
-% function chosen. The tests treat undefined floating points as zero,
-% as the comparison is intended for real numbers only.
+% This function compared the two \meta{floating point} values, which
+% may be stored as \texttt{fp} variables, using the \meta{relation}:
+% \begin{center}
+% \begin{tabular}{ll}
+% Equal & "=" \\
+% Greater than & ">" \\
+% Less than & "<" \\
+% \end{tabular}
+% \end{center}
+% Either \meta{true code} or \meta{false code} is then left in the
+% input stream, as appropriate to the truth of the test and the variant
+% of the function chosen. The tests treat undefined floating points as
+% zero as the comparison is intended for real numbers only.
%\end{function}
%
%\subsection{Unary operations}
@@ -567,7 +591,7 @@
% Divides the \meta{floating point} by the \meta{value}, making the
% assignment within the current \TeX\ group level. If the \meta{value}
% is zero, the \meta{floating point} will be set to
-% \cs{c_undefined_fp}.
+% \cs{c_undefined_fp}.The assignment is local.
%\end{function}
%
%\begin{function}{
@@ -580,12 +604,89 @@
% Divides the \meta{floating point} by the \meta{value}, making the
% assignment globally. If the \meta{value} is zero, the
% \meta{floating point} will be set to \cs{c_undefined_fp}.
+% The assignment is global.
+%\end{function}
+%
+%\subsection{Power operations}
+%
+%\begin{function}{
+% \fp_pow:Nn |
+% \fp_pow:cn |
+%}
+% \begin{syntax}
+% \cs{fp_pow:Nn} \meta{floating point} \Arg{value}
+% \end{syntax}
+% Raises the \meta{floating point} to the given \meta{value}, which
+% should be a positive real number or a negative integer.
+% Mathematically invalid operations such as \( 0^{0} \) will give
+% set the \meta{floating point} to to \cs{c_undefined_fp}. The
+% assignment is local.
+%\end{function}
+%
+%\begin{function}{
+% \fp_gpow:Nn |
+% \fp_gpow:cn |
+%}
+% \begin{syntax}
+% \cs{fp_gpow:Nn} \meta{floating point} \Arg{value}
+% \end{syntax}
+% Raises the \meta{floating point} to the given \meta{value}, which
+% should be a positive real number or a negative integer.
+% Mathematically invalid operations such as \( 0^{0} \) will give
+% set the \meta{floating point} to to \cs{c_undefined_fp}. The
+% assignment is global.
+%\end{function}
+%
+%\subsection{Exponential and logarithm functions}
+%
+%\begin{function}{
+% \fp_exp:Nn |
+% \fp_exp:cn |
+%}
+% \begin{syntax}
+% \cs{fp_exp:Nn} \meta{floating point} \Arg{value}
+% \end{syntax}
+% Calculates the exponential of the \meta{value} and assigns this
+% to the \meta{floating point}. The assignment is local.
+%\end{function}
+%
+%\begin{function}{
+% \fp_gexp:Nn |
+% \fp_gexp:cn |
+%}
+% \begin{syntax}
+% \cs{fp_gexp:Nn} \meta{floating point} \Arg{value}
+% \end{syntax}
+% Calculates the exponential of the \meta{value} and assigns this
+% to the \meta{floating point}. The assignment is global.
+%\end{function}
+%
+%\begin{function}{
+% \fp_ln:Nn |
+% \fp_ln:cn |
+%}
+% \begin{syntax}
+% \cs{fp_ln:Nn} \meta{floating point} \Arg{value}
+% \end{syntax}
+% Calculates the natural logarithm of the \meta{value} and assigns
+% this to the \meta{floating point}. The assignment is local.
+%\end{function}
+%
+%\begin{function}{
+% \fp_gln:Nn |
+% \fp_gln:cn |
+%}
+% \begin{syntax}
+% \cs{fp_gln:Nn} \meta{floating point} \Arg{value}
+% \end{syntax}
+% Calculates the natural logarithm of the \meta{value} and assigns
+% this to the \meta{floating point}. The assignment is global.
%\end{function}
%
%\subsection{Trigonometric functions}
%
% The trigonometric functions all work in radians. They accept a maximum
-% input value of \( 1 000 000 000\), as there are issues with range
+% input value of \( 100\,000\,000 \), as there are issues with range
% reduction and very large input values.
%
%\begin{function}{
@@ -662,6 +763,14 @@
%
%\subsection{Notes on the floating point unit}
%
+% As calculation of the elemental transcendental functions is
+% computationally expensive compared to storage of results, after
+% calculating a trigonometric function, exponent, \emph{etc}.~the module
+% stored the result for reuse. Thus the performance of the module for
+% repeated operations, most probably trigonometric functions, should be
+% much higher than if the values were re-calculated every time they
+% were needed.
+%
% Anyone with experience of programming floating point calculations will
% know that this is a complex area. The aim of the unit is to be
% accurate enough for the likely applications in a typesetting context.
@@ -709,20 +818,13 @@
%\begin{macro}{\c_one_thousand_million}
% There is some speed to gain by moving numbers into fixed positions.
% \begin{macrocode}
-\int_new:N \c_forty_four
-\int_set:Nn \c_forty_four { 44 }
-\int_new:N \c_one_hundred
-\int_set:Nn \c_one_hundred { 100 }
-\int_new:N \c_one_thousand
-\int_set:Nn \c_one_thousand { 1000 }
-\int_new:N \c_one_million
-\int_set:Nn \c_one_million { 1 000 000 }
-\int_new:N \c_one_hundred_million
-\int_set:Nn \c_one_hundred_million { 100 000 000 }
-\int_new:N \c_five_hundred_million
-\int_set:Nn \c_five_hundred_million { 500 000 000 }
-\int_new:N \c_one_thousand_million
-\int_set:Nn \c_one_thousand_million { 1 000 000 000 }
+\int_const:Nn \c_forty_four { 44 }
+\int_const:Nn \c_one_hundred { 100 }
+\int_const:Nn \c_one_thousand { 1000 }
+\int_const:Nn \c_one_million { 1 000 000 }
+\int_const:Nn \c_one_hundred_million { 100 000 000 }
+\int_const:Nn \c_five_hundred_million { 500 000 000 }
+\int_const:Nn \c_one_thousand_million { 1 000 000 000 }
% \end{macrocode}
%\end{macro}
%\end{macro}
@@ -738,7 +840,8 @@
%\begin{macro}{\c_fp_pi_extended_int}
%\begin{macro}{\c_fp_two_pi_decimal_int}
%\begin{macro}{\c_fp_two_pi_extended_int}
-% Parts of \( \pi \) for trigonometric range reduction.
+% Parts of \( \pi \) for trigonometric range reduction, implemented
+% as \texttt{int} variables for speed.
% \begin{macrocode}
\int_new:N \c_fp_pi_by_four_decimal_int
\int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 }
@@ -760,18 +863,26 @@
%\end{macro}
%\end{macro}
%
+%\begin{macro}{\c_e_fp}
+% The value \( \mathrm{e} \) as a `machine number'.
+% \begin{macrocode}
+\tl_new:N \c_e_fp
+\tl_set:Nn \c_e_fp { + 2.718281828 e 0 }
+% \end{macrocode}
+%\end{macro}
+%
%\begin{macro}{\c_one_fp}
% The constant value \( 1 \): used for fast comparisons.
% \begin{macrocode}
-\tl_new:N \c_one_fp
+\tl_new:N \c_one_fp
\tl_set:Nn \c_one_fp { + 1.000000000 e 0 }
% \end{macrocode}
%\end{macro}
%
%\begin{macro}{\c_pi_fp}
-% The value \( \pi \), as a `machine number'.
+% The value \( \pi \) as a `machine number'.
% \begin{macrocode}
-\tl_new:N \c_pi_fp
+\tl_new:N \c_pi_fp
\tl_set:Nn \c_pi_fp { + 3.141592654 e 0 }
% \end{macrocode}
%\end{macro}
@@ -779,7 +890,7 @@
%\begin{macro}{\c_undefined_fp}
% A marker for undefined values.
% \begin{macrocode}
-\tl_new:N \c_undefined_fp
+\tl_new:N \c_undefined_fp
\tl_set:Nn \c_undefined_fp { X 0.000000000 e 0 }
% \end{macrocode}
%\end{macro}
@@ -787,13 +898,21 @@
%\begin{macro}{\c_zero_fp}
% The constant zero value.
% \begin{macrocode}
-\tl_new:N \c_zero_fp
+\tl_new:N \c_zero_fp
\tl_set:Nn \c_zero_fp { + 0.000000000 e 0 }
% \end{macrocode}
%\end{macro}
%
%\subsection{Variables}
%
+%\begin{macro}{\l_fp_arg_tl}
+% A token list to store the formalised representation of the input
+% for transcendental functions.
+% \begin{macrocode}
+\tl_new:N \l_fp_arg_tl
+% \end{macrocode}
+%\end{macro}
+%
%\begin{macro}{\l_fp_count_int}
% A counter for things like the number of divisions possible.
% \begin{macrocode}
@@ -809,6 +928,22 @@
% \end{macrocode}
%\end{macro}
%
+%\begin{macro}{\l_fp_exp_integer_int}
+%\begin{macro}{\l_fp_exp_decimal_int}
+%\begin{macro}{\l_fp_exp_extended_int}
+%\begin{macro}{\l_fp_exp_exponent_int}
+% Used for the calculation of exponent values.
+% \begin{macrocode}
+\int_new:N \l_fp_exp_integer_int
+\int_new:N \l_fp_exp_decimal_int
+\int_new:N \l_fp_exp_extended_int
+\int_new:N \l_fp_exp_exponent_int
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
%\begin{macro}{\l_fp_input_a_sign_int}
%\begin{macro}{\l_fp_input_a_integer_int}
%\begin{macro}{\l_fp_input_a_decimal_int}
@@ -948,6 +1083,14 @@
%\end{macro}
%\end{macro}
%
+%\begin{macro}{\l_fp_sign_tl}
+% There are places where the sign needs to be set up `early',
+% so that the registers can be re-used.
+% \begin{macrocode}
+\tl_new:N \l_fp_sign_tl
+% \end{macrocode}
+%\end{macro}
+%
%\begin{macro}{\l_fp_split_sign_int}
% When splitting the input it is fastest to use a fixed name for the
% sign part, and to transfer it after the split is complete.
@@ -971,14 +1114,6 @@
% \end{macrocode}
%\end{macro}
%
-%\begin{macro}{\l_fp_trig_arg_tl}
-% A token list to store the formalised representation of the input
-% for trigonometry.
-% \begin{macrocode}
-\tl_new:N \l_fp_trig_arg_tl
-% \end{macrocode}
-%\end{macro}
-%
%\begin{macro}{\l_fp_trig_octant_int}
% To track which octant the trigonometric input is in.
% \begin{macrocode}
@@ -1008,7 +1143,7 @@
% value (register "a").
% \begin{macrocode}
\cs_new_protected_nopar:Npn \fp_read:N #1 {
- \exp_after:wN \fp_read_aux:w #1 \q_stop
+ \tex_expandafter:D \fp_read_aux:w #1 \q_stop
}
\cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 e #4 \q_stop {
\tex_if:D #1 -
@@ -1049,29 +1184,29 @@
\l_fp_split_sign_int \c_one
\fp_split_sign:
\use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
- \exp_after:wN \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1
+ \tex_expandafter:D \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1
}
\cs_new_protected_nopar:Npn \fp_split_sign: {
\tex_ifnum:D \pdf_strcmp:D
- { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { - }
+ { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { - }
= \c_zero
\tl_set:Nx \l_fp_tmp_tl
{
- \exp_after:wN
+ \tex_expandafter:D
\tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
}
\l_fp_split_sign_int -\l_fp_split_sign_int
- \exp_after:wN \fp_split_sign:
+ \tex_expandafter:D \fp_split_sign:
\tex_else:D
\tex_ifnum:D \pdf_strcmp:D
- { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { + }
+ { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { + }
= \c_zero
\tl_set:Nx \l_fp_tmp_tl
{
- \exp_after:wN
+ \tex_expandafter:D
\tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
}
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_split_sign:
\tex_fi:D
\tex_fi:D
@@ -1092,7 +1227,7 @@
}
\cs_new_protected_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop {
\l_fp_tmp_int 1 #1 \scan_stop:
- \exp_after:wN \fp_split_decimal:w
+ \tex_expandafter:D \fp_split_decimal:w
\int_use:N \l_fp_tmp_int 000000000 \q_stop
}
\cs_new_protected_nopar:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9 {
@@ -1111,7 +1246,7 @@
\tex_ifnum:D
\use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million
\tex_else:D
- \exp_after:wN \fp_overflow_msg:
+ \tex_expandafter:D \fp_overflow_msg:
\tex_fi:D
}
% \end{macrocode}
@@ -1137,9 +1272,9 @@
\etex_numexpr:D #2 + #3 = \c_zero
#1 \c_one
#4 \c_zero
- \exp_after:wN \use_none:nnnn
+ \tex_expandafter:D \use_none:nnnn
\tex_else:D
- \exp_after:wN \fp_standardise_aux:NNNN
+ \tex_expandafter:D \fp_standardise_aux:NNNN
\tex_fi:D
#1#2#3#4
}
@@ -1148,9 +1283,9 @@
{
\tex_ifnum:D #2 = \c_zero
\tex_advance:D #3 \c_one_thousand_million
- \exp_after:wN \fp_standardise_aux:w
+ \tex_expandafter:D \fp_standardise_aux:w
\int_use:N #3 \q_stop
- \exp_after:wN \fp_standardise_aux:
+ \tex_expandafter:D \fp_standardise_aux:
\tex_fi:D
}
\cs_set_protected_nopar:Npn
@@ -1165,9 +1300,9 @@
{
\tex_ifnum:D #2 > \c_nine
\tex_advance:D #2 \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_standardise_aux:w \int_use:N #2
- \exp_after:wN \fp_standardise_aux:
+ \tex_expandafter:D \fp_standardise_aux:
\tex_fi:D
}
\cs_set_protected_nopar:Npn
@@ -1179,7 +1314,7 @@
\tl_set:Nx \l_fp_tmp_tl
{
##9
- \exp_after:wN \use_none:n \int_use:N #3
+ \tex_expandafter:D \use_none:n \int_use:N #3
}
#3 \l_fp_tmp_tl \scan_stop:
\tex_advance:D #4 \c_one
@@ -1194,7 +1329,7 @@
#4 \c_zero
\tex_fi:D
\tex_else:D
- \exp_after:wN \fp_overflow_msg:
+ \tex_expandafter:D \fp_overflow_msg:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_standardise_aux: { }
@@ -1218,18 +1353,18 @@
% \begin{macrocode}
\cs_new_protected_nopar:Npn \fp_level_input_exponents: {
\tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
- \exp_after:wN \fp_level_input_exponents_a:
+ \tex_expandafter:D \fp_level_input_exponents_a:
\tex_else:D
- \exp_after:wN \fp_level_input_exponents_b:
+ \tex_expandafter:D \fp_level_input_exponents_b:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_level_input_exponents_a: {
\tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
\tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_level_input_exponents_a:NNNNNNNNN
\int_use:N \l_fp_input_b_integer_int
- \exp_after:wN \fp_level_input_exponents_a:
+ \tex_expandafter:D \fp_level_input_exponents_a:
\tex_fi:D
}
\cs_new_protected_nopar:Npn
@@ -1240,7 +1375,7 @@
\tl_set:Nx \l_fp_tmp_tl
{
#9
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_b_decimal_int
}
\l_fp_input_b_decimal_int \l_fp_tmp_tl \scan_stop:
@@ -1249,10 +1384,10 @@
\cs_new_protected_nopar:Npn \fp_level_input_exponents_b: {
\tex_ifnum:D \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
\tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_level_input_exponents_b:NNNNNNNNN
\int_use:N \l_fp_input_a_integer_int
- \exp_after:wN \fp_level_input_exponents_b:
+ \tex_expandafter:D \fp_level_input_exponents_b:
\tex_fi:D
}
\cs_new_protected_nopar:Npn
@@ -1263,7 +1398,7 @@
\tl_set:Nx \l_fp_tmp_tl
{
#9
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
}
\l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop:
@@ -1277,7 +1412,7 @@
%\end{macro}
%
%\begin{macro}{\fp_tmp:w}
-% Used for output of results, cutting down on \cs{exp_after:wN}.
+% Used for output of results, cutting down on \cs{tex_expandafter:D}.
% This is just a place holder definition.
% \begin{macrocode}
\cs_new_protected_nopar:Npn \fp_tmp:w #1#2 { }
@@ -1307,6 +1442,26 @@
%\end{macro}
%\end{macro}
%
+%\begin{macro}{\fp_const:Nn}
+%\begin{macro}{\fp_const:cn}
+% A simple wrapper.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_const:Nn #1#2 {
+ \cs_if_free:NTF #1
+ {
+ \fp_new:N #1
+ \fp_gset:Nn #1 {#2}
+ }
+ {
+ \msg_kernel_error:nx { variable-already-defined }
+ { \token_to_str:N #1 }
+ }
+}
+\cs_generate_variant:Nn \fp_const:Nn { c }
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%
%\begin{macro}{\fp_zero:N}
%\begin{macro}{\fp_zero:c}
%\begin{macro}{\fp_gzero:N}
@@ -1364,7 +1519,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -1408,7 +1563,7 @@
\l_fp_tmp_dim \l_fp_tmp_skip
\fp_split:Nn a
{
- \exp_after:wN \fp_set_from_dim_aux:w
+ \tex_expandafter:D \fp_set_from_dim_aux:w
\dim_use:N \l_fp_tmp_dim
}
\fp_standardise:NNNN
@@ -1429,7 +1584,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -1517,7 +1672,7 @@
% work out how big the input is.
% \begin{macrocode}
\cs_new_nopar:Npn \fp_use:N #1 {
- \exp_after:wN \fp_use_aux:w #1 \q_stop
+ \tex_expandafter:D \fp_use_aux:w #1 \q_stop
}
\cs_generate_variant:Nn \fp_use:N { c }
\cs_new_nopar:Npn \fp_use_aux:w #1#2 e #3 \q_stop {
@@ -1525,13 +1680,13 @@
-
\tex_fi:D
\tex_ifnum:D #3 > \c_zero
- \exp_after:wN \fp_use_large:w
+ \tex_expandafter:D \fp_use_large:w
\tex_else:D
\tex_ifnum:D #3 < \c_zero
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_use_small:w
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_use_none:w
\tex_fi:D
\tex_fi:D
@@ -1556,9 +1711,9 @@
% \begin{macrocode}
\cs_new_nopar:Npn \fp_use_large:w #1 . #2 e #3 \q_stop {
\tex_ifnum:D #3 < \c_ten
- \exp_after:wN \fp_use_large_aux_i:w
+ \tex_expandafter:D \fp_use_large_aux_i:w
\tex_else:D
- \exp_after:wN \fp_use_large_aux_ii:w
+ \tex_expandafter:D \fp_use_large_aux_ii:w
\tex_fi:D
#1#2 e #3 \q_stop
}
@@ -1651,7 +1806,7 @@
% simply using floating point variables, particularly in the lead-off.
% \begin{macrocode}
\cs_new_nopar:Npn \fp_to_int:N #1 {
- \exp_after:wN \fp_to_int_aux:w #1 \q_stop
+ \tex_expandafter:D \fp_to_int_aux:w #1 \q_stop
}
\cs_generate_variant:Nn \fp_to_int:N { c }
\cs_new_nopar:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop {
@@ -1659,9 +1814,9 @@
-
\tex_fi:D
\tex_ifnum:D #3 < \c_zero
- \exp_after:wN \fp_to_int_small:w
+ \tex_expandafter:D \fp_to_int_small:w
\tex_else:D
- \exp_after:wN \fp_to_int_large:w
+ \tex_expandafter:D \fp_to_int_large:w
\tex_fi:D
#2 e #3 \q_stop
}
@@ -1685,9 +1840,9 @@
% \begin{macrocode}
\cs_new_nopar:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop {
\tex_ifnum:D #3 < \c_ten
- \exp_after:wN \fp_to_int_large_aux_i:w
+ \tex_expandafter:D \fp_to_int_large_aux_i:w
\tex_else:D
- \exp_after:wN \fp_to_int_large_aux_ii:w
+ \tex_expandafter:D \fp_to_int_large_aux_ii:w
\tex_fi:D
#1#2 e #3 \q_stop
}
@@ -1783,7 +1938,7 @@
% simply using floating point variables, particularly in the lead-off.
% \begin{macrocode}
\cs_new_nopar:Npn \fp_to_tl:N #1 {
- \exp_after:wN \fp_to_tl_aux:w #1 \q_stop
+ \tex_expandafter:D \fp_to_tl_aux:w #1 \q_stop
}
\cs_generate_variant:Nn \fp_to_tl:N { c }
\cs_new_nopar:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop {
@@ -1791,9 +1946,9 @@
-
\tex_fi:D
\tex_ifnum:D #3 < \c_zero
- \exp_after:wN \fp_to_tl_small:w
+ \tex_expandafter:D \fp_to_tl_small:w
\tex_else:D
- \exp_after:wN \fp_to_tl_large:w
+ \tex_expandafter:D \fp_to_tl_large:w
\tex_fi:D
#2 e #3 \q_stop
}
@@ -1806,9 +1961,9 @@
% \begin{macrocode}
\cs_new_nopar:Npn \fp_to_tl_large:w #1 e #2 \q_stop {
\tex_ifnum:D #2 < \c_ten
- \exp_after:wN \fp_to_tl_large_aux_i:w
+ \tex_expandafter:D \fp_to_tl_large_aux_i:w
\tex_else:D
- \exp_after:wN \fp_to_tl_large_aux_ii:w
+ \tex_expandafter:D \fp_to_tl_large_aux_ii:w
\tex_fi:D
#1 e #2 \q_stop
}
@@ -1870,13 +2025,13 @@
% \begin{macrocode}
\cs_new_nopar:Npn \fp_to_tl_small:w #1 e #2 \q_stop {
\tex_ifnum:D #2 = \c_minus_one
- \exp_after:wN \fp_to_tl_small_one:w
+ \tex_expandafter:D \fp_to_tl_small_one:w
\tex_else:D
\tex_ifnum:D #2 = -\c_two
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_to_tl_small_two:w
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_to_tl_small_aux:w
\tex_fi:D
\tex_fi:D
@@ -1888,7 +2043,7 @@
\etex_numexpr:D #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
< \c_one_thousand_million
0.
- \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
+ \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN
\tex_number:D
\etex_numexpr:D
#1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
@@ -1907,7 +2062,7 @@
\etex_numexpr:D #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
< \c_one_thousand_million
0.0
- \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
+ \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN
\tex_number:D
\etex_numexpr:D
#1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
@@ -2073,7 +2228,7 @@
\fp_read:N #2
\int_set:Nn \l_fp_round_target_int { #3 - 1 }
\tex_ifnum:D \l_fp_round_target_int < \c_ten
- \exp_after:wN \fp_round:
+ \tex_expandafter:D \fp_round:
\tex_fi:D
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
\cs_set_protected_nopar:Npx \fp_tmp:w
@@ -2088,7 +2243,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -2125,7 +2280,7 @@
\int_set:Nn \l_fp_round_target_int
{ #3 + \l_fp_input_a_exponent_int }
\tex_ifnum:D \l_fp_round_target_int < \c_ten
- \exp_after:wN \fp_round:
+ \tex_expandafter:D \fp_round:
\tex_fi:D
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
\cs_set_protected_nopar:Npx \fp_tmp:w
@@ -2140,7 +2295,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -2170,7 +2325,7 @@
\l_fp_round_position_int \c_eight
\tl_clear:N \l_fp_round_decimal_tl
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int
}
\cs_new_protected_nopar:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
@@ -2207,7 +2362,7 @@
\tex_fi:D
\tex_advance:D \l_fp_round_position_int \c_minus_one
\tex_ifnum:D \l_fp_round_position_int > \c_minus_one
- \exp_after:wN \fp_round_loop:N
+ \tex_expandafter:D \fp_round_loop:N
\tex_fi:D
}
% \end{macrocode}
@@ -2245,7 +2400,7 @@
+
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -2289,13 +2444,13 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
}
- \exp_after:wN \group_end: \exp_after:wN
- #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+ \tex_expandafter:D \group_end: \tex_expandafter:D
+ #1 \tex_expandafter:D #2 \tex_expandafter:D { \l_fp_tmp_tl }
}
% \end{macrocode}
%\end{macro}
@@ -2351,9 +2506,9 @@
\l_fp_input_a_sign_int * \l_fp_input_b_sign_int
\scan_stop:
> \c_zero
- \exp_after:wN \fp_add_sum:
+ \tex_expandafter:D \fp_add_sum:
\tex_else:D
- \exp_after:wN \fp_add_difference:
+ \tex_expandafter:D \fp_add_difference:
\tex_fi:D
\l_fp_output_exponent_int \l_fp_input_a_exponent_int
\fp_standardise:NNNN
@@ -2373,7 +2528,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
e
@@ -2490,7 +2645,7 @@
%\begin{macro}{\fp_gmul:Nn}
%\begin{macro}{\fp_gmul:cn}
%\begin{macro}[aux]{\fp_mul_aux:NNn}
-%\begin{macro}[aux]{\fp_mul_int:}
+%\begin{macro}[aux]{\fp_mul_internal:}
%\begin{macro}[aux]{\fp_mul_split:NNNN}
%\begin{macro}[aux]{\fp_mul_split:w}
%\begin{macro}[aux]{\fp_mul_end_level:}
@@ -2522,7 +2677,7 @@
\l_fp_input_b_integer_int
\l_fp_input_b_decimal_int
\l_fp_input_b_exponent_int
- \fp_mul_int:
+ \fp_mul_internal:
\l_fp_output_exponent_int
\etex_numexpr:D
\l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
@@ -2554,7 +2709,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
e
@@ -2566,7 +2721,7 @@
% \end{macrocode}
% Done separately so that the internal use is a bit easier.
% \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_mul_int: {
+\cs_new_protected_nopar:Npn \fp_mul_internal: {
\fp_mul_split:NNNN \l_fp_input_a_decimal_int
\l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
\fp_mul_split:NNNN \l_fp_input_b_decimal_int
@@ -2610,7 +2765,7 @@
#3 ##5##6##7 \scan_stop:
#4 ##8##9 \scan_stop:
}
- \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop
+ \tex_expandafter:D \fp_mul_split_aux:w \int_use:N #1 \q_stop
\tex_advance:D #1 -\c_one_thousand_million
}
\cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2 {
@@ -2624,7 +2779,7 @@
% \begin{macrocode}
\cs_new_protected_nopar:Npn \fp_mul_end_level: {
\tex_advance:D \l_fp_mul_output_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int
}
\cs_new_protected_nopar:Npn \fp_mul_end_level:NNNNNNNNN
@@ -2649,7 +2804,7 @@
%\begin{macro}{\fp_gdiv:Nn}
%\begin{macro}{\fp_gdiv:cn}
%\begin{macro}[aux]{\fp_div_aux:NNn}
-%\begin{macro}[aux]{\fp_div_aux:}
+%\begin{macro}{\fp_div_internal:}
%\begin{macro}[aux]{\fp_div_loop:}
%\begin{macro}[aux]{\fp_div_divide:}
%\begin{macro}[aux]{\fp_div_divide_aux:}
@@ -2666,7 +2821,6 @@
}
\cs_generate_variant:Nn \fp_div:Nn { c }
\cs_generate_variant:Nn \fp_gdiv:Nn { c }
-
% \end{macrocode}
% Division proper starts with a couple of tests. If the denominator is
% zero then a error is issued. On the other hand, if the numerator is
@@ -2702,8 +2856,8 @@
#1 \exp_not:N #2 { \c_zero_fp }
}
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
- \fp_div_aux:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_div_internal:
\tex_fi:D
\tex_fi:D
\fp_tmp:w #1#2
@@ -2717,7 +2871,7 @@
% decimal place. Most of the process takes place in the loop function
% below.
% \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_div_aux: {
+\cs_new_protected_nopar:Npn \fp_div_internal: {
\l_fp_output_integer_int \c_zero
\l_fp_output_decimal_int \c_zero
\cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
@@ -2754,7 +2908,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
\scan_stop:
@@ -2774,14 +2928,14 @@
\fp_div_store:
\tex_multiply:D \l_fp_input_a_integer_int \c_ten
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
- \exp_after:wN \fp_div_loop_step:w
+ \tex_expandafter:D \fp_div_loop_step:w
\int_use:N \l_fp_input_a_decimal_int \q_stop
\tex_ifnum:D
\etex_numexpr:D
\l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
> \c_zero
\tex_ifnum:D \l_fp_div_offset_int > \c_zero
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_div_loop:
\tex_fi:D
\tex_fi:D
@@ -2795,16 +2949,16 @@
% \begin{macrocode}
\cs_new_protected_nopar:Npn \fp_div_divide: {
\tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
- \exp_after:wN \fp_div_divide_aux:
+ \tex_expandafter:D \fp_div_divide_aux:
\tex_else:D
\tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
\tex_else:D
\tex_ifnum:D
\l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
- \exp_after:wN \exp_after:wN \exp_after:wN
- \exp_after:wN \fp_div_divide_aux:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_div_divide_aux:
\tex_fi:D
\tex_fi:D
\tex_fi:D
@@ -2960,6 +3114,7 @@
\fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int
\fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int
\fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int
\fp_mul_end_level:
\fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int
\fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int
@@ -2983,6 +3138,73 @@
% \end{macrocode}
%\end{macro}
%
+%\begin{macro}{\fp_mul:NNNNNNNNN}
+% For internal multiplication where the integer does need to be
+% retained. This means of course that this code is quite slow, and so
+% is only used when necessary.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \fp_mul_split:NNNN #2
+ \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
+ \fp_mul_split:NNNN #3
+ \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
+ \fp_mul_split:NNNN #5
+ \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+ \fp_mul_split:NNNN #6
+ \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
+ \l_fp_mul_output_int \c_zero
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_vi_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_i_int
+ \tex_divide:D \l_fp_mul_output_int \c_one_thousand
+ \fp_mul_product:NN #1 \l_fp_mul_b_vi_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_vi_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int #4
+ \fp_mul_end_level:
+ #9 0 \l_fp_mul_output_tl \scan_stop:
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN #1 \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int #4
+ \fp_mul_end_level:
+ #8 0 \l_fp_mul_output_tl \scan_stop:
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN #1 #4
+ \fp_mul_end_level:
+ #7 0 \l_fp_mul_output_tl \scan_stop:
+}
+% \end{macrocode}
+%\end{macro}
+%
%\begin{macro}{\fp_div_integer:NNNNN}
% Here, division is always by an integer, and so it is possible to
% use \TeX's native calculations rather than doing it in macros.
@@ -3008,66 +3230,59 @@
}
% \end{macrocode}
%\end{macro}
-%
-%\subsection{Trigonometric functions}
%
-%\begin{macro}{\fp_trig_normalise:}
-%\begin{macro}[aux]{\fp_trig_normalise_aux_i:}
-%\begin{macro}[aux]{\fp_trig_normalise_aux:w}
-%\begin{macro}[aux]{\fp_trig_normalise_aux_ii:}
-%\begin{macro}[aux]{\fp_trig_normalise_aux:NNNNNNNNN}
-%\begin{macro}[aux]{\fp_trig_normalise_aux_iii:}
-% For normalisation, the code essentially switches to fixed-point
-% arithmetic. There is a shift of the exponent, then repeated
-% subtractions. The end result is a number in the range
-% \( -\pi < x \le \pi \).
+%\begin{macro}{\fp_extended_normalise:}
+%\begin{macro}[aux]{\fp_extended_normalise_aux_i:}
+%\begin{macro}[aux]{\fp_extended_normalise_aux_i:w}
+%\begin{macro}[aux]{\fp_extended_normalise_aux_ii:w}
+%\begin{macro}[aux]{\fp_extended_normalise_aux_ii:}
+%\begin{macro}[aux]{\fp_extended_normalise_aux:NNNNNNNNN}
+% The `extended' integers for internal use are mainly used in
+% fixed-point mode. This comes up in a few places, so a generalised
+% utility is made available to carry out the change. This function
+% simply calls the two loops to shift the input to the point of
+% having a zero exponent.
% \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_trig_normalise: {
- \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
- \l_fp_input_a_extended_int \c_zero
- \fp_trig_normalise_aux_i:
- \fp_trig_normalise_aux_ii:
- \fp_trig_normalise_aux_iii:
- \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero
- \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
- \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
- \tex_fi:D
- \exp_after:wN \fp_trig_octant:
- \tex_else:D
- \l_fp_input_a_sign_int \c_one
- \l_fp_output_integer_int \c_zero
- \l_fp_output_decimal_int \c_zero
- \l_fp_output_exponent_int \c_zero
- \exp_after:wN \fp_trig_overflow_msg:
- \tex_fi:D
+\cs_new_protected_nopar:Npn \fp_extended_normalise: {
+ \fp_extended_normalise_aux_i:
+ \fp_extended_normalise_aux_ii:
}
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_i: {
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i: {
\tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero
\tex_multiply:D \l_fp_input_a_integer_int \c_ten
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
- \exp_after:wN \fp_trig_normalise_aux:w
+ \tex_expandafter:D \fp_extended_normalise_aux_i:w
\int_use:N \l_fp_input_a_decimal_int \q_stop
- \exp_after:wN \fp_trig_normalise_aux_i:
+ \tex_expandafter:D \fp_extended_normalise_aux_i:
\tex_fi:D
}
\cs_new_protected_nopar:Npn
- \fp_trig_normalise_aux:w #1#2#3#4#5#6#7#8#9 \q_stop {
+ \fp_extended_normalise_aux_i:w #1#2#3#4#5#6#7#8#9 \q_stop {
\l_fp_input_a_integer_int
\etex_numexpr:D \l_fp_input_a_integer_int + #2 \scan_stop:
\l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+ \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+ \tex_expandafter:D \fp_extended_normalise_aux_ii:w
+ \int_use:N \l_fp_input_a_extended_int \q_stop
+}
+\cs_new_protected_nopar:Npn
+ \fp_extended_normalise_aux_ii:w #1#2#3#4#5#6#7#8#9 \q_stop {
+ \l_fp_input_a_decimal_int
+ \etex_numexpr:D \l_fp_input_a_decimal_int + #2 \scan_stop:
+ \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop:
\tex_advance:D \l_fp_input_a_exponent_int \c_minus_one
}
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_ii: {
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii: {
\tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
- \fp_trig_normalise_aux:NNNNNNNNN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
+ \fp_extended_normalise_ii_aux:NNNNNNNNN
\int_use:N \l_fp_input_a_decimal_int
- \exp_after:wN \fp_trig_normalise_aux_ii:
+ \tex_expandafter:D \fp_extended_normalise_aux_ii:
\tex_fi:D
}
\cs_new_protected_nopar:Npn
- \fp_trig_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \fp_extended_normalise_ii_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
\tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
\l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
\tex_else:D
@@ -3088,7 +3303,95 @@
\l_fp_input_a_extended_int \l_fp_tmp_tl \scan_stop:
\tex_advance:D \l_fp_input_a_exponent_int \c_one
}
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_iii: {
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_extended_normalise_output:}
+%\begin{macro}[aux]{\fp_extended_normalise_output_aux_i:NNNNNNNNN}
+%\begin{macro}[aux]{\fp_extended_normalise_output_aux_ii:NNNNNNNNN}
+%\begin{macro}[aux]{\fp_extended_normalise_output_aux:N}
+% At some stages in working out extended output, it is possible for the
+% value to need shifting to keep the integer part in range. This only
+% ever happens such that the integer needs to be made smaller.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output: {
+ \tex_ifnum:D \l_fp_output_integer_int > \c_nine
+ \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
+ \fp_extended_normalise_output_aux_i:NNNNNNNNN
+ \int_use:N \l_fp_output_integer_int
+ \tex_expandafter:D \fp_extended_normalise_output:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+ \fp_extended_normalise_output_aux_i:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \tex_expandafter:D \use_none:n
+ \int_use:N \l_fp_output_decimal_int
+ }
+ \tex_expandafter:D \fp_extended_normalise_output_aux_ii:NNNNNNNNN
+ \l_fp_tmp_tl
+}
+\cs_new_protected_nopar:Npn
+ \fp_extended_normalise_output_aux_ii:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop:
+ \fp_extended_normalise_output_aux:N
+}
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux:N #1 {
+ \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
+ \tex_divide:D \l_fp_output_extended_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #1
+ \tex_expandafter:D \use_none:n
+ \int_use:N \l_fp_output_extended_int
+ }
+ \l_fp_output_extended_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_output_exponent_int \c_one
+}
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\subsection{Trigonometric functions}
+%
+%\begin{macro}{\fp_trig_normalise:}
+%\begin{macro}[aux]{\fp_trig_normalise_aux:}
+% For normalisation, the code essentially switches to fixed-point
+% arithmetic. There is a shift of the exponent, then repeated
+% subtractions. The end result is a number in the range
+% \( -\pi < x \le \pi \).
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_trig_normalise: {
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+ \l_fp_input_a_extended_int \c_zero
+ \fp_extended_normalise:
+ \fp_trig_normalise_aux:
+ \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero
+ \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
+ \tex_fi:D
+ \tex_expandafter:D \fp_trig_octant:
+ \tex_else:D
+ \l_fp_input_a_sign_int \c_one
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \tex_expandafter:D \fp_trig_overflow_msg:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_trig_normalise_aux: {
\tex_ifnum:D \l_fp_input_a_integer_int > \c_three
\fp_sub:NNNNNNNNN
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
@@ -3096,7 +3399,7 @@
\c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
\l_fp_input_a_extended_int
- \exp_after:wN \fp_trig_normalise_aux_iii:
+ \tex_expandafter:D \fp_trig_normalise_aux:
\tex_else:D
\tex_ifnum:D \l_fp_input_a_integer_int > \c_two
\tex_ifnum:D \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int
@@ -3106,9 +3409,9 @@
\c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
\l_fp_input_a_extended_int
- \exp_after:wN \exp_after:wN \exp_after:wN
- \exp_after:wN \exp_after:wN \exp_after:wN
- \exp_after:wN \fp_trig_normalise_aux_iii:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_trig_normalise_aux:
\tex_fi:D
\tex_fi:D
\tex_fi:D
@@ -3116,10 +3419,6 @@
% \end{macrocode}
%\end{macro}
%\end{macro}
-%\end{macro}
-%\end{macro}
-%\end{macro}
-%\end{macro}
%
%\begin{macro}{\fp_trig_octant:}
%\begin{macro}[aux]{\fp_trig_octant_aux:}
@@ -3157,7 +3456,7 @@
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
\l_fp_input_a_extended_int
\tex_advance:D \l_fp_trig_octant_int \c_one
- \exp_after:wN \fp_trig_octant_aux:
+ \tex_expandafter:D \fp_trig_octant_aux:
\tex_else:D
\tex_ifnum:D
\l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int
@@ -3169,7 +3468,7 @@
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
\l_fp_input_a_extended_int
\tex_advance:D \l_fp_trig_octant_int \c_one
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_trig_octant_aux:
\tex_fi:D
\tex_fi:D
@@ -3211,7 +3510,7 @@
\l_fp_input_a_integer_int
\l_fp_input_a_decimal_int
\l_fp_input_a_exponent_int
- \tl_set:Nx \l_fp_trig_arg_tl
+ \tl_set:Nx \l_fp_arg_tl
{
\tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
-
@@ -3220,7 +3519,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_input_a_decimal_int + \c_one_thousand_million
e
@@ -3230,21 +3529,21 @@
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
- #1 \exp_not:N #2 { \l_fp_trig_arg_tl }
+ #1 \exp_not:N #2 { \l_fp_arg_tl }
}
\tex_else:D
\etex_ifcsname:D
- c_fp_sin ( \l_fp_trig_arg_tl ) _tl
+ c_fp_sin ( \l_fp_arg_tl ) _fp
\tex_endcsname:D
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_sin_aux_i:
\tex_fi:D
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
#1 \exp_not:N #2
- { \use:c { c_fp_sin ( \l_fp_trig_arg_tl ) _tl } }
+ { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } }
}
\tex_fi:D
\fp_tmp:w
@@ -3270,8 +3569,8 @@
\l_fp_output_integer_int
\l_fp_output_decimal_int
\l_fp_output_exponent_int
- \tl_new:c { c_fp_sin ( \l_fp_trig_arg_tl ) _tl }
- \tl_gset:cx { c_fp_sin ( \l_fp_trig_arg_tl ) _tl }
+ \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp }
{
\tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+
@@ -3280,7 +3579,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
\scan_stop:
@@ -3291,13 +3590,13 @@
\cs_new_protected_nopar:Npn \fp_sin_aux_ii: {
\tex_ifcase:D \l_fp_trig_octant_int
\tex_or:D
- \exp_after:wN \fp_trig_calc_sin:
+ \tex_expandafter:D \fp_trig_calc_sin:
\tex_or:D
- \exp_after:wN \fp_trig_calc_cos:
+ \tex_expandafter:D \fp_trig_calc_cos:
\tex_or:D
- \exp_after:wN \fp_trig_calc_cos:
+ \tex_expandafter:D \fp_trig_calc_cos:
\tex_or:D
- \exp_after:wN \fp_trig_calc_sin:
+ \tex_expandafter:D \fp_trig_calc_sin:
\tex_fi:D
}
% \end{macrocode}
@@ -3334,7 +3633,7 @@
\l_fp_input_a_integer_int
\l_fp_input_a_decimal_int
\l_fp_input_a_exponent_int
- \tl_set:Nx \l_fp_trig_arg_tl
+ \tl_set:Nx \l_fp_arg_tl
{
\tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
-
@@ -3343,21 +3642,21 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_input_a_decimal_int + \c_one_thousand_million
e
\int_use:N \l_fp_input_a_exponent_int
}
- \etex_ifcsname:D c_fp_cos ( \l_fp_trig_arg_tl ) _tl \tex_endcsname:D
+ \etex_ifcsname:D c_fp_cos ( \l_fp_arg_tl ) _fp \tex_endcsname:D
\tex_else:D
- \exp_after:wN \fp_cos_aux_i:
+ \tex_expandafter:D \fp_cos_aux_i:
\tex_fi:D
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
#1 \exp_not:N #2
- { \use:c { c_fp_cos ( \l_fp_trig_arg_tl ) _tl } }
+ { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } }
}
\fp_tmp:w
}
@@ -3380,8 +3679,8 @@
\l_fp_output_integer_int
\l_fp_output_decimal_int
\l_fp_output_exponent_int
- \tl_new:c { c_fp_cos ( \l_fp_trig_arg_tl ) _tl }
- \tl_gset:cx { c_fp_cos ( \l_fp_trig_arg_tl ) _tl }
+ \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp }
{
\tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+
@@ -3390,7 +3689,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
\scan_stop:
@@ -3401,13 +3700,13 @@
\cs_new_protected_nopar:Npn \fp_cos_aux_ii: {
\tex_ifcase:D \l_fp_trig_octant_int
\tex_or:D
- \exp_after:wN \fp_trig_calc_cos:
+ \tex_expandafter:D \fp_trig_calc_cos:
\tex_or:D
- \exp_after:wN \fp_trig_calc_sin:
+ \tex_expandafter:D \fp_trig_calc_sin:
\tex_or:D
- \exp_after:wN \fp_trig_calc_sin:
+ \tex_expandafter:D \fp_trig_calc_sin:
\tex_or:D
- \exp_after:wN \fp_trig_calc_cos:
+ \tex_expandafter:D \fp_trig_calc_cos:
\tex_fi:D
\tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
\tex_ifnum:D \l_fp_trig_octant_int > \c_two
@@ -3431,7 +3730,7 @@
%
%\begin{macro}{\fp_trig_calc_cos:}
%\begin{macro}{\fp_trig_calc_sin:}
-%\begin{macro}[aux]{\fp_trig_calc_aux:}
+%\begin{macro}[aux]{\fp_trig_calc_Taylor:}
% These functions actually do the calculation for sine and cosine.
% \begin{macrocode}
\cs_new_protected_nopar:Npn \fp_trig_calc_cos: {
@@ -3466,7 +3765,7 @@
\tex_fi:D
\tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int
\tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
- \exp_after:wN \fp_trig_calc_aux:
+ \tex_expandafter:D \fp_trig_calc_Taylor:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_trig_calc_sin: {
@@ -3480,7 +3779,7 @@
\l_fp_trig_decimal_int \l_fp_input_a_decimal_int
\l_fp_trig_extended_int \l_fp_input_a_extended_int
\l_fp_count_int \c_two
- \exp_after:wN \fp_trig_calc_aux:
+ \tex_expandafter:D \fp_trig_calc_Taylor:
\tex_fi:D
}
% \end{macrocode}
@@ -3488,7 +3787,7 @@
% functions. Lots of shuffling about as \TeX\ is not exactly a natural
% choice for this sort of thing.
% \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_trig_calc_aux: {
+\cs_new_protected_nopar:Npn \fp_trig_calc_Taylor: {
\l_fp_trig_sign_int -\l_fp_trig_sign_int
\fp_mul:NNNNNN
\l_fp_trig_decimal_int \l_fp_trig_extended_int
@@ -3538,7 +3837,7 @@
\tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
\tex_fi:D
\tex_fi:D
- \exp_after:wN \fp_trig_calc_aux:
+ \tex_expandafter:D \fp_trig_calc_Taylor:
\tex_fi:D
}
% \end{macrocode}
@@ -3577,7 +3876,7 @@
\l_fp_input_a_integer_int
\l_fp_input_a_decimal_int
\l_fp_input_a_exponent_int
- \tl_set:Nx \l_fp_trig_arg_tl
+ \tl_set:Nx \l_fp_arg_tl
{
\tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
-
@@ -3586,7 +3885,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_input_a_decimal_int + \c_one_thousand_million
e
@@ -3596,21 +3895,21 @@
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
- #1 \exp_not:N #2 { \l_fp_trig_arg_tl }
+ #1 \exp_not:N #2 { \l_fp_arg_tl }
}
\tex_else:D
\etex_ifcsname:D
- c_fp_tan ( \l_fp_trig_arg_tl ) _tl
+ c_fp_tan ( \l_fp_arg_tl ) _fp
\tex_endcsname:D
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_tan_aux_i:
\tex_fi:D
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
#1 \exp_not:N #2
- { \use:c { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } }
+ { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } }
}
\tex_fi:D
\fp_tmp:w
@@ -3624,11 +3923,11 @@
% \begin{macrocode}
\cs_new_protected_nopar:Npn \fp_tan_aux_i: {
\tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
- \exp_after:wN \fp_tan_aux_ii:
+ \tex_expandafter:D \fp_tan_aux_ii:
\tex_else:D
- \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
\c_zero_fp
- \exp_after:wN \fp_trig_overflow_msg:
+ \tex_expandafter:D \fp_trig_overflow_msg:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_tan_aux_ii: {
@@ -3636,14 +3935,14 @@
\fp_cos_aux_ii:
\tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
\tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
- \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
\c_undefined_fp
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_tan_aux_iii:
\tex_fi:D
\tex_else:D
- \exp_after:wN \fp_tan_aux_iii:
+ \tex_expandafter:D \fp_tan_aux_iii:
\tex_fi:D
}
% \end{macrocode}
@@ -3671,14 +3970,14 @@
\l_fp_input_a_exponent_int
\tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
\tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
- \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
\c_zero_fp
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_tan_aux_iv:
\tex_fi:D
\tex_else:D
- \exp_after:wN \fp_tan_aux_iv:
+ \tex_expandafter:D \fp_tan_aux_iv:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_tan_aux_iv: {
@@ -3701,8 +4000,8 @@
\l_fp_output_integer_int
\l_fp_output_decimal_int
\l_fp_output_exponent_int
- \tl_new:c { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
- \tl_gset:cx { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+ \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp }
{
\tex_ifnum:D \l_fp_output_sign_int > \c_zero
+
@@ -3711,7 +4010,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
\scan_stop:
@@ -3730,13 +4029,1432 @@
%\end{macro}
%\end{macro}
%
+%\subsection{Exponent and logarithm functions}
+%
+%\begin{macro}{\c_fp_exp_1_tl}
+%\begin{macro}{\c_fp_exp_2_tl}
+%\begin{macro}{\c_fp_exp_3_tl}
+%\begin{macro}{\c_fp_exp_4_tl}
+%\begin{macro}{\c_fp_exp_5_tl}
+%\begin{macro}{\c_fp_exp_6_tl}
+%\begin{macro}{\c_fp_exp_7_tl}
+%\begin{macro}{\c_fp_exp_8_tl}
+%\begin{macro}{\c_fp_exp_9_tl}
+%\begin{macro}{\c_fp_exp_10_tl}
+%\begin{macro}{\c_fp_exp_20_tl}
+%\begin{macro}{\c_fp_exp_30_tl}
+%\begin{macro}{\c_fp_exp_40_tl}
+%\begin{macro}{\c_fp_exp_50_tl}
+%\begin{macro}{\c_fp_exp_60_tl}
+%\begin{macro}{\c_fp_exp_70_tl}
+%\begin{macro}{\c_fp_exp_80_tl}
+%\begin{macro}{\c_fp_exp_90_tl}
+%\begin{macro}{\c_fp_exp_100_tl}
+%\begin{macro}{\c_fp_exp_200_tl}
+% Calculation of exponentials requires a number of precomputed values:
+% first the positive integers.
+% \begin{macrocode}
+\tl_new:c { c_fp_exp_1_tl }
+\tl_set:cn { c_fp_exp_1_tl }
+ { { 2 } { 718281828 } { 459045235 } { 0 } }
+\tl_new:c { c_fp_exp_2_tl }
+\tl_set:cn { c_fp_exp_2_tl }
+ { { 7 } { 389056098 } { 930650227 } { 0 } }
+\tl_new:c { c_fp_exp_3_tl }
+\tl_set:cn { c_fp_exp_3_tl }
+ { { 2 } { 008553692 } { 318766774 } { 1 } }
+\tl_new:c { c_fp_exp_4_tl }
+\tl_set:cn { c_fp_exp_4_tl }
+ { { 5 } { 459815003 } { 314423908 } { 1 } }
+\tl_new:c { c_fp_exp_5_tl }
+\tl_set:cn { c_fp_exp_5_tl }
+ { { 1 } { 484131591 } { 025766034 } { 2 } }
+\tl_new:c { c_fp_exp_6_tl }
+\tl_set:cn { c_fp_exp_6_tl }
+ { { 4 } { 034287934 } { 927351226 } { 2 } }
+\tl_new:c { c_fp_exp_7_tl }
+\tl_set:cn { c_fp_exp_7_tl }
+ { { 1 } { 096633158 } { 428458599 } { 3 } }
+\tl_new:c { c_fp_exp_8_tl }
+\tl_set:cn { c_fp_exp_8_tl }
+ { { 2 } { 980957987 } { 041728275 } { 3 } }
+\tl_new:c { c_fp_exp_9_tl }
+\tl_set:cn { c_fp_exp_9_tl }
+ { { 8 } { 103083927 } { 575384008 } { 3 } }
+\tl_new:c { c_fp_exp_10_tl }
+\tl_set:cn { c_fp_exp_10_tl }
+ { { 2 } { 202646579 } { 480671652 } { 4 } }
+\tl_new:c { c_fp_exp_20_tl }
+\tl_set:cn { c_fp_exp_20_tl }
+ { { 4 } { 851651954 } { 097902280 } { 8 } }
+\tl_new:c { c_fp_exp_30_tl }
+\tl_set:cn { c_fp_exp_30_tl }
+ { { 1 } { 068647458 } { 152446215 } { 13 } }
+\tl_new:c { c_fp_exp_40_tl }
+\tl_set:cn { c_fp_exp_40_tl }
+ { { 2 } { 353852668 } { 370199854 } { 17 } }
+\tl_new:c { c_fp_exp_50_tl }
+\tl_set:cn { c_fp_exp_50_tl }
+ { { 5 } { 184705528 } { 587072464 } { 21 } }
+\tl_new:c { c_fp_exp_60_tl }
+\tl_set:cn { c_fp_exp_60_tl }
+ { { 1 } { 142007389 } { 815684284 } { 26 } }
+\tl_new:c { c_fp_exp_70_tl }
+\tl_set:cn { c_fp_exp_70_tl }
+ { { 2 } { 515438670 } { 919167006 } { 30 } }
+\tl_new:c { c_fp_exp_80_tl }
+\tl_set:cn { c_fp_exp_80_tl }
+ { { 5 } { 540622384 } { 393510053 } { 34 } }
+\tl_new:c { c_fp_exp_90_tl }
+\tl_set:cn { c_fp_exp_90_tl }
+ { { 1 } { 220403294 } { 317840802 } { 39 } }
+\tl_new:c { c_fp_exp_100_tl }
+\tl_set:cn { c_fp_exp_100_tl }
+ { { 2 } { 688117141 } { 816135448 } { 43 } }
+\tl_new:c { c_fp_exp_200_tl }
+\tl_set:cn { c_fp_exp_200_tl }
+ { { 7 } { 225973768 } { 125749258 } { 86 } }
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\c_fp_exp_-1_tl}
+%\begin{macro}{\c_fp_exp_-2_tl}
+%\begin{macro}{\c_fp_exp_-3_tl}
+%\begin{macro}{\c_fp_exp_-4_tl}
+%\begin{macro}{\c_fp_exp_-5_tl}
+%\begin{macro}{\c_fp_exp_-6_tl}
+%\begin{macro}{\c_fp_exp_-7_tl}
+%\begin{macro}{\c_fp_exp_-8_tl}
+%\begin{macro}{\c_fp_exp_-9_tl}
+%\begin{macro}{\c_fp_exp_-10_tl}
+%\begin{macro}{\c_fp_exp_-20_tl}
+%\begin{macro}{\c_fp_exp_-30_tl}
+%\begin{macro}{\c_fp_exp_-40_tl}
+%\begin{macro}{\c_fp_exp_-50_tl}
+%\begin{macro}{\c_fp_exp_-60_tl}
+%\begin{macro}{\c_fp_exp_-70_tl}
+%\begin{macro}{\c_fp_exp_-80_tl}
+%\begin{macro}{\c_fp_exp_-90_tl}
+%\begin{macro}{\c_fp_exp_-100_tl}
+%\begin{macro}{\c_fp_exp_-200_tl}
+% Now the negative integers.
+% \begin{macrocode}
+\tl_new:c { c_fp_exp_-1_tl }
+\tl_set:cn { c_fp_exp_-1_tl }
+ { { 3 } { 678794411 } { 71442322 } { -1 } }
+\tl_new:c { c_fp_exp_-2_tl }
+\tl_set:cn { c_fp_exp_-2_tl }
+ { { 1 } { 353352832 } { 366132692 } { -1 } }
+\tl_new:c { c_fp_exp_-3_tl }
+\tl_set:cn { c_fp_exp_-3_tl }
+ { { 4 } { 978706836 } { 786394298 } { -2 } }
+\tl_new:c { c_fp_exp_-4_tl }
+\tl_set:cn { c_fp_exp_-4_tl }
+ { { 1 } { 831563888 } { 873418029 } { -2 } }
+\tl_new:c { c_fp_exp_-5_tl }
+\tl_set:cn { c_fp_exp_-5_tl }
+ { { 6 } { 737946999 } { 085467097 } { -3 } }
+\tl_new:c { c_fp_exp_-6_tl }
+\tl_set:cn { c_fp_exp_-6_tl }
+ { { 2 } { 478752176 } { 666358423 } { -3 } }
+\tl_new:c { c_fp_exp_-7_tl }
+\tl_set:cn { c_fp_exp_-7_tl }
+ { { 9 } { 118819655 } { 545162080 } { -4 } }
+\tl_new:c { c_fp_exp_-8_tl }
+\tl_set:cn { c_fp_exp_-8_tl }
+ { { 3 } { 354626279 } { 025118388 } { -4 } }
+\tl_new:c { c_fp_exp_-9_tl }
+\tl_set:cn { c_fp_exp_-9_tl }
+ { { 1 } { 234098040 } { 866795495 } { -4 } }
+\tl_new:c { c_fp_exp_-10_tl }
+\tl_set:cn { c_fp_exp_-10_tl }
+ { { 4 } { 539992976 } { 248451536 } { -5 } }
+\tl_new:c { c_fp_exp_-20_tl }
+\tl_set:cn { c_fp_exp_-20_tl }
+ { { 2 } { 061153622 } { 438557828 } { -9 } }
+\tl_new:c { c_fp_exp_-30_tl }
+\tl_set:cn { c_fp_exp_-30_tl }
+ { { 9 } { 357622968 } { 840174605 } { -14 } }
+\tl_new:c { c_fp_exp_-40_tl }
+\tl_set:cn { c_fp_exp_-40_tl }
+ { { 4 } { 248354255 } { 291588995 } { -18 } }
+\tl_new:c { c_fp_exp_-50_tl }
+\tl_set:cn { c_fp_exp_-50_tl }
+ { { 1 } { 928749847 } { 963917783 } { -22 } }
+\tl_new:c { c_fp_exp_-60_tl }
+\tl_set:cn { c_fp_exp_-60_tl }
+ { { 8 } { 756510762 } { 696520338 } { -27 } }
+\tl_new:c { c_fp_exp_-70_tl }
+\tl_set:cn { c_fp_exp_-70_tl }
+ { { 3 } { 975449735 } { 908646808 } { -31 } }
+\tl_new:c { c_fp_exp_-80_tl }
+\tl_set:cn { c_fp_exp_-80_tl }
+ { { 1 } { 804851387 } { 845415172 } { -35 } }
+\tl_new:c { c_fp_exp_-90_tl }
+\tl_set:cn { c_fp_exp_-90_tl }
+ { { 8 } { 194012623 } { 990515430 } { -40 } }
+\tl_new:c { c_fp_exp_-100_tl }
+\tl_set:cn { c_fp_exp_-100_tl }
+ { { 3 } { 720075976 } { 020835963 } { -44 } }
+\tl_new:c { c_fp_exp_-200_tl }
+\tl_set:cn { c_fp_exp_-200_tl }
+ { { 1 } { 383896526 } { 736737530 } { -87 } }
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_exp:Nn}
+%\begin{macro}{\fp_exp:cn}
+%\begin{macro}{\fp_gexp:Nn}
+%\begin{macro}{\fp_gexp:cn}
+%\begin{macro}[aux]{\fp_exp_aux:NNn}
+%\begin{macro}[aux]{\fp_exp_internal:}
+%\begin{macro}[aux]{\fp_exp_aux:}
+%\begin{macro}[aux]{\fp_exp_integer:}
+%\begin{macro}[aux]{\fp_exp_integer_tens:}
+%\begin{macro}[aux]{\fp_exp_integer_units:}
+%\begin{macro}[aux]{\fp_exp_integer_const:n}
+%\begin{macro}[aux]{\fp_exp_integer_const:nnnn}
+%\begin{macro}[aux]{\fp_exp_decimal:}
+%\begin{macro}[aux]{\fp_exp_Taylor:}
+%\begin{macro}[aux]{\fp_exp_const:Nx}
+%\begin{macro}[aux]{\fp_exp_const:cx}
+% The calculation of an exponent starts off starts in much the same
+% way as the trigonometric functions: normalise the input, look for
+% a pre-defined value and if one is not found hand off to the real
+% workhorse function. The test for a definition of the result is used
+% so that overflows do not result in any outcome being defined.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp:Nn {
+ \fp_exp_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gexp:Nn {
+ \fp_exp_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_exp:Nn { c }
+\cs_generate_variant:Nn \fp_gexp:Nn { c }
+\cs_new_protected_nopar:Npn \fp_exp_aux:NNn #1#2#3 {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \l_fp_input_a_extended_int \c_zero
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+ -
+ \tex_else:D
+ +
+ \tex_fi:D
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp \tex_endcsname:D
+ \tex_else:D
+ \tex_expandafter:D \fp_exp_internal:
+ \tex_fi:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp
+ \tex_endcsname:D
+ \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ \tex_else:D
+ \c_zero_fp
+ \tex_fi:D
+ }
+ }
+ \fp_tmp:w
+}
+% \end{macrocode}
+% The first real step is to convert the input into a fixed-point
+% representation for further calculation: anything which is dropped
+% here as too small would not influence the output in any case. There
+% are a couple of overflow tests: the maximum
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp_internal: {
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_three
+ \fp_extended_normalise:
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_aux:
+ \tex_else:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_overflow_msg:
+ \tex_fi:D
+ \tex_else:D
+ \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_aux:
+ \tex_else:D
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ { \c_zero_fp }
+ \tex_fi:D
+ \tex_fi:D
+ \tex_else:D
+ \tex_expandafter:D \fp_exp_overflow_msg:
+ \tex_fi:D
+}
+% \end{macrocode}
+% The main algorithm makes use of the fact that
+% \[
+% \mathrm{e}^{nmp.q} =
+% \mathrm{e}^{n}
+% \mathrm{e}^{m}
+% \mathrm{e}^{p}
+% \mathrm{e}^{0.q}
+% \]
+% and that there is a Taylor series that can be used to calculate
+% \( \mathrm{e}^{0.q} \). Thus the approach needed is in three parts.
+% First, the exponent of the integer part of the input is found
+% using the pre-calculated constants. Second, the Taylor series is
+% used to find the exponent for the decimal part of the input. Finally,
+% the two parts are multiplied together to give the result. As the
+% normalisation code will already have dealt with any overflowing
+% values, there are no further checks needed.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp_aux: {
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+ \tex_expandafter:D \fp_exp_integer:
+ \tex_else:D
+ \l_fp_output_integer_int \c_one
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_extended_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \tex_expandafter:D \fp_exp_decimal:
+ \tex_fi:D
+}
+% \end{macrocode}
+% The integer part calculation starts with the hundreds. This is
+% set up such that very large negative numbers can short-cut the entire
+% procedure and simply return zero. In other cases, the code either
+% recovers the exponent of the hundreds value or sets the appropriate
+% storage to one (so that multiplication works correctly).
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp_integer: {
+ \tex_ifnum:D \l_fp_input_a_integer_int < \c_one_hundred
+ \l_fp_exp_integer_int \c_one
+ \l_fp_exp_decimal_int \c_zero
+ \l_fp_exp_extended_int \c_zero
+ \l_fp_exp_exponent_int \c_zero
+ \tex_expandafter:D \fp_exp_integer_tens:
+ \tex_else:D
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \tex_expandafter:D \use_i:nnn
+ \int_use:N \l_fp_input_a_integer_int
+ }
+ \l_fp_input_a_integer_int
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int - \l_fp_tmp_tl 00
+ \scan_stop:
+ \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+ \tex_ifnum:D \l_fp_output_integer_int > 200 \scan_stop:
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ { \c_zero_fp }
+ \tex_else:D
+ \fp_exp_integer_const:n { - \l_fp_tmp_tl 00 }
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_integer_tens:
+ \tex_fi:D
+ \tex_else:D
+ \fp_exp_integer_const:n { \l_fp_tmp_tl 00 }
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_integer_tens:
+ \tex_fi:D
+ \tex_fi:D
+}
+% \end{macrocode}
+% The tens and units parts are handled in a similar way, with a
+% multiplication step to build up the final value. That also includes a
+% correction step to avoid an overflow of the integer part.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp_integer_tens: {
+ \l_fp_output_integer_int \l_fp_exp_integer_int
+ \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \l_fp_output_extended_int \l_fp_exp_extended_int
+ \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_nine
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \tex_expandafter:D \use_i:nn
+ \int_use:N \l_fp_input_a_integer_int
+ }
+ \l_fp_input_a_integer_int
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int - \l_fp_tmp_tl 0
+ \scan_stop:
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \fp_exp_integer_const:n { \l_fp_tmp_tl 0 }
+ \tex_else:D
+ \fp_exp_integer_const:n { - \l_fp_tmp_tl 0 }
+ \tex_fi:D
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \fp_extended_normalise_output:
+ \tex_fi:D
+ \fp_exp_integer_units:
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_units: {
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int }
+ \tex_else:D
+ \fp_exp_integer_const:n
+ { - \int_use:N \l_fp_input_a_integer_int }
+ \tex_fi:D
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \fp_extended_normalise_output:
+ \tex_fi:D
+ \fp_exp_decimal:
+}
+% \end{macrocode}
+% Recovery of the stored constant values into the separate registers
+% is done with a simple expansion then assignment.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp_integer_const:n #1 {
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_exp_integer_const:nnnn
+ \tex_csname:D c_fp_exp_ #1 _tl \tex_endcsname:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_const:nnnn #1#2#3#4 {
+ \l_fp_exp_integer_int #1 \scan_stop:
+ \l_fp_exp_decimal_int #2 \scan_stop:
+ \l_fp_exp_extended_int #3 \scan_stop:
+ \l_fp_exp_exponent_int #4 \scan_stop:
+}
+% \end{macrocode}
+% Finding the exponential for the decimal part of the number requires
+% a Taylor series calculation. The set up is done here with the loop
+% itself a separate function. Once the decimal part is available this
+% is multiplied by the integer part already worked out to give
+% the final result.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp_decimal: {
+ \tex_ifnum:D \l_fp_input_a_decimal_int > \c_zero
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \l_fp_exp_integer_int \c_one
+ \l_fp_exp_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_exp_extended_int \l_fp_input_a_extended_int
+ \tex_else:D
+ \l_fp_exp_integer_int \c_zero
+ \tex_ifnum:D \l_fp_exp_extended_int = \c_zero
+ \l_fp_exp_decimal_int
+ \etex_numexpr:D
+ \c_one_thousand_million - \l_fp_input_a_decimal_int
+ \scan_stop:
+ \l_fp_exp_extended_int \c_zero
+ \tex_else:D
+ \l_fp_exp_decimal_int
+ \etex_numexpr:D
+ 999999999 - \l_fp_input_a_decimal_int
+ \scan_stop:
+ \l_fp_exp_extended_int
+ \etex_numexpr:D
+ \c_one_thousand_million - \l_fp_input_a_extended_int
+ \scan_stop:
+ \tex_fi:D
+ \tex_fi:D
+ \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_extended_int \l_fp_input_a_extended_int
+ \l_fp_count_int \c_one
+ \fp_exp_Taylor:
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million
+ \tex_else:D
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+ \tex_else:D
+ \l_fp_output_decimal_int \c_zero
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_fi:D
+ \tex_fi:D
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ {
+ +
+ \int_use:N \l_fp_output_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ \scan_stop:
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+}
+% \end{macrocode}
+% The Taylor series for \( \exp(x) \) is
+%\[
+% 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots
+%\]
+% which converges for \( -1 < x < 1 \). The code above sets up
+% the \( x \) part, leaving the loop to multiply the running
+% value by \( x / n \) and add it onto the sum. The way that this is
+% done is that the running total is stored in the \texttt{exp} set of
+% registers, while the current item is stored as \texttt{input_b}.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp_Taylor: {
+ \tex_advance:D \l_fp_count_int \c_one
+ \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \fp_div_integer:NNNNN
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_count_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int
+ > \c_zero
+ \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+ \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int
+ \tex_advance:D \l_fp_exp_extended_int
+ \l_fp_input_b_extended_int
+ \tex_ifnum:D \l_fp_exp_extended_int < \c_one_thousand_million
+ \tex_else:D
+ \tex_advance:D \l_fp_exp_decimal_int \c_one
+ \tex_advance:D \l_fp_exp_extended_int
+ -\c_one_thousand_million
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_exp_decimal_int < \c_one_thousand_million
+ \tex_else:D
+ \tex_advance:D \l_fp_exp_integer_int \c_one
+ \tex_advance:D \l_fp_exp_decimal_int
+ -\c_one_thousand_million
+ \tex_fi:D
+ \tex_else:D
+ \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int
+ \tex_advance:D \l_fp_exp_extended_int
+ -\l_fp_input_a_extended_int
+ \tex_ifnum:D \l_fp_exp_extended_int < \c_zero
+ \tex_advance:D \l_fp_exp_decimal_int \c_minus_one
+ \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_exp_decimal_int < \c_zero
+ \tex_advance:D \l_fp_exp_integer_int \c_minus_one
+ \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
+ \tex_fi:D
+ \tex_fi:D
+ \tex_expandafter:D \fp_exp_Taylor:
+ \tex_fi:D
+}
+% \end{macrocode}
+% This is set up as a function so that the power code can redirect
+% the effect.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_exp_const:Nx #1#2 {
+ \tl_new:N #1
+ \tl_gset:Nx #1 {#2}
+}
+\cs_generate_variant:Nn \fp_exp_const:Nx { c }
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\c_fp_ln_10_1_tl}
+%\begin{macro}{\c_fp_ln_10_2_tl}
+%\begin{macro}{\c_fp_ln_10_3_tl}
+%\begin{macro}{\c_fp_ln_10_4_tl}
+%\begin{macro}{\c_fp_ln_10_5_tl}
+%\begin{macro}{\c_fp_ln_10_6_tl}
+%\begin{macro}{\c_fp_ln_10_7_tl}
+%\begin{macro}{\c_fp_ln_10_8_tl}
+%\begin{macro}{\c_fp_ln_10_9_tl}
+% Constants for working out logarithms: first those for the powers of
+% ten.
+% \begin{macrocode}
+\tl_new:c { c_fp_ln_10_1_tl }
+\tl_set:cn { c_fp_ln_10_1_tl }
+ { { 2 } { 302585092 } { 994045684 } { 0 } }
+\tl_new:c { c_fp_ln_10_2_tl }
+\tl_set:cn { c_fp_ln_10_2_tl }
+ { { 4 } { 605170185 } { 988091368 } { 0 } }
+\tl_new:c { c_fp_ln_10_3_tl }
+\tl_set:cn { c_fp_ln_10_3_tl }
+ { { 6 } { 907755278 } { 982137052 } { 0 } }
+\tl_new:c { c_fp_ln_10_4_tl }
+\tl_set:cn { c_fp_ln_10_4_tl }
+ { { 9 } { 210340371 } { 976182736 } { 0 } }
+\tl_new:c { c_fp_ln_10_5_tl }
+\tl_set:cn { c_fp_ln_10_5_tl }
+ { { 1 } { 151292546 } { 497022842 } { 1 } }
+\tl_new:c { c_fp_ln_10_6_tl }
+\tl_set:cn { c_fp_ln_10_6_tl }
+ { { 1 } { 381551055 } { 796427410 } { 1 } }
+\tl_new:c { c_fp_ln_10_7_tl }
+\tl_set:cn { c_fp_ln_10_7_tl }
+ { { 1 } { 611809565 } { 095831979 } { 1 } }
+\tl_new:c { c_fp_ln_10_8_tl }
+\tl_set:cn { c_fp_ln_10_8_tl }
+ { { 1 } { 842068074 } { 395226547 } { 1 } }
+\tl_new:c { c_fp_ln_10_9_tl }
+\tl_set:cn { c_fp_ln_10_9_tl }
+ { { 2 } { 072326583 } { 694641116 } { 1 } }
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\c_fp_ln_2_1_tl }
+%\begin{macro}{\c_fp_ln_2_2_tl }
+%\begin{macro}{\c_fp_ln_2_3_tl }
+% The smaller set for powers of two.
+% \begin{macrocode}
+\tl_new:c { c_fp_ln_2_1_tl }
+\tl_set:cn { c_fp_ln_2_1_tl }
+ { { 0 } { 693147180 } { 559945309 } { 0 } }
+\tl_new:c { c_fp_ln_2_2_tl }
+\tl_set:cn { c_fp_ln_2_2_tl }
+ { { 1 } { 386294361 } { 119890618 } { 0 } }
+\tl_new:c { c_fp_ln_2_3_tl }
+\tl_set:cn { c_fp_ln_2_3_tl }
+ { { 2 } { 079441541 } { 679835928 } { 0 } }
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_ln:Nn}
+%\begin{macro}{\fp_ln:cn}
+%\begin{macro}{\fp_gln:Nn}
+%\begin{macro}{\fp_gln:cn}
+%\begin{macro}[aux]{\fp_ln_aux:NNn}
+%\begin{macro}[aux]{\fp_ln_aux:}
+%\begin{macro}[aux]{\fp_ln_exponent:}
+%\begin{macro}[aux]{\fp_ln_internal:}
+%\begin{macro}[aux]{\fp_ln_exponent_units:}
+%\begin{macro}[aux]{\fp_ln_normalise:}
+%\begin{macro}[aux]{\fp_ln_nornalise_aux:NNNNNNNNN}
+%\begin{macro}[aux]{\fp_ln_mantissa:}
+%\begin{macro}[aux]{\fp_ln_mantissa_aux:}
+%\begin{macro}[aux]{\fp_ln_mantissa_divide_two:}
+%\begin{macro}[aux]{\fp_ln_integer_const:nn}
+%\begin{macro}[aux]{\fp_ln_Taylor:}
+%\begin{macro}[aux]{\fp_ln_fixed:}
+%\begin{macro}[aux]{\fp_ln_fixed_aux:NNNNNNNNN}
+%\begin{macro}[aux]{\fp_ln_Taylor_aux:}
+% The approach for logarithms is again based on a mix of tables and
+% Taylor series. Here, the initial validation is a bit easier and so it
+% is set up earlier, meaning less need to escape later on.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln:Nn {
+ \fp_ln_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gln:Nn {
+ \fp_ln_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_ln:Nn { c }
+\cs_generate_variant:Nn \fp_gln:Nn { c }
+\cs_new_protected_nopar:Npn \fp_ln_aux:NNn #1#2#3 {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ > \c_zero
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_ln_aux:
+ \tex_else:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2 { \c_zero_fp }
+ }
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_ln_error_msg:
+ \tex_fi:D
+ \tex_else:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2 { \c_zero_fp }
+ }
+ \tex_expandafter:D \fp_ln_error_msg:
+ \tex_fi:D
+ \fp_tmp:w #1 #2
+}
+% \end{macrocode}
+% As the input at this stage meets the validity criteria above, the
+% argument can now be saved for further processing. There is no need
+% to look at the sign of the input as it must be positive. The function
+% here simply sets up to either do the full calculation or recover
+% the stored value, as appropriate.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_aux: {
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ +
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \etex_ifcsname:D c_fp_ln ( \l_fp_arg_tl ) _fp \tex_endcsname:D
+ \tex_else:D
+ \tex_expandafter:D \fp_ln_exponent:
+ \tex_fi:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2
+ { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } }
+ }
+}
+% \end{macrocode}
+% The main algorithm here uses the fact the logarithm can be divided
+% up, first taking out the powers of ten, then powers of two and finally
+% using a Taylor series for the remainder.
+%\[
+% \ln ( 10^{n} \times 2^{m} \times x )
+% = \ln ( 10^{n} ) \times \ln ( 2^{m} ) \times \ln ( x )
+%\]
+% The second point to remember is that
+%\[
+% \ln ( x^{-1} ) = - \ln ( x )
+%\]
+% which means that for the powers of \( 10 \) and \( 2 \) constants
+% are only needed for positive powers.
+%
+% The first step is to set up the sign for the output functions and
+% work out the powers of ten in the exponent. First the larger powers
+% are sorted out. The values for the constants are the same as those
+% for the smaller ones, just with a shift in the exponent.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_exponent: {
+ \fp_ln_internal:
+ \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million
+ \tex_else:D
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+ \tex_else:D
+ \l_fp_output_decimal_int \c_zero
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_fi:D
+ \tex_fi:D
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \tl_new:c { c_fp_ln ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_ln ( \l_fp_arg_tl ) _fp }
+ {
+ \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+ +
+ \tex_else:D
+ -
+ \tex_fi:D
+ \int_use:N \l_fp_output_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ \scan_stop:
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+}
+\cs_new_protected_nopar:Npn \fp_ln_internal: {
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero
+ \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int
+ \l_fp_output_sign_int \c_minus_one
+ \tex_else:D
+ \l_fp_output_sign_int \c_one
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_input_a_exponent_int > \c_nine
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \tex_expandafter:D \use_i:nn
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \l_fp_input_a_exponent_int
+ \etex_numexpr:D
+ \l_fp_input_a_exponent_int - \l_fp_tmp_tl 0
+ \scan_stop:
+ \fp_ln_const:nn { 10 } { \l_fp_tmp_tl }
+ \tex_advance:D \l_fp_exp_exponent_int \c_one
+ \l_fp_output_integer_int \l_fp_exp_integer_int
+ \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \l_fp_output_extended_int \l_fp_exp_extended_int
+ \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \tex_else:D
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_extended_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \tex_fi:D
+ \fp_ln_exponent_units:
+}
+% \end{macrocode}
+% Next the smaller powers of ten, which will need to be combined
+% with the above: always an additive process.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_exponent_units: {
+ \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero
+ \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int }
+ \fp_ln_normalise:
+ \fp_add:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_fi:D
+ \fp_ln_mantissa:
+}
+% \end{macrocode}
+% The smaller table-based parts may need to be exponent shifted so that
+% they stay in line with the larger parts. This is similar to the
+% approach in other places, but here there is a need to watch the
+% extended part of the number.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_normalise: {
+ \tex_ifnum:D \l_fp_exp_exponent_int < \l_fp_output_exponent_int
+ \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
+ \fp_ln_normalise_aux:NNNNNNNNN
+ \int_use:N \l_fp_exp_decimal_int
+ \tex_expandafter:D \fp_ln_normalise:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+ \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \tex_ifnum:D \l_fp_exp_integer_int = \c_zero
+ \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_else:D
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \int_use:N \l_fp_exp_integer_int
+ #1#2#3#4#5#6#7#8
+ }
+ \l_fp_exp_integer_int \c_zero
+ \l_fp_exp_decimal_int \l_fp_tmp_tl \scan_stop:
+ \tex_fi:D
+ \tex_divide:D \l_fp_exp_extended_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \int_use:N \l_fp_exp_extended_int
+ }
+ \l_fp_exp_extended_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_exp_exponent_int \c_one
+}
+% \end{macrocode}
+% The next phase is to decompose the mantissa by division by two to
+% leave a value which is in the range \( 1 \le x < 2 \). The sum of the
+% two powers needs to take account of the sign of the output: if it
+% is negative then the result gets \emph{smaller} as the mantissa gets
+% \emph{bigger}.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa: {
+ \l_fp_count_int \c_zero
+ \l_fp_input_a_extended_int \c_zero
+ \fp_ln_mantissa_aux:
+ \tex_ifnum:D \l_fp_count_int > \c_zero
+ \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int }
+ \fp_ln_normalise:
+ \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+ \tex_expandafter:D \fp_add:NNNNNNNNN
+ \tex_else:D
+ \tex_expandafter:D \fp_sub:NNNNNNNNN
+ \tex_fi:D
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_fi:D
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one
+ \scan_stop:
+ \tex_expandafter:D \fp_ln_Taylor:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa_aux: {
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_one
+ \tex_advance:D \l_fp_count_int \c_one
+ \fp_ln_mantissa_divide_two:
+ \tex_expandafter:D \fp_ln_mantissa_aux:
+ \tex_fi:D
+}
+% \end{macrocode}
+% A fast one-shot division by two.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two: {
+ \tex_ifodd:D \l_fp_input_a_decimal_int
+ \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+ \tex_fi:D
+ \tex_ifodd:D \l_fp_input_a_integer_int
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \tex_fi:D
+ \tex_divide:D \l_fp_input_a_integer_int \c_two
+ \tex_divide:D \l_fp_input_a_decimal_int \c_two
+ \tex_divide:D \l_fp_input_a_extended_int \c_two
+}
+% \end{macrocode}
+% Recovering constants makes use of the same auxiliary code as for
+% exponents.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_const:nn #1#2 {
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_exp_integer_const:nnnn
+ \tex_csname:D c_fp_ln_ #1 _ #2 _tl \tex_endcsname:D
+}
+% \end{macrocode}
+% The Taylor series for the logarithm function is best implemented using
+% the identity
+%\[
+% \ln(x) = \ln\left( \frac{y + 1}{y - 1} \right)
+%\]
+% with
+%\[
+% y = \frac{x - 1}{x + 1}
+%\]
+% This leads to the series
+%\[
+% \ln(x)
+% = 2y
+% \left(
+% 1 + y^{2}
+% \left(
+% \frac{1}{3} + y^{2}
+% \left(
+% \frac{1}{5} + y^{2}
+% \left(
+% \frac{1}{7} + y^{2}
+% \left(
+% \frac{1}{9} + \cdots
+% \right)
+% \right)
+% \right)
+% \right)
+% \right)
+%\]
+% This expansion has the advantage that a lot of the work can be
+% loaded up early by finding \( y^{2} \) before the loop itself starts.
+% (In practice, the implementation does the multiplication by two at the
+% end of the loop, and expands out the brackets as this is an overall
+% more efficient approach.)
+%
+% At the implementation level, the code starts by calculating \( y \)
+% and storing that in input \texttt{a} (which is no longer needed
+% for other purposes). That is done using the full division system
+% avoiding the parsing step. The value is then switched to a fixed-point
+% representation. There is then some shuffling to get all of the working
+% space set up. At this stage, a lot of registers are in use and so
+% the Taylor series is calculated within a group so that the
+% \texttt{output} variables can be used to hold the result. The value
+% of \( y^{2} \) is held in input \texttt{b} (there are a few
+% assignments saved by choosing this over \texttt{a}), while input
+% \texttt{a} is used for the `loop value'.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_Taylor: {
+ \group_begin:
+ \l_fp_input_a_integer_int \c_zero
+ \l_fp_input_a_exponent_int \c_zero
+ \l_fp_input_b_integer_int \c_two
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_exponent_int \c_zero
+ \fp_div_internal:
+ \fp_ln_fixed:
+ \l_fp_input_a_integer_int \l_fp_output_integer_int
+ \l_fp_input_a_decimal_int \l_fp_output_decimal_int
+ \l_fp_input_a_exponent_int \l_fp_output_exponent_int
+ \l_fp_input_a_extended_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_output_extended_int \l_fp_input_a_extended_int
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_count_int \c_one
+ \fp_ln_Taylor_aux:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ \exp_not:N \l_fp_exp_decimal_int
+ \int_use:N \l_fp_output_decimal_int \scan_stop:
+ \exp_not:N \l_fp_exp_extended_int
+ \int_use:N \l_fp_output_extended_int \scan_stop:
+ \exp_not:N \l_fp_exp_exponent_int
+ \int_use:N \l_fp_output_exponent_int \scan_stop:
+ }
+ \fp_tmp:w
+% \end{macrocode}
+% After the loop part of the Taylor series, the factor of \( 2 \) needs
+% to be included. The total for the result can then be constructed.
+% \begin{macrocode}
+ \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int
+ \tex_ifnum:D \l_fp_exp_extended_int < \c_five_hundred_million
+ \tex_else:D
+ \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million
+ \tex_advance:D \l_fp_exp_decimal_int \c_one
+ \tex_fi:D
+ \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int
+ \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+ \tex_expandafter:D \fp_add:NNNNNNNNN
+ \tex_else:D
+ \tex_expandafter:D \fp_sub:NNNNNNNNN
+ \tex_fi:D
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+}
+% \end{macrocode}
+% The usual shifts to move to fixed-point working. This is done using
+% the \texttt{output} registers as this saves a reassignment here.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_fixed: {
+ \tex_ifnum:D \l_fp_output_exponent_int < \c_zero
+ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
+ \fp_ln_fixed_aux:NNNNNNNNN
+ \int_use:N \l_fp_output_decimal_int
+ \tex_expandafter:D \fp_ln_fixed:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+ \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \tex_ifnum:D \l_fp_output_integer_int = \c_zero
+ \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_else:D
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \int_use:N \l_fp_output_integer_int
+ #1#2#3#4#5#6#7#8
+ }
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \l_fp_tmp_tl \scan_stop:
+ \tex_fi:D
+ \tex_advance:D \l_fp_output_exponent_int \c_one
+}
+% \end{macrocode}
+% The main loop for the Taylor series: unlike some of the other similar
+% functions, the result here is not the final value and is therefore
+% subject to further manipulation outside of the loop.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_ln_Taylor_aux: {
+ \tex_advance:D \l_fp_count_int \c_two
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+ > \c_zero
+ \fp_div_integer:NNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_count_int
+ \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int
+ \tex_ifnum:D \l_fp_output_extended_int < \c_one_thousand_million
+ \tex_else:D
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \tex_advance:D \l_fp_output_extended_int
+ -\c_one_thousand_million
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+ \tex_else:D
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_advance:D \l_fp_output_decimal_int
+ -\c_one_thousand_million
+ \tex_fi:D
+ \tex_expandafter:D \fp_ln_Taylor_aux:
+ \tex_fi:D
+}
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_pow:Nn}
+%\begin{macro}{\fp_pow:cn}
+%\begin{macro}{\fp_gpow:Nn}
+%\begin{macro}{\fp_gpow:cn}
+%\begin{macro}[aux]{\fp_pow_aux:NNn}
+%\begin{macro}[aux]{\fp_pow_aux_i:}
+%\begin{macro}[aux]{\fp_pow_positive:}
+%\begin{macro}[aux]{\fp_pow_negative:}
+%\begin{macro}[aux]{\fp_pow_aux_ii:}
+%\begin{macro}[aux]{\fp_pow_aux_iii:}
+%\begin{macro}[aux]{\fp_pow_aux_iv:}
+% The approach used for working out powers is to first filter out the
+% various special cases and then do most of the work using the
+% logarithm and exponent functions. The two storage areas are used
+% in the reverse of the `natural' logic as this avoids some
+% re-assignment in the sanity checking code.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_pow:Nn {
+ \fp_pow_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gpow:Nn {
+ \fp_pow_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_pow:Nn { c }
+\cs_generate_variant:Nn \fp_gpow:Nn { c }
+\cs_new_protected_nopar:Npn \fp_pow_aux:NNn #1#2#3 {
+ \group_begin:
+ \fp_read:N #2
+ \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \l_fp_input_b_integer_int \l_fp_input_a_integer_int
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+ = \c_zero
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ = \c_zero
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \tex_else:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_zero_fp }
+ }
+ \tex_fi:D
+ \tex_else:D
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ = \c_zero
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_one_fp }
+ }
+ \tex_else:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_pow_aux_i:
+ \tex_fi:D
+ \tex_fi:D
+ \fp_tmp:w #1 #2
+}
+% \end{macrocode}
+% Simply using the logarithm function directly will fail when negative
+% numbers are raised to integer powers, which is a mathematically valid
+% operation. So there are some more tests to make, after forcing the
+% power into an integer and decimal parts, if necessary.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_pow_aux_i: {
+ \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+ \tl_set:Nn \l_fp_sign_tl { + }
+ \tex_expandafter:D \fp_pow_aux_ii:
+ \tex_else:D
+ \l_fp_input_a_extended_int \c_zero
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+ \group_begin:
+ \fp_extended_normalise:
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+ = \c_zero
+ \group_end:
+ \tl_set:Nn \l_fp_sign_tl { - }
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_pow_aux_ii:
+ \tex_else:D
+ \group_end:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \tex_fi:D
+ \tex_else:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \tex_fi:D
+ \tex_fi:D
+}
+% \end{macrocode}
+% The approach used here for powers works well in most cases but gives
+% poorer results for negative integer powers, which often have exact
+% values. So there is some filtering to do. For negative powers where
+% the power is small, an alternative approach is used in which the
+% positive value is worked out and the reciprocal is then taken. The
+% filtering is unfortunately rather long.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_pow_aux_ii: {
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \tex_expandafter:D \fp_pow_aux_iv:
+ \tex_else:D
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+ \group_begin:
+ \l_fp_input_a_extended_int \c_zero
+ \fp_extended_normalise:
+ \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_ten
+ \group_end:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_pow_aux_iv:
+ \tex_else:D
+ \group_end:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_pow_aux_iii:
+ \tex_fi:D
+ \tex_else:D
+ \group_end:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_pow_aux_iv:
+ \tex_fi:D
+ \tex_else:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_pow_aux_iv:
+ \tex_fi:D
+ \tex_fi:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2
+ {
+ \l_fp_sign_tl
+ \int_use:N \l_fp_output_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ \scan_stop:
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+}
+% \end{macrocode}
+% For the small negative integer powers, the calculation is done for
+% the positive power and the reciprocal is then taken.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_pow_aux_iii: {
+ \l_fp_input_a_sign_int \c_one
+ \fp_pow_aux_iv:
+ \l_fp_input_a_integer_int \c_one
+ \l_fp_input_a_decimal_int \c_zero
+ \l_fp_input_a_exponent_int \c_zero
+ \l_fp_input_b_integer_int \l_fp_output_integer_int
+ \l_fp_input_b_decimal_int \l_fp_output_decimal_int
+ \l_fp_input_b_exponent_int \l_fp_output_exponent_int
+ \fp_div_internal:
+}
+% \end{macrocode}
+% The business end of the code starts by finding the logarithm of the
+% given base. There is a bit of a shuffle so that this does not have
+% to be re-parsed and so that the output ends up in the correct place.
+% There is also a need to enable using the short-cut for a
+% pre-calculated result. The internal part of the multiplication
+% function can then be used to do the second part of the calculation
+% directly. There is some more set up before doing the exponential:
+% the idea here is to deactivate some internals so that everything works
+% smoothly.
+% \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_pow_aux_iv: {
+ \group_begin:
+ \l_fp_input_a_integer_int \l_fp_input_b_integer_int
+ \l_fp_input_a_decimal_int \l_fp_input_b_decimal_int
+ \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
+ \fp_ln_internal:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ \exp_not:N \l_fp_input_b_sign_int
+ \int_use:N \l_fp_output_sign_int \scan_stop:
+ \exp_not:N \l_fp_input_b_integer_int
+ \int_use:N \l_fp_output_integer_int \scan_stop:
+ \exp_not:N \l_fp_input_b_decimal_int
+ \int_use:N \l_fp_output_decimal_int \scan_stop:
+ \exp_not:N \l_fp_input_b_extended_int
+ \int_use:N \l_fp_output_extended_int \scan_stop:
+ \exp_not:N \l_fp_input_b_exponent_int
+ \int_use:N \l_fp_output_exponent_int \scan_stop:
+ }
+ \fp_tmp:w
+ \l_fp_input_a_extended_int \c_zero
+ \fp_mul:NNNNNNNNN
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \l_fp_input_b_integer_int \l_fp_input_b_decimal_int
+ \l_fp_input_b_extended_int
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \tex_advance:D \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn
+ \fp_exp_internal:
+}
+% \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
%\subsection{Tests for special values}
%
%\begin{macro}{\fp_if_undefined_p:N}
%\begin{macro}[TF]{\fp_if_undefined:N}
% Testing for an undefined value is easy.
% \begin{macrocode}
-\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF } {
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { T , F , TF , p } {
\tex_ifx:D #1 \c_undefined_fp
\prg_return_true:
\tex_else:D
@@ -3751,7 +5469,7 @@
%\begin{macro}[TF]{\fp_if_zero:N}
% Testing for a zero fixed-point is also easy.
% \begin{macrocode}
-\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF } {
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { T , F , TF , p } {
\tex_ifx:D #1 \c_zero_fp
\prg_return_true:
\tex_else:D
@@ -3777,7 +5495,8 @@
% faster. The lead off for both is the same: get the two numbers
% read and then look for a function to handle the comparison.
% \begin{macrocode}
-\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF }
+\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3
+ { T , F , TF }
{
\group_begin:
\fp_split:Nn a {#1}
@@ -3794,7 +5513,8 @@
\l_fp_input_b_exponent_int
\fp_compare_aux:N #2
}
-\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 { T , F , TF }
+\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3
+ { T , F , TF }
{
\group_begin:
\fp_read:N #3
@@ -4026,6 +5746,33 @@
% \end{macrocode}
%\end{macro}
%
+%\begin{macro}{\fp_exp_overflow_msg:}
+% A slightly more helpful message for exponent overflows.
+% \begin{macrocode}
+\msg_kernel_new:nnnn { fpu } { exponent-overflow }
+ { Number~too~big~for~exponent~unit. }
+ {
+ The~exponent~of~the~input~given~is~too~big~for~the~floating~point~
+ unit:~the~maximum~input~value~for~an~exponent~is~230.
+ }
+\cs_new_protected_nopar:Npn \fp_exp_overflow_msg: {
+ \msg_kernel_error:nn { fpu } { exponent-overflow }
+}
+% \end{macrocode}
+%\end{macro}
+%
+%\begin{macro}{\fp_ln_error_msg:}
+% Logarithms are only valid for positive number
+% \begin{macrocode}
+\msg_kernel_new:nnnn { fpu } { logarithm-input-error }
+ { Invalid~input~to~ln~function. }
+ { Logarithms~can~only~be~calculated~for~positive~numbers. }
+\cs_new_protected_nopar:Npn \fp_ln_error_msg: {
+ \msg_kernel_error:nn { fpu } { logarithm-input-error }
+}
+% \end{macrocode}
+%\end{macro}
+%
%\begin{macro}{\fp_trig_overflow_msg:}
% A slightly more helpful message for trigonometric overflows.
% \begin{macrocode}
@@ -4039,7 +5786,8 @@
\msg_kernel_error:nn { fpu } { trigonometric-overflow }
}
% \end{macrocode}
-%\end{macro}%
+%\end{macro}
+%
% \begin{macrocode}
%</initex|package>
% \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/expl3/l3tl.dtx b/Master/texmf-dist/source/latex/expl3/l3tl.dtx
index c77feb5b947..b436be36ab5 100644
--- a/Master/texmf-dist/source/latex/expl3/l3tl.dtx
+++ b/Master/texmf-dist/source/latex/expl3/l3tl.dtx
@@ -36,7 +36,7 @@
\RequirePackage{l3names}
%</driver|package>
%\fi
-\GetIdInfo$Id: l3tl.dtx 2084 2010-11-17 19:12:14Z joseph $
+\GetIdInfo$Id: l3tl.dtx 2103 2010-12-18 07:40:03Z joseph $
{L3 Experimental Token Lists}
%\iffalse
%<*driver>
@@ -1376,7 +1376,7 @@
\tl_set:Nn \l_tl_tmpb_tl {#2}
\tex_ifx:D \l_tl_tmpa_tl \l_tl_tmpb_tl
\group_end:
- \prg_return_false:
+ \prg_return_true:
\tex_else:D
\group_end:
\prg_return_false:
diff --git a/Master/texmf-dist/tex/latex/expl3/l3fp.sty b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
index 65366e3af16..b5bb0661edc 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3fp.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
@@ -48,25 +48,18 @@
%%
%% -----------------------------------------------------------------------
\RequirePackage{l3names}
-\GetIdInfo$Id: l3fp.dtx 2092 2010-11-25 20:44:04Z joseph $
+\GetIdInfo$Id: l3fp.dtx 2104 2010-12-18 09:29:34Z joseph $
{L3 Experimental floating-point operations}
\ProvidesExplPackage
{\filename}{\filedate}{\fileversion}{\filedescription}
\package_check_loaded_expl:
-\int_new:N \c_forty_four
-\int_set:Nn \c_forty_four { 44 }
-\int_new:N \c_one_hundred
-\int_set:Nn \c_one_hundred { 100 }
-\int_new:N \c_one_thousand
-\int_set:Nn \c_one_thousand { 1000 }
-\int_new:N \c_one_million
-\int_set:Nn \c_one_million { 1 000 000 }
-\int_new:N \c_one_hundred_million
-\int_set:Nn \c_one_hundred_million { 100 000 000 }
-\int_new:N \c_five_hundred_million
-\int_set:Nn \c_five_hundred_million { 500 000 000 }
-\int_new:N \c_one_thousand_million
-\int_set:Nn \c_one_thousand_million { 1 000 000 000 }
+\int_const:Nn \c_forty_four { 44 }
+\int_const:Nn \c_one_hundred { 100 }
+\int_const:Nn \c_one_thousand { 1000 }
+\int_const:Nn \c_one_million { 1 000 000 }
+\int_const:Nn \c_one_hundred_million { 100 000 000 }
+\int_const:Nn \c_five_hundred_million { 500 000 000 }
+\int_const:Nn \c_one_thousand_million { 1 000 000 000 }
\int_new:N \c_fp_pi_by_four_decimal_int
\int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 }
\int_new:N \c_fp_pi_by_four_extended_int
@@ -79,16 +72,23 @@
\int_set:Nn \c_fp_two_pi_decimal_int { 283 185 307 }
\int_new:N \c_fp_two_pi_extended_int
\int_set:Nn \c_fp_two_pi_extended_int { 179 586 477 }
-\tl_new:N \c_one_fp
+\tl_new:N \c_e_fp
+\tl_set:Nn \c_e_fp { + 2.718281828 e 0 }
+\tl_new:N \c_one_fp
\tl_set:Nn \c_one_fp { + 1.000000000 e 0 }
-\tl_new:N \c_pi_fp
+\tl_new:N \c_pi_fp
\tl_set:Nn \c_pi_fp { + 3.141592654 e 0 }
-\tl_new:N \c_undefined_fp
+\tl_new:N \c_undefined_fp
\tl_set:Nn \c_undefined_fp { X 0.000000000 e 0 }
-\tl_new:N \c_zero_fp
+\tl_new:N \c_zero_fp
\tl_set:Nn \c_zero_fp { + 0.000000000 e 0 }
+\tl_new:N \l_fp_arg_tl
\int_new:N \l_fp_count_int
\int_new:N \l_fp_div_offset_int
+\int_new:N \l_fp_exp_integer_int
+\int_new:N \l_fp_exp_decimal_int
+\int_new:N \l_fp_exp_extended_int
+\int_new:N \l_fp_exp_exponent_int
\int_new:N \l_fp_input_a_sign_int
\int_new:N \l_fp_input_a_integer_int
\int_new:N \l_fp_input_a_decimal_int
@@ -122,16 +122,16 @@
\tl_new:N \l_fp_round_decimal_tl
\int_new:N \l_fp_round_position_int
\int_new:N \l_fp_round_target_int
+\tl_new:N \l_fp_sign_tl
\int_new:N \l_fp_split_sign_int
\int_new:N \l_fp_tmp_int
\tl_new:N \l_fp_tmp_tl
-\tl_new:N \l_fp_trig_arg_tl
\int_new:N \l_fp_trig_octant_int
\int_new:N \l_fp_trig_sign_int
\int_new:N \l_fp_trig_decimal_int
\int_new:N \l_fp_trig_extended_int
\cs_new_protected_nopar:Npn \fp_read:N #1 {
- \exp_after:wN \fp_read_aux:w #1 \q_stop
+ \tex_expandafter:D \fp_read_aux:w #1 \q_stop
}
\cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 e #4 \q_stop {
\tex_if:D #1 -
@@ -150,29 +150,29 @@
\l_fp_split_sign_int \c_one
\fp_split_sign:
\use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
- \exp_after:wN \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1
+ \tex_expandafter:D \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1
}
\cs_new_protected_nopar:Npn \fp_split_sign: {
\tex_ifnum:D \pdf_strcmp:D
- { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { - }
+ { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { - }
= \c_zero
\tl_set:Nx \l_fp_tmp_tl
{
- \exp_after:wN
+ \tex_expandafter:D
\tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
}
\l_fp_split_sign_int -\l_fp_split_sign_int
- \exp_after:wN \fp_split_sign:
+ \tex_expandafter:D \fp_split_sign:
\tex_else:D
\tex_ifnum:D \pdf_strcmp:D
- { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { + }
+ { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { + }
= \c_zero
\tl_set:Nx \l_fp_tmp_tl
{
- \exp_after:wN
+ \tex_expandafter:D
\tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
}
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_split_sign:
\tex_fi:D
\tex_fi:D
@@ -193,7 +193,7 @@
}
\cs_new_protected_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop {
\l_fp_tmp_int 1 #1 \scan_stop:
- \exp_after:wN \fp_split_decimal:w
+ \tex_expandafter:D \fp_split_decimal:w
\int_use:N \l_fp_tmp_int 000000000 \q_stop
}
\cs_new_protected_nopar:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9 {
@@ -212,7 +212,7 @@
\tex_ifnum:D
\use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million
\tex_else:D
- \exp_after:wN \fp_overflow_msg:
+ \tex_expandafter:D \fp_overflow_msg:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_standardise:NNNN #1#2#3#4 {
@@ -220,9 +220,9 @@
\etex_numexpr:D #2 + #3 = \c_zero
#1 \c_one
#4 \c_zero
- \exp_after:wN \use_none:nnnn
+ \tex_expandafter:D \use_none:nnnn
\tex_else:D
- \exp_after:wN \fp_standardise_aux:NNNN
+ \tex_expandafter:D \fp_standardise_aux:NNNN
\tex_fi:D
#1#2#3#4
}
@@ -231,9 +231,9 @@
{
\tex_ifnum:D #2 = \c_zero
\tex_advance:D #3 \c_one_thousand_million
- \exp_after:wN \fp_standardise_aux:w
+ \tex_expandafter:D \fp_standardise_aux:w
\int_use:N #3 \q_stop
- \exp_after:wN \fp_standardise_aux:
+ \tex_expandafter:D \fp_standardise_aux:
\tex_fi:D
}
\cs_set_protected_nopar:Npn
@@ -248,9 +248,9 @@
{
\tex_ifnum:D #2 > \c_nine
\tex_advance:D #2 \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_standardise_aux:w \int_use:N #2
- \exp_after:wN \fp_standardise_aux:
+ \tex_expandafter:D \fp_standardise_aux:
\tex_fi:D
}
\cs_set_protected_nopar:Npn
@@ -262,7 +262,7 @@
\tl_set:Nx \l_fp_tmp_tl
{
##9
- \exp_after:wN \use_none:n \int_use:N #3
+ \tex_expandafter:D \use_none:n \int_use:N #3
}
#3 \l_fp_tmp_tl \scan_stop:
\tex_advance:D #4 \c_one
@@ -277,25 +277,25 @@
#4 \c_zero
\tex_fi:D
\tex_else:D
- \exp_after:wN \fp_overflow_msg:
+ \tex_expandafter:D \fp_overflow_msg:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_standardise_aux: { }
\cs_new_protected_nopar:Npn \fp_standardise_aux:w { }
\cs_new_protected_nopar:Npn \fp_level_input_exponents: {
\tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
- \exp_after:wN \fp_level_input_exponents_a:
+ \tex_expandafter:D \fp_level_input_exponents_a:
\tex_else:D
- \exp_after:wN \fp_level_input_exponents_b:
+ \tex_expandafter:D \fp_level_input_exponents_b:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_level_input_exponents_a: {
\tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
\tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_level_input_exponents_a:NNNNNNNNN
\int_use:N \l_fp_input_b_integer_int
- \exp_after:wN \fp_level_input_exponents_a:
+ \tex_expandafter:D \fp_level_input_exponents_a:
\tex_fi:D
}
\cs_new_protected_nopar:Npn
@@ -306,7 +306,7 @@
\tl_set:Nx \l_fp_tmp_tl
{
#9
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_b_decimal_int
}
\l_fp_input_b_decimal_int \l_fp_tmp_tl \scan_stop:
@@ -315,10 +315,10 @@
\cs_new_protected_nopar:Npn \fp_level_input_exponents_b: {
\tex_ifnum:D \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
\tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_level_input_exponents_b:NNNNNNNNN
\int_use:N \l_fp_input_a_integer_int
- \exp_after:wN \fp_level_input_exponents_b:
+ \tex_expandafter:D \fp_level_input_exponents_b:
\tex_fi:D
}
\cs_new_protected_nopar:Npn
@@ -329,7 +329,7 @@
\tl_set:Nx \l_fp_tmp_tl
{
#9
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
}
\l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop:
@@ -341,6 +341,18 @@
\tl_gset_eq:NN #1 \c_zero_fp
}
\cs_generate_variant:Nn \fp_new:N { c }
+\cs_new_protected_nopar:Npn \fp_const:Nn #1#2 {
+ \cs_if_free:NTF #1
+ {
+ \fp_new:N #1
+ \fp_gset:Nn #1 {#2}
+ }
+ {
+ \msg_kernel_error:nx { variable-already-defined }
+ { \token_to_str:N #1 }
+ }
+}
+\cs_generate_variant:Nn \fp_const:Nn { c }
\cs_new_protected_nopar:Npn \fp_zero:N #1 {
\tl_set_eq:NN #1 \c_zero_fp
}
@@ -376,7 +388,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -398,7 +410,7 @@
\l_fp_tmp_dim \l_fp_tmp_skip
\fp_split:Nn a
{
- \exp_after:wN \fp_set_from_dim_aux:w
+ \tex_expandafter:D \fp_set_from_dim_aux:w
\dim_use:N \l_fp_tmp_dim
}
\fp_standardise:NNNN
@@ -419,7 +431,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -447,7 +459,7 @@
\cs_new_eq:NN \fp_show:N \tl_show:N
\cs_new_eq:NN \fp_show:c \tl_show:c
\cs_new_nopar:Npn \fp_use:N #1 {
- \exp_after:wN \fp_use_aux:w #1 \q_stop
+ \tex_expandafter:D \fp_use_aux:w #1 \q_stop
}
\cs_generate_variant:Nn \fp_use:N { c }
\cs_new_nopar:Npn \fp_use_aux:w #1#2 e #3 \q_stop {
@@ -455,13 +467,13 @@
-
\tex_fi:D
\tex_ifnum:D #3 > \c_zero
- \exp_after:wN \fp_use_large:w
+ \tex_expandafter:D \fp_use_large:w
\tex_else:D
\tex_ifnum:D #3 < \c_zero
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_use_small:w
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_use_none:w
\tex_fi:D
\tex_fi:D
@@ -475,9 +487,9 @@
}
\cs_new_nopar:Npn \fp_use_large:w #1 . #2 e #3 \q_stop {
\tex_ifnum:D #3 < \c_ten
- \exp_after:wN \fp_use_large_aux_i:w
+ \tex_expandafter:D \fp_use_large_aux_i:w
\tex_else:D
- \exp_after:wN \fp_use_large_aux_ii:w
+ \tex_expandafter:D \fp_use_large_aux_ii:w
\tex_fi:D
#1#2 e #3 \q_stop
}
@@ -516,7 +528,7 @@
\cs_new_nopar:Npn \fp_to_dim:N #1 { \fp_use:N #1 pt }
\cs_generate_variant:Nn \fp_to_dim:N { c }
\cs_new_nopar:Npn \fp_to_int:N #1 {
- \exp_after:wN \fp_to_int_aux:w #1 \q_stop
+ \tex_expandafter:D \fp_to_int_aux:w #1 \q_stop
}
\cs_generate_variant:Nn \fp_to_int:N { c }
\cs_new_nopar:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop {
@@ -524,9 +536,9 @@
-
\tex_fi:D
\tex_ifnum:D #3 < \c_zero
- \exp_after:wN \fp_to_int_small:w
+ \tex_expandafter:D \fp_to_int_small:w
\tex_else:D
- \exp_after:wN \fp_to_int_large:w
+ \tex_expandafter:D \fp_to_int_large:w
\tex_fi:D
#2 e #3 \q_stop
}
@@ -542,9 +554,9 @@
}
\cs_new_nopar:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop {
\tex_ifnum:D #3 < \c_ten
- \exp_after:wN \fp_to_int_large_aux_i:w
+ \tex_expandafter:D \fp_to_int_large_aux_i:w
\tex_else:D
- \exp_after:wN \fp_to_int_large_aux_ii:w
+ \tex_expandafter:D \fp_to_int_large_aux_ii:w
\tex_fi:D
#1#2 e #3 \q_stop
}
@@ -590,7 +602,7 @@
\prg_replicate:nn { #2 - 9 } { 0 }
}
\cs_new_nopar:Npn \fp_to_tl:N #1 {
- \exp_after:wN \fp_to_tl_aux:w #1 \q_stop
+ \tex_expandafter:D \fp_to_tl_aux:w #1 \q_stop
}
\cs_generate_variant:Nn \fp_to_tl:N { c }
\cs_new_nopar:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop {
@@ -598,17 +610,17 @@
-
\tex_fi:D
\tex_ifnum:D #3 < \c_zero
- \exp_after:wN \fp_to_tl_small:w
+ \tex_expandafter:D \fp_to_tl_small:w
\tex_else:D
- \exp_after:wN \fp_to_tl_large:w
+ \tex_expandafter:D \fp_to_tl_large:w
\tex_fi:D
#2 e #3 \q_stop
}
\cs_new_nopar:Npn \fp_to_tl_large:w #1 e #2 \q_stop {
\tex_ifnum:D #2 < \c_ten
- \exp_after:wN \fp_to_tl_large_aux_i:w
+ \tex_expandafter:D \fp_to_tl_large_aux_i:w
\tex_else:D
- \exp_after:wN \fp_to_tl_large_aux_ii:w
+ \tex_expandafter:D \fp_to_tl_large_aux_ii:w
\tex_fi:D
#1 e #2 \q_stop
}
@@ -664,13 +676,13 @@
\cs_new_nopar:cpn { fp_to_tl_large_9:w } #1 . #2 \q_stop {#1#2}
\cs_new_nopar:Npn \fp_to_tl_small:w #1 e #2 \q_stop {
\tex_ifnum:D #2 = \c_minus_one
- \exp_after:wN \fp_to_tl_small_one:w
+ \tex_expandafter:D \fp_to_tl_small_one:w
\tex_else:D
\tex_ifnum:D #2 = -\c_two
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_to_tl_small_two:w
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_to_tl_small_aux:w
\tex_fi:D
\tex_fi:D
@@ -682,7 +694,7 @@
\etex_numexpr:D #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
< \c_one_thousand_million
0.
- \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
+ \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN
\tex_number:D
\etex_numexpr:D
#1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
@@ -701,7 +713,7 @@
\etex_numexpr:D #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
< \c_one_thousand_million
0.0
- \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
+ \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN
\tex_number:D
\etex_numexpr:D
#1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
@@ -817,7 +829,7 @@
\fp_read:N #2
\int_set:Nn \l_fp_round_target_int { #3 - 1 }
\tex_ifnum:D \l_fp_round_target_int < \c_ten
- \exp_after:wN \fp_round:
+ \tex_expandafter:D \fp_round:
\tex_fi:D
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
\cs_set_protected_nopar:Npx \fp_tmp:w
@@ -832,7 +844,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -854,7 +866,7 @@
\int_set:Nn \l_fp_round_target_int
{ #3 + \l_fp_input_a_exponent_int }
\tex_ifnum:D \l_fp_round_target_int < \c_ten
- \exp_after:wN \fp_round:
+ \tex_expandafter:D \fp_round:
\tex_fi:D
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
\cs_set_protected_nopar:Npx \fp_tmp:w
@@ -869,7 +881,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -882,7 +894,7 @@
\l_fp_round_position_int \c_eight
\tl_clear:N \l_fp_round_decimal_tl
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int
}
\cs_new_protected_nopar:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
@@ -919,7 +931,7 @@
\tex_fi:D
\tex_advance:D \l_fp_round_position_int \c_minus_one
\tex_ifnum:D \l_fp_round_position_int > \c_minus_one
- \exp_after:wN \fp_round_loop:N
+ \tex_expandafter:D \fp_round_loop:N
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_abs:N {
@@ -942,7 +954,7 @@
+
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
@@ -971,13 +983,13 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\int_use:N \l_fp_input_a_decimal_int
e
\int_use:N \l_fp_input_a_exponent_int
}
- \exp_after:wN \group_end: \exp_after:wN
- #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+ \tex_expandafter:D \group_end: \tex_expandafter:D
+ #1 \tex_expandafter:D #2 \tex_expandafter:D { \l_fp_tmp_tl }
}
\cs_new_protected_nopar:Npn \fp_add:Nn {
\fp_add_aux:NNn \tl_set:Nn
@@ -1006,9 +1018,9 @@
\l_fp_input_a_sign_int * \l_fp_input_b_sign_int
\scan_stop:
> \c_zero
- \exp_after:wN \fp_add_sum:
+ \tex_expandafter:D \fp_add_sum:
\tex_else:D
- \exp_after:wN \fp_add_difference:
+ \tex_expandafter:D \fp_add_difference:
\tex_fi:D
\l_fp_output_exponent_int \l_fp_input_a_exponent_int
\fp_standardise:NNNN
@@ -1028,7 +1040,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
e
@@ -1121,7 +1133,7 @@
\l_fp_input_b_integer_int
\l_fp_input_b_decimal_int
\l_fp_input_b_exponent_int
- \fp_mul_int:
+ \fp_mul_internal:
\l_fp_output_exponent_int
\etex_numexpr:D
\l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
@@ -1153,7 +1165,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
e
@@ -1162,7 +1174,7 @@
}
\fp_tmp:w
}
-\cs_new_protected_nopar:Npn \fp_mul_int: {
+\cs_new_protected_nopar:Npn \fp_mul_internal: {
\fp_mul_split:NNNN \l_fp_input_a_decimal_int
\l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
\fp_mul_split:NNNN \l_fp_input_b_decimal_int
@@ -1199,7 +1211,7 @@
#3 ##5##6##7 \scan_stop:
#4 ##8##9 \scan_stop:
}
- \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop
+ \tex_expandafter:D \fp_mul_split_aux:w \int_use:N #1 \q_stop
\tex_advance:D #1 -\c_one_thousand_million
}
\cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2 {
@@ -1208,7 +1220,7 @@
}
\cs_new_protected_nopar:Npn \fp_mul_end_level: {
\tex_advance:D \l_fp_mul_output_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
\fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int
}
\cs_new_protected_nopar:Npn \fp_mul_end_level:NNNNNNNNN
@@ -1224,7 +1236,6 @@
}
\cs_generate_variant:Nn \fp_div:Nn { c }
\cs_generate_variant:Nn \fp_gdiv:Nn { c }
-
\cs_new_protected_nopar:Npn \fp_div_aux:NNn #1#2#3 {
\group_begin:
\fp_read:N #2
@@ -1254,13 +1265,13 @@
#1 \exp_not:N #2 { \c_zero_fp }
}
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
- \fp_div_aux:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_div_internal:
\tex_fi:D
\tex_fi:D
\fp_tmp:w #1#2
}
-\cs_new_protected_nopar:Npn \fp_div_aux: {
+\cs_new_protected_nopar:Npn \fp_div_internal: {
\l_fp_output_integer_int \c_zero
\l_fp_output_decimal_int \c_zero
\cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
@@ -1297,7 +1308,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
\scan_stop:
@@ -1312,30 +1323,30 @@
\fp_div_store:
\tex_multiply:D \l_fp_input_a_integer_int \c_ten
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
- \exp_after:wN \fp_div_loop_step:w
+ \tex_expandafter:D \fp_div_loop_step:w
\int_use:N \l_fp_input_a_decimal_int \q_stop
\tex_ifnum:D
\etex_numexpr:D
\l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
> \c_zero
\tex_ifnum:D \l_fp_div_offset_int > \c_zero
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_div_loop:
\tex_fi:D
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_div_divide: {
\tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
- \exp_after:wN \fp_div_divide_aux:
+ \tex_expandafter:D \fp_div_divide_aux:
\tex_else:D
\tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
\tex_else:D
\tex_ifnum:D
\l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
- \exp_after:wN \exp_after:wN \exp_after:wN
- \exp_after:wN \fp_div_divide_aux:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_div_divide_aux:
\tex_fi:D
\tex_fi:D
\tex_fi:D
@@ -1430,6 +1441,7 @@
\fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int
\fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int
\fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int
\fp_mul_end_level:
\fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int
\fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int
@@ -1450,6 +1462,65 @@
\fp_mul_end_level:
#5 0 \l_fp_mul_output_tl \scan_stop:
}
+\cs_new_protected_nopar:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \fp_mul_split:NNNN #2
+ \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
+ \fp_mul_split:NNNN #3
+ \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
+ \fp_mul_split:NNNN #5
+ \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+ \fp_mul_split:NNNN #6
+ \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
+ \l_fp_mul_output_int \c_zero
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_vi_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_i_int
+ \tex_divide:D \l_fp_mul_output_int \c_one_thousand
+ \fp_mul_product:NN #1 \l_fp_mul_b_vi_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_vi_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int #4
+ \fp_mul_end_level:
+ #9 0 \l_fp_mul_output_tl \scan_stop:
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN #1 \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int #4
+ \fp_mul_end_level:
+ #8 0 \l_fp_mul_output_tl \scan_stop:
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN #1 #4
+ \fp_mul_end_level:
+ #7 0 \l_fp_mul_output_tl \scan_stop:
+}
\cs_new_protected_nopar:Npn \fp_div_integer:NNNNN #1#2#3#4#5 {
\l_fp_tmp_int #1
\tex_divide:D \l_fp_tmp_int #3
@@ -1466,52 +1537,46 @@
\tex_advancd:D #5 -\c_one_thousand_million
\tex_fi:D
}
-\cs_new_protected_nopar:Npn \fp_trig_normalise: {
- \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
- \l_fp_input_a_extended_int \c_zero
- \fp_trig_normalise_aux_i:
- \fp_trig_normalise_aux_ii:
- \fp_trig_normalise_aux_iii:
- \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero
- \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
- \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
- \tex_fi:D
- \exp_after:wN \fp_trig_octant:
- \tex_else:D
- \l_fp_input_a_sign_int \c_one
- \l_fp_output_integer_int \c_zero
- \l_fp_output_decimal_int \c_zero
- \l_fp_output_exponent_int \c_zero
- \exp_after:wN \fp_trig_overflow_msg:
- \tex_fi:D
+\cs_new_protected_nopar:Npn \fp_extended_normalise: {
+ \fp_extended_normalise_aux_i:
+ \fp_extended_normalise_aux_ii:
}
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_i: {
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i: {
\tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero
\tex_multiply:D \l_fp_input_a_integer_int \c_ten
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
- \exp_after:wN \fp_trig_normalise_aux:w
+ \tex_expandafter:D \fp_extended_normalise_aux_i:w
\int_use:N \l_fp_input_a_decimal_int \q_stop
- \exp_after:wN \fp_trig_normalise_aux_i:
+ \tex_expandafter:D \fp_extended_normalise_aux_i:
\tex_fi:D
}
\cs_new_protected_nopar:Npn
- \fp_trig_normalise_aux:w #1#2#3#4#5#6#7#8#9 \q_stop {
+ \fp_extended_normalise_aux_i:w #1#2#3#4#5#6#7#8#9 \q_stop {
\l_fp_input_a_integer_int
\etex_numexpr:D \l_fp_input_a_integer_int + #2 \scan_stop:
\l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+ \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+ \tex_expandafter:D \fp_extended_normalise_aux_ii:w
+ \int_use:N \l_fp_input_a_extended_int \q_stop
+}
+\cs_new_protected_nopar:Npn
+ \fp_extended_normalise_aux_ii:w #1#2#3#4#5#6#7#8#9 \q_stop {
+ \l_fp_input_a_decimal_int
+ \etex_numexpr:D \l_fp_input_a_decimal_int + #2 \scan_stop:
+ \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop:
\tex_advance:D \l_fp_input_a_exponent_int \c_minus_one
}
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_ii: {
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii: {
\tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero
\tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
- \exp_after:wN \use_i:nn \exp_after:wN
- \fp_trig_normalise_aux:NNNNNNNNN
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
+ \fp_extended_normalise_ii_aux:NNNNNNNNN
\int_use:N \l_fp_input_a_decimal_int
- \exp_after:wN \fp_trig_normalise_aux_ii:
+ \tex_expandafter:D \fp_extended_normalise_aux_ii:
\tex_fi:D
}
\cs_new_protected_nopar:Npn
- \fp_trig_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \fp_extended_normalise_ii_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
\tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
\l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
\tex_else:D
@@ -1532,7 +1597,64 @@
\l_fp_input_a_extended_int \l_fp_tmp_tl \scan_stop:
\tex_advance:D \l_fp_input_a_exponent_int \c_one
}
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_iii: {
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output: {
+ \tex_ifnum:D \l_fp_output_integer_int > \c_nine
+ \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
+ \fp_extended_normalise_output_aux_i:NNNNNNNNN
+ \int_use:N \l_fp_output_integer_int
+ \tex_expandafter:D \fp_extended_normalise_output:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+ \fp_extended_normalise_output_aux_i:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \tex_expandafter:D \use_none:n
+ \int_use:N \l_fp_output_decimal_int
+ }
+ \tex_expandafter:D \fp_extended_normalise_output_aux_ii:NNNNNNNNN
+ \l_fp_tmp_tl
+}
+\cs_new_protected_nopar:Npn
+ \fp_extended_normalise_output_aux_ii:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop:
+ \fp_extended_normalise_output_aux:N
+}
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux:N #1 {
+ \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
+ \tex_divide:D \l_fp_output_extended_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #1
+ \tex_expandafter:D \use_none:n
+ \int_use:N \l_fp_output_extended_int
+ }
+ \l_fp_output_extended_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_output_exponent_int \c_one
+}
+\cs_new_protected_nopar:Npn \fp_trig_normalise: {
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+ \l_fp_input_a_extended_int \c_zero
+ \fp_extended_normalise:
+ \fp_trig_normalise_aux:
+ \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero
+ \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
+ \tex_fi:D
+ \tex_expandafter:D \fp_trig_octant:
+ \tex_else:D
+ \l_fp_input_a_sign_int \c_one
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \tex_expandafter:D \fp_trig_overflow_msg:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_trig_normalise_aux: {
\tex_ifnum:D \l_fp_input_a_integer_int > \c_three
\fp_sub:NNNNNNNNN
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
@@ -1540,7 +1662,7 @@
\c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
\l_fp_input_a_extended_int
- \exp_after:wN \fp_trig_normalise_aux_iii:
+ \tex_expandafter:D \fp_trig_normalise_aux:
\tex_else:D
\tex_ifnum:D \l_fp_input_a_integer_int > \c_two
\tex_ifnum:D \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int
@@ -1550,9 +1672,9 @@
\c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
\l_fp_input_a_extended_int
- \exp_after:wN \exp_after:wN \exp_after:wN
- \exp_after:wN \exp_after:wN \exp_after:wN
- \exp_after:wN \fp_trig_normalise_aux_iii:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_trig_normalise_aux:
\tex_fi:D
\tex_fi:D
\tex_fi:D
@@ -1583,7 +1705,7 @@
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
\l_fp_input_a_extended_int
\tex_advance:D \l_fp_trig_octant_int \c_one
- \exp_after:wN \fp_trig_octant_aux:
+ \tex_expandafter:D \fp_trig_octant_aux:
\tex_else:D
\tex_ifnum:D
\l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int
@@ -1595,7 +1717,7 @@
\l_fp_input_a_integer_int \l_fp_input_a_decimal_int
\l_fp_input_a_extended_int
\tex_advance:D \l_fp_trig_octant_int \c_one
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_trig_octant_aux:
\tex_fi:D
\tex_fi:D
@@ -1616,7 +1738,7 @@
\l_fp_input_a_integer_int
\l_fp_input_a_decimal_int
\l_fp_input_a_exponent_int
- \tl_set:Nx \l_fp_trig_arg_tl
+ \tl_set:Nx \l_fp_arg_tl
{
\tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
-
@@ -1625,7 +1747,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_input_a_decimal_int + \c_one_thousand_million
e
@@ -1635,21 +1757,21 @@
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
- #1 \exp_not:N #2 { \l_fp_trig_arg_tl }
+ #1 \exp_not:N #2 { \l_fp_arg_tl }
}
\tex_else:D
\etex_ifcsname:D
- c_fp_sin ( \l_fp_trig_arg_tl ) _tl
+ c_fp_sin ( \l_fp_arg_tl ) _fp
\tex_endcsname:D
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_sin_aux_i:
\tex_fi:D
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
#1 \exp_not:N #2
- { \use:c { c_fp_sin ( \l_fp_trig_arg_tl ) _tl } }
+ { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } }
}
\tex_fi:D
\fp_tmp:w
@@ -1669,8 +1791,8 @@
\l_fp_output_integer_int
\l_fp_output_decimal_int
\l_fp_output_exponent_int
- \tl_new:c { c_fp_sin ( \l_fp_trig_arg_tl ) _tl }
- \tl_gset:cx { c_fp_sin ( \l_fp_trig_arg_tl ) _tl }
+ \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp }
{
\tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+
@@ -1679,7 +1801,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
\scan_stop:
@@ -1690,13 +1812,13 @@
\cs_new_protected_nopar:Npn \fp_sin_aux_ii: {
\tex_ifcase:D \l_fp_trig_octant_int
\tex_or:D
- \exp_after:wN \fp_trig_calc_sin:
+ \tex_expandafter:D \fp_trig_calc_sin:
\tex_or:D
- \exp_after:wN \fp_trig_calc_cos:
+ \tex_expandafter:D \fp_trig_calc_cos:
\tex_or:D
- \exp_after:wN \fp_trig_calc_cos:
+ \tex_expandafter:D \fp_trig_calc_cos:
\tex_or:D
- \exp_after:wN \fp_trig_calc_sin:
+ \tex_expandafter:D \fp_trig_calc_sin:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_cos:Nn {
@@ -1715,7 +1837,7 @@
\l_fp_input_a_integer_int
\l_fp_input_a_decimal_int
\l_fp_input_a_exponent_int
- \tl_set:Nx \l_fp_trig_arg_tl
+ \tl_set:Nx \l_fp_arg_tl
{
\tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
-
@@ -1724,21 +1846,21 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_input_a_decimal_int + \c_one_thousand_million
e
\int_use:N \l_fp_input_a_exponent_int
}
- \etex_ifcsname:D c_fp_cos ( \l_fp_trig_arg_tl ) _tl \tex_endcsname:D
+ \etex_ifcsname:D c_fp_cos ( \l_fp_arg_tl ) _fp \tex_endcsname:D
\tex_else:D
- \exp_after:wN \fp_cos_aux_i:
+ \tex_expandafter:D \fp_cos_aux_i:
\tex_fi:D
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
#1 \exp_not:N #2
- { \use:c { c_fp_cos ( \l_fp_trig_arg_tl ) _tl } }
+ { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } }
}
\fp_tmp:w
}
@@ -1757,8 +1879,8 @@
\l_fp_output_integer_int
\l_fp_output_decimal_int
\l_fp_output_exponent_int
- \tl_new:c { c_fp_cos ( \l_fp_trig_arg_tl ) _tl }
- \tl_gset:cx { c_fp_cos ( \l_fp_trig_arg_tl ) _tl }
+ \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp }
{
\tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+
@@ -1767,7 +1889,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
\scan_stop:
@@ -1778,13 +1900,13 @@
\cs_new_protected_nopar:Npn \fp_cos_aux_ii: {
\tex_ifcase:D \l_fp_trig_octant_int
\tex_or:D
- \exp_after:wN \fp_trig_calc_cos:
+ \tex_expandafter:D \fp_trig_calc_cos:
\tex_or:D
- \exp_after:wN \fp_trig_calc_sin:
+ \tex_expandafter:D \fp_trig_calc_sin:
\tex_or:D
- \exp_after:wN \fp_trig_calc_sin:
+ \tex_expandafter:D \fp_trig_calc_sin:
\tex_or:D
- \exp_after:wN \fp_trig_calc_cos:
+ \tex_expandafter:D \fp_trig_calc_cos:
\tex_fi:D
\tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
\tex_ifnum:D \l_fp_trig_octant_int > \c_two
@@ -1829,7 +1951,7 @@
\tex_fi:D
\tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int
\tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
- \exp_after:wN \fp_trig_calc_aux:
+ \tex_expandafter:D \fp_trig_calc_Taylor:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_trig_calc_sin: {
@@ -1843,10 +1965,10 @@
\l_fp_trig_decimal_int \l_fp_input_a_decimal_int
\l_fp_trig_extended_int \l_fp_input_a_extended_int
\l_fp_count_int \c_two
- \exp_after:wN \fp_trig_calc_aux:
+ \tex_expandafter:D \fp_trig_calc_Taylor:
\tex_fi:D
}
-\cs_new_protected_nopar:Npn \fp_trig_calc_aux: {
+\cs_new_protected_nopar:Npn \fp_trig_calc_Taylor: {
\l_fp_trig_sign_int -\l_fp_trig_sign_int
\fp_mul:NNNNNN
\l_fp_trig_decimal_int \l_fp_trig_extended_int
@@ -1896,7 +2018,7 @@
\tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
\tex_fi:D
\tex_fi:D
- \exp_after:wN \fp_trig_calc_aux:
+ \tex_expandafter:D \fp_trig_calc_Taylor:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_tan:Nn {
@@ -1915,7 +2037,7 @@
\l_fp_input_a_integer_int
\l_fp_input_a_decimal_int
\l_fp_input_a_exponent_int
- \tl_set:Nx \l_fp_trig_arg_tl
+ \tl_set:Nx \l_fp_arg_tl
{
\tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
-
@@ -1924,7 +2046,7 @@
\tex_fi:D
\int_use:N \l_fp_input_a_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_input_a_decimal_int + \c_one_thousand_million
e
@@ -1934,32 +2056,32 @@
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
- #1 \exp_not:N #2 { \l_fp_trig_arg_tl }
+ #1 \exp_not:N #2 { \l_fp_arg_tl }
}
\tex_else:D
\etex_ifcsname:D
- c_fp_tan ( \l_fp_trig_arg_tl ) _tl
+ c_fp_tan ( \l_fp_arg_tl ) _fp
\tex_endcsname:D
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_tan_aux_i:
\tex_fi:D
\cs_set_protected_nopar:Npx \fp_tmp:w
{
\group_end:
#1 \exp_not:N #2
- { \use:c { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } }
+ { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } }
}
\tex_fi:D
\fp_tmp:w
}
\cs_new_protected_nopar:Npn \fp_tan_aux_i: {
\tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
- \exp_after:wN \fp_tan_aux_ii:
+ \tex_expandafter:D \fp_tan_aux_ii:
\tex_else:D
- \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
\c_zero_fp
- \exp_after:wN \fp_trig_overflow_msg:
+ \tex_expandafter:D \fp_trig_overflow_msg:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_tan_aux_ii: {
@@ -1967,14 +2089,14 @@
\fp_cos_aux_ii:
\tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
\tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
- \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
\c_undefined_fp
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_tan_aux_iii:
\tex_fi:D
\tex_else:D
- \exp_after:wN \fp_tan_aux_iii:
+ \tex_expandafter:D \fp_tan_aux_iii:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_tan_aux_iii: {
@@ -1997,14 +2119,14 @@
\l_fp_input_a_exponent_int
\tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
\tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
- \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
\c_zero_fp
\tex_else:D
- \exp_after:wN \exp_after:wN \exp_after:wN
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
\fp_tan_aux_iv:
\tex_fi:D
\tex_else:D
- \exp_after:wN \fp_tan_aux_iv:
+ \tex_expandafter:D \fp_tan_aux_iv:
\tex_fi:D
}
\cs_new_protected_nopar:Npn \fp_tan_aux_iv: {
@@ -2027,8 +2149,563 @@
\l_fp_output_integer_int
\l_fp_output_decimal_int
\l_fp_output_exponent_int
- \tl_new:c { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
- \tl_gset:cx { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+ \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp }
+ {
+ \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+ +
+ \tex_else:D
+ -
+ \tex_fi:D
+ \int_use:N \l_fp_output_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ \scan_stop:
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+}
+\tl_new:c { c_fp_exp_1_tl }
+\tl_set:cn { c_fp_exp_1_tl }
+ { { 2 } { 718281828 } { 459045235 } { 0 } }
+\tl_new:c { c_fp_exp_2_tl }
+\tl_set:cn { c_fp_exp_2_tl }
+ { { 7 } { 389056098 } { 930650227 } { 0 } }
+\tl_new:c { c_fp_exp_3_tl }
+\tl_set:cn { c_fp_exp_3_tl }
+ { { 2 } { 008553692 } { 318766774 } { 1 } }
+\tl_new:c { c_fp_exp_4_tl }
+\tl_set:cn { c_fp_exp_4_tl }
+ { { 5 } { 459815003 } { 314423908 } { 1 } }
+\tl_new:c { c_fp_exp_5_tl }
+\tl_set:cn { c_fp_exp_5_tl }
+ { { 1 } { 484131591 } { 025766034 } { 2 } }
+\tl_new:c { c_fp_exp_6_tl }
+\tl_set:cn { c_fp_exp_6_tl }
+ { { 4 } { 034287934 } { 927351226 } { 2 } }
+\tl_new:c { c_fp_exp_7_tl }
+\tl_set:cn { c_fp_exp_7_tl }
+ { { 1 } { 096633158 } { 428458599 } { 3 } }
+\tl_new:c { c_fp_exp_8_tl }
+\tl_set:cn { c_fp_exp_8_tl }
+ { { 2 } { 980957987 } { 041728275 } { 3 } }
+\tl_new:c { c_fp_exp_9_tl }
+\tl_set:cn { c_fp_exp_9_tl }
+ { { 8 } { 103083927 } { 575384008 } { 3 } }
+\tl_new:c { c_fp_exp_10_tl }
+\tl_set:cn { c_fp_exp_10_tl }
+ { { 2 } { 202646579 } { 480671652 } { 4 } }
+\tl_new:c { c_fp_exp_20_tl }
+\tl_set:cn { c_fp_exp_20_tl }
+ { { 4 } { 851651954 } { 097902280 } { 8 } }
+\tl_new:c { c_fp_exp_30_tl }
+\tl_set:cn { c_fp_exp_30_tl }
+ { { 1 } { 068647458 } { 152446215 } { 13 } }
+\tl_new:c { c_fp_exp_40_tl }
+\tl_set:cn { c_fp_exp_40_tl }
+ { { 2 } { 353852668 } { 370199854 } { 17 } }
+\tl_new:c { c_fp_exp_50_tl }
+\tl_set:cn { c_fp_exp_50_tl }
+ { { 5 } { 184705528 } { 587072464 } { 21 } }
+\tl_new:c { c_fp_exp_60_tl }
+\tl_set:cn { c_fp_exp_60_tl }
+ { { 1 } { 142007389 } { 815684284 } { 26 } }
+\tl_new:c { c_fp_exp_70_tl }
+\tl_set:cn { c_fp_exp_70_tl }
+ { { 2 } { 515438670 } { 919167006 } { 30 } }
+\tl_new:c { c_fp_exp_80_tl }
+\tl_set:cn { c_fp_exp_80_tl }
+ { { 5 } { 540622384 } { 393510053 } { 34 } }
+\tl_new:c { c_fp_exp_90_tl }
+\tl_set:cn { c_fp_exp_90_tl }
+ { { 1 } { 220403294 } { 317840802 } { 39 } }
+\tl_new:c { c_fp_exp_100_tl }
+\tl_set:cn { c_fp_exp_100_tl }
+ { { 2 } { 688117141 } { 816135448 } { 43 } }
+\tl_new:c { c_fp_exp_200_tl }
+\tl_set:cn { c_fp_exp_200_tl }
+ { { 7 } { 225973768 } { 125749258 } { 86 } }
+\tl_new:c { c_fp_exp_-1_tl }
+\tl_set:cn { c_fp_exp_-1_tl }
+ { { 3 } { 678794411 } { 71442322 } { -1 } }
+\tl_new:c { c_fp_exp_-2_tl }
+\tl_set:cn { c_fp_exp_-2_tl }
+ { { 1 } { 353352832 } { 366132692 } { -1 } }
+\tl_new:c { c_fp_exp_-3_tl }
+\tl_set:cn { c_fp_exp_-3_tl }
+ { { 4 } { 978706836 } { 786394298 } { -2 } }
+\tl_new:c { c_fp_exp_-4_tl }
+\tl_set:cn { c_fp_exp_-4_tl }
+ { { 1 } { 831563888 } { 873418029 } { -2 } }
+\tl_new:c { c_fp_exp_-5_tl }
+\tl_set:cn { c_fp_exp_-5_tl }
+ { { 6 } { 737946999 } { 085467097 } { -3 } }
+\tl_new:c { c_fp_exp_-6_tl }
+\tl_set:cn { c_fp_exp_-6_tl }
+ { { 2 } { 478752176 } { 666358423 } { -3 } }
+\tl_new:c { c_fp_exp_-7_tl }
+\tl_set:cn { c_fp_exp_-7_tl }
+ { { 9 } { 118819655 } { 545162080 } { -4 } }
+\tl_new:c { c_fp_exp_-8_tl }
+\tl_set:cn { c_fp_exp_-8_tl }
+ { { 3 } { 354626279 } { 025118388 } { -4 } }
+\tl_new:c { c_fp_exp_-9_tl }
+\tl_set:cn { c_fp_exp_-9_tl }
+ { { 1 } { 234098040 } { 866795495 } { -4 } }
+\tl_new:c { c_fp_exp_-10_tl }
+\tl_set:cn { c_fp_exp_-10_tl }
+ { { 4 } { 539992976 } { 248451536 } { -5 } }
+\tl_new:c { c_fp_exp_-20_tl }
+\tl_set:cn { c_fp_exp_-20_tl }
+ { { 2 } { 061153622 } { 438557828 } { -9 } }
+\tl_new:c { c_fp_exp_-30_tl }
+\tl_set:cn { c_fp_exp_-30_tl }
+ { { 9 } { 357622968 } { 840174605 } { -14 } }
+\tl_new:c { c_fp_exp_-40_tl }
+\tl_set:cn { c_fp_exp_-40_tl }
+ { { 4 } { 248354255 } { 291588995 } { -18 } }
+\tl_new:c { c_fp_exp_-50_tl }
+\tl_set:cn { c_fp_exp_-50_tl }
+ { { 1 } { 928749847 } { 963917783 } { -22 } }
+\tl_new:c { c_fp_exp_-60_tl }
+\tl_set:cn { c_fp_exp_-60_tl }
+ { { 8 } { 756510762 } { 696520338 } { -27 } }
+\tl_new:c { c_fp_exp_-70_tl }
+\tl_set:cn { c_fp_exp_-70_tl }
+ { { 3 } { 975449735 } { 908646808 } { -31 } }
+\tl_new:c { c_fp_exp_-80_tl }
+\tl_set:cn { c_fp_exp_-80_tl }
+ { { 1 } { 804851387 } { 845415172 } { -35 } }
+\tl_new:c { c_fp_exp_-90_tl }
+\tl_set:cn { c_fp_exp_-90_tl }
+ { { 8 } { 194012623 } { 990515430 } { -40 } }
+\tl_new:c { c_fp_exp_-100_tl }
+\tl_set:cn { c_fp_exp_-100_tl }
+ { { 3 } { 720075976 } { 020835963 } { -44 } }
+\tl_new:c { c_fp_exp_-200_tl }
+\tl_set:cn { c_fp_exp_-200_tl }
+ { { 1 } { 383896526 } { 736737530 } { -87 } }
+\cs_new_protected_nopar:Npn \fp_exp:Nn {
+ \fp_exp_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gexp:Nn {
+ \fp_exp_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_exp:Nn { c }
+\cs_generate_variant:Nn \fp_gexp:Nn { c }
+\cs_new_protected_nopar:Npn \fp_exp_aux:NNn #1#2#3 {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \l_fp_input_a_extended_int \c_zero
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+ -
+ \tex_else:D
+ +
+ \tex_fi:D
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp \tex_endcsname:D
+ \tex_else:D
+ \tex_expandafter:D \fp_exp_internal:
+ \tex_fi:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp
+ \tex_endcsname:D
+ \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ \tex_else:D
+ \c_zero_fp
+ \tex_fi:D
+ }
+ }
+ \fp_tmp:w
+}
+\cs_new_protected_nopar:Npn \fp_exp_internal: {
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_three
+ \fp_extended_normalise:
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_aux:
+ \tex_else:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_overflow_msg:
+ \tex_fi:D
+ \tex_else:D
+ \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_aux:
+ \tex_else:D
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ { \c_zero_fp }
+ \tex_fi:D
+ \tex_fi:D
+ \tex_else:D
+ \tex_expandafter:D \fp_exp_overflow_msg:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_aux: {
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+ \tex_expandafter:D \fp_exp_integer:
+ \tex_else:D
+ \l_fp_output_integer_int \c_one
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_extended_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \tex_expandafter:D \fp_exp_decimal:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer: {
+ \tex_ifnum:D \l_fp_input_a_integer_int < \c_one_hundred
+ \l_fp_exp_integer_int \c_one
+ \l_fp_exp_decimal_int \c_zero
+ \l_fp_exp_extended_int \c_zero
+ \l_fp_exp_exponent_int \c_zero
+ \tex_expandafter:D \fp_exp_integer_tens:
+ \tex_else:D
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \tex_expandafter:D \use_i:nnn
+ \int_use:N \l_fp_input_a_integer_int
+ }
+ \l_fp_input_a_integer_int
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int - \l_fp_tmp_tl 00
+ \scan_stop:
+ \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+ \tex_ifnum:D \l_fp_output_integer_int > 200 \scan_stop:
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ { \c_zero_fp }
+ \tex_else:D
+ \fp_exp_integer_const:n { - \l_fp_tmp_tl 00 }
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_integer_tens:
+ \tex_fi:D
+ \tex_else:D
+ \fp_exp_integer_const:n { \l_fp_tmp_tl 00 }
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_exp_integer_tens:
+ \tex_fi:D
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_tens: {
+ \l_fp_output_integer_int \l_fp_exp_integer_int
+ \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \l_fp_output_extended_int \l_fp_exp_extended_int
+ \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_nine
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \tex_expandafter:D \use_i:nn
+ \int_use:N \l_fp_input_a_integer_int
+ }
+ \l_fp_input_a_integer_int
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int - \l_fp_tmp_tl 0
+ \scan_stop:
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \fp_exp_integer_const:n { \l_fp_tmp_tl 0 }
+ \tex_else:D
+ \fp_exp_integer_const:n { - \l_fp_tmp_tl 0 }
+ \tex_fi:D
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \fp_extended_normalise_output:
+ \tex_fi:D
+ \fp_exp_integer_units:
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_units: {
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int }
+ \tex_else:D
+ \fp_exp_integer_const:n
+ { - \int_use:N \l_fp_input_a_integer_int }
+ \tex_fi:D
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \fp_extended_normalise_output:
+ \tex_fi:D
+ \fp_exp_decimal:
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_const:n #1 {
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_exp_integer_const:nnnn
+ \tex_csname:D c_fp_exp_ #1 _tl \tex_endcsname:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_const:nnnn #1#2#3#4 {
+ \l_fp_exp_integer_int #1 \scan_stop:
+ \l_fp_exp_decimal_int #2 \scan_stop:
+ \l_fp_exp_extended_int #3 \scan_stop:
+ \l_fp_exp_exponent_int #4 \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_exp_decimal: {
+ \tex_ifnum:D \l_fp_input_a_decimal_int > \c_zero
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \l_fp_exp_integer_int \c_one
+ \l_fp_exp_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_exp_extended_int \l_fp_input_a_extended_int
+ \tex_else:D
+ \l_fp_exp_integer_int \c_zero
+ \tex_ifnum:D \l_fp_exp_extended_int = \c_zero
+ \l_fp_exp_decimal_int
+ \etex_numexpr:D
+ \c_one_thousand_million - \l_fp_input_a_decimal_int
+ \scan_stop:
+ \l_fp_exp_extended_int \c_zero
+ \tex_else:D
+ \l_fp_exp_decimal_int
+ \etex_numexpr:D
+ 999999999 - \l_fp_input_a_decimal_int
+ \scan_stop:
+ \l_fp_exp_extended_int
+ \etex_numexpr:D
+ \c_one_thousand_million - \l_fp_input_a_extended_int
+ \scan_stop:
+ \tex_fi:D
+ \tex_fi:D
+ \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_extended_int \l_fp_input_a_extended_int
+ \l_fp_count_int \c_one
+ \fp_exp_Taylor:
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million
+ \tex_else:D
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+ \tex_else:D
+ \l_fp_output_decimal_int \c_zero
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_fi:D
+ \tex_fi:D
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ {
+ +
+ \int_use:N \l_fp_output_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ \scan_stop:
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+}
+\cs_new_protected_nopar:Npn \fp_exp_Taylor: {
+ \tex_advance:D \l_fp_count_int \c_one
+ \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \fp_div_integer:NNNNN
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_count_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int
+ > \c_zero
+ \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+ \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int
+ \tex_advance:D \l_fp_exp_extended_int
+ \l_fp_input_b_extended_int
+ \tex_ifnum:D \l_fp_exp_extended_int < \c_one_thousand_million
+ \tex_else:D
+ \tex_advance:D \l_fp_exp_decimal_int \c_one
+ \tex_advance:D \l_fp_exp_extended_int
+ -\c_one_thousand_million
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_exp_decimal_int < \c_one_thousand_million
+ \tex_else:D
+ \tex_advance:D \l_fp_exp_integer_int \c_one
+ \tex_advance:D \l_fp_exp_decimal_int
+ -\c_one_thousand_million
+ \tex_fi:D
+ \tex_else:D
+ \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int
+ \tex_advance:D \l_fp_exp_extended_int
+ -\l_fp_input_a_extended_int
+ \tex_ifnum:D \l_fp_exp_extended_int < \c_zero
+ \tex_advance:D \l_fp_exp_decimal_int \c_minus_one
+ \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_exp_decimal_int < \c_zero
+ \tex_advance:D \l_fp_exp_integer_int \c_minus_one
+ \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
+ \tex_fi:D
+ \tex_fi:D
+ \tex_expandafter:D \fp_exp_Taylor:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_const:Nx #1#2 {
+ \tl_new:N #1
+ \tl_gset:Nx #1 {#2}
+}
+\cs_generate_variant:Nn \fp_exp_const:Nx { c }
+\tl_new:c { c_fp_ln_10_1_tl }
+\tl_set:cn { c_fp_ln_10_1_tl }
+ { { 2 } { 302585092 } { 994045684 } { 0 } }
+\tl_new:c { c_fp_ln_10_2_tl }
+\tl_set:cn { c_fp_ln_10_2_tl }
+ { { 4 } { 605170185 } { 988091368 } { 0 } }
+\tl_new:c { c_fp_ln_10_3_tl }
+\tl_set:cn { c_fp_ln_10_3_tl }
+ { { 6 } { 907755278 } { 982137052 } { 0 } }
+\tl_new:c { c_fp_ln_10_4_tl }
+\tl_set:cn { c_fp_ln_10_4_tl }
+ { { 9 } { 210340371 } { 976182736 } { 0 } }
+\tl_new:c { c_fp_ln_10_5_tl }
+\tl_set:cn { c_fp_ln_10_5_tl }
+ { { 1 } { 151292546 } { 497022842 } { 1 } }
+\tl_new:c { c_fp_ln_10_6_tl }
+\tl_set:cn { c_fp_ln_10_6_tl }
+ { { 1 } { 381551055 } { 796427410 } { 1 } }
+\tl_new:c { c_fp_ln_10_7_tl }
+\tl_set:cn { c_fp_ln_10_7_tl }
+ { { 1 } { 611809565 } { 095831979 } { 1 } }
+\tl_new:c { c_fp_ln_10_8_tl }
+\tl_set:cn { c_fp_ln_10_8_tl }
+ { { 1 } { 842068074 } { 395226547 } { 1 } }
+\tl_new:c { c_fp_ln_10_9_tl }
+\tl_set:cn { c_fp_ln_10_9_tl }
+ { { 2 } { 072326583 } { 694641116 } { 1 } }
+\tl_new:c { c_fp_ln_2_1_tl }
+\tl_set:cn { c_fp_ln_2_1_tl }
+ { { 0 } { 693147180 } { 559945309 } { 0 } }
+\tl_new:c { c_fp_ln_2_2_tl }
+\tl_set:cn { c_fp_ln_2_2_tl }
+ { { 1 } { 386294361 } { 119890618 } { 0 } }
+\tl_new:c { c_fp_ln_2_3_tl }
+\tl_set:cn { c_fp_ln_2_3_tl }
+ { { 2 } { 079441541 } { 679835928 } { 0 } }
+\cs_new_protected_nopar:Npn \fp_ln:Nn {
+ \fp_ln_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gln:Nn {
+ \fp_ln_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_ln:Nn { c }
+\cs_generate_variant:Nn \fp_gln:Nn { c }
+\cs_new_protected_nopar:Npn \fp_ln_aux:NNn #1#2#3 {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ > \c_zero
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_ln_aux:
+ \tex_else:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2 { \c_zero_fp }
+ }
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_ln_error_msg:
+ \tex_fi:D
+ \tex_else:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2 { \c_zero_fp }
+ }
+ \tex_expandafter:D \fp_ln_error_msg:
+ \tex_fi:D
+ \fp_tmp:w #1 #2
+}
+\cs_new_protected_nopar:Npn \fp_ln_aux: {
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ +
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \etex_ifcsname:D c_fp_ln ( \l_fp_arg_tl ) _fp \tex_endcsname:D
+ \tex_else:D
+ \tex_expandafter:D \fp_ln_exponent:
+ \tex_fi:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2
+ { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } }
+ }
+}
+\cs_new_protected_nopar:Npn \fp_ln_exponent: {
+ \fp_ln_internal:
+ \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million
+ \tex_else:D
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+ \tex_else:D
+ \l_fp_output_decimal_int \c_zero
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_fi:D
+ \tex_fi:D
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \tl_new:c { c_fp_ln ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_ln ( \l_fp_arg_tl ) _fp }
{
\tex_ifnum:D \l_fp_output_sign_int > \c_zero
+
@@ -2037,7 +2714,7 @@
\tex_fi:D
\int_use:N \l_fp_output_integer_int
.
- \exp_after:wN \use_none:n
+ \tex_expandafter:D \use_none:n
\tex_number:D \etex_numexpr:D
\l_fp_output_decimal_int + \c_one_thousand_million
\scan_stop:
@@ -2045,21 +2722,445 @@
\int_use:N \l_fp_output_exponent_int
}
}
-\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF } {
+\cs_new_protected_nopar:Npn \fp_ln_internal: {
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero
+ \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int
+ \l_fp_output_sign_int \c_minus_one
+ \tex_else:D
+ \l_fp_output_sign_int \c_one
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_input_a_exponent_int > \c_nine
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \tex_expandafter:D \use_i:nn
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \l_fp_input_a_exponent_int
+ \etex_numexpr:D
+ \l_fp_input_a_exponent_int - \l_fp_tmp_tl 0
+ \scan_stop:
+ \fp_ln_const:nn { 10 } { \l_fp_tmp_tl }
+ \tex_advance:D \l_fp_exp_exponent_int \c_one
+ \l_fp_output_integer_int \l_fp_exp_integer_int
+ \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \l_fp_output_extended_int \l_fp_exp_extended_int
+ \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \tex_else:D
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_extended_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \tex_fi:D
+ \fp_ln_exponent_units:
+}
+\cs_new_protected_nopar:Npn \fp_ln_exponent_units: {
+ \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero
+ \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int }
+ \fp_ln_normalise:
+ \fp_add:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_fi:D
+ \fp_ln_mantissa:
+}
+\cs_new_protected_nopar:Npn \fp_ln_normalise: {
+ \tex_ifnum:D \l_fp_exp_exponent_int < \l_fp_output_exponent_int
+ \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
+ \fp_ln_normalise_aux:NNNNNNNNN
+ \int_use:N \l_fp_exp_decimal_int
+ \tex_expandafter:D \fp_ln_normalise:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+ \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \tex_ifnum:D \l_fp_exp_integer_int = \c_zero
+ \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_else:D
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \int_use:N \l_fp_exp_integer_int
+ #1#2#3#4#5#6#7#8
+ }
+ \l_fp_exp_integer_int \c_zero
+ \l_fp_exp_decimal_int \l_fp_tmp_tl \scan_stop:
+ \tex_fi:D
+ \tex_divide:D \l_fp_exp_extended_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \int_use:N \l_fp_exp_extended_int
+ }
+ \l_fp_exp_extended_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_exp_exponent_int \c_one
+}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa: {
+ \l_fp_count_int \c_zero
+ \l_fp_input_a_extended_int \c_zero
+ \fp_ln_mantissa_aux:
+ \tex_ifnum:D \l_fp_count_int > \c_zero
+ \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int }
+ \fp_ln_normalise:
+ \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+ \tex_expandafter:D \fp_add:NNNNNNNNN
+ \tex_else:D
+ \tex_expandafter:D \fp_sub:NNNNNNNNN
+ \tex_fi:D
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_fi:D
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one
+ \scan_stop:
+ \tex_expandafter:D \fp_ln_Taylor:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa_aux: {
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_one
+ \tex_advance:D \l_fp_count_int \c_one
+ \fp_ln_mantissa_divide_two:
+ \tex_expandafter:D \fp_ln_mantissa_aux:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two: {
+ \tex_ifodd:D \l_fp_input_a_decimal_int
+ \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+ \tex_fi:D
+ \tex_ifodd:D \l_fp_input_a_integer_int
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \tex_fi:D
+ \tex_divide:D \l_fp_input_a_integer_int \c_two
+ \tex_divide:D \l_fp_input_a_decimal_int \c_two
+ \tex_divide:D \l_fp_input_a_extended_int \c_two
+}
+\cs_new_protected_nopar:Npn \fp_ln_const:nn #1#2 {
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_exp_integer_const:nnnn
+ \tex_csname:D c_fp_ln_ #1 _ #2 _tl \tex_endcsname:D
+}
+\cs_new_protected_nopar:Npn \fp_ln_Taylor: {
+ \group_begin:
+ \l_fp_input_a_integer_int \c_zero
+ \l_fp_input_a_exponent_int \c_zero
+ \l_fp_input_b_integer_int \c_two
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_exponent_int \c_zero
+ \fp_div_internal:
+ \fp_ln_fixed:
+ \l_fp_input_a_integer_int \l_fp_output_integer_int
+ \l_fp_input_a_decimal_int \l_fp_output_decimal_int
+ \l_fp_input_a_exponent_int \l_fp_output_exponent_int
+ \l_fp_input_a_extended_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_output_extended_int \l_fp_input_a_extended_int
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_count_int \c_one
+ \fp_ln_Taylor_aux:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ \exp_not:N \l_fp_exp_decimal_int
+ \int_use:N \l_fp_output_decimal_int \scan_stop:
+ \exp_not:N \l_fp_exp_extended_int
+ \int_use:N \l_fp_output_extended_int \scan_stop:
+ \exp_not:N \l_fp_exp_exponent_int
+ \int_use:N \l_fp_output_exponent_int \scan_stop:
+ }
+ \fp_tmp:w
+ \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int
+ \tex_ifnum:D \l_fp_exp_extended_int < \c_five_hundred_million
+ \tex_else:D
+ \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million
+ \tex_advance:D \l_fp_exp_decimal_int \c_one
+ \tex_fi:D
+ \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int
+ \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+ \tex_expandafter:D \fp_add:NNNNNNNNN
+ \tex_else:D
+ \tex_expandafter:D \fp_sub:NNNNNNNNN
+ \tex_fi:D
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+}
+\cs_new_protected_nopar:Npn \fp_ln_fixed: {
+ \tex_ifnum:D \l_fp_output_exponent_int < \c_zero
+ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+ \tex_expandafter:D \use_i:nn \tex_expandafter:D
+ \fp_ln_fixed_aux:NNNNNNNNN
+ \int_use:N \l_fp_output_decimal_int
+ \tex_expandafter:D \fp_ln_fixed:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+ \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+ \tex_ifnum:D \l_fp_output_integer_int = \c_zero
+ \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_else:D
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \int_use:N \l_fp_output_integer_int
+ #1#2#3#4#5#6#7#8
+ }
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \l_fp_tmp_tl \scan_stop:
+ \tex_fi:D
+ \tex_advance:D \l_fp_output_exponent_int \c_one
+}
+\cs_new_protected_nopar:Npn \fp_ln_Taylor_aux: {
+ \tex_advance:D \l_fp_count_int \c_two
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+ > \c_zero
+ \fp_div_integer:NNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_count_int
+ \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int
+ \tex_ifnum:D \l_fp_output_extended_int < \c_one_thousand_million
+ \tex_else:D
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \tex_advance:D \l_fp_output_extended_int
+ -\c_one_thousand_million
+ \tex_fi:D
+ \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+ \tex_else:D
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_advance:D \l_fp_output_decimal_int
+ -\c_one_thousand_million
+ \tex_fi:D
+ \tex_expandafter:D \fp_ln_Taylor_aux:
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_pow:Nn {
+ \fp_pow_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gpow:Nn {
+ \fp_pow_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_pow:Nn { c }
+\cs_generate_variant:Nn \fp_gpow:Nn { c }
+\cs_new_protected_nopar:Npn \fp_pow_aux:NNn #1#2#3 {
+ \group_begin:
+ \fp_read:N #2
+ \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \l_fp_input_b_integer_int \l_fp_input_a_integer_int
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+ = \c_zero
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ = \c_zero
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \tex_else:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_zero_fp }
+ }
+ \tex_fi:D
+ \tex_else:D
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ = \c_zero
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_one_fp }
+ }
+ \tex_else:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_pow_aux_i:
+ \tex_fi:D
+ \tex_fi:D
+ \fp_tmp:w #1 #2
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_i: {
+ \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+ \tl_set:Nn \l_fp_sign_tl { + }
+ \tex_expandafter:D \fp_pow_aux_ii:
+ \tex_else:D
+ \l_fp_input_a_extended_int \c_zero
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+ \group_begin:
+ \fp_extended_normalise:
+ \tex_ifnum:D
+ \etex_numexpr:D
+ \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+ = \c_zero
+ \group_end:
+ \tl_set:Nn \l_fp_sign_tl { - }
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_pow_aux_ii:
+ \tex_else:D
+ \group_end:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \tex_fi:D
+ \tex_else:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \tex_fi:D
+ \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_ii: {
+ \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+ \tex_expandafter:D \fp_pow_aux_iv:
+ \tex_else:D
+ \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+ \group_begin:
+ \l_fp_input_a_extended_int \c_zero
+ \fp_extended_normalise:
+ \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
+ \tex_ifnum:D \l_fp_input_a_integer_int > \c_ten
+ \group_end:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_pow_aux_iv:
+ \tex_else:D
+ \group_end:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_pow_aux_iii:
+ \tex_fi:D
+ \tex_else:D
+ \group_end:
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \tex_expandafter:D \fp_pow_aux_iv:
+ \tex_fi:D
+ \tex_else:D
+ \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+ \fp_pow_aux_iv:
+ \tex_fi:D
+ \tex_fi:D
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2
+ {
+ \l_fp_sign_tl
+ \int_use:N \l_fp_output_integer_int
+ .
+ \tex_expandafter:D \use_none:n
+ \tex_number:D \etex_numexpr:D
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ \scan_stop:
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_iii: {
+ \l_fp_input_a_sign_int \c_one
+ \fp_pow_aux_iv:
+ \l_fp_input_a_integer_int \c_one
+ \l_fp_input_a_decimal_int \c_zero
+ \l_fp_input_a_exponent_int \c_zero
+ \l_fp_input_b_integer_int \l_fp_output_integer_int
+ \l_fp_input_b_decimal_int \l_fp_output_decimal_int
+ \l_fp_input_b_exponent_int \l_fp_output_exponent_int
+ \fp_div_internal:
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_iv: {
+ \group_begin:
+ \l_fp_input_a_integer_int \l_fp_input_b_integer_int
+ \l_fp_input_a_decimal_int \l_fp_input_b_decimal_int
+ \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
+ \fp_ln_internal:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ \exp_not:N \l_fp_input_b_sign_int
+ \int_use:N \l_fp_output_sign_int \scan_stop:
+ \exp_not:N \l_fp_input_b_integer_int
+ \int_use:N \l_fp_output_integer_int \scan_stop:
+ \exp_not:N \l_fp_input_b_decimal_int
+ \int_use:N \l_fp_output_decimal_int \scan_stop:
+ \exp_not:N \l_fp_input_b_extended_int
+ \int_use:N \l_fp_output_extended_int \scan_stop:
+ \exp_not:N \l_fp_input_b_exponent_int
+ \int_use:N \l_fp_output_exponent_int \scan_stop:
+ }
+ \fp_tmp:w
+ \l_fp_input_a_extended_int \c_zero
+ \fp_mul:NNNNNNNNN
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \l_fp_input_b_integer_int \l_fp_input_b_decimal_int
+ \l_fp_input_b_extended_int
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \tex_advance:D \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn
+ \fp_exp_internal:
+}
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { T , F , TF , p } {
\tex_ifx:D #1 \c_undefined_fp
\prg_return_true:
\tex_else:D
\prg_return_false:
\tex_fi:D
}
-\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF } {
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { T , F , TF , p } {
\tex_ifx:D #1 \c_zero_fp
\prg_return_true:
\tex_else:D
\prg_return_false:
\tex_fi:D
}
-\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF }
+\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3
+ { T , F , TF }
{
\group_begin:
\fp_split:Nn a {#1}
@@ -2076,7 +3177,8 @@
\l_fp_input_b_exponent_int
\fp_compare_aux:N #2
}
-\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 { T , F , TF }
+\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3
+ { T , F , TF }
{
\group_begin:
\fp_read:N #3
@@ -2265,6 +3367,21 @@
\cs_new_protected_nopar:Npn \fp_overflow_msg: {
\msg_kernel_error:nn { fpu } { overflow }
}
+\msg_kernel_new:nnnn { fpu } { exponent-overflow }
+ { Number~too~big~for~exponent~unit. }
+ {
+ The~exponent~of~the~input~given~is~too~big~for~the~floating~point~
+ unit:~the~maximum~input~value~for~an~exponent~is~230.
+ }
+\cs_new_protected_nopar:Npn \fp_exp_overflow_msg: {
+ \msg_kernel_error:nn { fpu } { exponent-overflow }
+}
+\msg_kernel_new:nnnn { fpu } { logarithm-input-error }
+ { Invalid~input~to~ln~function. }
+ { Logarithms~can~only~be~calculated~for~positive~numbers. }
+\cs_new_protected_nopar:Npn \fp_ln_error_msg: {
+ \msg_kernel_error:nn { fpu } { logarithm-input-error }
+}
\msg_kernel_new:nnnn { fpu } { trigonometric-overflow }
{ Number~too~big~for~trigonometry~unit. }
{
diff --git a/Master/texmf-dist/tex/latex/expl3/l3tl.sty b/Master/texmf-dist/tex/latex/expl3/l3tl.sty
index 14719daf74b..cd8125b8d1b 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3tl.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3tl.sty
@@ -48,7 +48,7 @@
%%
%% -----------------------------------------------------------------------
\RequirePackage{l3names}
-\GetIdInfo$Id: l3tl.dtx 2084 2010-11-17 19:12:14Z joseph $
+\GetIdInfo$Id: l3tl.dtx 2103 2010-12-18 07:40:03Z joseph $
{L3 Experimental Token Lists}
\ProvidesExplPackage
{\filename}{\filedate}{\fileversion}{\filedescription}
@@ -235,7 +235,7 @@
\tl_set:Nn \l_tl_tmpb_tl {#2}
\tex_ifx:D \l_tl_tmpa_tl \l_tl_tmpb_tl
\group_end:
- \prg_return_false:
+ \prg_return_true:
\tex_else:D
\group_end:
\prg_return_false: