diff options
Diffstat (limited to 'Master/texmf-dist/source/latex/l3kernel/l3fp.dtx')
-rw-r--r-- | Master/texmf-dist/source/latex/l3kernel/l3fp.dtx | 268 |
1 files changed, 134 insertions, 134 deletions
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx index 9f871243bd5..e7214655937 100644 --- a/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx +++ b/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx @@ -49,7 +49,7 @@ % }^^A % } % -% \date{Released 2023-02-07} +% \date{Released 2023-02-22} % % \maketitle % @@ -58,8 +58,8 @@ % A decimal floating point number is one which is stored as a significand and a % separate exponent. The module implements expandably a wide set of % arithmetic, trigonometric, and other operations on decimal floating point -% numbers, to be used within floating point expressions. Floating point -% expressions support the following operations with their usual +% numbers, to be used within floating point expressions. \emph{Floating point +% expressions} (\enquote{\meta{fp expr}}) support the following operations with their usual % precedence. % \begin{itemize} % \item Basic arithmetic: addition $x+y$, subtraction $x-y$, @@ -170,11 +170,11 @@ % \begin{function}[updated = 2012-05-08, tested = m3fp001] % {\fp_const:Nn, \fp_const:cn} % \begin{syntax} -% \cs{fp_const:Nn} \meta{fp~var} \Arg{floating point expression} +% \cs{fp_const:Nn} \meta{fp~var} \Arg{fp expr} % \end{syntax} % Creates a new constant \meta{fp~var} or raises an error if the name % is already taken. The \meta{fp~var} is set globally equal to -% the result of evaluating the \meta{floating point expression}. +% the result of evaluating the \meta{fp expr}. % \end{function} % % \begin{function}[updated = 2012-05-08, tested = m3fp001] @@ -200,10 +200,10 @@ % \begin{function}[updated = 2012-05-08, tested = m3fp002] % {\fp_set:Nn, \fp_set:cn, \fp_gset:Nn, \fp_gset:cn} % \begin{syntax} -% \cs{fp_set:Nn} \meta{fp~var} \Arg{floating point expression} +% \cs{fp_set:Nn} \meta{fp~var} \Arg{fp expr} % \end{syntax} % Sets \meta{fp~var} equal to the result of computing the -% \meta{floating point expression}. +% \meta{fp expr}. % \end{function} % % \begin{function}[updated = 2012-05-08, tested = m3fp002] @@ -221,9 +221,9 @@ % \begin{function}[updated = 2012-05-08, tested = m3fp002] % {\fp_add:Nn, \fp_add:cn, \fp_gadd:Nn, \fp_gadd:cn} % \begin{syntax} -% \cs{fp_add:Nn} \meta{fp~var} \Arg{floating point expression} +% \cs{fp_add:Nn} \meta{fp~var} \Arg{fp expr} % \end{syntax} -% Adds the result of computing the \meta{floating point expression} to +% Adds the result of computing the \meta{fp expr} to % the \meta{fp~var}. % This also applies if \meta{fp~var} and \meta{floating point % expression} evaluate to tuples of the same size. @@ -232,7 +232,7 @@ % \begin{function}[updated = 2012-05-08, tested = m3fp002] % {\fp_sub:Nn, \fp_sub:cn, \fp_gsub:Nn, \fp_gsub:cn} % \begin{syntax} -% \cs{fp_sub:Nn} \meta{fp~var} \Arg{floating point expression} +% \cs{fp_sub:Nn} \meta{fp~var} \Arg{fp expr} % \end{syntax} % Subtracts the result of computing the \meta{floating point % expression} from the \meta{fp~var}. @@ -245,9 +245,9 @@ % \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08, % tested = m3fp-convert003]{\fp_eval:n} % \begin{syntax} -% \cs{fp_eval:n} \Arg{floating point expression} +% \cs{fp_eval:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression} and expresses the +% Evaluates the \meta{fp expr} and expresses the % result as a decimal number with no % exponent. Leading or trailing zeros may be inserted to compensate % for the exponent. Non-significant trailing zeros are trimmed, and @@ -262,9 +262,9 @@ % % \begin{function}[EXP, added = 2018-11-03]{\fp_sign:n} % \begin{syntax} -% \cs{fp_sign:n} \Arg{fpexpr} +% \cs{fp_sign:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{fpexpr} and leaves its sign in the input stream +% Evaluates the \meta{fp expr} and leaves its sign in the input stream % using \cs{fp_eval:n} |{sign(|\meta{result}|)}|: $+1$ for positive % numbers and for $+\infty$, $-1$ for negative numbers and for % $-\infty$, $\pm 0$ for $\pm 0$. If the operand is a tuple or is @@ -276,9 +276,9 @@ % {\fp_to_decimal:N, \fp_to_decimal:c, \fp_to_decimal:n} % \begin{syntax} % \cs{fp_to_decimal:N} \meta{fp~var} -% \cs{fp_to_decimal:n} \Arg{floating point expression} +% \cs{fp_to_decimal:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression} and expresses the +% Evaluates the \meta{fp expr} and expresses the % result as a decimal number with no % exponent. Leading or trailing zeros may be inserted to compensate % for the exponent. Non-significant trailing zeros are trimmed, and @@ -294,9 +294,9 @@ % {\fp_to_dim:N, \fp_to_dim:c, \fp_to_dim:n} % \begin{syntax} % \cs{fp_to_dim:N} \meta{fp~var} -% \cs{fp_to_dim:n} \Arg{floating point expression} +% \cs{fp_to_dim:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression} and expresses the +% Evaluates the \meta{fp expr} and expresses the % result as a dimension (in~\texttt{pt}) suitable for use in dimension % expressions. The output is identical to \cs{fp_to_decimal:n}, with % an additional trailing~\texttt{pt} (both letter tokens). @@ -311,9 +311,9 @@ % {\fp_to_int:N, \fp_to_int:c, \fp_to_int:n} % \begin{syntax} % \cs{fp_to_int:N} \meta{fp~var} -% \cs{fp_to_int:n} \Arg{floating point expression} +% \cs{fp_to_int:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression}, and rounds the +% Evaluates the \meta{fp expr}, and rounds the % result to the closest integer, rounding exact ties to an even % integer. % The result may be outside the range $[- 2^{31} + 1, 2^{31} - 1]$ of @@ -326,9 +326,9 @@ % {\fp_to_scientific:N, \fp_to_scientific:c, \fp_to_scientific:n} % \begin{syntax} % \cs{fp_to_scientific:N} \meta{fp~var} -% \cs{fp_to_scientific:n} \Arg{floating point expression} +% \cs{fp_to_scientific:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression} and expresses the +% Evaluates the \meta{fp expr} and expresses the % result in scientific notation: % \begin{quote} % \meta{optional \texttt{-}}\meta{digit}\texttt{.}\meta{15 digits}\texttt{e}\meta{optional sign}\meta{exponent} @@ -346,9 +346,9 @@ % {\fp_to_tl:N, \fp_to_tl:c, \fp_to_tl:n} % \begin{syntax} % \cs{fp_to_tl:N} \meta{fp~var} -% \cs{fp_to_tl:n} \Arg{floating point expression} +% \cs{fp_to_tl:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression} and expresses the +% Evaluates the \meta{fp expr} and expresses the % result in (almost) the shortest possible form. Numbers in the % ranges $(0,10^{-3})$ and $[10^{16},\infty)$ are expressed in % scientific notation with trailing zeros trimmed and no decimal @@ -398,10 +398,10 @@ % \begin{function}[EXP, pTF, updated = 2012-05-08, % tested = m3fp-logic001]{\fp_compare:nNn} % \begin{syntax} -% \cs{fp_compare_p:nNn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} -% \cs{fp_compare:nNnTF} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{true code} \Arg{false code} +% \cs{fp_compare_p:nNn} \Arg{fp expr_1} \meta{relation} \Arg{fp expr_2} +% \cs{fp_compare:nNnTF} \Arg{fp expr_1} \meta{relation} \Arg{fp expr_2} \Arg{true code} \Arg{false code} % \end{syntax} -% Compares the \meta{fpexpr_1} and the \meta{fpexpr_2}, and returns +% Compares the \meta{fp expr_1} and the \meta{fp expr_2}, and returns % \texttt{true} if the \meta{relation} is obeyed. Two floating points % $x$ and~$y$ may obey four mutually exclusive relations: % $x<y$, $x=y$, $x>y$, or $x?y$ (\enquote{not ordered}). The last @@ -430,30 +430,30 @@ % \begin{syntax} % \cs{fp_compare_p:n} \\ % ~~\{ \\ -% ~~~~\meta{fpexpr_1} \meta{relation_1} \\ +% ~~~~\meta{fp expr_1} \meta{relation_1} \\ % ~~~~\ldots{} \\ -% ~~~~\meta{fpexpr_N} \meta{relation_N} \\ -% ~~~~\meta{fpexpr_{N+1}} \\ +% ~~~~\meta{fp expr_N} \meta{relation_N} \\ +% ~~~~\meta{fp expr_{N+1}} \\ % ~~\} \\ % \cs{fp_compare:nTF} % ~~\{ \\ -% ~~~~\meta{fpexpr_1} \meta{relation_1} \\ +% ~~~~\meta{fp expr_1} \meta{relation_1} \\ % ~~~~\ldots{} \\ -% ~~~~\meta{fpexpr_N} \meta{relation_N} \\ -% ~~~~\meta{fpexpr_{N+1}} \\ +% ~~~~\meta{fp expr_N} \meta{relation_N} \\ +% ~~~~\meta{fp expr_{N+1}} \\ % ~~\} \\ % ~~\Arg{true code} \Arg{false code} % \end{syntax} -% Evaluates the \meta{floating point expressions} as described for +% Evaluates the \meta{fp exprs} as described for % \cs{fp_eval:n} and compares consecutive result using the -% corresponding \meta{relation}, namely it compares \meta{fpexpr_1} -% and \meta{fpexpr_2} using the \meta{relation_1}, then -% \meta{fpexpr_2} and \meta{fpexpr_3} using the \meta{relation_2}, -% until finally comparing \meta{fpexpr_N} and \meta{fpexpr_{N+1}} +% corresponding \meta{relation}, namely it compares \meta{fp expr_1} +% and \meta{fp expr_2} using the \meta{relation_1}, then +% \meta{fp expr_2} and \meta{fp expr_3} using the \meta{relation_2}, +% until finally comparing \meta{fp expr_N} and \meta{fp expr_{N+1}} % using the \meta{relation_N}. The test yields \texttt{true} if all % comparisons are \texttt{true}. Each \meta{floating point % expression} is evaluated only once. Contrarily to -% \cs{int_compare:nTF}, all \meta{floating point expressions} are +% \cs{int_compare:nTF}, all \meta{fp exprs} are % computed, even if one comparison is \texttt{false}. Two floating % points $x$ and~$y$ may obey four mutually exclusive % relations: $x<y$, $x=y$, $x>y$, or $x?y$ (\enquote{not ordered}). @@ -481,7 +481,7 @@ % \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003] % {\fp_do_until:nNnn} % \begin{syntax} -% \cs{fp_do_until:nNnn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{code} +% \cs{fp_do_until:nNnn} \Arg{fp expr_1} \meta{relation} \Arg{fp expr_2} \Arg{code} % \end{syntax} % Places the \meta{code} in the input stream for \TeX{} to process, % and then evaluates the relationship between the two \meta{floating @@ -494,7 +494,7 @@ % \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003] % {\fp_do_while:nNnn} % \begin{syntax} -% \cs{fp_do_while:nNnn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{code} +% \cs{fp_do_while:nNnn} \Arg{fp expr_1} \meta{relation} \Arg{fp expr_2} \Arg{code} % \end{syntax} % Places the \meta{code} in the input stream for \TeX{} to process, % and then evaluates the relationship between the two \meta{floating @@ -507,7 +507,7 @@ % \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003] % {\fp_until_do:nNnn} % \begin{syntax} -% \cs{fp_until_do:nNnn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{code} +% \cs{fp_until_do:nNnn} \Arg{fp expr_1} \meta{relation} \Arg{fp expr_2} \Arg{code} % \end{syntax} % Evaluates the relationship between the two \meta{floating point % expressions} as described for \cs{fp_compare:nNnTF}, and then @@ -520,7 +520,7 @@ % \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003] % {\fp_while_do:nNnn} % \begin{syntax} -% \cs{fp_while_do:nNnn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{code} +% \cs{fp_while_do:nNnn} \Arg{fp expr_1} \meta{relation} \Arg{fp expr_2} \Arg{code} % \end{syntax} % Evaluates the relationship between the two \meta{floating point % expressions} as described for \cs{fp_compare:nNnTF}, and then @@ -533,7 +533,7 @@ % \begin{function}[rEXP, added = 2012-08-16, updated = 2013-12-14, tested = m3fp-logic003] % {\fp_do_until:nn} % \begin{syntax} -% \cs{fp_do_until:nn} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{code} +% \cs{fp_do_until:nn} \{ \meta{fp expr_1} \meta{relation} \meta{fp expr_2} \} \Arg{code} % \end{syntax} % Places the \meta{code} in the input stream for \TeX{} to process, % and then evaluates the relationship between the two \meta{floating @@ -546,7 +546,7 @@ % \begin{function}[rEXP, added = 2012-08-16, updated = 2013-12-14, tested = m3fp-logic003] % {\fp_do_while:nn} % \begin{syntax} -% \cs{fp_do_while:nn} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{code} +% \cs{fp_do_while:nn} \{ \meta{fp expr_1} \meta{relation} \meta{fp expr_2} \} \Arg{code} % \end{syntax} % Places the \meta{code} in the input stream for \TeX{} to process, % and then evaluates the relationship between the two \meta{floating @@ -559,7 +559,7 @@ % \begin{function}[rEXP, added = 2012-08-16, updated = 2013-12-14, tested = m3fp-logic003] % {\fp_until_do:nn} % \begin{syntax} -% \cs{fp_until_do:nn} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{code} +% \cs{fp_until_do:nn} \{ \meta{fp expr_1} \meta{relation} \meta{fp expr_2} \} \Arg{code} % \end{syntax} % Evaluates the relationship between the two \meta{floating point % expressions} as described for \cs{fp_compare:nTF}, and then places @@ -572,7 +572,7 @@ % \begin{function}[rEXP, added = 2012-08-16, updated = 2013-12-14, tested = m3fp-logic003] % {\fp_while_do:nn} % \begin{syntax} -% \cs{fp_while_do:nn} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{code} +% \cs{fp_while_do:nn} \{ \meta{fp expr_1} \meta{relation} \meta{fp expr_2} \} \Arg{code} % \end{syntax} % Evaluates the relationship between the two \meta{floating point % expressions} as described for \cs{fp_compare:nTF}, and then places @@ -773,9 +773,9 @@ % tested = m3fp002]{\fp_show:N, \fp_show:c, \fp_show:n} % \begin{syntax} % \cs{fp_show:N} \meta{fp~var} -% \cs{fp_show:n} \Arg{floating point expression} +% \cs{fp_show:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression} and displays the +% Evaluates the \meta{fp expr} and displays the % result in the terminal. % \end{function} % @@ -783,9 +783,9 @@ % {\fp_log:N, \fp_log:c, \fp_log:n} % \begin{syntax} % \cs{fp_log:N} \meta{fp~var} -% \cs{fp_log:n} \Arg{floating point expression} +% \cs{fp_log:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression} and writes the +% Evaluates the \meta{fp expr} and writes the % result in the log file. % \end{function} % @@ -1036,27 +1036,27 @@ % % \begin{function}[tested = m3fp-basics004]{abs} % \begin{syntax} -% \cs{fp_eval:n} \{ |abs(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |abs(| \meta{fp expr} |)| \} % \end{syntax} -% Computes the absolute value of the \meta{fpexpr}. If the operand is +% Computes the absolute value of the \meta{fp expr}. If the operand is % a tuple, \enquote{invalid operation} occurs. This operation does % not raise exceptions in other cases. See also \cs{fp_abs:n}. % \end{function} % % \begin{function}[tested = m3fp-expo001]{exp} % \begin{syntax} -% \cs{fp_eval:n} \{ |exp(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |exp(| \meta{fp expr} |)| \} % \end{syntax} -% Computes the exponential of the \meta{fpexpr}. \enquote{Underflow} +% Computes the exponential of the \meta{fp expr}. \enquote{Underflow} % and \enquote{overflow} occur when appropriate. % If the operand is a tuple, \enquote{invalid operation} occurs. % \end{function} % % \begin{function}[tested = m3fp-expo001]{fact} % \begin{syntax} -% \cs{fp_eval:n} \{ |fact(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |fact(| \meta{fp expr} |)| \} % \end{syntax} -% Computes the factorial of the \meta{fpexpr}. If the \meta{fpexpr} +% Computes the factorial of the \meta{fp expr}. If the \meta{fp expr} % is an integer between $-0$ and $3248$ included, the result is finite % and correctly rounded. Larger positive integers give $+\infty$ with % \enquote{overflow}, while $|fact(|{+\infty}|)|=+\infty$ and @@ -1066,9 +1066,9 @@ % % \begin{function}[tested = m3fp-expo001]{ln} % \begin{syntax} -% \cs{fp_eval:n} \{ |ln(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |ln(| \meta{fp expr} |)| \} % \end{syntax} -% Computes the natural logarithm of the \meta{fpexpr}. Negative +% Computes the natural logarithm of the \meta{fp expr}. Negative % numbers have no (real) logarithm, hence the \enquote{invalid % operation} is raised in that case, including for $\ln(-0)$. % \enquote{Division by zero} occurs when evaluating @@ -1079,9 +1079,9 @@ % % \begin{function}[EXP, added = 2018-11-03]{logb} % \begin{syntax} -% \cs{fp_eval:n} \{ |logb(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |logb(| \meta{fp expr} |)| \} % \end{syntax} -% Determines the exponent of the \meta{fpexpr}, namely the floor of +% Determines the exponent of the \meta{fp expr}, namely the floor of % the base-$10$ logarithm of its absolute value. \enquote{Division by % zero} occurs when evaluating $\operatorname{logb}(\pm 0) = -\infty$. % Other special values are $\operatorname{logb}(\pm\infty)=+\infty$ @@ -1092,11 +1092,11 @@ % % \begin{function}[tested = m3fp-logic002]{max, min} % \begin{syntax} -% \cs{fp_eval:n} \{ |max(| \meta{fpexpr_1} |,| \meta{fpexpr_2} |,| \ldots{} |)| \} -% \cs{fp_eval:n} \{ |min(| \meta{fpexpr_1} |,| \meta{fpexpr_2} |,| \ldots{} |)| \} +% \cs{fp_eval:n} \{ |max(| \meta{fp expr_1} |,| \meta{fp expr_2} |,| \ldots{} |)| \} +% \cs{fp_eval:n} \{ |min(| \meta{fp expr_1} |,| \meta{fp expr_2} |,| \ldots{} |)| \} % \end{syntax} -% Evaluates each \meta{fpexpr} and computes the largest (smallest) of -% those. If any of the \meta{fpexpr} is a \nan{} or tuple, the result +% Evaluates each \meta{fp expr} and computes the largest (smallest) of +% those. If any of the \meta{fp expr} is a \nan{} or tuple, the result % is \nan{}. If any operand is a tuple, \enquote{invalid operation} % occurs; these operations do not raise exceptions in other cases. % \end{function} @@ -1105,19 +1105,19 @@ % [tested = {m3fp-round001, m3fp-round002}, added = 2013-12-14, updated = 2015-08-08] % {round, trunc, ceil, floor} % \begin{syntax} -% \cs{fp_eval:n} \{ |round| |(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |round| |(| \meta{fpexpr_1} , \meta{fpexpr_2} |)| \} -% \cs{fp_eval:n} \{ |round| |(| \meta{fpexpr_1} , \meta{fpexpr_2} , \meta{fpexpr_3} |)| \} +% \cs{fp_eval:n} \{ |round| |(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |round| |(| \meta{fp expr_1} , \meta{fp expr_2} |)| \} +% \cs{fp_eval:n} \{ |round| |(| \meta{fp expr_1} , \meta{fp expr_2} , \meta{fp expr_3} |)| \} % \end{syntax} % Only |round| accepts a third argument. -% Evaluates $\meta{fpexpr_1}=x$ and $\meta{fpexpr_2}=n$ and $\meta{fpexpr_3}=t$ then rounds +% Evaluates $\meta{fp expr_1}=x$ and $\meta{fp expr_2}=n$ and $\meta{fp expr_3}=t$ then rounds % $x$~to $n$~places. If $n$~is an integer, this rounds~$x$ to a % multiple of~$10^{-n}$; if $n=+\infty$, this always yields~$x$; if % $n=-\infty$, this yields one of $\pm 0$, $\pm\infty$, or~\nan{}; if % $n=\nan{}$, this yields \nan{}; if % $n$~is neither $\pm\infty$ nor an integer, then an \enquote{invalid -% operation} exception is raised. When \meta{fpexpr_2} is omitted, -% $n=0$, \emph{i.e.}, \meta{fpexpr_1} is rounded to an integer. The +% operation} exception is raised. When \meta{fp expr_2} is omitted, +% $n=0$, \emph{i.e.}, \meta{fp expr_1} is rounded to an integer. The % rounding direction depends on the function. % \begin{itemize} % \item |round| yields the multiple of~$10^{-n}$ closest to~$x$, @@ -1139,15 +1139,15 @@ % zero}). % \end{itemize} % \enquote{Overflow} occurs if $x$~is finite and the result is -% infinite (this can only happen if $\meta{fpexpr_2}\string<-9984$). +% infinite (this can only happen if $\meta{fp expr_2}\string<-9984$). % If any operand is a tuple, \enquote{invalid operation} occurs. % \end{function} % % \begin{function}[tested = m3fp-logic002]{sign} % \begin{syntax} -% \cs{fp_eval:n} \{ |sign(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |sign(| \meta{fp expr} |)| \} % \end{syntax} -% Evaluates the \meta{fpexpr} and determines its sign: $+1$ for +% Evaluates the \meta{fp expr} and determines its sign: $+1$ for % positive numbers and for $+\infty$, $-1$ for negative numbers and % for $-\infty$, $\pm 0$ for $\pm 0$, and \nan{} for \nan{}. % If the operand is a tuple, \enquote{invalid operation} occurs. @@ -1157,15 +1157,15 @@ % \begin{function}[updated = 2013-11-17, tested = m3fp-trig001] % {sin, cos, tan, cot, csc, sec} % \begin{syntax} -% \cs{fp_eval:n} \{ |sin(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |cos(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |tan(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |cot(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |csc(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |sec(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |sin(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |cos(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |tan(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |cot(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |csc(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |sec(| \meta{fp expr} |)| \} % \end{syntax} % Computes the sine, cosine, tangent, cotangent, cosecant, or secant -% of the \meta{fpexpr} given in radians. For arguments given in +% of the \meta{fp expr} given in radians. For arguments given in % degrees, see \texttt{sind}, \texttt{cosd}, \emph{etc.} Note that % since $\pi$~is irrational, $\operatorname{sin}(8\mathrm{pi})$ is not quite % zero, while its analogue $\operatorname{sind}(8\times 180)$ is exactly @@ -1181,15 +1181,15 @@ % \begin{function}[added = 2013-11-02, tested = m3fp-trig003] % {sind, cosd, tand, cotd, cscd, secd} % \begin{syntax} -% \cs{fp_eval:n} \{ |sind(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |cosd(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |tand(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |cotd(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |cscd(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |secd(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |sind(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |cosd(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |tand(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |cotd(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |cscd(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |secd(| \meta{fp expr} |)| \} % \end{syntax} % Computes the sine, cosine, tangent, cotangent, cosecant, or secant -% of the \meta{fpexpr} given in degrees. For arguments given in +% of the \meta{fp expr} given in degrees. For arguments given in % radians, see \texttt{sin}, \texttt{cos}, \emph{etc.} Note that % since $\pi$~is irrational, $\operatorname{sin}(8\mathrm{pi})$ is not quite % zero, while its analogue $\operatorname{sind}(8\times 180)$ is exactly @@ -1205,13 +1205,13 @@ % \begin{function}[added = 2013-11-02, tested = m3fp-trig002] % {asin, acos, acsc, asec} % \begin{syntax} -% \cs{fp_eval:n} \{ |asin(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |acos(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |acsc(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |asec(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |asin(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |acos(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |acsc(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |asec(| \meta{fp expr} |)| \} % \end{syntax} % Computes the arcsine, arccosine, arccosecant, or arcsecant of the -% \meta{fpexpr} and returns the result in radians, in the range +% \meta{fp expr} and returns the result in radians, in the range % $[-\pi/2,\pi/2]$ for \texttt{asin} and \texttt{acsc} and $[0,\pi]$ % for \texttt{acos} and \texttt{asec}. For a result in degrees, use % \texttt{asind}, \emph{etc.} If the argument of |asin| or |acos| @@ -1225,13 +1225,13 @@ % \begin{function}[added = 2013-11-02, tested = m3fp-trig004] % {asind, acosd, acscd, asecd} % \begin{syntax} -% \cs{fp_eval:n} \{ |asind(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |acosd(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |acscd(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |asecd(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |asind(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |acosd(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |acscd(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |asecd(| \meta{fp expr} |)| \} % \end{syntax} % Computes the arcsine, arccosine, arccosecant, or arcsecant of the -% \meta{fpexpr} and returns the result in degrees, in the range +% \meta{fp expr} and returns the result in degrees, in the range % $[-90,90]$ for \texttt{asin} and \texttt{acsc} and $[0,180]$ for % \texttt{acos} and \texttt{asec}. For a result in radians, use % \texttt{asin}, \emph{etc.} If the argument of |asin| or |acos| lies @@ -1245,26 +1245,26 @@ % \begin{function}[added = 2013-11-02, tested = m3fp-trig002] % {atan, acot} % \begin{syntax} -% \cs{fp_eval:n} \{ |atan(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |atan(| \meta{fpexpr_1} , \meta{fpexpr_2} |)| \} -% \cs{fp_eval:n} \{ |acot(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |acot(| \meta{fpexpr_1} , \meta{fpexpr_2} |)| \} +% \cs{fp_eval:n} \{ |atan(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |atan(| \meta{fp expr_1} , \meta{fp expr_2} |)| \} +% \cs{fp_eval:n} \{ |acot(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |acot(| \meta{fp expr_1} , \meta{fp expr_2} |)| \} % \end{syntax} % Those functions yield an angle in radians: \texttt{atand} and % \texttt{acotd} are their analogs in degrees. The one-argument % versions compute the arctangent or arccotangent of the -% \meta{fpexpr}: arctangent takes values in the range +% \meta{fp expr}: arctangent takes values in the range % $[-\pi/2,\pi/2]$, and arccotangent in the range $[0,\pi]$. The % two-argument arctangent computes the angle in polar coordinates of -% the point with Cartesian coordinates $(\meta{fpexpr_2}, -% \meta{fpexpr_1})$: this is the arctangent of -% $\meta{fpexpr_1}/\meta{fpexpr_2}$, possibly shifted by~$\pi$ -% depending on the signs of \meta{fpexpr_1} and \meta{fpexpr_2}. The +% the point with Cartesian coordinates $(\meta{fp expr_2}, +% \meta{fp expr_1})$: this is the arctangent of +% $\meta{fp expr_1}/\meta{fp expr_2}$, possibly shifted by~$\pi$ +% depending on the signs of \meta{fp expr_1} and \meta{fp expr_2}. The % two-argument arccotangent computes the angle in polar coordinates of -% the point $(\meta{fpexpr_1}, \meta{fpexpr_2})$, equal to the -% arccotangent of $\meta{fpexpr_1}/\meta{fpexpr_2}$, possibly shifted +% the point $(\meta{fp expr_1}, \meta{fp expr_2})$, equal to the +% arccotangent of $\meta{fp expr_1}/\meta{fp expr_2}$, possibly shifted % by~$\pi$. Both two-argument functions take values in the wider -% range $[-\pi,\pi]$. The ratio $\meta{fpexpr_1}/\meta{fpexpr_2}$ +% range $[-\pi,\pi]$. The ratio $\meta{fp expr_1}/\meta{fp expr_2}$ % need not be defined for the two-argument arctangent: when both % expressions yield~$\pm 0$, or when both yield~$\pm\infty$, the % resulting angle is one of $\{\pm\pi/4,\pm 3\pi/4\}$ depending on @@ -1275,26 +1275,26 @@ % \begin{function}[added = 2013-11-02, tested = m3fp-trig004] % {atand, acotd} % \begin{syntax} -% \cs{fp_eval:n} \{ |atand(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |atand(| \meta{fpexpr_1} , \meta{fpexpr_2} |)| \} -% \cs{fp_eval:n} \{ |acotd(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |acotd(| \meta{fpexpr_1} , \meta{fpexpr_2} |)| \} +% \cs{fp_eval:n} \{ |atand(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |atand(| \meta{fp expr_1} , \meta{fp expr_2} |)| \} +% \cs{fp_eval:n} \{ |acotd(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |acotd(| \meta{fp expr_1} , \meta{fp expr_2} |)| \} % \end{syntax} % Those functions yield an angle in degrees: \texttt{atand} and % \texttt{acotd} are their analogs in radians. The one-argument % versions compute the arctangent or arccotangent of the -% \meta{fpexpr}: arctangent takes values in the range $[-90,90]$, and +% \meta{fp expr}: arctangent takes values in the range $[-90,90]$, and % arccotangent in the range $[0,180]$. The two-argument arctangent % computes the angle in polar coordinates of the point with Cartesian -% coordinates $(\meta{fpexpr_2}, \meta{fpexpr_1})$: this is the -% arctangent of $\meta{fpexpr_1}/\meta{fpexpr_2}$, possibly shifted -% by~$180$ depending on the signs of \meta{fpexpr_1} and -% \meta{fpexpr_2}. The two-argument arccotangent computes the angle -% in polar coordinates of the point $(\meta{fpexpr_1}, -% \meta{fpexpr_2})$, equal to the arccotangent of -% $\meta{fpexpr_1}/\meta{fpexpr_2}$, possibly shifted by~$180$. Both +% coordinates $(\meta{fp expr_2}, \meta{fp expr_1})$: this is the +% arctangent of $\meta{fp expr_1}/\meta{fp expr_2}$, possibly shifted +% by~$180$ depending on the signs of \meta{fp expr_1} and +% \meta{fp expr_2}. The two-argument arccotangent computes the angle +% in polar coordinates of the point $(\meta{fp expr_1}, +% \meta{fp expr_2})$, equal to the arccotangent of +% $\meta{fp expr_1}/\meta{fp expr_2}$, possibly shifted by~$180$. Both % two-argument functions take values in the wider range $[-180,180]$. -% The ratio $\meta{fpexpr_1}/\meta{fpexpr_2}$ need not be defined for +% The ratio $\meta{fp expr_1}/\meta{fp expr_2}$ need not be defined for % the two-argument arctangent: when both expressions yield~$\pm 0$, or % when both yield~$\pm\infty$, the resulting angle is one of $\{\pm % 45,\pm 135\}$ depending on signs. The \enquote{underflow} @@ -1304,10 +1304,10 @@ % % \begin{function}[added = 2013-12-14, tested = m3fp-basics005]{sqrt} % \begin{syntax} -% \cs{fp_eval:n} \{ |sqrt(| \meta{fpexpr} |)| \} +% \cs{fp_eval:n} \{ |sqrt(| \meta{fp expr} |)| \} % \end{syntax} -% Computes the square root of the \meta{fpexpr}. The \enquote{invalid -% operation} is raised when the \meta{fpexpr} is negative or is a tuple; no other +% Computes the square root of the \meta{fp expr}. The \enquote{invalid +% operation} is raised when the \meta{fp expr} is negative or is a tuple; no other % exception can occur. Special values yield $\sqrt{-0} = -0$, % $\sqrt{+0} = +0$, $\sqrt{+\infty} = +\infty$ and % $\sqrt{\text{\nan{}}}=\text{\nan{}}$. @@ -1338,11 +1338,11 @@ % % \begin{function}[added = 2016-12-05]{randint} % \begin{syntax} -% \cs{fp_eval:n} \{ |randint(| \meta{fpexpr} |)| \} -% \cs{fp_eval:n} \{ |randint(| \meta{fpexpr_1} , \meta{fpexpr_2} |)| \} +% \cs{fp_eval:n} \{ |randint(| \meta{fp expr} |)| \} +% \cs{fp_eval:n} \{ |randint(| \meta{fp expr_1} , \meta{fp expr_2} |)| \} % \end{syntax} -% Produces a pseudo-random integer between $1$~and \meta{fpexpr} or -% between \meta{fpexpr_1} and \meta{fpexpr_2} inclusive. The bounds +% Produces a pseudo-random integer between $1$~and \meta{fp expr} or +% between \meta{fp expr_1} and \meta{fp expr_2} inclusive. The bounds % must be integers in the range $(-10^{16},10^{16})$ and the first % must be smaller or equal to the second. See \texttt{rand} for % important comments on how these pseudo-random numbers are generated. @@ -1392,9 +1392,9 @@ % \begin{function}[EXP, added = 2012-05-14, updated = 2012-07-08, % tested = m3fp-convert003]{\fp_abs:n} % \begin{syntax} -% \cs{fp_abs:n} \Arg{floating point expression} +% \cs{fp_abs:n} \Arg{fp expr} % \end{syntax} -% Evaluates the \meta{floating point expression} as described for +% Evaluates the \meta{fp expr} as described for % \cs{fp_eval:n} and leaves the absolute value of the result in the % input stream. If the argument is $\pm\infty$, \nan{} or a tuple, % \enquote{invalid operation} occurs. Within floating point @@ -1407,7 +1407,7 @@ % \begin{syntax} % \cs{fp_max:nn} \Arg{fp expression 1} \Arg{fp expression 2} % \end{syntax} -% Evaluates the \meta{floating point expressions} as described for +% Evaluates the \meta{fp exprs} as described for % \cs{fp_eval:n} and leaves the resulting larger (\texttt{max}) or % smaller (\texttt{min}) value in the input stream. If the argument % is a tuple, \enquote{invalid operation} occurs, but no other case @@ -1427,7 +1427,7 @@ % \item Decide what exponent range to consider. % \item Support signalling \texttt{nan}. % \item Modulo and remainder, and rounding function |quantize| (and its friends analogous to |trunc|, |ceil|, |floor|). -% \item \cs{fp_format:nn} \Arg{fpexpr} \Arg{format}, but what should +% \item \cs{fp_format:nn} \Arg{fp expr} \Arg{format}, but what should % \meta{format} be? More general pretty printing? % \item Add |and|, |or|, |xor|? Perhaps under the names \texttt{all}, % \texttt{any}, and \texttt{xor}? |