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-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx22
1 files changed, 11 insertions, 11 deletions
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
index d5c48436db4..4ff2e34c2bd 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
@@ -38,7 +38,7 @@
% {latex-team@latex-project.org}^^A
% }^^A
% }
-% \date{Released 2017/05/29}
+% \date{Released 2017/07/15}
%
% \maketitle
%
@@ -158,7 +158,7 @@
% an invalid operation exception with the appropriate function name.
% Otherwise, call the \texttt{trig} function to perform argument
% reduction and if necessary convert the reduced argument to radians.
-% Then, \cs{@@_sin_series_o:NNwwww} will be called to compute the
+% Then, \cs{@@_sin_series_o:NNwwww} is called to compute the
% Taylor series: this function receives a sign~|#3|, an initial octant
% of~$0$, and the function \cs{@@_ep_to_float_o:wwN} which converts the
% result of the series to a floating point directly rather than taking
@@ -187,7 +187,7 @@
% invalid operation exception. The cosine of \nan{} is itself.
% Otherwise, the \texttt{trig} function reduces the argument to at
% most half a right-angle and converts if necessary to radians. We
-% will then call the same series as for sine, but using a positive
+% then call the same series as for sine, but using a positive
% sign~|0| regardless of the sign of~$x$, and with an initial octant
% of~$2$, because $\cos(x) = + \sin(\pi/2 + \lvert x\rvert)$.
% \begin{macrocode}
@@ -382,7 +382,7 @@
% converts it to a fixed point number. Some trailing digits may be
% lost in the conversion, so we keep the original floating point
% number around: when computing sine or tangent (or their inverses),
-% the last step will be to multiply by the floating point number (as
+% the last step is to multiply by the floating point number (as
% an extended-precision number) rather than the fixed point number.
% The period serves to end the integer expression for the octant.
% \begin{macrocode}
@@ -516,7 +516,7 @@
% \begin{variable}[aux, EXP]{\@@_trig_inverse_two_pi:}
% This macro expands to |,,!| or~|,!| followed by $10112$~decimals of
% $10^{-16}/(2\pi)$. The number of decimals we really need is the
-% maximum exponent plus the number of digits we will need later,~$52$,
+% maximum exponent plus the number of digits we later need,~$52$,
% plus~$12$ ($4-1$~groups of $4$~digits). We store the decimals as a
% control sequence name, and convert it to a token list when required:
% strings take up less memory than their token list representation.
@@ -864,7 +864,7 @@
% \item the conversion function~|#1|;
% \item the final sign, which depends on the octant~|#3| and the
% sign~|#2|;
-% \item the octant~|#3|, which will control the series we use;
+% \item the octant~|#3|, which controls the series we use;
% \item the square |#4 * #4| of the argument as a fixed point number,
% computed with \cs{@@_fixed_mul:wwn};
% \item the number itself as an extended-precision number.
@@ -1046,7 +1046,7 @@
% / x)$ is the angular coordinate of the point $(x, y)$.
%
% As for direct trigonometric functions, the first step in computing
-% $\operatorname{atan}(y, x)$ is argument reduction. The sign of~$y$ will give that
+% $\operatorname{atan}(y, x)$ is argument reduction. The sign of~$y$ gives that
% of the result. We distinguish eight regions where the point $(x,
% \lvert y\rvert)$ can lie, of angular size roughly $\pi/8$,
% characterized by their \enquote{octant}, between $0$ and~$7$ included. In
@@ -1080,7 +1080,7 @@
% $\operatorname{atan}\frac{\lvert y\rvert}{x}
% = \pi-\operatorname{atan}\frac{\lvert y\rvert}{-x}$.
% \end{itemize}
-% In the following, we will denote by~$z$ the ratio among
+% In the following, we denote by~$z$ the ratio among
% $\lvert\frac{y}{x}\rvert$, $\lvert\frac{x}{y}\rvert$,
% $\lvert\frac{x+y}{x-y}\rvert$, $\lvert\frac{x-y}{x+y}\rvert$ which
% appears in the right-hand side above.
@@ -1171,8 +1171,8 @@
% \cs{@@_atan_combine_o:NwwwwwN}, with arguments the final sign~|#2|;
% the octant~|#3|; $\operatorname{atan} z/z=1$ as a fixed point number; $z=0$~as a
% fixed point number; and $z=0$~as an extended-precision number.
-% Given the values we provide, $\operatorname{atan} z$ will be computed to be~$0$,
-% and the result will be $[|#3|/2]\cdot\pi/4$ if the sign~|#5| of~$x$
+% Given the values we provide, $\operatorname{atan} z$ is computed to be~$0$,
+% and the result is $[|#3|/2]\cdot\pi/4$ if the sign~|#5| of~$x$
% is positive, and $[(7-|#3|)/2]\cdot\pi/4$ for negative~$x$, where
% the divisions are rounded up.
% \begin{macrocode}
@@ -1215,7 +1215,7 @@
% both as a fixed point number and as an extended-precision floating
% point number with a mantissa in $[0.01,1)$. For now, we place |#1|
% as a first argument, and start an integer expression for the octant.
-% The sign of $x$ does not affect what~$z$ will be, so we simply leave
+% The sign of $x$ does not affect~$z$, so we simply leave
% a contribution to the octant: $\meta{octant} \to 7 - \meta{octant}$
% for negative~$x$. Then we order $\lvert y\rvert$ and $\lvert
% x\rvert$ in a non-decreasing order: if $\lvert y\rvert > \lvert