diff options
Diffstat (limited to 'Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx')
-rw-r--r-- | Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx | 22 |
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 |