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-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx20
1 files changed, 10 insertions, 10 deletions
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx
index 8a8e233edc5..ae6a2ad07b0 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx
@@ -38,7 +38,7 @@
% {latex-team@latex-project.org}^^A
% }^^A
% }
-% \date{Released 2017/05/29}
+% \date{Released 2017/07/15}
%
% \maketitle
%
@@ -614,7 +614,7 @@
% $10$, namely the first digit of $x$ is $1$, and all others vanish
% when subtracting $y$. Then the \meta{rounding} |#3| and the
% \meta{final sign} |#4| control whether we get $1$ or $0.9999 9999
-% 9999 9999$. In the usual round-to-nearest mode, we will get $1$
+% 9999 9999$. In the usual round-to-nearest mode, we get $1$
% whenever the \meta{rounding} digit is less than or equal to $5$
% (remember that the \meta{rounding} digit is only equal to $5$ if
% there was no further non-zero digit).
@@ -922,7 +922,7 @@
% \end{macro}
%
% \begin{macro}[aux, rEXP]{\@@_mul_significand_small_f:NNwwwN}
-% In this branch, \meta{digit 1} is zero. Our result will thus be
+% In this branch, \meta{digit 1} is zero. Our result is thus
% \meta{digits 2--17}, plus some rounding which depends on the digits
% $17$, $18$, and whether all subsequent digits are zero or not.
% The $8$ digits |1#3| are followed, after expansion of the
@@ -1038,7 +1038,7 @@
% + 10^{-16} Q_{D} + \text{rounding}$. Since the $Q_{i}$ are integers,
% $B$, $C$, $D$, and~$E$ are all exact multiples of $10^{-16}$, in other
% words, computing with $16$ digits after the decimal separator yields
-% exact results. The problem will be overflow: in general $B$, $C$,
+% exact results. The problem is the risk of overflow: in general $B$, $C$,
% $D$, and $E$ may be greater than $1$.
%
% Unfortunately, things are not as easy as they seem. In particular, we
@@ -1143,7 +1143,7 @@
% All of those bounds are less than $2.147\cdot 10^{5}$, and we are thus
% within \TeX{}'s bounds in all cases!
%
-% We will later need to have a bound on the $Q_{i}$. Their definitions
+% We later need to have a bound on the $Q_{i}$. Their definitions
% imply that $Q_{A} < 10^{9} A/y - 1/2 < 10^{5} A$ and similarly for the
% other $Q_{i}$. Thus, all of them are less than $177770$.
%
@@ -1151,7 +1151,7 @@
% \begin{equation*}
% A/Z = \sum_{i=1}^{4} \left(10^{-4i} Q_{i}\right) + 10^{-16} E/Z
% \end{equation*}
-% exactly. Furthermore, we know that the result will be in $[0.1,10)$,
+% exactly. Furthermore, we know that the result is in $[0.1,10)$,
% hence will be rounded to a multiple of $10^{-16}$ or of $10^{-15}$, so
% we only need to know the integer part of $E/Z$, and a
% \enquote{rounding} digit encoding the rest. Equivalently, we need to
@@ -1194,7 +1194,7 @@
% Compute $10^{6} + Q_{A}$ (a $7$~digit number thanks to the shift),
% unbrace \meta{A_1} and \meta{A_2}, and prepare the
% \meta{continuation} arguments for $4$ consecutive calls to
-% \cs{@@_div_significand_calc:wwnnnnnnn}. Each of these calls will need
+% \cs{@@_div_significand_calc:wwnnnnnnn}. Each of these calls needs
% \meta{y} (|#1|), and it turns out that we need post-expansion there,
% hence the \cs{__int_value:w}. Here, |#4| is six brace groups, which
% give the six first |n|-type arguments of the \texttt{calc} function.
@@ -1328,7 +1328,7 @@
% \meta{continuations} \meta{sign}
% \end{quote}
% Compute $Q_{B}$ by evaluating $\meta{B_1}\meta{B_2}0 / y - 1$. The
-% result will be output to the left, in an \cs{__int_eval:w} which we
+% result is output to the left, in an \cs{__int_eval:w} which we
% start now. Once that is evaluated (and the other $Q_{i}$ also,
% since later expansions are triggered by this one), a packing
% auxiliary takes care of placing the digits of $Q_{B}$ in an
@@ -1353,7 +1353,7 @@
% \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
% \end{quote}
% We compute $P \simeq 2E/Z$ by rounding $2 E_{1} E_{2}/Z_{1}Z_{2}$.
-% Note the first $0$, which multiplies $Q_{D}$ by $10$: we will later
+% Note the first $0$, which multiplies $Q_{D}$ by $10$: we later
% add (roughly) $5\cdot P$, which amounts to adding $P/2 \simeq E/Z$
% to $Q_{D}$, the appropriate correction from a hypothetical $Q_{E}$.
% \begin{macrocode}
@@ -1692,7 +1692,7 @@
% < 3.2 \cdot 10^{-8} \,,
% \]
% and $\sqrt{a} - y = (a - y^2)/(\sqrt{a} + y) \leq 16 \cdot 10^{-8}$.
-% Next, \cs{@@_sqrt_auxii_o:NnnnnnnnN} will be called several times to
+% Next, \cs{@@_sqrt_auxii_o:NnnnnnnnN} is called several times to
% get closer and closer underestimates of~$\sqrt{a}$. By
% construction, the underestimates~$y$ are always increasing, $a - y^2
% < 3.2 \cdot 10^{-8}$ for all. Also, $y<1$.