diff options
Diffstat (limited to 'Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx')
-rw-r--r-- | Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx | 20 |
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, $y<1$. |