% CHANGES TO VOLUME 2 OF THE ART OF COMPUTER PROGRAMMING
%
% Copyright (C) 2011, 2012, 2013 by Donald E. Knuth
% This file may be freely copied provided that no modifications are made.
% All other rights are reserved.
%
% Three levels of changes to the books are distinguished here:
%
% "\bugonpage" introduces the correction of an error;
% "\amendpage" introduces new material for future editions;
% "\improvepage" introduces ameliorations of lesser importance.
%
% (Changes introduced by \improvepage do not appear in the hardcopy listing.)
%
% Also, "\planforpage" introduces some of the author's half-baked intentions.
%

% NOTE: TO PUT THE INDEX ON A SEPARATE PAGE, RUN THIS WITH THE COMMAND LINE
%   tex "\let\indexeject+ \input err2"

\newif\ifall % \alltrue means show the trivial items too
\relax % hook

\def\vertical{|}
\def\inref#1 #{\expandafter\def\csname\vertical#1\endcsname}
\catcode`|=\active
\let|\inref \input \jobname.ref
\catcode`|=12

\input taocpmac % use the format for TAOCP, with modifications below

\def\becomes{\ifmmode\ \hbox\fi{\manfnt y}\ } % wiggly arrow indicates a change

\def\bugonpage#1.#2 #3 (#4) {
  \medbreak\defaultpointsize
  \line{\kern-5pt\llap{\manfnt x}% print a black triangle in left margin
   {\bf Page #2}\enspace #3
   \leaders\hrule\hfill\ \eightrm\date#4.}
  \nobreak\smallskip\iftrue\noindent}
\def\amendpage#1.#2 #3 (#4) {
  \medbreak\defaultpointsize
  \line{\kern-5pt{\bf Page #2}\enspace #3
   \leaders\hrule\hfill\ \eightrm\date#4.}
  \nobreak\smallskip\iftrue\noindent}
\def\improvepage#1.#2 #3 (#4) {\ifall
  \medbreak\ninepoint
  \line{\kern-6pt{\sl Page #2\enspace #3\/}
   \leaders\hrule\hfill\ \eightrm\date#4.}
  \nobreak\smallskip\noindent}
\def\planforpage#1.#2 #3 (#4) {
  \medbreak\defaultpointsize
  \line{\kern-5pt{\bf Page #2}\enspace #3
   \leaders\hbox to 5pt{\hss.\hss}\hfill\ \eightrm\date#4.}
  \nobreak\smallskip\begingroup\let\endchange=\endgroup\sl\noindent}
\let\endchange=\fi
\def\nl{\par\noindent}
\def\nlh{\par\noindent\hangit}
\def\hangit{\hangindent2em}
\def\cutpar{{\parfillskip=0pt\par}}

\def\date#1.#2.#3.{% convert "yy.mm.dd." to "dd Mon 19yy"
  #3
  \ifcase#2\or Jan\or Feb\or Mar\or Apr\or May\or Jun\or
               Jul\or Aug\or Sep\or Oct\or Nov\or Dec\fi
  \ \ifnum #1<97 \hundred#1\else19#1\fi}
\def\hundred{20} % the "century" for dates before '97

\def\ex #1. [#2]{\ninepoint
  \textindent{\bf#1.}[{\it#2\/}]\kern6pt}
\def\EX #1. [#2]{\ninepoint
  \textindent{\llap{\manfnt x}\bf#1.}[{\it#2\/}]\kern6pt}

\def\foottext#1{\medskip
        \hrule height\ruleht width5pc \kern-\ruleht \kern3pt \eightpoint
        \smallskip\textindent{#1}}
\def\volheadline#1{\line{\cleaders\hbox{\raise3pt\hbox{\manfnt\char'36}}\hfill
       \titlefont\ #1\ \cleaders\hbox{\raise3pt\hbox{\manfnt\char'36}}\hfill}}
\def\refin#1 {\let|\inref \input #1.ref \let|\crossref}

\let\defaultpointsize=\tenpoint

%%%%%%%%%%%%%% opening remarks %%%%%%%%%%%%%%%%%%%%%%%%

\def\lhead{INTRODUCTION}
\let\rhead=\lhead
\titlepage
\volheadline{THE ART OF COMPUTER PROGRAMMING}
\bigskip
\volheadline{ERRATA TO VOLUME 2 (after 2010)}
\bigskip

\noindent This document is a transcript of the notes that I have been making
in my personal copy of {\sl The Art of Computer Programming}, Volume~2 (third
edition, 26th printing) since it was first printed in 2011.
Previous errata are recorded in another file `{\tt all2-pre.ps}'.

\ifall Four levels of updates\dash---``errors,'' ``amendments,'' ``plans,''
   and ``improvements''\dash---appear, indicated by four
\else Three levels of updates\dash---``errors,'' ``amendments,'' and
   ``plans''\dash---appear, indicated by three \fi
different typographic conventions:
\begingroup\def\hundred{17}

\bugonpage 0.666 line 1 (76.07.04)
Technical or typographical errors (aka bugs) are the most critical items, so
they are flagged with a `\thinspace{\manfnt x}\thinspace' preceding the page
number. The date on which I first was told about the bug is shown; this is the
effective date on which I paid the finder's fee. The necessary
corrections are indicated in
a straightforward way. If,~for example, the book says
`$n$' where it should have said `$n+1$', the change is shown thus:
\smallskip
$n$ \becomes $n+1$
\endchange

\amendpage 0.666 line 2 (89.07.14)
Amendments to the text appear in the same format as bugs, but without
the~`\thinspace{\manfnt x}\thinspace'. These are things I wish I had known
about or thought of when I wrote the original text, so I added them later.
The date is the date I drafted the new text.
\endchange

\def\hundred{19}

\planforpage 0.666 line 3 (17.11.20)
Plans for the future represent a third kind of item. In such notes I~sketched
my intentions about things that I wasn't ready to flesh out further when
I~wrote them down. You can identify these items because they're written in
slanted type, and preceded by a bunch of dots
`\hbox to 6em{\leaders\hbox to 5pt{\hss.\hss}\hfill}' leading to the date on
which I recorded the plan in my files.
\endchange

\improvepage 0.666 line 4 (38.01.10)
The fourth and final category\dash---indicated by page and line number in
smaller, slanted type\dash---consists of minor corrections or improvements
that most readers don't want to know about, because they are so trivial.
You wouldn't even
be seeing these items if you hadn't specifically chosen to print the complete
errata list in all its gory details.
Are you sure you wanted to do that?
\endchange

\endgroup
\ifall\else\medskip\ninepoint
My personal file of updates also includes a fourth category of items, not
shown in this list. They are miscellaneous minor corrections or improvements
that most readers don't want to know about, because they are so trivial.
If you really want to see all of the gory details,
you can download the full list from Internet webpage
$$\.{http://www-cs-faculty.stanford.edu/\char`\~knuth/taocp.html}$$
by selecting the ``long form'' of the errata.
\fi

\medskip
\tenpoint
My shelves at home are
bursting with preprints and reprints of significant research results that I
want to digest and summarize, where appropriate, in the ultimate edition of
Volume~2. I didn't do that in the third edition because I would surely have to do
it over again later: New results continue to pour forth at a great rate, and I
will have time to rewrite that volume only~once. Volumes 4 and~5 need to be
finished first. So I've put most of my effort so far into writing up
those parts of the total picture that seem to have converged to their
near-final form. It follows, somewhat paradoxically, that the updates in this
document are most current in the areas where there has been least activity.

On the other hand I do believe that the changes listed here bring Volume~2
completely up to date in two respects: (1)~All of the research problems in the
previous edition\dash---i.e., all exercises that were rated 46 and
above\dash---have received new ratings of 45 or less whenever I learned of a
solution; and in such cases, the answer now refers to that solution.
(2)~All of the historical information about pioneering developments has been
amended whenever new details have come to my attention.

\beginconstruction
The ultimate, glorious, 100\% perfect editions of Volumes 1--4A are works in progress.
Please let me know of any improvements that you think I ought to make.
Send your comments either by snail mail to D.~E. Knuth, Computer
Science, Gates Building 4B, Stanford University, Stanford CA~94305-9045,
or by email to
{\tt taocp{\char`\@}cs.stanford.edu}. (Use email for book suggestions
only, please\dash---all
other correspondence is returned unread to the sender, or discarded,
because I have no time to
read ordinary email.) Although I'm working full time on
Volume~4B these days, I~will try to reply to all such messages
within a year of receipt. Current news about {\sl The Art of Computer
Programming\/} is posted on
$$\.{http://www-cs-faculty.stanford.edu/\char`~knuth/taocp.html}$$
and updated regularly.
\par\endconstruction
\rightline{\dash---Don Knuth, January 2011}

\bigskip
\bigskip
{\quoteformat
Oh! If only someone would give me time, time,
time to do everything\/ {\rm properly},
to read everything at\/ {\rm my own\/} tempo,
to take it apart and put it together again.
\author KARL BARTH (1922)
% letter to Edvard Thurneysen, spring 1922
% found in Revolutionary Theology in the Making: Barth-Thurneysen
% Correspondence 1914--1925, tr by Jas. D. Smart
% Richmond VA: John Knox Press, 1964, p43
\vfill\eject
}

\def\today{\number\day\space\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
  \space\number\year}

%%%%%%%%%%%%%%% CHANGES FOR VOLUME 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\lhead{CHANGES TO VOLUME 2: SEMINUMERICAL ALGORITHMS}
\let\rhead=\lhead
\titlepage
\volheadline{SEMINUMERICAL ALGORITHMS}
\bigskip
\rightline{Copyright \copyright\ 2011, 2012, 2013
 Addison\with Wesley; all rights reserved}
\rightline{Last updated \today}
\bigskip
\rightline{\sl Most of these corrections have already been made in
                  recent printings.}
\smallskip
\let\defaultpointsize=\tenpoint

\amendpage 2.x line 16 (11.06.16)
a {\it 45\/} rating \becomes
a {\it 40\/} rating
\endchange

\amendpage 2.x line 20 (13.01.30)
creativity.\ \becomes
creativity. All exercises with ratings of {\it46\/} or more are open problems
for future research, rated according to the number of
different attacks that they've resisted so far.
\endchange

\improvepage 2.13 lines 1 and 2 (11.09.15)
overflow will be on after program \eq(2) if and only if the result equals~$w$
\becomes
the result equals $w$ if and only if program~\eq(2) turns overflow on
\endchange

\amendpage 2.117 line $-4$ (13.04.02)
\ninepoint [\HM47] (I. Borosh.) \becomes 
[\HM48] (I. Borosh and H. Niederreiter.)
\endchange

\improvepage 2.145 line 25 (12.02.23)
Let $X_1$, $X_2$, \dots, $X_t$ be a set \becomes
Let $(X_1,X_2,\ldots,X_t)$ be a sequence
\endchange

\amendpage 2.189 a new quotation to insert before the exercises (13.02.06)
{\quoteformat
Almost all good computer programs 
contain at least one random-number generator.
\author DONALD E. KNUTH, {\sl Seminumerical Algorithms\/} (1969)
% first edition p157
}
\endchange

\bugonpage 2.196 line $-11$ (11.06.08)
Pratiche del calcolo \becomes Pratiche di calcolo
\endchange

\bugonpage 2.200 line 20 (13.01.24)
an appendix to his little book {\sl Rhabdologia\/} \becomes
part three of his little book {\sl Rabdologi\ae\/}
\endchange

\bugonpage 2.200 line $-15$ (11.09.13)
K. Gehrhardt \becomes C. I. Gerhardt
\endchange

\bugonpage 2.275 line 19 (11.04.04)
$235@M$ \becomes $23.5@M$
\endchange

\amendpage 2.280 line 26 (13.03.08)
Stay tuned for new records as we move into a new millennium. \becomes
By 2011 the world record had risen to ten {\it trillion\/} digits(!),
obtained by A.~J. Yee and S.~Kondo using the Chudnovsky formula
together with exercise~39.
\endchange

\amendpage 2.293 line 4 of exercise 13 (12.11.26)
{\bf 218} \becomes
{\bf 218},\thinspace1
\endchange

\amendpage 2.311 line $-5$ (11.03.02)
(1988) \becomes (International Supercomputing Institute, 1988)
\endchange

\amendpage 2.367 replacement for line $-8$ (11.09.18)
Furthermore $r_n\le\vert{\cal I}\cap P_n\vert\le r_n+t_n$, because
${\cal I}_N\subseteq{\cal I}\subseteq{\cal I}_N\cup{\cal K}$. Consequently
\endchange

\amendpage 2.367 replacement for line $-5$ (11.09.18)
Given $\epsilon$, this holds for all $n$; so
$\lim_{@n\to \infty } r_n/n =
\lim_{@n\to \infty } (r_n+t_n)/n = \mu ({\cal I})$.\quad\slug\tighten
\endchange

\amendpage 2.382 replacement for {\eq(5)} (11.12.09)
$$\pi(x)\;\approx\;\sum_{k=1}^{\lg x}
{\mu(k)\over k}L\bigl(\!\root k\of x\,\bigr)
\;=\; L(x) - {1\over2}L\bigl(\sqrt x\,\bigr)
   - {1\over3}L\bigl(\root3\of x\,\bigr) + \cdots \eqno (5)$$
\endchange

%\amendpage 2.395 line 8 (12.10.23)
%$1<x<n$ \becomes $1<x<n-1$
%\endchange

\improvepage 2.404 line 18 (11.11.06)
is between 0 and $N$ \becomes lies in the range $0\le x_i<N$
\endchange

\improvepage 2.404 line 22 (11.10.05)
$(x^3)^d\mod N=x$ \becomes
each secret component $(x_i^3\mod N)^d\mod N=x_i$
\endchange

\amendpage 2.409 another Mersenne prime (13.02.16)
[add `57885161' to \eq(26), and use it instead of 43112609 in the
remarks below, noting that $2^{57885161}-1$ has 17,425,170 decimal digits]
\endchange

\amendpage 2.417 replacement for lines 3--9 of exercise 47 (12.10.23)
\ninepoint\noindent$$\advance\baselineskip-1pt
\vcenter{\halign{\seventt #\cr
\llap{\sevenrm(}8372e6cadf564a9ee347092daefc242058b804422859%
7e5f2326bbbff1583ea4200d895d9564d39229c79af8\cr
72a72e38bb92852a22679080e269c30690fab0ec19f7%
8e9ef8bae74b600f4ebef42a1dd5a6d806dc70b96de2\cr
bf4a6c7d2ebb51bfd156dd8ac3cb0ae1c1c38d76a342%
7bcc3f12af7d4d04314c0d8377a0c79db1b1f0cd1702\rlap{\sevenrm,}\cr
2aabcd0f9f1f9fb382313246de168bae6a28d177963a%
8ebe6023f1c5bd8632caee9604f63c6a6e33ceb1e1bd\cr
4732a2973f5021e96e05e0da932b5b1d2bc618351ca5%
84bb6e49255ba22dca55ebd6b93a9c94d8749bb53be2\cr
90650878b17f4fe30bbb08453929a94a2efe3367e2cd%
92ea31a5e0d9f466870b162272e9e164e8c3238da519\rlap{\sevenrm)}\cr}}$$
in hexadecimal notation, where $N$ is
$$\advance\baselineskip-1pt
\vcenter{\halign{\seventt #\cr
c97d1cbcc3b67d1ba197100df7dbd2d2864c4fef4a78%
e62ddd1423d972bc7a420f66046386462d260d68a8b2\cr
3fbf12354705d874f79c22698f750c1b4435bc99174e%
58180bd18560a5c69c4eafb573446f79f588f624ec18\cr
4c3e7098e65ac7b88f89e1fadcdc3558c878dde6bc7c%
32be57c5e7e8d95d697ad3c6c343485132dcbb74f411\rlap{\sevenrm.}\cr}}$$
\endchange

\amendpage 2.435 lines 6 and 7 (13.03.09)
{\sl derived by C.~L. Dodgson (aka Lewis Carroll) from a theorem
of Jacobi, is also highly relevant to these methods.} \becomes
{\sl published in 1853 by Felice Chi\`o and rediscovered
by C.~L. ^{Dodgson} (aka Lewis ^{Carroll}), is also
highly relevant.}
\endchange

\bugonpage 2.453 replacement for line 5 (12.04.22)
\noindent$$\textstyle\deg(v_{i_1})+\cdots+\deg(v_{i_d})\in\bigcap D_j.$$
\endchange

\bugonpage 2.478 line 6 (11.08.30)
$c(33)$ \becomes $c(39)$
\endchange

\amendpage 2.478 lines $-11$ through $-5$ (11.08.30)
Computer calculations \dots~Arnold Scholz \becomes\nl
Notice that $2^n-1$ is the worst case for the binary method, because
$\nu(2^n-1)=n$. E.~G. Thurber
[{\sl Discrete Math.\ \bf 16} (1976), 279--289] has shown that several of
these values, including the case $n = 32$, can actually be calculated by hand.
Computer calculations by Neill Clift [{\sl Computing\/ \bf91} (2011), 265--284]
show that $l(2^n-1)$ is in fact exactly equal to
$n-1+l(n)$ for $1\le n\le64$. % but he doesn't think it will hold in general
Arnold Scholz
\endchange

\bugonpage 2.478 line $-3$ (11.03.30)
{\sl deutschen\/} \becomes {\sl Deutschen}
\endchange

\improvepage 2.490 line 6 after {\eq(9)} (13.04.29)
savings is worthwhile \becomes change is worthwhile
\endchange

\amendpage 2.537 a new quotation to append here (12.12.03)
\vskip3pt
{\quoteformat
This business of series, the most disagreeable thing in mathematics,
is no more than a game for the English;
Stirling's book, and the one by de Moivre, are proof.
\author PIERRE DE MAUPERTUIS, letter to d'Ortous de Mairan (30 Oct 1730)
% "Cette affaire de suites qui est tout ce qu'il y a de plus d\'esagr\'eable
% dans les math\'ematiques n'est qu'un jeu pour les Anglois;
% ce livre [of Stirling] et celui de M. de Moivre en sont une preuve."
% see Mary Terrall, The Man Who Flattened the Earth (2002), p43
}
\endchange

\amendpage 2.537 another new quotation to append here (12.10.23)
{\quoteformat
He was daunted and bewildered by their almost infinite series.
\author G. K. CHESTERTON, {\sl The Man Who Was Thursday\/} (1907)
%early in chapter 9
}
\endchange

\amendpage 2.524 last line of exercise 73 (11.02.16)
\ninepoint steps. \becomes steps. How big can their determinants be?
\endchange

\bugonpage 2.579 bottom line (12.07.10)
{\bf 5} (1848) \becomes {\bf 13} (1848)
\endchange

\amendpage 2.584 line 5 of answer 31 (13.04.02)
172. \becomes
172, and an excellent survey of later work has been prepared by
A.~Kontorovich in {\sl Bull.\ Amer.\ Math.\ Soc.\ \bf50} (2013), 187--228.
\endchange

\bugonpage 2.584 line $-3$ of answer 31 (13.04.02)
{\sl BIT\/ \bf25} (1980), 193--208 \becomes
{\sl BIT\/ \bf23} (1983), 65--74
\endchange

\improvepage 2.591 lines 6 and 7 of answer 8 (11.09.17)
$(N-j-k)/(N-j)$ \becomes $\bigl((N-j-k)/(N-j)\bigr)$
\endchange

\let\defaultpointsize=\ninepoint % get ready for answer pages

\bugonpage 2.618 first line of answer 5 (12.11.24)
lines 22 \becomes lines 23
\endchange

\bugonpage 2.618 line 4 of answer 7 (12.11.24)
.99999999 \becomes $-.99999999$
\endchange

\bugonpage 2.619 line $-2$ of answer 8 (12.11.24)
better then \becomes better than
\endchange

\bugonpage 2.626 line {\it 008\/} of answer 25 (11.04.04)
\.{V+N+1} \becomes \.{TEMP}
\qquad and\qquad $(v+1)$ \becomes $(v_{n-1}+1)$
\endchange

\bugonpage 2.626 lines {\it 110\/} and {\it 111\/} of answer 26 (11.04.04)
\.{DEC2} \becomes \.{DEC1}
\qquad and\qquad
$j+1$ \becomes $j-1$
\qquad and\qquad
\.{J2NN} \becomes \.{J1NN}
\endchange

\bugonpage 2.633 line 5 of answer 4 (12.07.09)
$\half\bigl(W(j)-W(-j)\bigr)$ \becomes
$\bigl(W(j)-W(-j)\bigr)/(2j)$.
\endchange

\amendpage 2.635 line 1 of answer 3 (11.02.19)
Jon L. White \becomes Jon L White
\endchange

\bugonpage 2.663 line 2 of answer 25 (11.12.10)
if $n$ \becomes if $x$
\endchange

\amendpage 2.671 new answer (12.10.23)
\ans47. Earlier printings of this book had a 211-digit~$N$, which was cracked
in 2012 using the elliptic curve method and the general number field
method by Greg Childers and about 500 volunteers(!).
\endchange

\bugonpage 2.715 replacement for lines 2, 3, 4 of answer 64 (11.12.21)
\noindent $(x_{k1}+u^2x_{k2})(y_{2k}+u^2y_{1k})@z_{kk}
  +(x_{k1}+u^2x_{k3})@y_{3k}\bigl((1+u)@z_{kk}-u(z_{1k}+z_{2k}+z_{3k})\bigr)
       -x_{k1}(y_{2k}+y_{3k})(z_{k1}+z_{k2}+z_{k3})$ and
$g_{jk}(u)=(x_{k1}+u^2x_{j3})(y_{3k}+uy_{1j})(z_{kj}+uz_{jk})
       +   (x_{k1}+u^2x_{j2})(y_{2k}-uy_{1j}) z_{kj}$.
[The best upper bound known for $\\(T(3,3,3))$ is 23;{\parfillskip=0pt\par}
\endchange

\amendpage 2.717 last line of answer 67 (12.02.01)
492.] \becomes
492. The best bound currently known, $\omega<2.3727$, is due to
V.~Vassilevska Williams (2012, to appear).]
\endchange

\let\defaultpointsize=\tenpoint % begin appendices

\amendpage 2.730 through page 734 (12.04.07)
[replace the notation $(R\Relbar\joinrel\joinrel\joinrel\Rightarrow x;\;y)$
 by $(R{?}\ x{:}\ y)$ in fourteen places]
\endchange

\amendpage 2.735 and 736 new entries for Appendix C (11.04.17)
\ninepoint\noindent
Program 4.3.1A$'$, 623.\nl
Program 4.3.1B, 624.\nl
Program 4.5.2A$'$, 373.
\endchange

\bugonpage 2.735 in Appendix C (11.04.17)
\ninepoint\noindent
Algorithm 3.3.4S, 101--103.\nl
Program 4.2.3D, 251--252.\nl
Program 4.3.1D, 273--275, 626.\nl
Algorithm 4.5.4F, 659--660.\nl
Theorem 4.6.4C, 496.\nl
Theorem 4.6.4W, 513--514.
\endchange

\expandafter\ifx\csname indexeject\endcsname\relax\else\vfill\eject\fi
\amendpage 2.737 and following (11.01.01)
Miscellaneous changes to the existing index of Volume~2 are collected here,
including corrections and amendments to the old entries as well as new entries
that are occasioned by the new material. Thus, the lines of the full index
that have changed serve also as an index to the present document. However,
when a correction or amendment has caused an old index entry to be deleted,
the deletion is usually not indicated.

\input exotic
\begindoublecolumns
\indexformat
\gdef\Uni1.08:{\bitmap24:1.08:}
\hangindent 2em
Chebyshev (= Tschebyscheff), Pafnutii Lvovich ({\rus Chebyshebp2, Pafnut{\char12}i0 Lp1vovichp2} = {\rus Chebyshev, Pafnutii0 Lp1vovich}), inequality, 183, 669. % 30th
Chesterton, Gilbert Keith, 417, 537. % 29th
Childers, James Gregory, 671. % 29th
Chi\`o, Felice, 435. % 30th
Chor, Benny ({\heb\Hrr/\Hvv/\Hsh/ \Hfn/\Hvv/\Hyy/\Hts/}\thinspace-{\heb\Hfn/\Hbb/}), 669. % 27th
de Mairan, Jean-Jacques d'Ortous, 537. % 30th
de Maupertuis, Pierre-Louis Moreau, 537. % 30th
de Moivre, Abraham, 537. % 30th
$e$ (base of natural logarithms), 12, 76, 359, 726--727, 733. % 29th
Elliptic curve method, 402, 671. % 29th
Fuss, Paul Heinrich von ({\rus Fuss, Pavel Nikolaevich}), 392, 651. % 29th
Gerhardt, Carl Immanuel, 200. % 28th
Gray, Herbert Lee Roy, 242. % 29th
Ja'Ja' (= JaJa), Joseph Farid \indexbreak ({\arab\Afai/\Amj/\Amai/\Aij/ \Afd/\Aiy/\Afr/\Aif/ \Aff/\Aiy/\Az/\Afw/\Aij/}), 514. % 27th
Kannan, Ravindran ({\tm\\205\\270\\151\\227\\205\\150 \\170\\146\\176\\150}), 599. % 30th
Kondo, Shigeru (\JC48:48:0:40% J2265
<0000000000800000000001800000000007c0000000003ff038000c00ffe01f000e0ffe00%
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 00f00f00000000000f00000000000f00000c00000f00001e00000fffffff00000fffffff%
 00000f003c0000600f003c0000f00f003c00fff80f003c007ff80f003c0000f00f003c00%
 00f00f003c0000f00f003c0000f00f003c0000f00f003c0000f00f003c0000f00f003c00%
 00f01e003c0000f01e003c0000f01e003c0000f03c003c0000f03c003c0000f078003c00%
 00f070003c0000f0e0003c0000f1c0003c0001fb8000180003dc000000000fcf00000000%
 3f87ffffffffff03fffffffffe00fffffffe7c003ffffffe780000000000300000000000%
 >%% unicode char "8fd1
\JC48:48:0:40% J3803
<0000c00c00000000f00f00000000f80f800c0000f00f001effffffffffff7fffffffffff%
 0000f00f00000000f00f00000000f00600000000600000000c06000c03000f0f3e0f07c0%
 0fff8f8f8fe00fff87cf1f800f0f07ef3e000f0f03ef38000f0f01cf60300f0f000f0078%
 0f0f3ffffffc0f0f1ffffffc0f0f001f60000f0f003e70000fff003e300c0fff007c381e%
 0f0fffffffff0f0f7fffffff0f0f01f00f800f0f03e607c00f0f07c787f80f0f0f07c3ff%
 0f0f1fe7c1ff0f0f39f784ff0fffe0ff8e7f0fff00ff9f1e0f0f007fbf800f0f0037f000%
 1f0f000780001e0f000780001e0f003ff0001e0f03f7be001c0f1fe79f803c0f0fc78fc0%
 380f0f878fe0381f060787e031ff043f83e0707e001f81c0603e000f8000c01c00070000%
 >%% unicode char "85e4
\JC48:48:0:40% J4448
<0001800600000001e00780000001f007c0000001f007c0000001e007800c0001e007801e%
 ffffffffffff7fffffffffff0001e00780000001e00780000001e00780000001e0078000%
 0000c003000000000003c00000001c00f00000001f00780000001e007c0000001f007e00%
 00000f003e0006000f803e1807800f800c3c07fffffffffe07fffffffffe078007c00000%
 078003e00000078003e01800078001f01e00078001f03f80078001f83f00078000f87e00%
 078000fc7c000780007cf8000780003ff0040780003fe0040780001fe0040780000fc00c%
 0780000fc00c0780001fe00c0780003ff01c0700007ff81c0f0000fcfe1e0e0001f87f9e%
 1e0007e03fff1c000fc01fff38003f0007ff3800fc0003fe7007c000007cc00000000000%
 >%% unicode char "8302
), 280. % 30th
Kontorovich, Alex Vladimir ({\rus Kontorovich, Aleksandr Vladimirovich}), 584. % 30th
Lalescu, Gheorghe Liviu, 186. % 28th
Left multiple, least common, 437--438. % 29th
MacMillan, Donald Bashford, 226. % 30th
Mairan, Jean-Jacques d'Ortous de, 537. % 30th
Maupertuis, Pierre-Louis Moreau de, 537. % 30th
Moivre, Abraham de, 537. % 30th
Number field sieve, 403, 671. %29th
Right divisor, greatest common, 437--438. % 29th
Stirling, James, 537. % 30th
Vassilevska Williams, Virginia Panayotova ({\rus Vasilevska, Virginiya Panai0otova}), 717. % 29th
Ville, Jean Andr\'e, 597. % 29th
Wald, Abraham (= \'Abrah\'am), 163, 177--178. % 30th
Williams, Virginia Panayotova Vassilevska ({\rus Virginiya Panai0otova Vasilevska}), 717. % 29th
Yee, Alexander Jih-Hing (\GC79:80:-1:64% G5164
<000000001e0000000000000000001f8000000000000000003fc000000000000000003ff0%
 00000000000000007ff000000000000000007ff00000000000000000ffe0000000000000%
 0000fff00000000000000001ff780000000000000001fc7c0000000000000003f83c0000%
 000000000003f83e0000000000000007f01f000000000000000fe01f000000000000001f%
 c00f800000000000001f800fc00000000000003f8007f00000000000007f0007f8000000%
 000000fe0003fc000000000001fc0001fe000000000003f80000ff800000000003f00000%
 ffc00000000007e000007ff0000000000fc000003ff8000000001fc000001ffe00000000%
 3f80000007ff000000007f00000003ffc0000000fe0000000fffe0000001fc0000001fff%
 fc000001f80000003fbfff800003f00000007fdfffe00007ffffffffffe7fffc000f8fff%
 ffffffe3fffe001f04001f800000fff8003e00001f8000003ff000fc00001f8000000fc0%
 01f800001f800000078007e000001f80000001000fc000001f80000000001f0000001f80%
 000000007e0000001f8000070000f80000001f80000f8000f00000001f80001fc000c000%
 00001f80003fc000007fffffffffffffe000003ffffffffffffff000003fffffffffffff%
 f000000000001f8000000000000000001f8000000000000000001f8000000000000001c0%
 1f8000000000000001e01f8000000000000003f81f8380000000000003fc1f87e0000000%
 000007fe1f83f8000000000007fe1f81fe00000000000ffc1f807f00000000000ff81f80%
 3fc0000000001fc01f801ff0000000003f801f800ffc000000007f801f8007ff00000000%
 7f001f8003ff80000000fe001f8001ffe0000001fc001f8000fff0000003fc001f80007f%
 f8000007f8001f80003ff800001ff0001f80001ffc00003fc0001f80000ffc00007f8000%
 1f800007fc0000ff0fe01f800003fe0003fc1ffc1f800003fe0007f803ffff800001fe00%
 1fe000ffff800000fc003f00003fff800000fc003c00001fff800000700010000007ff80%
 0000000010000003ff000000000000000003fe000000000000000001f800000000000000%
 0001f00000000000>%% unicode "4f59
\GC72:79:-2:63% G5439
<0003c00000000000000003f80000000000000003f80000000000000007f8000000000000%
 0007f80000000000000007f00000000000000007f00007000000700007e0000f83c000f8%
 0007e0001fc3f801fc000f80003fe3fffffe000ffffffff3ffffff001ffffffffbffffff%
 001ffffffffbe0007e003e03f00003e0007c003c03f00003e0007c007c03f00003e0007c%
 007c07f00003e0007c00f807f00003e0007c01f007f00383e0007c01e007f007c3e0007c%
 038007f00fe3e0007c030007e01ff3e0007c7ffffffffffbe0007c3fffffffffffe0007c%
 1fffffffffffe0007c000007e00003e0007c000007c00003e0007c000007f00003e0007c%
 000007fc0003e0007c00000fff0003e0007c00000fbfc003e0007c00001f1ff003e0007c%
 00001f07fc03fffffc00003e03fe03fffffc00007e00ff83fffffc0000fc007f83e0007e%
 0001fc003f87e0007e0003f8001fc7e0007e0007f0000fc7e0007e000fe00007c7e0007e%
 003fc00007c7e0007c00ff1c000307e0e00003fe1e00000001f0000ff81f80000003f800%
 3fe01ffffffffffc00ff801ffffffffffe00fe001ffffffffffe0040001f80000001fc00%
 00000f80000001f80000000f80000001f80000000f80000001f80000000f80000001f800%
 00000f80000001f80000000f80000001f80000000f80000001f80000000f80000001f800%
 00000f80000001f80000000ffffffffff80000000ffffffffff80000000f80000001f800%
 00000f80000001f80000000f80000001f80000000f80000001f80000000f80000001f800%
 00000f80000001f80000000f80000001f80000000f80000001f80000000f80000001f800%
 00001f80000001f80000001ffffffffff80000001ffffffffff80000001ffffffffffc00%
 00001f80000001fc0000001f80000001fc0000003f80000001fc0000003f80000001fc00%
 00003f80000001fc0000003f00000001f80000003f00000001f800>%% unicode "667a
\GC78:78:-1:63% G2667
<000e0000000000000000000fc000000000000000000ff000000000000000000ff8000000%
 00000000000ff800000000000000000ff000000000000e00000fe000000000003f00000f%
 c000000000007f80000fc00000000000ffc0000fc03fffffffffffe0000fc01fffffffff%
 fff0000fc00ffffffffffff0000fc00e000000000000000fc000000000000000000fc000%
 000000000000000fc000000000000000000fc000000000000000000fc000000000000000%
 000ff800700000078000000fff007800000fc000000fffc07e00000fe000020fdfe07f00%
 001ff000030fcff07ffffffff800030fc7f87ffffffffc00030fc3f87ffffffffc00038f%
 c1fc7e00000ff000038fc1fc7e00000fc000078fc0fc7e00000fc000078fc0fc7e00000f%
 c0000f8fc0787e00000fc0000f8fc0707e00000fc0001f8fc0007e00000fc0001f8fc000%
 7e00000fe0003f0fc0007e00000fe0007f0fc0007e00000fe000ff0fc0007e00000fe000%
 ff0fc0007e00000fe0007f0fc0007e00000fe0007f0fc0007fffffffe0003c0fc0007fff%
 ffffe000000fc0007e00000fe000000fc0007e00000fe000000fc0007e00000fe000000f%
 c0007e00000fe000000fc0007e00000fe000000fc0007e00000fe000000fc0007e00000f%
 e000000fc0007e00000fe000000fc0007e00000fe000000fc0007e00000fe000000fc000%
 7e00000fe000000fc0007e00000fe000000fc0007e00000fe000000fc0007e00000fe000%
 000fc0007fffffffe000000fc0007fffffffe000000fc0007fffffffe000000fc0007e00%
 000fe000000fc0007e00000fe000000fc0007e00000fc000000fc0007e00000fc000000f%
 c0007c0000000000000fc0007c0000000000000fc000000000000000000fc00000000000%
 0380000fc0000000000007c0000fc000000000000fe0000fc000000000001ff0000fc000%
 000000003ff8000fcffffffffffffffc000fc7fffffffffffffc000fc200000000000000%
 000fc000000000000000000fc000000000000000001fc000000000000000001fc0000000%
 00000000001fc000000000000000001e0000000000000000>%% unicode "6052
), 280. % 30th

\vfill
\enddoublecolumns
\endchange

\bye

[The next printing will be the 30th.]
not listed above:
pages 184--189 revised to accommodate a new quote; (v) on p 185 shortened
the index entries for Ferrenberg, Knuth, and Pitfalls are affected
index entry for Jacobi loses page 435 


ARTICLES "TO APPEAR" THAT ARE STILL PENDING:
Virginia's paper on matrix multiplication