Graham !11
Knuth !11
Patashnik !11
CMath !11
induction-- !11
arithmetic progression !11
partitions !12
Hardy !12
Ramanujan !12
Fibonacci sequence !13
golden ratio !13
proofs of algorithms-- !13
Euclid's algorithm extended-- !13
greatest common divisor-- !13
--Euclid's algorithm extended !14
--greatest common divisor !14
flow chart-- !15
assertions+++ !15
algorithms, how to read !16
algorithms, communication of !16
proof of termination-- !16
--proof of termination !17
--proofs of algorithms !17
Henkin !17
Maurolico !17
Fermat !17
Pascal !17
De Morgan !17
P\'olya !17
Floyd !17
Naur !17
invariants !17
Hoare !17
weakest precondition !17
Dijkstra !17
Goldstine !18
von~Neumann !18
Turing !18
Morris !18
Jones !18
--flow chart !18
TURING !18
Ferranti Mark I !18
fallacious reasoning !18
Fibonacci numbers !18
golden ratio !18
prime number !19
Nicomachus !19
Lushbaugh !19
Gardner !19
Conway !19
Guy !19
proof of termination-- !19
Carlitz !96
binomial coefs, sums !96
--generating functions !96
analysis of algorithms-- !96
maximum algorithm-- !96
execution time, methods for studying !96
Kirchhoff's first law !97
left-to-right max or min-- !97
average-- !97
permutations-- !97
probability distribution-- !98
--permutations !98
mean !98
expected !98
--average !98
variance !98
standard deviation !98
Chebyshev's inequality !98
Bienaym\'e !98
generating functions for probabilities-- !99
Stirling numbers-- !99
mean from gf-- !100
variance from gf-- !100
Roes !100
Foster !100
Stuart !100
--Stirling numbers !100
--left-to-right max or min !101
--maximum algorithm !101
coin tossing-- !101
binomial distribution-- !101
--binomial distribution !102
--coin tossing !102
uniform distribution !102
probability generating function !103
characteristic function !103
convolution !103
Iverson's convention !103
--variance from gf !103
--mean from gf !103
semi-invariants !103
semi-invariants-- !103
cumulants-- !103
Thiele !103
Hald !103
normal distribution !104
Chebyshev's inequality !104
tail inequalities !104
Kolmogorov !104
left-to-right max or min-- !104
moment !105
central moment !105
Arbogast !105
normal distribution, approximate-- !105
L\'evy !105
Gnedenko !105
Kolmogorov !105
Chung !105
de Moivre !106
Poisson distribution !106
--normal distribution, approximate !106
--cumulants !106
--semi-invariants !106
mixture !106
inverse permutation !106
maximum norm !106
--left-to-right max or min !106
coin tosses, tail !106
binomial distribution, tail !106
tail inequalities-- !106
negative binomial distribution !107
--analysis of algorithms !107
--probability distribution !107
--generating functions for probabilities !107
--tail inequalities !107
asymptotics-- !107
Bachmann !107
O-notation-- !107
Euler's constant !107
polynomial !108
one-way equalities !108
transitive relation !108
factorial powers-- !109
--factorial powers !110
root !110
Big Omega-- !110
Big Theta !110
Dull !111
fallacious reasoning !111
--Big Omega !111
--O-notation !111
Euler's summation formula-- !111
Euler !111
integration and summation-- !111
integration by parts-- !112
Bernoulli numbers-- !112
Bernoulli !112
Seki !112
Bernoulli polynomial-- !113
--integration by parts !113
Euler's constant !114
harmonic numbers !114
Stirling's approximation-- !115
Stirling !115
Sums of powers !115
Bernoulli !115
Seki !115
--Bernoulli numbers !115
--Bernoulli polynomial !115
Wallis's product !116
gamma function !116
absolute error !116
relative error !116
--Euler's summation formula !116
--integration and summation !116
--Stirling's approximation !116
Taylor's formula with remainder !117
incomplete gamma function-- !117
gamma function-- !117
power series manipulations !118
O-notation !118
--gamma function !119
Euler's summation formula !120
Demuth !120
Knuth !120
Ramanujan !121
Furch !121
Tricomi !121
Temme !121
Gould !121
de Bruijn !121
Odlyzko !121
Tricomi !122
normal distribution !122
--incomplete gamma function !122
Ramanujan !122
de Bruijn !122
Euler's summation formula !123
Miller !123
Watson's lemma !123
KELLER !123
--asymptotics !123
Floyd !20
King !20
induction, generalized !20
well-ordering !20
linear order !20
Lexicographic order !20
--induction !21
--proof of termination !21
number definitions !21
integers !21
rational number !21
real number !21
pi !21
golden ratio !21
complex number !21
real part !21
imaginary part !21
absolute value !21
complex conjugate !21
intervals !21
exponents, laws of !22
root of number !22
power of number !22
Oresme !22
Wallis !22
Newton !22
logarithm-- !22
logarithms, common !23
binary logarithms !23
Reingold !23
natural logarithms !23
Napier !23
compound interest-- !23
--compound interest !24
Cajori !24
computational error-- !24
root of number !25
exponents, laws of !25
rational number !25
Hamming !26
natural logarithms !26
logarithms, common !26
binary logarithms !26
hardware-oriented algorithms !26
Briggs !26
--logarithm !26
Feynman !26
--computational error !26
summation-- !27
index variable !27
dummy variable !27
Fourier !27
infinite series-- !27
divergent !28
convergent !28
distributive law !28
Change of variable !28
Apostol !28
Interchanging order of summation !29
absolutely convergent !29
convergence, absolute !29
--infinite series !29
geometric progression !31
arithmetic progression-- !31
--arithmetic progression !32
Induction !32
bracket notation, for statements-- !32
change of variable-- !32
--change of variable !33
Kronecker !33
Iverson !33
Knuth !33
--bracket notation, for statements !33
sums, multiple-- !33
interchanging order !33
partitions !34
interchange the order of summation !35
Matrix !35
Binet !36
Schwarz !36
Cauchy's inequality !36
--sums, multiple !36
Matrix !36
supremum !37
distributive law !37
determinants-- !37
cofactor !37
inverse of matrix-- !37
Vandermonde matrix-- !37
combinatorial matrix-- !37
Cauchy matrix-- !37
elementary symmetric functions !38
--combinatorial matrix !38
--Vandermonde matrix !38
--inverse of matrix !38
--Cauchy matrix !38
Hilbert matrix !38
Krattenthaler !39
--summation !39
--determinants !39
floor-- !39
ceiling !39
Iverson !39
mod-- !39
remainder !40
quotient !40
--mod !40
fractional part !40
number theory-- !40
modulo !40
congruence-- !40
relatively prime !40
greatest common divisor !40
Fermat's theorem !41
prime number !41
ceiling !41
rounding !41
--floor !41
distributive law !42
inverse modulo $m$ !42
Euclid's algorithm extended !42
Fundamental theorem of arithmetic !42
prime factorization !42
totient function !42
Euler's theorem !42
--congruence !42
multiplicative function-- !42
--multiplicative function !43
interchange order !43
Busche !43
replicative function-- !43
--replicative function !44
Bernoulli polynomials !44
trigonometric functions !44
Hurwitz !44
zeta function !44
psi function !44
summation by parts !44
reciprocity-- !44
prime number !45
Legendre symbol !45
quadratic reciprocity !45
--reciprocity !45
--number theory !45
permutations-- !45
Pratt !45
terminology !45
--permutations !46
factorials-- !46
Stirling-- !47
prime numbers-- !47
Legendre !48
--prime numbers !48
termial !48
Knopp !48
Euler !49
Goldbach !49
Hermite !49
--Stirling !49
Gauss !49
Kramp !49
Legendre !49
gamma function-- !49
factorial related to gamma !49
Hankel !49
factorial powers !50
falling !50
rising !50
Capelli !50
Toscano !50
Davis !50
Euler !50
Dutka !50
cards, playing !51
permutations !51
Stirling's approxi\-mation !51
termial !51
Legendre !51
Wilson's theorem !51
Leibniz !51
prime !51
Stickelberger !51
permanent !51
Wallis's product !52
Wallis !52
Arbogast !52
chain rule !52
Euler !52
factorial powers !52
exponents, law !52
--factorials !52
--gamma function !52
combinations-- !52
binomial coefficients-- !52
--combinations !53
binomial coefs defined !53
Pascal's triangle-- !53
Chu !53
Yang !53
Chia !53
Hal\=ayudha !53
Pi\:ngala !53
Chakra\-varti !53
prosody !54
Mah\=av{\ii }ra !54
Bh\=askara !54
von Ettings\-hausen !54
--Pascal's triangle !54
figurate numbers !54
binomial coefs, table !54
tables of numerical quantities !54
Twain !54
jokes !54
factorials !55
polynomials !55
binomial coefs in sums-- !56
arithmetic progression !56
polynomial !57
binomial theorem-- !57
Newton !57
Oldenburg !57
Struik !57
Euler !57
Gauss !58
infinite sums !58
Abel !58
Crelle !58
Gould !58
--binomial theorem !58
Vandermonde !59
Chu !59
Needham !59
Iverson's convention !61
Kronecker delta !61
partial fractions-- !62
--partial fractions !63
Rothe !63
Gould !63
Kauck\'y !63
inversion problem-- !63
--inversion problem !64
polynomial !64
differences of polynomials !64
Gosper !65
Zeilberger !65
Petkov\v {s}ek !65
Wilf !65
Zeilberger !65
hypergeometric functions !65
Dutka !65
binomial coefs generalized !65
$q$-nomial coefficients !65
multi\-nomial coefficient !65
multinomial theorem !65
Temme !66
Wilf !66
Hwang !66
Stirling numbers-- !66
Stirling numbers table !66
tables of numbers !66
Stirling numbers, asymptotic !66
Moser !66
Wyman !66
Barton !66
David !66
Merrington !66
Temme !66
Wilf !66
Hwang !66
Karamata !66
Knuth !66
Stirling numbers combinatorially !66
factorial powers !67
falling powers !67
polynomials !67
Stirling !67
polynomials !68
duality law !68
Stirling !69
falling powers !69
--Stirling numbers !69
combinations !69
cards, playing !69
primes-- !69
Pascal's triangle !69
Lucas !69
Kummer !70
--primes !70
Chu !70
Vandermonde !70
polynomials !70
binomial theorem generalized !70
rising !71
factorial power !71
Vandermonde !71
Torelli !71
Abel's binomial theorem !71
Stirling numbers-- !71
Pascal's triangle !71
Ramus !71
beta function !72
gamma function !72
binomial coefs generalized !72
binomial coefs, asymptotic !72
partial fraction !72
Abel's binomial formula-- !72
--Abel's binomial formula !73
Pascal's triangle !73
inverse of matrix !73
combinatorial number system !73
Stirling !73
Rothe !73
$q$-nomial theorem !73
$q$-nomial coefficients !73
binomial coefs combinatorially !73
combinations with repetitions !73
--Stirling numbers !74
partitions of set !74
Stirling numbers combinatorially !74
Logan !74
binomial coefficient inequalities !74
binomial coefs, bounds !74
de Moivre !74
--binomial coefficients !74
--binomial coefs in sums !74
harmonic numbers-- !75
psi function !75
divergent series !75
Euler's constant !75
Euler !75
Riemann !76
zeta function !76
Bernoulli number !76
Euler !76
summation by parts-- !76
binomial coefs in sums-- !76
integration by parts !77
Stirling numbers !78
--summation by parts !78
--binomial coefs in sums !78
Waring !78
Selfridge !78
gamma function !79
--harmonic numbers !79
Fibonacci numbers-- !79
Leonardo !79
Pisano !79
Fibonacci-- !79
al-Khw\=arizm\ii  !79
Boncompagni !79
--Fibonacci !80
prosody !80
Gop\=ala !80
Hemacandra !80
Singh !80
Kepler !80
phyllotaxis !80
Conway !80
Guy !80
L\'eger !80
Euclid's algorithm !80
Lucas !80
golden ratio !80
extreme and mean ratio !80
Wythoff !80
Coxeter !80
Gardner !80
Markowsky !80
Jacob !81
Schreiber !81
phi !81
Phidias !81
Dickson !81
Kepler !81
Cassini !81
determinant !81
greatest common divisor-- !81
Lucas !81
--greatest common divisor !82
generating functions-- !82
Fibonacci gf-- !82
partial fractions !83
phi-- !83
Bernoulli, Daniel !83
de Moivre !83
linear recurrences !83
--Fibonacci gf !83
rounding !83
Fibonacci !84
prime numbers-- !84
--generating functions !84
Pascal's triangle !85
sum of binomial coefs !85
--prime numbers !85
Fibonomial coefficients !85
Lucas !85
binomial coefs generalized !85
Jarden !85
Motzkin !85
Fibonacci number system !86
phi number system !86
Fibonacci strings !86
strings !86
Gaskell !86
Whinihan !86
game !86
Matiyasevich !86
Klarner !86
--phi !86
--Fibonacci numbers !86
generating functions-- !87
de Moivre !87
recurrences-- !87
Stirling !87
Euler !87
partitions !87
Laplace !87
convergence of power series !87
Bell !87
Niven !87
Henrici !88
linear recurrence !88
geometric progression !88
binomial co\-effi\-cients !89
--recurrences !89
exponential generating function !89
roots of unity !89
Differentiation !90
integration !90
derivative !90
harmonic numbers gf !90
Binomial theorem !90
binomial coefs, gf !90
binomial theorem generalized !90
Stirling numbers, gf !91
logarithm power series !91
Zave !91
Spie\ss  !91
Bernoulli numbers !91
bracket notation for coefficients !92
coefficient extraction !92
Cauchy !92
symmetric functions-- !92
partitions !93
P\'olya !93
Wilf !93
WILF !94
partitions gf !94
elementary symmetric function !94
--symmetric functions !94
binomial coefs, gf !94
double generating function !94
Laplace transform !94
combinations with restricted repetitions !95
Gauss !95
Abel's limit theorem !95
MIX-- !124
machine language !124
RISC !124
MMIX !124
System/360 !124
IBM 650 !124
IBM 709 !124
IBM 7070 !124
UNIVAC III !124
UNIVAC SS80 !124
UNIVAC 1107 !124
CDC 1604 !124
Bendix G20 !124
Burroughs B220 !124
Philco S2000 !124
XDS 920 !124
RCA 601 !124
Honeywell H800 !124
PDP-4 !124
Recomp II !124
byte in MIX-- !124
byte !125
--byte in MIX !125
word-- !125
A-register of MIX !125
X-register of MIX !125
J-register of MIX !125
I1-register of MIX !125
index registers !125
GO button !126
overflow toggle !126
comparison indicator !126
memory !126
field, partial-- !126
--word !127
instructions in MIX-- !127
address portion of MIX instruction !127
index register !127
cell !127
CONTENTS !127
instructions in MIX, symbolic !128
--field, partial !128
packed data !128
loading operators of MIX !129
LDA !129
LDX !129
LD1 !129
LDAN !129
LDXN !129
LD1N !129
storing operators of MIX !130
STA !130
STX !130
ST1 !130
STJ !130
STZ !130
arithmetic operators of MIX-- !131
floating point !131
ADD-- !131
sideways addition !131
SUB-- !131
MUL-- !131
DIV-- !131
--MUL !132
--ADD !132
--SUB !132
--DIV !133
--arithmetic operators of MIX !133
ENTA !133
ENTX !133
ENT1 !133
ENNA !133
ENNX !133
ENN1 !133
INCA !133
INCX !133
INC1 !133
DECA !134
DECX !134
DEC1 !134
comparison operators of MIX !134
comparison indicator !134
CMPA !134
CMPX !134
CMP1 !134
jump operators of MIX-- !134
JMP !134
JSJ !134
JOV !134
overflow toggle !134
JNOV !134
JL !135
JE !135
JG !135
JGE !135
JNE !135
JLE !135
JAN !135
JAZ !135
JAP !135
JANN !135
JANZ !135
JANP !135
JXN !135
JXZ !135
JXP !135
JXNN !135
JXNZ !135
JXNP !135
J1N !135
J1Z !135
J1P !135
J1NN !135
J1NZ !135
J1NP !135
--jump operators of MIX !135
shift operators of MIX !135
SRA !135
SLA !135
SLAX !135
SRAX !135
SLC !135
SRC !135
circulating shift !135
MOVE !135
NOP !136
HLT !136
input operators of MIX-- !136
output operators of MIX-- !136
disk-- !136
drum-- !136
magnetic tape-- !136
line printer-- !136
typewriter-- !136
paper tape-- !136
cards, punched-- !136
peripheral devices !136
block-- !136
alphameric codes for MIX !136
IN !137
OUT !137
IOC !137
--block !137
--cards, punched !137
--paper tape !137
--typewriter !137
--line printer !137
--magnetic tape !137
--drum !137
--disk !137
JRED !137
JBUS !137
--output operators of MIX !138
--input operators of MIX !138
NUM !138
conversion operators of MIX !138
alphameric codes of MIX !138
CHAR !138
execution time for MIX instructions-- !138
WORDSWORTH !139
alphameric codes (TABLE 1) !139
MIX instructions, summary (TABLE 1) !139
--execution time (TABLE 1) !139
GO button !139
trits !139
byte in MIX !139
field, partial !139
loading operators of MIX !139
DIV !139
overflow toggle !142
compar\-ison indicator !142
I1-register of MIX !142
JOV !142
JNOV !142
MOVE !142
HLT !143
J-register of MIX !143
field, partial !143
MIX extensions !143
bootstrapping !143
GO button !143
MMIX-- !2
machine language !2
CRAY I !2
IBM 801 !2
RISC II !2
Clipper C300 !2
AMD 29000 !2
Motorola 88000 !2
IBM 601 !2
Intel i960 !2
Alpha 21164 !2
POWER 2 !2
MIPS R4000 !2
Hitachi SuperH4 !2
StrongArm 110 !2
Sparc 64 !2
Roman numerals !2
bits !2
hexadecimal digits !3
byte !3
ASCII !3
ISO: The International Organization for Standardization\sic / !3
Yossarian !3
HELLER !3
Unicode !3
IEC: The International Electrotechnical Commission !3
UCS: Universal Multiple-Octet Coded Character Set !3
Roman numerals !3
wyde !4
tetrabytes !4
octabytes !4
binary number system !4
unsigned integers !4
two's complement notation !4
signed integers !4
registers !4
memory+ !4
Big-endian convention-- !4
special registers !5
instructions in MMIX-- !5
opcode !5
operands !5
notation s(x) !6
\s (x) !6
integer overflow !6
overflow !6
loading operators of MMIX+ !6
memory address !6
notation u(x) !6
\u (x) !6
LDB !6
LDW !6
LDT !6
LDO !6
signed integers+ !6
unsigned integers++ !6
sign extension !7
extending the sign bit !7
LDBU !7
LDWU !7
LDTU !7
LDOU !7
LDHT !7
LDA !7
STB !7
STW !7
STT !7
STO !7
storing operators of MMIX+ !7
Overflow !7
--Big-endian convention !7
STBU !8
STWU !8
STTU !8
STOU !8
STHT !8
STCO !8
arithmetic operators of MMIX+ !8
addition !8
subtraction !8
multiplication !8
ADD !8
SUB !8
MUL !8
DIV !8
remainder register !8
rR !8
divide check !8
ADDU !8
SUBU !8
MULU !8
DIVU !8
himult register !8
rH !8
binary radix point !8
phi !8
Division !9
dividend register !9
rD !9
2ADDU !9
4ADDU !9
8ADDU !9
16ADDU !9
multiplication by small constants !9
small constants !9
NEG !9
NEGU !9
negation !9
SL !9
SLU !9
SR !9
SRU !9
shift operators of MMIX !9
extending the sign bit !9
sign extension !9
notation $\ll $ !9
notation $\gg $ !9
CMP !9
CMPU !9
comparison operators of MMIX !9
conditional operators of MMIX !10
CSN !10
CSZ !10
CSP !10
CSOD !10
CSNN !10
CSNZ !10
CSNP !10
CSEV !10
ZSN !10
zero or set !10
ZSZ !10
ZSP !10
ZSOD !10
ZSNN !10
ZSNZ !10
ZSNP !10
ZSEV !10
bitwise operators of MMIX !10
bit vectors !10
vector !10
AND !10
OR !10
XOR !10
ANDN !10
ORN !10
NAND !10
NOR !10
NXOR !10
complement !10
notation v(x) !10
notation vbar(x) !10
notation $\band $ !10
notation $\bor $ !10
notation $\oplus $ !10
MUX !11
multiplex mask register !11
rM !11
SADD !11
sideways add !11
counting bits !11
population counting !11
BDIF !11
byte difference !11
WDIF !11
wyde difference !11
TDIF !11
tetra difference !11
ODIF !11
octa difference !11
saturating subtraction !11
notation dotminus !11
notation b(x) !11
notation w(x) !11
notation t(x) !11
graphics !11
pixel values !11
Boolean matrix !11
notation m(x) !11
generalized matrix product !11
Iverson !11
associative !11
MOR !12
MXOR !12
byte reversal !12
reversal !12
floating point operators of MMIX+ !12
IEEE: The Institute of Electrical and Electronics Engineers !12
ANSI: The American National Standards Institute !12
floating binary number !12
notation f(x) !12
exponent !12
fraction !12
sign of floating point number !12
NaN (Not-a-Number) !12
short float+ !12
FADD !12
addition !12
FSUB !12
subtraction !12
FMUL !12
multiplication !12
FDIV !12
division !12
FREM !12
remainder !12
FSQRT !13
square root !13
FINT !13
FCMP !13
comparison !13
FEQL !13
FUN !13
FCMPE !13
rE !13
epsilon register !13
FEQLE !13
FUNE !13
FIX !13
conversion operators of MMIX !13
FIXU !13
FLOT !13
FLOTU !13
SFLOT !13
SFLOTU !13
LDSF !13
STSF !13
ROUND\_OFF !13
ROUND\_UP !13
ROUND\_DOWN !13
ROUND\_NEAR !13
ceiling !13
notation rem !13
notation int !13
minus zero !13
immediate constants+ !13
small constant numbers !13
NEG !14
wyde immediate !14
SETH !14
SETMH !14
SETML !14
SETL !14
INCH !14
addition !14
INCMH !14
INCML !14
INCL !14
ORH !14
bitwise or !14
bitwise operations !14
ORMH !14
ORML !14
ORL !14
ANDNH !14
bitwise and-not !14
bitwise difference !14
ANDNMH !14
ANDNML !14
ANDNL !14
SET !14
jump operators of MMIX !15
@ !15
JMP !15
RA !15
relative addresses-- !15
GO !15
absolute address !15
BN !15
BZ !15
BP !15
BOD !15
BNN !15
BNZ !15
BNP !15
BEV !15
branch operators of MMIX !15
PBN !15
probable branch+ !15
PBZ !15
PBP !15
PBOD !15
PBNN !15
PBNZ !16
PBNP !16
PBEV !16
hints+ !16
register stack !16
PUSHJ !16
PUSHGO !16
stack operators of MMIX !16
--relative addresses !16
return-jump register !16
rJ !16
rG !16
global threshold register !16
global registers !16
rL !16
local threshold register !16
local registers !16
marginal registers !16
POP !16
SAVE !16
UNSAVE !16
register stack !16
register stack offset !17
rO !17
register stack pointer !17
rS !17
system operators of MMIX !17
LDUNC !17
cache memory !17
STUNC !17
PRELD !17
PREST !17
PREGO !17
prefetching !17
SYNCID !17
SYNCD !17
SYNC !17
CSWAP !17
rP !17
prediction register !17
atomic !17
LDVTS !17
virtual address translation !17
interrupts+ !18
trip handler !18
trap handler !18
divide check !18
overflow !18
invalid floating operation !18
overflow !18
under\-flow !18
division by zero !18
inexact !18
arithmetic status register !18
rA !18
excep\-tions !18
event bits !18
DVWIOUZX !18
enable bits !18
rounding mode !18
TRIP !18
bootstrap register !18
rB !18
where-interrupted register !18
rW !18
execution register !18
rX !18
Y operand register !18
rY !18
Z operand register !18
rZ !18
TRAP+ !18
rBB !18
rWW !18
rXX !18
rYY !18
rZZ !18
trap address register !18
rT !18
input/output operations !18
end of program !19
termination !19
halt !19
exit from program !19
interrupt mask register !19
rK !19
interrupt request register !19
rQ !19
Dynamic traps !19
rTT !19
RESUME !19
ropcode !19
hexadecimal notation !19
opcodes+ !19
immediate constant !19
GET !19
PUT !19
special registers of MMIX !19
clock register !19
cycle counter !19
rC !19
failure register !19
rF !19
interval counter !19
rI !19
serial number register !19
rN !19
usage counter !20
rU !20
virtual translation register !20
rV !20
opcode chart !20
running time-- !20
GETA !20
relative address !20
special registers !21
SWYM !21
no-op !21
pipelined !22
prefetching !22
notation $\mu $ !22
notation $\upsilon $ !22
upsilon !22
oops !22
mems !22
probable branch !22
cache memory+ !22
meta-simulator+ !22
MMIX simulator+ !22
--running time !23
KERNIGHAN !23
VAN WYK !23
FINT !23
FREM !23
MOR !23
MXOR !23
registers !23
WORDSWORTH !24
RISC !24
hexadecimal !24
half-bytes !24
nybbles !24
bytes !24
kilobyte !24
megabyte !24
\s (x) !24
\u (x) !24
negating !24
two's complement notation !24
LDHT !24
STHT !24
binary radix point !24
DIV+ !24
division+ !24
overflow !25
carry !25
addition !25
subtraction !25
multiplication !25
signed integers !25
MULU !25
division by small constants !25
multiplication by small constants !25
SL !25
SLU !25
SR !25
SRU !25
Dull !25
comparison operators of MMIX !25
subset representation !25
bitwise operations !25
set intersection !25
set union !25
set difference !25
bit difference !26
BDIF !26
maximum !26
minimum !26
pixel !26
absolute value !26
saturating addition !26
ASCII !26
blank spaces !26
string manipulation !26
parity !26
generalized matrix product !26
cyclic shift !26
ASCII !26
Unicode !26
MOR !26
bit reversal !26
reversal !26
Finite fields !26
MXOR !26
conditional operators of MMIX !26
probable branch !26
GO !26
absolute value !27
tetrabytes, arithmetic on !27
overflow !27
DVWIOUZX !27
Fuchs !27
instruction, numeric form++ !27
loading routine !144
--MIX !144
--instructions in MIX !144
MIXAL-- !144
assembly language for MIX-- !144
instruction in MIX, symbolic !144
maximum algorithm/program !145
location field of MIXAL line !145
opcode field of MIXAL line !145
address field of MIXAL line !145
assembly program !145
comments !145
profile !145
EQU !146
ORIG !146
pseudo-operations !146
asterisk !146
prime numbers, algorithm to compute-- !147
buffer swapping !147
--prime numbers, program to compute !149
asterisk !149
comment !149
EQU !149
CON-- !149
constants in assembly language !150
literal constant !150
--CON !150
local symbols-- !150
Conway !151
--local symbols !151
UNIVAC~I !151
address field of MIXAL line-- !151
ALF !151
ORIG !151
END !151
prime program !152
cards, punched !152
location field of MIXAL line !152
ALF !152
--address field of MIXAL line !153
assembly program !153
defined symbol !153
future reference !153
asterisk !153
W-value-- !154
--W-value !155
location counter !155
opcode field of MIXAL line !155
EQU !155
ORIG !155
CON !155
ALF !155
END !156
Literal constants !156
future reference !156
equivalent of MIXAL symbol !156
future reference restrictions !156
PL/MIX !156
JBUS !157
local symbols !157
--MIXAL !157
--assembly language for MIX !157
switching tables !158
multiway decisions !158
index registers !158
matrix representation-- !158
sequential arrays-- !158
packed data !158
fixed point arithmetic !158
subroutines !158
buffering of I/O !158
row major order !159
--sequential arrays !159
--matrix representation !159
saddle point !159
English letter frequencies !159
buffer swapping !159
Lilius !159
Clavius !159
Easter-- !159
calendar !160
--Easter !160
harmonic series-- !160
rounding !160
--harmonic series !161
Farey series !161
rational numbers !161
traffic signals-- !161
--traffic signals !162
magic square !162
Ibn al-Haytham !162
Ball !162
Coxeter !162
Josephus problem !162
Ahrens !162
graphical display !163
crossword puzzle !163
no-op !28
rH !28
rA !28
rL !28
exponentiation !28
evaluation of powers !28
self-modifying code !28
SYNCID !28
NNIX !28
RANDOLPH !28
WILSON !28
--MMIX !28
--instructions in MMIX !28
MMIXAL-- !28
assembly language for MMIX-- !28
instruction in MMIX, symbolic !28
maximum algorithm/program+ !28
label field of MMIXAL line !29
opcode field of MMIXAL line !29
expression field of MMIXAL line !29
assembly program !29
comments !29
profile !29
IS !30
LOC !30
pseudo-operations !30
relative addresses !30
subroutine !30
complete MMIX program !30
Hello, world++ !30
MMIX simulator !30
object file+ !30
mms !30
mmo !30
NNIX !31
profile !31
Main !31
\$0 !31
command line arguments !31
\$1 !31
string !31
input-output !31
standard output !31
terminate a program !31
BYTE !31
pseudo-operation !31
double-quote !31
string constant !31
ASCII !32
newline !32
prime numbers, program to compute-- !32
ASCII !34
--prime numbers, program to compute !34
Comments !34
IS !34
register number !34
global register !34
\$255 !34
GREG+ !34
base addresses !35
@ !35
local symbols++ !35
Conway !35
UNIVAC~I !35
user space !36
kernel space !36
operating system !36
text segment !36
data segment !36
pool segment !36
stack segment !36
read-only !36
loader !36
binary-to-decimal conversion !37
prime program !37
underscore !37
Unicode !37
decimal constant !37
hexadecimal constant !37
character constant !37
ASCII !37
string constant !37
double-quote !37
defined symbol !37
future reference !37
forward reference, see future reference !37
predefined symbols+ !37
equivalent of MMIXAL symbol !38
primary !38
@ !38
term !38
expression !38
strong binary operators !38
weak binary operators !38
LABEL field of MMIXAL line !38
OP field of MMIXAL line !38
EXPR field of MMIXAL line !38
aligned !39
IS !39
GREG !39
base address !39
LOC !39
BYTE !39
WYDE !39
TETRA !39
OCTA !39
future references !39
blank space !40
comment !40
input-output-- !40
\$255-- !40
TRAP !40
Fopen !41
handle !41
binary file !41
text file !41
standard input file !41
standard output file !41
standard error file !41
Fclose !41
Fread !42
Fgets !42
Fgetws !42
wide strings !42
newline !42
Fwrite !42
Fputs !42
Fputws !42
Fseek !42
rewind !42
Ftell !43
predefined !43
Fopen !43
Fclose !43
Fread !43
Fgets !43
Fgetws !43
Fwrite !43
Fputs !43
Fputws !43
Fseek !43
Ftell !43
TextRead !43
TextWrite !43
BinaryRead !43
BinaryWrite !43
BinaryReadWrite !43
Halt !43
--input-output !43
--\$255 !43
local symbols !43
Fread !43
Fwrite !43
double-quote !44
Quick !44
align !44
Unicode !44
Arabic numerals !44
ASCII !44
Arabic script !44
bidirectional !44
floating point arithmetic !44
FREM !44
--MMIXAL !44
--assembly language for MMIX !44
C !45
Java !45
Wirth !45
PL/360 !45
PL/MMIX !45
System/360 !45
literate programming !45
Knuth !45
switching tables !45
multiway decisions !45
fixed point arithmetic !45
floating point arithmetic !45
subroutines !45
complete MMIX program !45
privileged !46
valid !46
multiway decisions !46
switching table !46
table-driven computation !46
matrix representation !46
sequential arrays !46
row major order !46
saddle point !46
Farey series !47
rational numbers !47
optimization of loops !47
meta-simulator !47
string manipulation !47
pipeline simulator !47
copying a string !47
cryptanalysis !47
optimization of loops !47
meta-simulator !47
pipeline !47
Fibonacci !47
rounding !47
phi !47
magic square+ !47
Ibn al-Haytham !48
Ball !48
Coxeter !48
Josephus problem !48
Ahrens !48
harmonic convergence !48
harmonic series-- !48
rounding !48
--harmonic series !49
Lilius !49
Clavius !49
Easter !49
calendar !49
remainder !49
division !49
traffic signals !50
graphical display+ !50
crossword puzzle+ !50
permutations-- !164
two-line notation !164
cycle notation-- !164
cycles in perms-- !164
singleton cycles !164
identity permutation !164
() !164
permutation in place !165
multiplication of permutations-- !165
commutative !165
--multiplication of permutations !167
--cycle notation !167
--cycles in perms !167
analysis of algorithms-- !170
execution time, methods for finding-- !170
profile !170
Kirchhoff's first law-- !170
conservative law !170
--Kirchhoff's first law !171
singleton cycle !171
--execution time, methods for finding !172
--analysis of algorithms !172
cycle notation-- !172
multiplication of permutations-- !172
--multiplication of permutations !173
--cycle notation !175
symbol table algorithms !175
inverse of perm-- !175
identity permutation !175
cycles in perms-- !176
Huang !176
Boothroyd !177
--cycles in perms !178
--inverse of perm !178
unusual correspondence-- !178
canonical cycle notation-- !178
--canonical cycle notation !179
left-to-right minimum !179
--unusual correspondence !179
analysis of algorithms !179
cycles in random permutation-- !179
Stirling numbers combinatorially !179
singleton cycles-- !180
derangements !180
Stirling !181
probability generating function !181
inclusion and exclusion !181
--singleton cycles !181
de Moivre !182
Todhunter !182
Whitworth !182
exchange !182
cycles in perms-- !182
two-line notation !182
inverse of permutation !182
cycle notation !182
Transposing a rectangular matrix !182
row major order !182
derangements !183
rounding !183
Shepp !183
Lloyd !183
Golomb !184
Shepp !184
Lloyd !184
--cycles in random permutation !184
--cycles in perms !184
inclusion and exclusion !184
totient function !184
Kaplansky !184
Josephus !184
orthogonal vectors of permutations !184
permutations, orthogonal vectors of !184
permutation in place-- !185
transposing blocks-- !185
--transposing blocks !185
--permutation in place !185
strings !185
--permutations !185
subroutines-- !186
subroutine linkage !186
J-register of MIX !186
maximum algorithm/program !186
entrances to subroutines-- !186
exits from subroutines-- !186
MMIX !187
self-modifying code !187
STJ !187
JMP !187
parameters !187
calling sequence-- !187
arguments !187
saving and restoring registers !188
multiple entrances !189
JSJ !189
J-register of MIX !189
arguments of subroutines !189
parameters of subroutines !189
System/360 !189
multiple exits !190
--calling sequence !190
recursive use of subroutines !191
--entrances to subroutines !191
--exits from subroutines !191
large programs-- !191
program construction-- !191
Dijkstra !191
Wirth !191
temporary storage !191
debugging-- !192
trace routine !192
reachability !51
METAPOST !51
\MMIX masters !51
subroutines-- !52
subroutine linkage-- !52
library !52
maximum algorithm/program-- !52
entrances to subroutines-- !52
exits from subroutines-- !52
PUSHJ !53
POP !53
GO-- !53
parameters !54
calling sequence-- !54
arguments !54
saving and restoring registers !55
\$255 !56
multiple entrances !56
multiple exits+ !56
--maximum algorithm/program !56
--calling sequence !56
recursive use of subroutines !57
--entrances to subroutines !57
--exits from subroutines !57
memory stack+ !57
stack pointer+ !57
stack !57
data segment !57
leaf subroutine !57
frame pointer !58
--GO !58
register stack-- !58
register stack !58
local registers !58
rL !58
\$0 !58
\$1 !58
global registers !58
rG !58
marginal !58
PUSHJ !59
POP !59
multiple exits !60
rJ !60
calling sequence !60
nonleaf subroutines+ !60
scalar !61
stack segment !61
SAVE !61
UNSAVE !61
--subroutine linkage !61
--register stack !61
MMIXAL+ !61
PREFIX+ !61
structured symbols+ !61
library !61
current prefix !61
LOCAL !62
GREG !62
BSPEC !62
ESPEC !62
compilers !62
library !62
large programs-- !63
program construction-- !63
Dijkstra !63
Wirth !63
programming languages !63
PL/MMIX !63
rewrites !64
debugging-- !64
trace routine !64
Knuth !65
literate programming !65
TeX !65
--debugging !65
--program construction !65
--large programs !65
TURING !65
ACE !65
leaf subroutine !65
PUSHGO !65
marginal registers !65
trip interrupt !65
overflow !65
handler !65
local registers !65
global registers !65
register stack+ !65
current prefix !65
PREFIX !65
Knuth !193
literate programming !193
TeX !193
--debugging !193
--program construction !193
--large programs !193
TURING !193
ACE !193
calling sequence !193
MOVE !193
self-modifying code !193
coroutines-- !193
chess !194
coroutine linkage !194
calling sequence-- !196
--calling sequence !197
--subroutines !197
saving and restoring registers !198
multipass algorithms-- !198
pass-- !198
UNIX !198
pipe !198
filters !198
memory hierarchy !199
Fibonacci number !66
recursive !66
Nonlocal\/ {\ninebfi goto} statements !66
coroutines-- !66
chess !66
coroutine linkage !66
whitespace character !67
character constant !67
subroutine !68
calling sequence-- !68
\$255 !68
--calling sequence !70
Initialization !70
starting a program !70
--subroutines !70
register stack !70
multipass algorithms-- !70
pass-- !70
UNIX !71
pipe !71
filters !71
memory hierarchy !72
joke !72
threads !72
replicated coroutines !72
--pass !72
--multipass algorithms !72
TETRA !72
double-quote !72
coroutine linkage+ !72
joke !200
--pass !200
--multipass algorithms !200
coroutine linkage !200
--coroutines !200
interpreter-- !200
virtual machine !201
debugging !201
Knuth !201
multipass program-- !201
--multipass program !202
ALGOL !202
Randell !202
Russell !202
compiler algorithms !202
Evans !202
Fuchs !202
TeX !202
Knuth !202
Rokicki !202
Adobe Systems !202
PostScript !202
subroutines !202
--interpreter !202
simulation of computers-- !202
emulator !202
reprogramming !203
MIX simulator-- !203
discrete system simulators !203
--simulation of computers !203
switching table-- !205
--switching table !206
subroutines-- !206
field, partial !207
--subroutines !207
arithmetic operators of MIX !208
ADD !208
SUB !208
MUL !208
DIV !208
overflow toggle !208
loading operators of MIX !208
LDA !208
LDX !208
LDAN !208
LDXN !208
LD1 !208
LD1N !208
storing operators of MIX !209
STA !209
STX !209
ST1 !209
STJ !209
STZ !209
jump operators of MIX !209
JMP !209
JOV !209
JNOV !209
JLE !209
JGE !209
JNE !209
JL !209
JE !209
JG !209
switching table !209
JSJ !210
JAN !210
JAZ !210
JAP !210
JANN !210
JANZ !210
JANP !210
JXN !210
JXZ !210
JXP !210
JXNN !210
JXNZ !210
JXNP !210
J1N !210
J1Z !210
J1P !210
J1NN !210
J1NZ !210
J1NP !210
switching table !210
ENTA !210
ENNA !210
INCA !210
DECA !210
ENTX !210
ENNX !210
INCX !210
DECX !210
ENT1 !210
ENN1 !210
INC1 !210
DEC1 !210
comparison operators of MIX-- !210
CMPA-- !210
CMPX-- !210
CMP1-- !210
comparison indicator !211
--comparison operators of MIX !211
--CMPA !211
--CMPX !211
--CMP1 !211
subroutines !211
shift operators of MIX !211
MOVE !211
GO button !211
JBUS !212
--MIX simulator !212
simulation of self-- !212
trace routine-- !212
J-register of MIX-- !212
monitor !212
saving and restoring registers !213
comparison indicator !213
PUSH !73
POP !73
register stack !73
--coroutines !73
interpreter-- !73
virtual machine !73
debugging !73
Knuth !74
multipass program !74
ALGOL !74
Randell !74
Russell !74
compiler algorithms !74
Evans !74
Fuchs !74
TeX+ !74
Knuth !74
Rokicki !74
Adobe Systems !74
PostScript !74
subroutines !75
--interpreter !75
simulation of computers-- !75
emulator !75
reprogramming !75
MMIX simulator in MMIX-- !75
discrete system simulators !76
--simulation of computers !76
Pipeline processing !76
meta-simulator !76
privileged instructions !76
clock !76
data segment+ !76
local register ring !76
text segment !77
subroutines-- !77
MemFind subroutine+ !77
chunks !77
linked allocation+ !77
self-organizing !77
PREFIX+ !77
register stack-- !78
local register ring++ !79
stack pointer !79
rS !79
stack offset !79
rO !79
rL !79
global registers !79
global !80
local !80
marginal !80
colon !80
prefix !80
rJ !80
leaf subroutines !80
rJ !81
--subroutines !81
--register stack !81
@ !81
text segment !81
data segment !81
packed data !82
unpacking !82
table-driven programs !82
Flag bits !82
relative address !83
operands+ !83
register stack !84
marginal !84
local !84
global !84
RESUME !84
overflow !84
enable bits !85
event bits !85
rH !85
multiplication !85
branch !85
probable branch !85
PUSHJ+ !85
PUSHGO+ !85
register stack+ !85
SYNC !86
switching table+ !86
multiway switching+ !86
jump table+ !86
TRAP+ !86
packed data+ !87
table-driven computation+ !87
flags !87
arithmetic exceptions !89
label !89
IEEE standard !89
floating point arithmetic !89
underflow !89
inexact exception !89
trip handler !89
DVWIOUZX !89
denormal !89
command line !90
binary file !90
UNSAVE !90
library !91
Main !91
initialization !91
starting a program !91
rK !91
rT !91
rTT !91
rV !91
error recovery !91
debugging !91
MemFind !91
nonlocal goto !91
division !91
CSWAP !91
GET !92
PUT !92
POP !92
rL !92
rG !92
SAVE !92
local registers !92
global registers !92
UNSAVE !92
trip interrupts !92
RESUME !92
ropcode !92
DVWIOUZX !92
Fputs !92
Fopen !92
Fread !92
local register ring !92
subroutines !92
binary files+ !92
--MMIX simulator in MMIX !93
jump trace !93
trace routine !93
profiling !93
self-modification !93
overflow toggle !214
omphaloskepsis !214
jump trace !214
profiling !214
--J-register of MIX !214
--trace routine !214
--simulation of self !214
input-- !215
output-- !215
MMIX !215
dictionaries of English !215
I/O !215
reading !215
writing !215
data !215
IN-- !215
input operators of MIX-- !215
JBUS !216
busy waiting !216
--input operators of MIX !216
--IN !216
anticipated input !216
end of file !216
buffering-- !216
Webster's New World Dictionary !216
critical path time !217
buffer swapping-- !217
sentinel !218
--buffer swapping !218
blocking of records !218
circle of buffers-- !218
assigning a buffer-- !219
releasing a buffer-- !219
coroutines-- !222
JRED-- !222
coroutine linkage !223
--JRED !223
--coroutines !223
--releasing a buffer !223
--assigning a buffer !223
pooled buffers !224
channel !224
forecasting !224
OUT !225
buffer swapping !225
blocking of records !225
assigning a buffer-- !226
releasing a buffer-- !226
--releasing a buffer !227
--assigning a buffer !227
end of file !227
--circle of buffers !227
pooled buffers !227
MIX extensions !228
interrupt !228
overflow toggle !228
comparison indicator !228
saving and restoring registers !228
clock for real time !228
INT !228
latency !228
rotating memory !228
disk input, buffered !228
--output !228
--input !228
--buffering !228
subroutine history-- !229
Babbage !229
Analytical Engine !229
Morrison !229
Hopper !229
trigonometric functions !229
Mark I calculator !229
open subroutines !229
Jacquard !229
cards, punched !229
paper tapes !229
subroutine linkage !229
Goldstine !229
von Neumann !229
parameters !229
Turing !229
Carpenter !229
Doran !229
Wilkes !229
Wheeler !229
Gill !229
Conway !229
coroutine history !229
Erdwinn !229
Merner !229
UNIVAC I !229
Dahl !229
ALGOL !229
SIMULA I !229
Nygaard !229
Dahl !230
Dijkstra !230
Hoare !230
interpretive routine !230
Turing machine !230
automata theory !230
Mauchly !230
Moore School !230
Whirlwind I !230
Adams !230
Illiac~I !230
Wheeler !230
Turing !230
Pilot ACE !230
Bennett !230
Prinz !230
Woods !230
Office of Naval Research !230
Backus !230
IBM 701 !230
Speedcoding !230
IBM 650 !230
Wolontis !230
Bell Interpretive System !230
IPL !230
Newell !230
Shaw !230
Simon !230
tracing !230
Gill !230
Wilkes !230
Wheeler !230
--subroutine history !230
Meek !230
IBM 705 !230
System/360 !230
McKeeman !230
Horning !230
Wortman !230
Satterthwaite !231
buffering history-- !231
UNIVAC I !231
--buffering history !231
DYSEAC !231
Leiner !231
Mock !231
Swift !231
Dijkstra !231
Loopstra !231
Scholten !231
X-1 !231
paper tape !231
typewriter !231
semaphores !231
Genuys !231
Ferguson !231
FORTRAN !231
circles of buffers !231
GOLDSTINE !231
VON NEUMANN !231