Multiple-precision arithmetic→250f
addition→250f
subtraction→250
multiplication→250f
division→250f
quotient→250
remainder→250
places→250
conversion of representations→250
carry→251f
induction on the computation→251
borrow→252
\hbox {\:tWM1}→253
multiplication,→253f
carry→254f
induction→254
division,→255f
borrow→258
carry→258
complement notation→261f
two's complement→261f
ones' complement→261f
analysis of algorithms→261f
carries→261f
generating functions→262f
Lehmer→263
Ballantine,→263
von Neumann→263
Goldstine→263
Pope→263
Stein→263
Cox→263
Luther,→263
Stein,→264
Krishnamurthy→264
Nandi→264
Collins→264
Musser→264
Fourier division→264
Fourier,→264
Lehmer,→264
Uspensky,→264
Newton's method→264
reciprocal→264
Krishnamurthy→264
Laughlin,→264
ones' complement→265
Stroud→265
Secrest,→265
Blum,→265
Tienari→265
Suokonautio,→265
Collins,→265
Brent,→265
hardware→265f
Reitwiesner,→265
MacSorley→265
Metz,→265
Garner,→265
Winograd,→265
Brent→265
Floyd,→265
Sun Ts\u u→265
al-Khow\A arizm\A \i →265
al-Uql\A \i dis\A \i →265
Fibonacci→265
Robert Recorde→265
proof→265f
inductive assertions→265f
Hindu→265
Arabic→265
al-Uql\A \i dis\A \i →265
linked memory→266
linear lists→266
carry→266
mixed-radix→266
addition, mixed-radix→266
borrow→266
subtraction→266
multiplication of fractions→266
division→266f
Svoboda,→267
balanced ternary→268
division, balanced ternary→268
quater-imaginary number system→268
division, quater-imaginary→268
Nadler,→268
Pawlak→268
Wakulicz,→268
square roots→268
linked memory→268
decuple-precision→268
floating point→268
pi→268
Shanks→268
Wrench,→268
Salamin→268
Modular Arithmetic→268f
Chinese Remainder Theorem→269f
parallel computers→270
real-time→270
Euler's theorem→270
Sun→271
Needham→271
Chhin→271
Dickson→271
addition, mod m→271
subtraction, mod m→271
ones' complement→272
conversion of representations→273
casting out nines→273
proofs, constructive versus nonconstructive→273
Euler's totient function $\varphi (n)$→273
Garner→274
Fraenkel,→274
Szab\'o→275
Takahasi→275
Ishibashi,→275
linear equations→276
Borosh→276
Fraenkel→276
CDC 1604→276
McClellan,→276
Bareiss,→276
Svoboda→276
Valach→276
Garner→276
Fraenkel→276
Sch\"onhage→276
Szab\'o→276
Tanaka→276
Chinese remainder theorem, generalized→276
Automorphic numbers→278
multiplication→278f
recursive process→279f
Karatsuba→279
calculating prodigies→279
mental arithmetic→279
Toom→280
Cook→280
interpolation→281
Stirling number→282
Toom→282
Cook→282
recursive→283f
Toom→284
Cook→284
modular→287f
Sch\"onhage→287f
Chinese remainder theorem→288f
Euclid's algorithm→289
convolution→290f
Fourier transform→290f
Toom→290
Strassen→290f
FFT, see Fast Fourier Transform→290
fast Fourier transform→290f
inverse Fourier transform→291
fixed point arithmetic→292f
error estimates→293
absolute error→293
truncate→293
pointer machine→295
storage modification machines→295
linking automata→295
division→295f
Newton's method→295
reciprocal→295
Cook→296
Anderson→296
Earle,→296
Goldschmidt,→296
Powers,→296
Brent→297
linear iterative array→297f
automata→297f
hardware, suitable algorithms for→297f
integrated circuit module→297
Atrubin,→299
Winograd→299
Wallace,→299
Baker→300
fast Fourier transform→300
convolution→300
Sch\"onhage→300f
Strassen→300
pointer machine→301
Cook→301
Fischer→301
Stockmeyer→301
Paterson→301
Fischer,→301
Meyer→301
pointer machines→301