arithmetic   746

« earlier    

What Every Computer Scientist Should Know About Floating-Point Arithmetic
This appendix is an edited reprint of the paper What Every Computer Scientist Should Know About Floating-Point Arithmetic, by David Goldberg, published in the March, 1991 issue of Computing Surveys. Copyright 1991, Association for Computing Machinery, Inc., reprinted by permission.
arithmetic  math  paper  programming 
8 days ago by jchris
Continued Fractions
I like con­tin­ued frac­tions for their elegance, their finite closure under a wider set of oper­a­tions than dec­imal expan­sion, and their most-sig­nif­icant-part-first arithmetic. But they run for unpre­dictable and pos­si­bly non-ter­minat­ing time before pro­vid­ing any informa­tion at all.
I pro­pose that a useful real-number rep­re­senta­tion would be equiv­a­lent to inter­vals that could be narrowed by applying a compu­ta­tion. Con­tin­ued frac­tions are such a narrow­ing inter­val: truncat­ing at an odd number of val­ues gives a lower bound, while truncat­ing at an even number gives an upper bound. The prob­lem is that not every answer gives such a narrow­ing inter­val because not all con­tin­ued frac­tions con­tin­ue. [1; 2, 2, …] is a narrow­ing inter­val, but [2], it’s square, must appear in an all-or-noth­ing way.
All of which begs the ques­tion, what rep­re­senta­tion should be used? It clearly will not be canon­ical, since we want to be able to rep­re­sent two as both an finite inte­ger and an infi­nitely-narrow­ing inter­val converg­ing on two. Beyond that, it isn’t clear. Some­thing to think about.
continued-fractions  algorithms  arithmetic  to-write-about  nudge-targets  consider:looking-to-see 
28 days ago by Vaguery
Arithmetic with Continued Fractions
Multiprecision arithmetic algorithms usually represent real numbers as decimals, or perhaps as their base-2n analogues. But this representation has some puzzling properties. For example, there is no exact representation of even as simple a number as one-third. Continued fractions are a practical but little-known alternative.

Continued fractions are a representation of the real numbers that are in many ways more mathematically natural than the usual decimal or binary representations. All rational numbers have simple representations, and so do many irrational numbers, such as sqrt(2) and e1. One reason that continued fractions are not often used, however, is that it's not clear how to involve them in basic operations like addition and multiplication. This was an unsolved problem until 1972, when Bill Gosper found practical algorithms for continued fraction arithmetic.

In this talk, I explain what continued fractions are and why they are interesting, how to represent them in computer programs, and how to calculate with them.
continued-fractions  arithmetic  nudge-targets  consider:looking-to-see  to-write-about 
28 days ago by Vaguery
RT : So here's a new free resource to boost KS2 - 5 minutes of questions every day every week Y3-6. USP is f…
arithmetic  from twitter_favs
9 weeks ago by sophiebessemer
Beast Academy
Math learning for kids with a novel approach. I've seen the way this guy asks people to think about math and it's pretty challenging.
math  education  learning  arithmetic  kids 
10 weeks ago by drhayes
GitHub - attaswift/BigInt: Arbitrary-precision arithmetic in pure Swift
This repository provides integer types of arbitrary width implemented in 100% pure Swift. The underlying representation is in base 2^64, using Array<UInt64>. This module is handy when you need an integer type that's wider than UIntMax, but you don't want to add The GNU Multiple Precision Arithmetic Library as a dependency.
swift  bigint  arithmetic 
october 2017 by dlkinney

« earlier    

related tags

!zsh  #  -  academia  access  after  ai  algebra  algorithm  algorithms  alias  and  arbitrar-precision  architecture  arm  array  arrays  artificial  assembly  assoc  associative  authentication  awaymsgused  backquotes  bash  bc  before  bigint  binary  bit-tricks  bits  bitwise  blog  bonn  book  brace  brain  breakfast  brucedawson  bytes  c++  c  calculation  calculator  calculus  calendar  cereal  challenge  child  children  closure  closures  code  coding  coinduction  comic  command  compute  computer  computerscience  computing  condition-code  consider:looking-to-see  continued-fractions  continued  corps-fini  cs  daniel-lemire  data  date  day  dictionary  differential  dir  divide  division  double  drycode  economy  education  embedded  engineering-design  equations  error  ethereum  exercise  expansion  expression  expressions  fair-mapping  fairness  fft  file  filename  filesize  finite-field  fixedpoint  flags  float  floating-point  floating  floatingpoint  formats  fractal  fraction  fw  game  generation  geometric  geometry  glob  globbing  go  golang  group  head  hexa  hexadecimal  history  ieee  in  increment  indexing  integer  intelligence  interesting  interval  is:repo  issue  java  javascript  johnregehr  join  kids  lang:swift  languages  learning  library  line  linear  linux  logarithm  logic  mac  manycore  material  math  mathematical-recreations  mathematics  maths  matrix  memory  mental  merriam-webster  modification  modular  modulo  month  morning  multi-core  mw  negative  notation  nudge-targets  number-theory  number  numbers  numeracy  numerical  of  operations  or  origins  other  overflow  paper  parallelism  parameter  parentheses  parser  pattern  perfectoid  perpetual  peter  phishing  point  pointer  posit  precision  primitive  probability  problem  proceedings  process  processor  program  programming  proof  puzzle  puzzle24  python  qualcomm  qualifiers  quotes  rather-interesting  read  recursive  reduce  reference  removal  replacement  representations  research  reverse  rfw  roots  rosie  rounding  ruby  saturday  scary  scholze  school  science  security  sequence  sh  shared  shell  signalprocessing  signals  singularity  size  smbc  sorting  spaces  spirograph  split  splitting  stream  structures  subscript  subscripts  substitution  subtitution  subtract  swift  swiftlang  symlink  symposium  system  tail  tank  teach  technique  terms  testing  the  theory  to-write-about  tolearn  tool  toolbox  toread  totry  tounderstand  transforms  tree  trick  tricks  tutorial  unix  unum  user  variable  weak  web  webcomic  wetcode  word-splitting  word  wordsplitting  xor  zero  zsh  | 

Copy this bookmark: