How Google designed a smarter calculator than Apple скачать в хорошем качестве

How Google designed a smarter calculator than Apple

Self-study with Brilliant at https://brilliant.org/TreforBazett to get started for free for 30 days, and to get 20% off an annual premium subscription! Paper by Hans Boehm: https://research.google/pubs/towards-... Useful blog post also covering the paper: https://chadnauseam.com/coding/random... The iOS calculator occasionally gives errors like saying that 10^100+1-10^100=0. This is because it uses floating point arithmetic, which is great because it uses little memory, can represent a huge range of numbers, and allows for very efficient calculations. But Hans Boehm at google uses a hybrid approach with recursive real arithmetic to create a calculator app that avoids these errors and, while not perfect, is pretty good at identifying user experience issues like deciding between 0 and 0.00000000. 0:00 Apple vs Google 0:38 Floating Point Arithmetic 4:11 Rationals and Dyadic Rational Approximations 7:23 Recursive Reals 9:48 Addition of Recursive Reals 15:05 Decidability 18:00 Implementation 24:53 Check out Brilliant.org/TreforBazett Correction: 8:42 I say we can UNIQUELY choose a dyadic rational within that error bound that has the denominator 2^n. It isn't quite unique. Take 1/3 rounding to the nearest 1/4. Both 1/4 and 2/4 are within the error range. But that's ok, you can choose either of them and ultimately all we care about is choosing something within the error bound that is as small (from a memory perspective, i.e. smaller denominator) as possible. I can't tell from paper, but I suspect in the implementation it spends a bit of computational time to adjudicate that 1/4 is closer than 2/4 and so chooses that one BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS I LOVE (affilliate link): ► https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line In...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems...   ►Cool Math Series:    • Cool Math Series   SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok:   / drtrefor   ►Instagram (photography based):   / treforphotography