Nauseam (in sf!) (@ChadNauseam) / X

Nauseam (in sf!)

3,864 posts

Nauseam (in sf!)

@ChadNauseam

If I sound lazy just ignore my tone cause I’m always gonna answer when you call my phone (at @WaferSystems)

Joined January 2020

Pinned
Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
"A calculator app? Anyone could make that." Not true. A calculator should show you the result of the mathematical expression you entered. That's much, much harder than it sounds. What I'm about to tell you is the greatest calculator app development story ever told.
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Nauseam (in sf!)
@ChadNauseam
Jun 6, 2025
scott alexander makes a good point here:
Emma Camp
@emmma_camp_
Jun 5, 2025
This tech does not *prevent* any children from going blind. It ensures that children who may go blind will never be born.
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Nauseam (in sf!)
@ChadNauseam
Aug 17, 2025
imagine you're 15 and just want to make your own programming language and then you get stunlocked by this
zack
@zack_overflow
Aug 17, 2025
Every programmer I’ve talked to who’s into types and programming language development has the shared trauma of being recommended to read “Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism” only to discover it not being complete nor easy at all
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
Even for him, this must have been a challenge. The purpose of a calculator app is to give you correct answers. Floating point numbers are imprecise - they cannot represent 0.3 or 10^100. This means a calculator built on floating point numbers is like a house built on sand.
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
Google hired Hans-J. Boehm, of the "Boehm garbage collector" fame. They needed an elite coder to fix garbage collection and concurrent programming. He led the effort to define C++ shared variable semantics. But then they gave him an impossible task: write a calculator app.
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
That picture is from iOS calculator. Notice anything? It's wrong. (10^100) + 1 − (10^100) is 0, not 1. Android gets it right. And the story for how is absolutely insane.
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Nauseam (in sf!)
@ChadNauseam
May 15, 2025
when I was in 2nd grade, I thought I was cooking by inventing the "negative penny" to make it easier to pay with exact change when you buy something for 99 cents
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
It bears repeating. To give correct answers to mathematical expressions, a calculator must represent numbers. And almost all numbers cannot be expressed in IEEE floating points. Even simple operations with floating point numbers requires careful thought for an accurate answer
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
Now THAT is engineering! You should read his paper, buff.ly/3EGs7Bm I hope you appreciate your android calculator a little more next time you use it! (Also I decided to try writing this thread in the style of a linkedin influencer lol, sorry about that.)
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
So Boehm had no choice but to go even deeper. It was time to get serious. We started off with integers (bignum), went to rational numbers, then algebraic numbers. What's next? Constructive real numbers.
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
Math goes much deeper than fractions. What about π or √2? A calculator that is based on arbitrary-precision fractions still can't tell you the circumference of a circle, since π is not expressible as a fraction. If your calculator can't handle 9th grade math, what good is it?
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
Some problems can be avoided if you use bignums. Most numeric types are always 2 or 4 bytes. Not so for bignums. These are integers without bounds. They grow in memory as needed. This solves the (10^100) + 1 - (10^100) example. But bignums are integers. How about fractions?
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
So Boehm began to consider "recursive real arithmetic" (RRA). Given an expression and how precise you want the answer, RRA gives you an answer at least that precise. Check out the cover of this classic textbook. See how the rulers get smaller and smaller?
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Nauseam (in sf!)
@ChadNauseam
Feb 15, 2025
Replying to @ChadNauseam
Algebraic arithmetic would get him closer. Forget about representing numbers as numerators and denominators. You can represent them as the polynomial equation they satisfy. For √2, it would be x² - 2 = 0. (Plus you'd store that you want the positive root.)
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