The Array Cast

Raul Miller - Precision

Aug 5, 2023

01:05:10

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Quick takeaways

Floating point numbers have limitations in accuracy and precision, while extended integers in J provide a workaround by maximizing precision within the available bit space.

Parsing numbers accurately and maintaining precision can be challenging, but recent improvements in languages like BQN allow for more accurate representation of large numbers by splitting them into integer and floating point components.

Extended precision and integer types, like those supported by J, excel in fields like number theory, cryptography, simulation, and precise mathematical calculations.

Deep dives

The Challenges of Representing Numbers on Computers

Representing numbers on computers can be challenging due to the limitations of finite representation. Infinities are not numbers per se, but rather used in mathematical concepts and cannot be precisely represented on computers. Floating point numbers, for instance, have limitations in accuracy and precision, and algebraic properties like associativity are not always preserved. Extended integers in J, which represent polynomials, provide a workaround by using a representation that maximizes precision while still fitting into the available bit space. However, even with extended integers or rational numbers, computations involving square roots or trigonometric functions can introduce inaccuracies. Nevertheless, for many practical use cases, the precision of floating point numbers is sufficient.

Introduction

2min

The Double Strike X in BQN

2min

Raw Miller Raw Is a Veteran of the J Programming Language and Has a Long Background With the Language

2min

The History of a Polyglot Programmer

3min

How I Discovered the Array Languages in College

2min

The Story of Coming Back to Jay

2min

The Relationship Between Henry and Jay

5min

The Importance of Stability in Computers

2min

The Problems With Infinite Numbers

2min

10.

How to Use NANs in KQ

2min

11.

The Problem With Extended Forms in Calculations

2min

12.

The Importance of Exact Calculations in Banking Calculations

1min

13.

The Difference Between a Rational Type and a Fixed Point Type

2min

14.

The Problem With Floating Point Types

2min

15.

The North 2000: APL With All Kinds of Fancy Features

2min

16.

The Importance of Precision in Advertising

2min

17.

NASA's Limit Problems

2min

18.

The JPL and the Hilbert Matrix

3min

19.

The Problem With Idioms in Mathematica

2min

20.

The Importance of Knowing Where You Want to Go

2min

21.

How to Parse a Number

2min

22.

How to Handle the French Republican Calendar

2min

23.

The Problem With the Gregorian Calendar

2min

24.

The History of Calendars

4min

25.

The Importance of Second Since the Unix Epoch

2min

26.

The Importance of J

2min

27.

Zagging vs. Rust: The Differences

2min

28.

The Importance of Community in JavaScript

2min

29.

The Proliferation of Extended Integer Types

3min

30.

The Proliferation of the APLK Community

3min

Array Cast - August 4, 2023
Show Notes

Thanks to Bob Therriault and AdámBrudzewsky for gathering these links:

[01] 00:01:49 Stephen's book contributions sjt AT 5jt DOT com

Dyalog User Meeting https://www.dyalog.com/user-meetings/dyalog23.htm

[02] 00:04:19 Henry ArrayCast episodes
ArrayCast Episode #6 https://www.arraycast.com/episodes/episode-06-henry-richs-deep-dive-into-j

ArrayCast Episode #18 https://www.arraycast.com/episodes/episode18-henry-rich-presents-j903

ArrayCast Episode #48 https://www.arraycast.com/episodes/episode48-henry-rich

ArrayCast Episode #50 https://www.arraycast.com/episodes/episode50-fold

APL Farm Discord https://aplwiki.com/wiki/APL_Farm

[03] 00:10:40 Todd Rundgren https://en.wikipedia.org/wiki/Todd_Rundgren

[04] 00:13:00 J's Extended Integer type https://code.jsoftware.com/wiki/Vocabulary/Constants#Extended_Integers

lib.gmp https://gmplib.org/

Infinity in J https://code.jsoftware.com/wiki/Vocabulary/Constants#Infinity

Endianness https://en.wikipedia.org/wiki/Endianness

[05] 00:20:25 NaN or Indeterminate in J https://code.jsoftware.com/wiki/Essays/Indeterminate

Null in K https://k.miraheze.org/wiki/Null%3F

[06] 00:25:46 Fixed point type https://en.wikipedia.org/wiki/Fixed-point_arithmetic

[07] 00:29:30 Floating Point Math https://0.30000000000000004.com

NARS2000 https://aplwiki.com/wiki/NARS2000

J constants https://code.jsoftware.com/wiki/Guides/Constants

[08] 00:35:20 Hilbert Matrix https://en.wikipedia.org/wiki/Hilbert_matrix

[09] 00:37:00 Kamila Lisp https://aplwiki.com/wiki/KamilaLisp

Euler's Formula https://en.wikipedia.org/wiki/Euler%27s_formula

Dyalog Idioms https://help.dyalog.com/latest/#Language/Introduction/Idiom%20Recognition/Idiom%20List.htm

Roger's Comments https://www.dyalog.com/blog/2015/12/apl-puns/

[10] 00:39:00 World Math Day https://www.jsoftware.com/papers/APLQA.htm#worldmathsday

Complex Floor https://aplwiki.com/wiki/Complex_floor

[11] 00:44:50 Dyalog Time Functions https://help.dyalog.com/latest/#Language/System%20Functions/dt.htm

French Republican Calendar https://en.wikipedia.org/wiki/French_Republican_calendar

Proleptic Gregorian calendar https://en.wikipedia.org/wiki/Proleptic_Gregorian_calendar

Leap year rules https://en.wikipedia.org/wiki/Leap_year

Microsoft Date Time Picker https://learn.microsoft.com/en-us/dotnet/api/system.datetime.ticks?view=net-7.0

[12] 00:48:20 Ben Deane Calendrical C++ https://www.youtube.com/watch?v=qD8HQl1fU5Y

[13] 00:53:24 Rosetta Code https://rosettacode.org/wiki/Rosetta_Code

J Wiki https://code.jsoftware.com/wiki/Main_Page

[14] 00:59:13 Ktye https://aplwiki.com/wiki/APL%5Civ

April https://aplwiki.com/wiki/April

ArrayCast Episode #23 https://www.arraycast.com/episodes/episode23-andrew-sengul

[15] 01:00:47 Scrabble word list Collins https://en.wikipedia.org/wiki/Collins_Scrabble_Words

NWL https://en.wikipedia.org/wiki/NASPA_Word_List

Official Scrabble Players Dictionary https://en.wikipedia.org/wiki/Official_Scrabble_Players_Dictionary

[16] 01:03:50 Contact AT ArrayCast DOT com

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The Array Cast

Raul Miller - Precision

Podcast summary created with Snipd AI

Quick takeaways

Deep dives

The Challenges of Representing Numbers on Computers

Parsing Numbers and Dealing with Precision Issues

Personal Use and Fun Projects with J

Limitations of Floating Point Numbers

Extended Precision and Numerical Accuracy

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AI-powered
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The Array Cast

Raul Miller - Precision

Podcast summary created with Snipd AI

Quick takeaways

Deep dives

The Challenges of Representing Numbers on Computers

Parsing Numbers and Dealing with Precision Issues

Personal Use and Fun Projects with J

Limitations of Floating Point Numbers

Extended Precision and Numerical Accuracy

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Discoverhighlights

Save anymoment

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