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Talk:Generalised floating point addition: Difference between revisions
Talk:Generalised floating point addition (view source)
Revision as of 21:41, 19 February 2020
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:BCD was a great hack when you had to fit all of your code into a few kilobytes of memory. But (for example) representing dollars as cents, to avoid the binary fraction issues, is also a great hack. Nowadays, BCD is mostly useful for backwards compatability and in systems that have included BCD support without supporting other options.
:So, anyways, if I wanted to illustrate polynomial multiplication, I would not bother with BCD. Instead, I would focus on something like the [[wp:Chain rule (probability)|chain rule]]. For example: ''If you flip a coin ten times, with 50% odds each for "Heads" and "Tails" on one coin flip, what are the odds that the total number of "Heads" is a prime number?''. Or something like that that involves summing cumulative probabilities -- perhaps involving dice or perhaps even something with uneven base chances. If you like, I could draft up a task on that subject. (Or feel free to do so yourself.) --[[User:Rdm|Rdm]] 10:33, 31 October 2011 (UTC)
:: That task already exists (morally) at [[Count the coins]]. [[User:CRGreathouse|CRGreathouse]] 17:40, 8 May 2012 (UTC)
:: FWIW, a fair number of languages have built-in arbitrary precision integers; they can do generalised floating point math without needing to fuss around with BCD. ''Requiring'' the use of non-idiomatic techniques when a high-quality idiomatic technique lies close by is a little odd. I'll look into rewriting the task a bit to make this possible. (BCD ''can'' be a possible implementation strategy, of course; I've no problem with that.) –[[User:Dkf|Donal Fellows]] ([[User talk:Dkf|talk]]) 18:41, 23 December 2013 (UTC)
::: After some thought I think I'd like to draw several distinctions here. One distinction has to do with the number base (BCD vs Binary, for example). Another distinction has to do with precision (53 bits of mantissa? arbitrary precision integers?). Another distinction has to do with the represented range of numbers (integers are different from rational numbers). And yet another distinction has to do with "floating point".
::: Floating point, as I understand them, give us numbers of the form x*y^z where y is typically a constant and where x and z typically have constrained ranges. So one way of representing floating point numbers is using the pair (x,z) along with a specification of the remaining constraints. One might imagine this specification as being a part of an external standard, or a given for users of either certain computing hardware or a specific programming language, library or environment, or we might want a floating point number where each floating point number is an object and a representation of these constraints is embedded in each such object. But, of course, there will always be limits. If you have a floating point number that takes 16 gigabytes to represent you will not be able to have as many of those as you would a floating point number that takes 4 bytes to represent.
::: Anyways, to meaningfully choose tradeoffs, it's usually a good idea to express the purpose of the representation. As I understand it, floating point numbers are based off "scientific notation" where numbers are typically the result of measurements (and, thus, limited in precision while often needing to treat a wide variety of magnitudes). Another aspect of floating point numbers is that they can efficiently represent approximate results of transcendental functions (sine, cosine, logarithm, ...). For many practical purposes approximations are more than adequate - excessive precision can be thought of as distracting attention from the important issues.
::: Hopefully some of these musings will help you in your rewrite? And, thank you. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 19:17, 23 December 2013 (UTC)
== Edit Or Delete Task ==
I suggest editing the task to demonstrate the arbitrary precision arithmetic provided by the language. If not provided by the language, then the task would be to implement this in your language.
Otherwise, delete the task. Today, there is no need to re-invent what is provided by the language. I lean towards this recommendation. Many other Rosetta Code tasks require arbitrary precision arithmetic. Those tasks would not use the algorithms presented here. In addition, Internet users of Rosetta Code need to find useful, not misleading, information.
--[[User:DavidFashion|DavidFashion]] ([[User talk:DavidFashion|talk]]) 21:41, 19 February 2020 (UTC)
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