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14h
awarded  Popular Question
Jan
19
comment Is there a better representation than p-adics for exact computer arithmetic?
I see. I suppose that is the answer then: Do it the usual way. Sorry for the noise.
Jan
18
comment Is there a better representation than p-adics for exact computer arithmetic?
It's hard for me to clarify because I don't really know what I'm talking about in this area. I'm trying to balance these factors: ease of implementation, average memory/time performance, worst-case memory/time performance. And the comments suggest that unless I invest a lot more effort in implementation, my worst-case performance is going to be really bad, even if I choose $p = 2 000 000 001$. So I'm trying to understand what the problem is and/or mitigate it. But I also want to avoid a straight p/q representation because I fear the cost of the normalization step there too. Does that help?
Jan
18
comment Is there a better representation than p-adics for exact computer arithmetic?
So practically, I should go ahead with the project? I'm very keen to use this representation for an APL interpreter since it gives me multiprecision integers and approximations of floating-point (if I bound the digits and avoid loss of significance in the calculations) and "natural" results like (1/3)*3 = 1. The other option to achieve these features would be orchestrating 3 different number types (MP ints, floats, rationals) the last one a derived type of the first. So I really want p-adics to be the right answer ... since I've already begun the research into it. :)
Jan
17
asked Is there a better representation than p-adics for exact computer arithmetic?
Dec
28
asked Can a bicubic Bezier surface be represented as a Bernstein polynomial?
Dec
20
awarded  Constituent
Dec
16
awarded  Caucus
Aug
30
comment Reference for book on fundamental abstract algebra topics
@user45552 Use the 'Ask Question' link to ask a new question.
Aug
30
awarded  Citizen Patrol
Aug
30
awarded  Autobiographer
Aug
4
awarded  Critic
Aug
4
answered Why do we still do symbolic math?
Mar
10
revised How are the Taylor Series derived?
added 87 characters in body
Mar
10
revised How are the Taylor Series derived?
added 82 characters in body
Mar
10
answered How are the Taylor Series derived?
Mar
6
awarded  Announcer
Feb
10
comment How elliptic arc can be represented by cubic Bézier curve?
+1. I wish I had seen this post earlier. I've recently implemented circular arcs in PostScript.
Sep
30
comment Surprising identities / equations
postscript source code for the image.
Sep
29
answered Surprising identities / equations