Talk:Thiele's interpolation formula: Difference between revisions
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(“Can you define triangular arrays?” someone (Tony Hoare?)) |
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How many entries should the trig table have? --[[User:Short Circuit|Michael Mol]] 14:46, 2 October 2010 (UTC) |
How many entries should the trig table have? --[[User:Short Circuit|Michael Mol]] 14:46, 2 October 2010 (UTC) |
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: I make it 16, with ''x'' varying by steps of 0.05 from 0 to 1.55. (Now, if only I could make my version of this ''work'', but that algol68 code is deeply gnarly; does it really have different base indices in different dimensions?!?) –[[User:Dkf|Donal Fellows]] 16:01, 2 October 2010 (UTC) |
: I make it 16, with ''x'' varying by steps of 0.05 from 0 to 1.55. (Now, if only I could make my version of this ''work'', but that algol68 code is deeply gnarly; does it really have different base indices in different dimensions?!?) –[[User:Dkf|Donal Fellows]] 16:01, 2 October 2010 (UTC) |
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I picked 32 rows to the table. Basically "'''from''' 0 '''to''' 1.55 '''by''' 0.05 ..." as 0.05 seems to give the full single precision answer (on an i686 CPU at least). Ideally this size would be calculated from the desired precision, but I don't have a formula for this precision calculation. [[User:NevilleDNZ|NevilleDNZ]] 21:31, 2 October 2010 (UTC) |
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=== re:base indices in different dimensions === |
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Yes. Here is a quote from the 1968 Congress: [http://www.cs.ru.nl/~kees/home/papers/psi96.pdf C.H.A. Koster (1993). "The Making of Algol 68" (PDF)]. |
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The IFIP 1968 Congress took place that August in Edinburgh, just a few hours drive |
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away from North Berwick. Van Wijngaarden’s invited lecture on Algol 68 was to me |
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the high point of the conference, and not only to me. The auditorium was packed, |
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people were standing on all sides, even in the corridors and outside, in front of the |
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hall. Van Wijngaarden appeared in the centre, smiling radiantly. “Let me sell you |
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a language”, he started, and proceeded to outline the ideas behind the language. He |
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showed some examples. “Can you define triangular arrays?” someone (Tony Hoare?) |
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interrupted. “Not just triangular, but even elliptical” replied Aad, and showed how. |
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He carried the listeners with him, from scepsis to enthusiasm. There was a prolonged |
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applause. |
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Vehemently discussing, people streamed out of the hall. A small man pushed |
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through the throng, straight at me. “Conkratulations, your Master hass done it” |
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said Niklaus Wirth in his inimitable Swiss-German English. |
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Basically, Algol 68 is agnostic about where an array starts, although the default starting point for both an array and a '''do''' ~ '''od''' loop is <u>one</u>. Hence - for convenience - in the [[wp:User:Hair_Commodore|Hair Commodore]]'s ALGOL 68 code specimen s/he pushes some array base indices to 1 using the [@1] construct. |
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[[User:NevilleDNZ|NevilleDNZ]] 21:31, 2 October 2010 (UTC) |