Talk:Thiele's interpolation formula: Difference between revisions
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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) |
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Revision as of 21:31, 2 October 2010
How many entries should the trig table have? --Michael Mol 14:46, 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?!?) –Donal Fellows 16:01, 2 October 2010 (UTC)
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. NevilleDNZ 21:31, 2 October 2010 (UTC)
re:base indices in different dimensions
Yes. Here is a quote from the 1968 Congress: C.H.A. Koster (1993). "The Making of Algol 68" (PDF).
The IFIP 1968 Congress took place that August in Edinburgh, just a few hours drive away from North Berwick. Van Wijngaarden’s invited lecture on Algol 68 was to me the high point of the conference, and not only to me. The auditorium was packed, people were standing on all sides, even in the corridors and outside, in front of the hall. Van Wijngaarden appeared in the centre, smiling radiantly. “Let me sell you a language”, he started, and proceeded to outline the ideas behind the language. He showed some examples. “Can you define triangular arrays?” someone (Tony Hoare?) interrupted. “Not just triangular, but even elliptical” replied Aad, and showed how. He carried the listeners with him, from scepsis to enthusiasm. There was a prolonged applause. Vehemently discussing, people streamed out of the hall. A small man pushed through the throng, straight at me. “Conkratulations, your Master hass done it” said Niklaus Wirth in his inimitable Swiss-German English.
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 one. Hence - for convenience - in the Hair Commodore's ALGOL 68 code specimen s/he pushes some array base indices to 1 using the [@1] construct.
NevilleDNZ 21:31, 2 October 2010 (UTC)