What would be the ultimate calculator in 2017?

General discussion about calculators, SwissMicros or otherwise
toml_12953
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Re: What would be the ultimate calculator in 2017?

Post by toml_12953 »

rprosperi wrote:
Sat Sep 09, 2017 2:57 am
toml_12953 wrote:
Sat Sep 09, 2017 2:12 am
I get -1.24138E-11 when I do this:

atan(acos(asin(sin(cos(tan(9))))))-9
Is this using the the NumWorks machine?

On the DM42, I get -2.86934E-28 !
Amazing!
I got that result using the online simulator (which is slightly behind the shipping calculator's firmware version).
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pauli
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Re: What would be the ultimate calculator in 2017?

Post by pauli »

On the 34S I get -1.71086E-28 for the sequence atan(acos(asin(sin(cos(tan(9)))))) - 9 in double precision mode. I'm reasonably confident that this is the proper correctly rounded result.

This isn't the usual trig forensic. That is asin(acos(atan(tan(cos(sin(9)))))) - 9 which equals -6,2465E-29. Again, I believe this to be the correctly rounded result at this precision.

The difference between the Free 42 result and the 34S result has to do with how the Intel decimal library calculates its results (in binary with a decimal conversion). The Intel library is known to round results incorrectly in some circumstances.


- Pauli
rprosperi
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Re: What would be the ultimate calculator in 2017?

Post by rprosperi »

pauli wrote:
Sat Sep 09, 2017 2:08 pm
This isn't the usual trig forensic. That is asin(acos(atan(tan(cos(sin(9)))))) - 9 which equals -6,2465E-29. Again, I believe this to be the correctly rounded result at this precision.
Using the format toml posted didn't feel quite right/familiar, as I recall it starts/ends with sin() but I used it as shown for comparison. I'm pretty sure this means I've used this forensic way too many times...
--bob p

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Dani R.
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Re: What would be the ultimate calculator in 2017?

Post by Dani R. »

toml_12953 wrote:
Sat Sep 09, 2017 2:12 am
Dani R. wrote:
Thu Aug 31, 2017 10:29 pm

A friend of mine has ordered an NunWorks. I told him to play with the simulator till his calculator arrives. So he entered tan(cos(sin(9))), then asin(acos(atan(ans))) and then ans-9. Result when using intermediat results from the "stack" (ans) gives -0.010082. He wrote an issue on gitub. Maybe there are difference between simulator and physical device.
I get -1.24138E-11 when I do this:

atan(acos(asin(sin(cos(tan(9))))))-9
They have an rounding issue on Ans. When you use Ans, you still will get the result i have posted using the simulator. I always go over the intermediat (Ans) result when I make the forensic test. In my experiance often a calculation is done by several part calculation. To get a result in one step is suspect for me, but maybe I using too long RPN calculator.

Wolfram Alpha delivers 0! ( asind(acosd(atand(tand(cosd(sind(9))))))-9 )
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pauli
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Re: What would be the ultimate calculator in 2017?

Post by pauli »

rprosperi wrote:
Sat Sep 09, 2017 4:31 pm
I'm pretty sure this means I've used this forensic way too many times...
It could be argued that once is too many times :)


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rprosperi
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Re: What would be the ultimate calculator in 2017?

Post by rprosperi »

pauli wrote:
Sun Sep 10, 2017 3:02 am
It could be argued that once is too many times :)
While I don't disagree, this near-useless 'forensic test', which really doesn't tell one much of any real use, is the gold standard useless benchmark by which we judge all machines. It's popular because it's easy to remember and so easy to do. It's real value, to me at least, is to reveal if the s/w under the hood of different model and manufacturer labels is the same.
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Walter
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Re: What would be the ultimate calculator in 2017?

Post by Walter »

rprosperi wrote:
Sun Sep 10, 2017 3:13 pm
pauli wrote:
Sun Sep 10, 2017 3:02 am
It could be argued that once is too many times :)
While I don't disagree, this near-useless 'forensic test', which really doesn't tell one much of any real use, is the gold standard useless benchmark by which we judge all machines. It's popular because it's easy to remember and so easy to do. It's real value, to me at least, is to reveal if the s/w under the hood of different model and manufacturer labels is the same.
In a way, certainly. As far as I understood it, it's also telling you something about the precision (not accuracy!) of the s/w.
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rprosperi
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Re: What would be the ultimate calculator in 2017?

Post by rprosperi »

Walter wrote:
Sun Sep 10, 2017 3:26 pm
In a way, certainly. As far as I understood it, it's also telling you something about the precision (not accuracy!) of the s/w.
Well that is superficially true, however it only reveals a small amount about a small amount of the s/w, I think. The basic trig functions, and anti-functions (well, you know what I mean) are only a tiny portion of the s/w, and being in degrees (vs. radians) is probably also less indicative of the core systems, but I'm only speculating.

I've no idea at all how the guts of the 34S or Free42 are assembled (and no, reading the code won't help; me that is) but it doesn't seem as if the routines exercised in this test is a meaningful representation of the full machine's precision. In terms of directly-called end-user functions, it's obviously a tiny percentage; I suppose it may actually utilize a large percentage of the actual worker routines inside, but I doubt it. I just don't know.

But I do know who does know...

Pauli - in rough terms, how much of the inner core (math foundations) of the 34s f/w is exercised in this test?

Thomas - same question about Free42?
--bob p

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Thomas Okken
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Re: What would be the ultimate calculator in 2017?

Post by Thomas Okken »

In a nutshell: the trigs (in radians), logarithms, exponentials, hyperbolics, and gamma, are all handled by the Intel Decimal Floating-Point Math Library. The trigs in degrees and grads are handled by reducing the arguments to the first octant before converting them to radians, and then passing them on to the Intel library. Y^X has special-case logic for integer exponents.

Everything else is built on top of this: complex, matrices, statistics, the solver, and the integrator.
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dm319
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Re: What would be the ultimate calculator in 2017?

Post by dm319 »

Thomas Okken wrote:
Mon Sep 11, 2017 6:13 am
the trigs (in radians), logarithms, exponentials, hyperbolics, and gamma, are all handled by the Intel Decimal Floating-Point Math Library.
That's really interesting Thomas - I assume the basic operators are also handled by the library? Can you tell me why sqrt(-9) and (-9)^0.5 give different answers, though sqrt(9) and 9^0.5 give the same?
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