I got that result using the online simulator (which is slightly behind the shipping calculator's firmware version).rprosperi wrote: ↑Sat Sep 09, 2017 2:57 amIs this using the the NumWorks machine?toml_12953 wrote: ↑Sat Sep 09, 2017 2:12 amI get -1.24138E-11 when I do this:
atan(acos(asin(sin(cos(tan(9))))))-9
On the DM42, I get -2.86934E-28 !
Amazing!
What would be the ultimate calculator in 2017?
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Re: What would be the ultimate calculator in 2017?
Tom L
Some people call me inept but I'm as ept as anybody!
DM10L SN: 059/100
DM41X SN: 00023 (Beta)
DM41X SN: 00506 (Shipping)
DM42 SN: 00025 (Beta)
DM42 SN: 00221 (Shipping)
WP43 SN: 00025 (Prototype)
Some people call me inept but I'm as ept as anybody!
DM10L SN: 059/100
DM41X SN: 00023 (Beta)
DM41X SN: 00506 (Shipping)
DM42 SN: 00025 (Beta)
DM42 SN: 00221 (Shipping)
WP43 SN: 00025 (Prototype)
Re: What would be the ultimate calculator in 2017?
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
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
Re: What would be the ultimate calculator in 2017?
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
DM42: β00071 & 00282, DM41X: β00071 & 00656, DM10L: 071/100
DM42: β00071 & 00282, DM41X: β00071 & 00656, DM10L: 071/100
Re: What would be the ultimate calculator in 2017?
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.toml_12953 wrote: ↑Sat Sep 09, 2017 2:12 amI get -1.24138E-11 when I do this: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.
atan(acos(asin(sin(cos(tan(9))))))-9
Wolfram Alpha delivers 0! ( asind(acosd(atand(tand(cosd(sind(9))))))-9 )
C47(DM42) SN:00032 WP43 SN:00016
https://47calc.com
https://47calc.com
Re: What would be the ultimate calculator in 2017?
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.
--bob p
DM42: β00071 & 00282, DM41X: β00071 & 00656, DM10L: 071/100
DM42: β00071 & 00282, DM41X: β00071 & 00656, DM10L: 071/100
Re: What would be the ultimate calculator in 2017?
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.rprosperi wrote: ↑Sun Sep 10, 2017 3:13 pmWhile 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.
WP43 SN00000, 34S, and 31S for obvious reasons; HP-35, 45, ..., 35S, 15CE, DM16L S/N# 00093, DM42β SN:00041
Re: What would be the ultimate calculator in 2017?
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
DM42: β00071 & 00282, DM41X: β00071 & 00656, DM10L: 071/100
DM42: β00071 & 00282, DM41X: β00071 & 00656, DM10L: 071/100
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Re: What would be the ultimate calculator in 2017?
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.
Everything else is built on top of this: complex, matrices, statistics, the solver, and the integrator.
Re: What would be the ultimate calculator in 2017?
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?Thomas Okken wrote: ↑Mon Sep 11, 2017 6:13 amthe trigs (in radians), logarithms, exponentials, hyperbolics, and gamma, are all handled by the Intel Decimal Floating-Point Math Library.
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