Hello,
In FriCAS, airyAi has a problem of precision. Here is the output using
DoubleFloat, MathLink (Wolfram engine) with Julia, and Maxima:
(15) -> airyAi 3.7
(15) 0.0017455720028082336
Type: DoubleFloat
(16) -> airyAi jWSReal "3.7"
(16) 0.0017455720006099784
Type: JuliaWSReal
(17) -> airyBi 3.7
(17) 47.5607474995892
Type: DoubleFloat
(18) -> airyBi jWSReal "3.7"
(18) 47.560747499589446
Type: JuliaWSReal
In Maxima:
(%i1) airy_ai(3.7);
(%o1) 0.0017455720006099781
(%i2) airy_bi(3.7);
(%o2) 47.56074749958946
So as you can see it is not the coercion to DoubleFloat that is to
blame. It seems at first glance that the airyAi computation occurs on
a ~32 bits floating point number. I have not checked. I have another
package that operates also on 64 bits floats that comforts this but
with different function naming schemes, and I plan to uniformize this
right now.
(32) -> )expose JF64SF2
JuliaFloat64SpecialFunctions2 is now explicitly exposed in frame
frame0
(32) -> airyai(jf64 3.7)
(32) 0.001745572000609978
Type: JuliaFloat64
So my question is, do I fill an issue for this particular special
function, and populate later this issue with other function issues
after I encounter others like this one? Or do I open separate issues?
It is also probable that even if I fill an issue for different
functions tested, I encounter some other later. Frankly I would prefer
not to encounter the airyAy imprecision problem for other functions.
And yes, I know machine floating point numbers are inherently
imprecise to represent real numbers.
I have a test file for the other package on 64 bits floats mentioned
above*, I can modify and use it to have a better view if necessary on
a set of special functions.
- Greg
* I use it to test yet another package, sorry, that operates on high
precision floating point numbers.
(33) -> )expose JFSF2
JuliaFloatSpecialFunctions2 is now explicitly exposed in frame
frame0
(33) -> airyai(jfloat "3.7")
(33)
0.001745572000609979136759728232445420447338438146589128698021602847417405690
988777
Type: JuliaFloat
(34) -> airyAi jWSReal "3.7"
(34) 0.0017455720006099784
Type: JuliaWSReal
(35) -> airyAi 3.7
(35) 0.0017455720028082336
Type: DoubleFloat
--
You received this message because you are subscribed to the Google Groups
"FriCAS - computer algebra system" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/fricas-devel/CAHnU2dZFdGUGuUfD7RH3xpGuSn%3D0jrhS1wd5KaP0pXi%2BL-TMKg%40mail.gmail.com.
