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[SOLVED] Lua math.cos issue
Posted: Mon Mar 02, 2020 5:42 pm
by XHH
I simply want to get cos(90 deg) using the following:
This is giving me a nasty 6.1232339957368e-17.
I thought cos(90 deg) was 0. My calculator IRL and google also gives me 0.
Re: Lua math.cos issue
Posted: Mon Mar 02, 2020 6:11 pm
by zorg
Code: Select all
return ('%0.19f'):format(math.cos(math.pi/2)) -- same as if you pass in math.rad(90)
> 0.0000000000000000612
That's just how it's formatted; for all intents and purposes, that is zero, with some floating point error.
Re: Lua math.cos issue
Posted: Mon Mar 02, 2020 6:41 pm
by XHH
Interesting! Thanks for explaining.
Re: [SOLVED] Lua math.cos issue
Posted: Mon Mar 02, 2020 7:05 pm
by monolifed
Also don't forget that math.pi is just an approximation of the number pi
Re: [SOLVED] Lua math.cos issue
Posted: Mon Mar 02, 2020 9:24 pm
by raidho36
Welcome to the world of floating point numbers. It patently sucks but it's the best we have.
Re: [SOLVED] Lua math.cos issue
Posted: Mon Mar 02, 2020 11:40 pm
by pgimeno
ingsoc451 wrote: ↑Mon Mar 02, 2020 7:05 pm
Also don't forget that math.pi is just an approximation of the number pi
This is exactly the reason. The value returned is the cosine of that approximation. Something similar happens with math.sin(math.pi).
Re: [SOLVED] Lua math.cos issue
Posted: Tue Mar 03, 2020 1:55 am
by raidho36
pgimeno wrote: ↑Mon Mar 02, 2020 11:40 pm
This is exactly the reason. The value returned is the cosine of that approximation. Something similar happens with math.sin(math.pi).
Nevermind that math.cos function itself only returns approximate cosine values (and of not particularly great accuracy, FYI).
Re: [SOLVED] Lua math.cos issue
Posted: Tue Mar 03, 2020 2:41 am
by pgimeno
raidho36 wrote: ↑Tue Mar 03, 2020 1:55 am
pgimeno wrote: ↑Mon Mar 02, 2020 11:40 pm
This is exactly the reason. The value returned is the cosine of that approximation. Something similar happens with math.sin(math.pi).
Nevermind that math.cos function itself only returns approximate cosine values (and of not particularly great accuracy, FYI).
Apparently that happens on LuaJIT only. The closest number to Pi/2 that can be exactly represented in double precision floating point is:
1.5707963267948965579989817342720925807952880859375
whose cosine is:
0.0000000000000000612323399573676588613032966137500138418265969...
In my system, Lua reports:
Code: Select all
$ lua
Lua 5.1.5 Copyright (C) 1994-2012 Lua.org, PUC-Rio
> =("%.17g"):format(math.cos(math.pi/2))
6.123233995736766e-17
which is accurate up to the maximum precision of the type, but LuaJIT's result is disastrous:
Code: Select all
$ luajit
LuaJIT 2.0.4 -- Copyright (C) 2005-2015 Mike Pall. http://luajit.org/
JIT: ON CMOV SSE2 SSE3 SSE4.1 fold cse dce fwd dse narrow loop abc sink fuse
> =("%.17g"):format(math.cos(math.pi/2))
6.1230317691118863e-17
which is accurate only up to the fourth significant digit.
That said, it's a function for which the IEEE standard gives no guarantees of precision, unlike +,-,*,/,%,sqrt.
Re: [SOLVED] Lua math.cos issue
Posted: Tue Mar 03, 2020 5:08 am
by raidho36
Lua uses C standard library (by design) and it usually provides fairly good scientific functions, horrendously slow though. LuaJIT uses hardware acceleration whenever available (by design) and hardware accelerated floating point math tends to not be very accurate, particularly the transcendental functions such as trigonometry, it's really fast though. I would also argue that 4 significant digits is good enough if you're not trying to do anything silly, like trying to rotate a 100 million mile stick to move 1/8" at the tip; 1 part in 10 000 is equivalent to instrument-grade precision in real life.