Re: Deviation in math functions

[KHMan <keinhong@...>]

On 2/10/2012 4:18 PM, roman.maire@besonet.ch wrote:
> [snip]
> angle = 270
> originx = 0
> originy = 100
> distance = 100
>
> x = (originx + (math.cos(math.rad(angle)) * distance))
> y = (originy + (math.sin(math.rad(angle)) * distance))
> print("x: ".. x ..", y: ".. y)
>
> Output:
> -> x: -1.836970198721e-014, y: 0
>
> I was expecting that x should be 0 too.
>
> am I missing something here?

It's near the expected error magnitude. A double has about 16 
digits of precision with 53 significand bits. For the calculation 
you used, each of the following are not perfectly precise so error 
accumulates:

(1) #define PI (3.14159265358979323846) in lmathlib.c
(2) #define RADIANS_PER_DEGREE (PI/180.0) in lmathlib.c
(3) luaL_checknumber(L, 1)*RADIANS_PER_DEGREE in lmathlib.c
    -- for math.rad(angle)
(4) math.sin(...)
(5) math.sin(... * distance)
(6) (originx + ...)

Each operation adds to the amount of error. So 14-15 digits is 
about right. But it should be enough for almost everyone, after 
all, 1000km to 1mm is only a magnitude of 9. As HyperHacker 
suggests, some Googling and study on the Internet should sort it 
out...

--
Cheers,
Kein-Hong Man (esq.)
Kuala Lumpur, Malaysia