Hi,


I've been wondering how it is that computers analytically calculate
such functions as roots, fractional exponents and other such "magic"
such as trig functions.

Thanks,
Adam

Hi Adam,

a common way to compute sine and cosine functions is to use a taylor series expansion. http://en.wikipedia.org/wiki/Taylor_series

For the root function a Newton iteration is sometimes used http://en.wikipedia.org/wiki/Newton%27s_method

C/C++ uses the Floating-Point-Unit of the processor and so references the functions directly implemented in Hardware/microcode. FPU's use the CORDIC algorithm http://en.wikipedia.org/wiki/Cordic

Best,
Martin

Am 14.03.2013 um 19:43 schrieb Adam Puckett:

> Hi,
> 
> 
> I've been wondering how it is that computers analytically calculate
> such functions as roots, fractional exponents and other such "magic"
> such as trig functions.
> 
> Thanks,
> Adam
> 
> 
> Send bugs reports to the Sourceforge bug tracker
>            https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
> 

_________________________
Martin Hünniger
a_s_tarantoga@yahoo.de
a-s-tarantoga.tumblr.com
soundcloud.com/a_s_tarantoga

> Hi Adam,
>
> a common way to compute sine and cosine functions is to use a taylor
> series expansion. http://en.wikipedia.org/wiki/Taylor_series
>

But tghe wrong way if you want any decent speed.  Tchebychev polynomials
is the correct way.  Try Code & Waite's book.


> For the root function a Newton iteration is sometimes used
> http://en.wikipedia.org/wiki/Newton%27s_method
>
> C/C++ uses the Floating-Point-Unit of the processor and so references the
> functions directly implemented in Hardware/microcode. FPU's use the CORDIC
> algorithm http://en.wikipedia.org/wiki/Cordic
>
> Best,
> Martin
>
> Am 14.03.2013 um 19:43 schrieb Adam Puckett:
>
>> Hi,
>>
>>
>> I've been wondering how it is that computers analytically calculate
>> such functions as roots, fractional exponents and other such "magic"
>> such as trig functions.
>>
>> Thanks,
>> Adam
>>
>>
>> Send bugs reports to the Sourceforge bug tracker
>>            https://sourceforge.net/tracker/?group_id=81968&atid=564599
>> Discussions of bugs and features can be posted here
>> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe
>> csound"
>>
>
> _________________________
> Martin Hünniger
> a_s_tarantoga@yahoo.de
> a-s-tarantoga.tumblr.com
> soundcloud.com/a_s_tarantoga
>
>
>
>
>
>
> Send bugs reports to the Sourceforge bug tracker
>             https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe
> csound"
>
>
>
>