Replace sine table with 5th order approximation

[ndsl7109256]

The previous implementation used the pre-calculated fixed-point arithmetic table for sine values, which added over 2 KiB to the code size.

To solve this issue, I implemented the 5th order polynomial approximation for sine, which reduced the code size from 2556 bytes to 494 bytes (by about 80%) while maintaining acceptable error (RMS error is 8.866 observed with 0-90 degrees, 0-1024 in fixed-point representation)

Original code size with sine table.

$ size .libtwin.a/src/trig.c.o
   text    data     bss     dec     hex filename
   2556       0       0    2556     9fc .libtwin.a/src/trig.c.o

Code size after using 5th order approximation

$ size .libtwin.a/src/trig.c.o
   text    data     bss     dec     hex filename
   494        0       0    494      1ee .libtwin.a/src/trig.c.o

I initially tried a 3rd order approximation, but the error was slightly large, causing the drawn circle to appear not perfectly round. Below is some analysis.

RMS Error Comparing with Sine table (valued from 0-65536, observed with 0-90 degrees, 0-1024 in fixed-point representation)		3rd approximation	5th approximation
RMS	878.000907	8.8665040

ref: https://www.nullhardware.com/blog/fixed-point-sine-and-cosine-for-embedded-systems/ https://hackmd.io/@rickywu0421/FinalProject#透過-3rd-order-sine-approximation-模擬-RSSI

[jserv]

glibc implementation of sincos:

• sysdeps/ieee754/flt-32/s_sincosf.h
• sysdeps/ieee754/flt-32/s_sincosf_data.c
• sysdeps/ieee754/flt-32/s_sincosf.c

[jouae]

@ndsl7109256 Hey! You do a great job!

Here is a suggestion make your report getting better.

When mentioning RMS or MSE, be sure to include the number of observations.

[ndsl7109256]

Enhancement: Implement CORDIC algorithm for tan calculation

Currently, the twin_tan function uses division, which may be computationally expensive. A potential improvement would be to implement the CORDIC algorithm for calculating tan. This would avoid the use of the divider and potentially improve performance.

References: https://github.com/Max-Gulda/Cordic-Math/blob/main/lib/cordicMath/src/cordic-math.c#L290-L332 https://hackmd.io/@sysprog/linux-intdiv

[jserv]

Thank @ndsl7109256 for contributing!