Use Pythagorean identity to shrink sine table

[ndsl7109256]

The sine table contribute a large code size. To optimize this, the Pythagorean identity has been applied to minimize the size of sine table. The adjustment decreases code size while preserving the accuracy of sine calculations.

[jserv]

Run clang-format -i to ensure consistent indention.

[jserv]

Don't change this line. Minimize the necessary changes.

[jouae]

@ndsl7109256 Can you briefly explain how the Pythagorean identity can reduce the size of the table, or provide a comment in the code explaining how it works?

And you can use the size command as mentioned in #13 to check how much memory overhead has been reduced compared to the original.

Thanks

[jserv]

Improve the git commit message. In particular, make it grammatically correct.

As @jouae mentioned, prove that the proposed method is beneficial and maintains the desired precision. You may consider introducing the CORDIC method for sine computation without using expensive lookup tables. Check the following:

• Why the CORDIC algorithm lives rent-free in my head
• How to use the CORDIC to perform mathematical functions on STM32 MCUs
• 5th Order Polynomial Fixed-Point Sine Approximation
• A performance test for trigonometric functions, computed with the CORDIC method
• Simple C source for CORDIC
• How do Trigonometric functions work?

[jouae]

@ndsl7109256
By the way, the __sin_s3() function used in vwifi is a third-order fixed-point approximation of the sine function. However, the reference documentation Another fast fixed-point sine approximation seems to be unavailable now. The principle is similar to the 5th Order Polynomial Fixed-Point Sine Approximation mentioned by @jserv.

For a Chinese explanation of __sin_s3(), you can refer to the document written by @rickywu0421 at 2022q1 vwifi.

[ndsl7109256]

@jserv @jouae Thanks for the advice. I would open another pull request to use third-order approximation to compute sine values.