(I thought it would be better to make it a comment instead of a simple reply)
After a quick look into the code, I would like to make some suggestions/remarks :
1) Where is my_pi() defined?? (used line 137)
2) There could be some improvements in the algorithms, like:
- You should save the result of "bcpow($num, 2)" and using only multiplications instead of "bcpow($num,2 * $i + 1,$sc)"
- The exp algorithm is highly divergent for negative input, you'll need some tricks( e^-x = 1/e^x and e4.8 = (((e^0.6)^2)^2) for example).
- don't use "($i/2 != floor($i/2))" but ($i & 1) -> much faster
- you should warn the user about invalid input: acos(), asin(), ln()...
- the atan() taylor's developpement only works with input in the interval [-1;1], you'll need some tricks (trigonometric transformations) to allow a wider range.
- some algorithms **need** at lot of loops to become relevant, I don't see the point using $scale as a brake condition, you should break the loop on a relative error basis.
3) I don't really like the way you get the Pi value, especially if its the only reason to have zlib in dependencies. There is also a way to calculate this value.
4) Applying P.C.S would make the code much more readable.
5) I can imagine unexpected results, because of the intermediary simplifications using $scale+<arbitrary number>. There's probably a better way to do it.