Added some series-based functions (exp, cos, sin, ...)

ionspin / kotlin-multiplatform-bignum

A Kotlin multiplatform library for arbitrary precision arithmetics

Apache License 2.0

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Added some series-based functions (exp, cos, sin, ...) #235

Open hakanai opened 2 years ago

hakanai commented 2 years ago

Added:

exp (by infinite series)
cos (by infinite series)
sin (by infinite series)
tan (by cos/sin)
cosh (by infinite series)
sinh (by infinite series)
tanh (by cosh/sinh)

Not added:

ln - might not be too hard but converges very slowly so need another trick
arcsin(x) = arctan(x / √(1 - x²))
arccos(x) = arctan(√(1 - x²) / x)
arctan - conceivably possible to do similarly, but the series only converges for small values, so need to use Euler's trick
arsinh(x) = ln(√(1 + x²) + x)
arcosh(x) = ln(x + √(x - 1)√(x + 1)) = ln(√(x² - 1) + x)
artanh(x) = ½ ln(x + 1) - ½ ln(1 - x)

hakanai commented 2 years ago

I'm still unsure about the way I handled precision here.

I could have tried to use the precision of the number used as input, but the problem is that the decimal mode can currently be null, which can't work for these things because they always need to know when to stop.

Also I haven't actually signed the commit, but it isn't a complete solution either, so I'll worry about that if it gets even remotely close to usable. :(

CLAassistant commented 2 years ago

All committers have signed the CLA.

ionspin commented 2 years ago

Awesome, thanks for the contribution! It will take me some time to go through it in detail and understand everything so please have patience, especially since I can only get some time to work on the library on the weekend. And don't worry about the signature.

The decimal mode was long overdue for a refactor so I'll try to combine that with changes here.

ionspin commented 2 years ago

I haven't forgotten about this, but I'm still short on time. It's top of my priority list for the library.

sergeych commented 1 month ago

why isn't it yet merged? any problems with it? Btw, missing precision could be taken from the decimal size of the argument + n, usually it works fairy well. Also you can provide some kind of epsilon parameter instead.

@ionspin could you please merge it or like?

ionspin commented 1 month ago

@sergeych Unfortunately I haven't had the time to properly go through this pull request and it's also related to decimal mode refactor which is a big undertaking, so that's why this pull request hasn't been merged for a long time, and by the way things are looking it's going to stay that way for some time to come.