Replace SpiderMonkey's Math functions with platform consistent versions

[historic_bruno]

As Philip reported on ​Bugzilla, there are differences in SpiderMonkey's floating point ​Math functions on different platforms. Even a small discrepancy can cause OOS errors in multiplayer games, if those functions are used in e.g. simulation, map generation, or AI code. We already use fixed point approximations for sin/cos and atan2 in the engine, but not yet for scripts. Currently no scripts appear to use atan, acos, or asin.

(There may also be differences in pow and exp which we do use rarely, but I wasn't able to reproduce them with the above test cases.)

[Jonathan Waller]

The sin/cos approximations which are accurate to about 10^{-9 have been added with commit ​http://trac.wildfiregames.com/changeset/11226 . I will look at writing a good approximation for atan2.}

[historic_bruno]

Updated title and description since fixed point is no longer the focus.

Also [11220] is relevant, it introduced a new rmgen function GetAngle, which calls Math.acos. I don't know if acos is even a problem, I simply mentioned all the trig functions :)

[Jonathan Waller]

In 11231:

Added atan and atan2. Refs #1193

[historic_bruno]

This ticket is probably solved well enough for Alpha 9. Would be nice to add some tests eventually.

[Jonathan Waller]

These changes should fix the ticket, will wait till after A9 to commit them

[Kieran P]

Bump. Can we get this finished up easily?

[leper]

A slightly modified version of the last diff was applied in [11363].

[Jonathan Waller]

This is not closed because we were wanting to add some tests. I should get round to this sometime soon.

[historic_bruno]

I would suggest that as described in #433, the Math tests be run at game startup by everyone, not only in the standard test suite. That way we can hopefully detect problems like [11857] sooner and with more explicit errors.

[ben]

In 12056:

Implements global tech modification function. Fixes #1358, refs #1520.
Applies tech modifications to template data returned by GuiInterface.
Extends engine to load arbitrary global scripts, separates this from RNG replacement. Refs #1193.
Loads global scripts for most script contexts for consistency.
Adds simulation tests for global scripts.

[historic_bruno]

Should also replace Math.pow and Math.exp at some point.

[historic_bruno]

Replying to historic_bruno:

Should also replace Math.pow and Math.exp at some point.

This is in fact rather important, see #1990.

[sanderd17]

There are some implementations of Math.pow, Math.exp and Math.log in #1990 now.

[Yves]

I found this in Spidermonkey's configure script:

--enable-more-deterministic Enable changes that make the shell more deterministic"

I don't know what it does and the word "more" looks suspicious.

[ben]

In 13515:

Adds JS implementations of Math.pow, exp, and log, by sanderd17, refs #1193.
Fixes #1990 (OOS caused by Math.pow).
Adds tests and documentation for Math functions.

[sanderd17]

As a reference, link to a sqrt algorithm: ​http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29

Of course, there is also a very simple way to just define sqrt(x)=pow(x,0.5). But a native sqrt algorithm would be more optimal.

[wraitii]

There are a few cases where Aegis and qBot use Math.sqrt, Math.round, Math.min, Math.max, and Math.floor/Math.ceil.

If their behaviors can be inconsistent too, this might explain both #1966 and #2000.

[sanderd17]

I hope Math.round/ceil/floor don't give problems, as I use them for pow and exp calculation. And I don't know how we can replace those functions, as we can't read the internal values.

For Math.sqrt, you could try defining it as pow(x,0.5) and see if those problems still occur (although they're hard to test).

[historic_bruno]

Current plan: test before A14 release, if there are no OOS errors with Aegis, push this to backlog. Otherwise experiment with replacing Math.pow, but note it's much slower than the native Math.sqrt (by 600x or so)

[historic_bruno]

No recent OOS reports with Aegis, so I'm pushing this back to A15 and lowering priority. All that remains is deciding if we want to replace Math.sqrt and adding some runtime tests like #433.

[historic_bruno]

Replacing Math.sqrt doesn't solve #2000.

[sanderd17]

It has been working a long time now, so I don't think there are issues with the remaining functions.