Comment #53 on issue 3006 by [email protected]: Inaccurate sin/cos values
https://code.google.com/p/v8/issues/detail?id=3006
Thanks for all the hard work on coming to an excellent solution to this
issue.
For future decision making, I'd like to register a vote for 1 ulp as a
target precision where possible, or a small handful of ulps if the tradeoff
is considered very carefully. Max error is important here. RMS is not a
good measure.
Note that rounding sin(-1e-16) to 0 is not a matter of being off by a few
ulps--it's a matter of being off by all of them! All 54 bits of the
mantissa, down the toilet, when they could have all been retained by just
returning the input.
Application developers can choose to ignore numbers below some *absolute*
threshold, like 1e-16 or whatever is appropriate in their circumstances,
but as language implementers, it's important to be conservative about
*relative* precision, because you don't know when numbers of a certain
scale will be used in someone else's application. IEEE arithmetic gives us
wonderful tools to achieve this--we just have to respect them and use them
correctly.
I came across this issue because some of our unit tests on www.desmos.com
have been failing for a while in Chrome. We're proud of offering a very
high quality graphing calculator implemented in JS, and we're counting on
you as language implementers to give us good foundations to build on. We
love the performance improvements, but correctness comes first.
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