Incorrect value of sin(13.11250158914107) on x87

[eduardosm]

On x87, sin(13.11250158914107) returns 0.00003381429460243744, when the correct value is 0.51938488614424543.

The following command can be used to build for x87:

RUSTFLAGS="-C target-cpu=pentium" cargo build --target i686-unknown-linux-gnu

[eduardosm]

It looks like the issue is in the floor function.

[plugwash]

I'm also seeing issues with the floor and ceiling functions in the Debian package of this library on i386 (Debian i386 uses x87).

Taking a read of the source, I suspect that the issue is that calculations are being performed with excess precision and this is breaking some of the tricks used in the floor/ceiling implementations. Specifically I suspect that the following construction is not producing the correct result.

/* y = int(x) - x, where int(x) is an integer neighbor of x */
let y = if (ui >> 63) != 0 {
    x - TOINT + TOINT - x
} else {
    x + TOINT - TOINT - x
};

Doing some reading I can't find a clear statement either way on whether such excess precision should be considered a bug in rustc or not.

I suspect the pragmatic way to fix this would be to reimplement this function with a different approach, i,e, converting to an integer and back, then adjusing as nessacery as proposed in #219

[plugwash]

I just whipped up a patch which made cargo test pass on x87, it's not particularly pretty though.

floor, ceil, round, roundf and rem_pio2f (but not floorf or ceilf) use an add/sub trick to round stuff to the nearest integer. Unfortunately this seems to break due to excess precision on x87.

For floor and ceil I made the functions use alternative implementations based on the proposal at #219

For the other functions I added a conversion to/from bits, this seems to force rounding, though I don't know for sure how robust that soloution is.

Finally I loosened the test slightly for j1f

I've pushed my changes at https://github.com/plugwash/libm if anyone wants to comment on them or clean them up.

[Lokathor]

opening it as a pr would allow for an easier review process, but i won't have time to look until Sunday or Monday

[plugwash]

PR filed at #249

[tgross35]

I believe this was fixed by #249.