[PATCH 2/6] Remove slow paths from sin/cos

[Steve Ellcey]

On Fri, 2018-03-09 at 13:52 -0500, Zack Weinberg wrote:
>Â 
> More concretely, for IEEE single, the gap between representable values
> is bigger than 2π for values whose exponent is 2^26 or above.  Since
> the sine function is periodic over 2Ï€, that means the result of sinf()
> is effectively meaningless for any input at least that big - _any
> value_ within the input period could have been rounded to the
> representable, so the "true" answer could be anything.  (I am tempted
> to suggest that we return NaN for inputs this large, without even
> bothering to do argument reduction.)
> 
> For double, this happens at 2^55, and for x86-64 long double it
> happens at 2^66.  I _think_ x86-64 long double is 80-bit IEEE
> extended, not quad, but I could be wrong.
> 
> zw

And yet we have tests for large numbers in auto-libm-test-out-sin
and auto-libm-test-out-cos. Â I was testing a different vector sin/cos
implementation on aarch64 and I got some big diffs on very large
output. Â Maybe we shouldn't test for these values if they are not
of any value.

testing double (vector length 2)
Failure: Test: sin_vlen2 (-0x2p+64)
Result:
 is:         -0.0000000000000000e+00  -0x0.0000000000000p+0
 should be:   4.7183876212354675e-02   0x1.8287c2a760e04p-5
 difference:  4.7183876212354675e-02   0x1.8287c2a760e04p-5
 ulp       :  6799913194491396.0000
 max.ulp   :  1.0000
Failure: Test: sin_vlen2 (-0x3.3de320f6be87ep+1020)
Result:
 is:         -0.0000000000000000e+00  -0x0.0000000000000p+0
 should be:  -9.9219562491895441e-01  -0x1.fc0110a085bafp-1
 difference:  9.9219562491895441e-01   0x1.fc0110a085bafp-1
 ulp       :  8936903693327279.0000
 max.ulp   :  1.0000