math: avoid assumption of denormalized math mode in Sincos
math: avoid assumption of denormalized math mode in Sincos

The extra-clever code in Sincos is trying to do

        if v&2 == 0 {
                mask = 0xffffffffffffffff
        } else {
                mask = 0
        }

It does this by turning v&2 into a float64 X0 and then using

        MOVSD $0.0, X3
        CMPSD X0, X3, 0

That CMPSD is defined to behave like:

        if X0 == X3 {
                X3 = 0xffffffffffffffff
        } else {
                X3 = 0
        }

which gives the desired mask in X3. The goal in using the
CMPSD was to avoid a conditional branch.

This code fails when called from a PortAudio callback.
In particular, the failure behavior is exactly as if the
CMPSD always chose the 'true' execution.

Notice that the comparison X0 == X3 is comparing as
floating point values the 64-bit pattern v&2 and the actual
floating point value zero. The only possible values for v&2
are 0x0000000000000000 (floating point zero)
and 0x0000000000000002 (floating point 1e-323, a denormal).
If they are both comparing equal to zero, I conclude that
in a PortAudio callback (whatever that means), the processor
is running in "denormals are zero" mode.

I confirmed this by placing the processor into that mode
and running the test case in the bug; it produces the
incorrect output reported in the bug.

In general, if a Go program changes the floating point math
modes to something other than what Go expects, the math
library is not going to work exactly as intended, so we might
be justified in not fixing this at all.

However, it seems reasonable that the client code might
have expected "denormals are zero" mode to only affect
actual processing of denormals. This code has produced
what is in effect a gratuitous denormal by being extra clever.
There is nothing about the computation being requested
that fundamentally requires a denormal.

It is also easy to do this computation in integer math instead:

        mask = ((v&2)>>1)-1

Do that.

For the record, the other math tests that fail if you put the
processor in "denormals are zero" mode are the tests for
Frexp, Ilogb, Ldexp, Logb, Log2, and FloatMinMax, but all
fail processing denormal inputs. Sincos was the only function
for which that mode causes incorrect behavior on non-denormal inputs.

The existing tests check that the new assembly is correct.
There is no test for behavior in "denormals are zero" mode,
because I don't want to add assembly to change that.

Fixes issue 8623.

LGTM=josharian
R=golang-codereviews, josharian
CC=golang-codereviews, iant, r
https://codereview.appspot.com/151750043

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