Allow small deviation in builtin tests

[jpf91]

On systems where real is just an alias for double (e.g. ARM) the exact literal values might not be representable, so allow a deviation of real.epsilon.

[yebblies]

Do we really need to loosen the tests? Could it be done using a version statement to compare with the exact value double precision produces on those platforms?

[jpf91]

Probably, but I'm not sure if we can expect exactly the same result on all CPUs (even if they have the same architecture). There are lots of floating point implementations on ARM (vfp1-3, VFPLite, FPA, FPE, iwMMXt, software emulated) and I don't know if they all produce the same results for sin/cos/...

[donc]

Actually, the existing tests are wrong. x86 is wrong in the last two bits.
static assert(sin(6.8) == 0x1.f9f8d9aea10fdf1cp-2); Should be:
static assert(sin(6.8) == 0x1.f9f8d9aea10fdf10p-2); // precise value is 0x1.f9f8d9aea10fdf10d323f9c7p-2
But this will fail, so it will need the epsilon test.

Likewise cos(6.8) should be:
0x1.bd21aaf88dcfa13ap-1 // existing
0x1.bd21aaf88dcfa13ep-1 // new
0x1.bd21aaf88dcfa13d1879e9a5f2f02p-1 // precise

tan(6.8) should be:
0x1.22fd752af75cd08cp-1 // existing
0x1.22fd752af75cd084p-1 // new
0x1.22fd752af75cd083fbe4115c995ep-1 //precise

Please change the tests to use the 'new' numbers, with the epsilon tests, and include the comment below in the file.
/*
Precise values:
sin(6.8) = 0x1.f9f8d9aea10fdf10d323f9c7p-2
cos(6.8) = 0x1.bd21aaf88dcfa13d1879e9a5f2f02p-1
tan(6.8) = 0x1.22fd752af75cd083fbe4115c995ep-1
*/

[jpf91]

Closed. I'll reopen this pull when I've implemented Don's suggestions.