std.math: proper support for 64-bit real in exp()

[kinke]

No description provided.

[kinke]

13 lowest mantissa bits allowed to diverge - 13 has been chosen based on an LDC run on Linux x64 with LLVM 3.6 llvm.exp.f80 intrinsic (supposedly following libm implementation).

[WalterBright]

add as comment in code

[WalterBright]

Please explain what is meant by "proper" 64 bit support. Does it mean reducing precision from 80 bits for intermediate results to 64 bits?

[ibuclaw]

I assume this allows targets whose real type have a maximum significand precision of 53 bits to pass these tests?

[kinke]

I thought the changes are pretty self-explaining, but here's a quick summary:

The 1st commit fixes a serious bug in feqrel() wrt. subnormal diffs, an issue which arised when preparing the 2nd commit, which mainly fixes exp() for double-precision real by (1) using proper over-/underflow limits for exp() and (2) adding a proper test set for that precision. Additionally, the 2nd commit relaxes the tests a bit by NOT checking for bitwise equality of the exp() results and NOT caring about whether the overflow bit was set when the input was real.infinity (based on the LLVM intrinsic which is supposed to mimic the libm implementation).

There are other places assuming 80-bit reals, so that's only a start for platforms/targets without x87 support.

[kinke]

I've added some appropriate comments and tightened the tests again, this time allowing a relative diff of max 2 mantissa bits (3 ulp). That limit is declared as variable so that other backends like LDC may easily relax them.

[WalterBright]

Auto-merge toggled on

[ibuclaw]

I've just had another look, and I found something wrong, see comment.

[ibuclaw]

I tested this (albeit on 64bit) with -mlong-double-64 and get slightly different result to here. I even double-checked against libm, and it agrees with me.

expected = 0x0.06f84920bb2d300p-1022 (6.05799464199889e-310)
std.math = 0x0.06f84920bb2d400p-1022 (6.05799464199894e-310)
libm     = 0x0.06f84920bb2d400p-1022 (6.05799464199894e-310)

[ibuclaw]

Ping on the failing unittest!

[ibuclaw]

Regression raised https://issues.dlang.org/show_bug.cgi?id=14732