[Bug go/63269] libgo/math test failures in TestLog2

["vogt at linux dot vnet.ibm.com" <gcc-bugzilla@gcc.gnu.org>]

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=63269

--- Comment #5 from Dominik Vogt <vogt at linux dot vnet.ibm.com> ---
regarding 1)

My earlier explanation of the problem was wrong.  Multiply and add is not
generated; it probably only was in the artificial test case that I made and
certainly did not compile with -ffp-contract=off.

In this calculation in log2(),

  Log(frac)*(1/Ln2) + float64(exp)

Gcc does constant folding for (1/Ln2) and generates a multiply instruction and
then adds the second term.  Same result if you write "*Log2E" instead of
"*(1/Ln2)").  But with

  Log(frac)/Ln2 + float64(exp)

it generates a divide instruction.  The multiplication and the division yield
results that differ in the least significant bit, and I don't see how this
could be prevented in general; it's just an artifact of the floating point
format.  I've verified that the constants Ln2, 1/Ln2 and Log2E are bit correct.

The "easy" way to fix this is increasing the allowed tolerance as my patch does
(note that the arguments of the veryclose() call need to be swapped, see
previous comment).

The "right" way to fix this is to calculate platform specific ULPs for all the
algorithms from the math library and use these.  That's what glibc does.