Implement fma in soft-fp

[Joseph S. Myers]

On Tue, 25 Jun 2013, Richard Henderson wrote:

> With the following patch, I get
> 
> > testing long double (without inline functions)
> > Failure: fma (0x1.fffffffffffffffffffffffffffcp-16382, 0x1.0000000000000000000000000001p-1, 0x1p-16494): Exception "Underflow" set
> > Failure: fma (-0x1.fffffffffffffffffffffffffffcp-16382, 0x1.0000000000000000000000000001p-1, -0x1p-16494): Exception "Underflow" set
> > Failure: fma (0x1p-16494, -0x1p-16494, 0x1p-16382): Exception "Underflow" set
> > Failure: fma (0x1p-16494, 0x1p-16494, -0x1p-16382): Exception "Underflow" set
> > Failure: fma_downward (-0x1.fffffffffffffffffffffffffffcp-16382, 0x1.0000000000000000000000000001p-1, -0x1p-16494): Exception "Underflow" set
> > Failure: fma_downward (-0x1p-16494, 0x1.1p-1, -0x0.ffffffffffffffffffffffffffffp-16382): Exception "Underflow" set
> > Failure: fma_downward (0x1p-16494, 0x1p-16494, -0x1p-16382): Exception "Underflow" set
> > Failure: fma_upward (0x1.fffffffffffffffffffffffffffcp-16382, 0x1.0000000000000000000000000001p-1, 0x1p-16494): Exception "Underflow" set
> > Failure: fma_upward (0x1p-16494, 0x1.1p-1, 0x0.ffffffffffffffffffffffffffffp-16382): Exception "Underflow" set
> > Failure: fma_upward (0x1p-16494, -0x1p-16494, 0x1p-16382): Exception "Underflow" set
> 
> but I thought you'd already committed the patch to solve this
> as commit 695c378f81263640618bdebf56eaa065f578251f ?

No, that fix was about incorrect results rather than exceptions.  The 
above is what I was referring to about soft-fp not supporting 
after-rounding tininess detection.  _FP_PACK_SEMIRAW and 
_FP_PACK_CANONICAL will need, for results whose before-rounding exponent 
is the largest underflowing exponent, to check some new soft-fp macro for 
after-rounding architectures and if it's true then determine whether the 
result would still underflow if rounded to the normal precision (*not* if 
rounded to the subnormal precision with one less bit, so this involves an 
extra trial rounding in a temporary variable to determine whether the 
result counts as tiny).  See what stdlib/strtod_l.c does in 
round_and_return if (TININESS_AFTER_ROUNDING && shift == 1), for example.  
(But soft-fp would use its own macro definition from sfp-machine.h instead 
of the existing tininess.h since it's supposed to be usable outside glibc 
and independent of glibc internal headers.)

MIPS is an after-rounding architecture but this issue doesn't cause test 
failures there because the testsuite knows not to test exceptions for MIPS 
software floating point (which uses fp-bit in libgcc), via math-tests.h.

-- 
Joseph S. Myers
joseph@codesourcery.com