Fused multiply add and default rounding modes

Question

With GCC 5.3 the following code compield with -O3 -fma

float mul_add(float a, float b, float c) {
  return a*b + c;
}

produces t

Answer 1

When you quoted that fused multiply-add is allowed, you left out the important condition "unless pragma FP_CONTRACT is off". Which is a newish feature in C (I think introduced in C99) and was made absolutely necessary by PowerPC, which all had fused multiply-add from the start - actually, x*y was equivalent to fma (x, y, 0) and x+y was equivalent to fma (1.0, x, y).

FP_CONTRACT is what controls fused multiply/add, not FLT_EVAL_METHOD. Although if FLT_EVAL_METHOD allows higher precision, then contracting is always legal; just pretend that the operations were performed with very high precision and then rounded.

The fma function is useful if you don't want the speed, but the precision. It will calculate the contracted result slowly but correctly even if it isn't available in hardware. And should be inlined if it is available in hardware.

Answer 2

It doesn't violate IEEE-754, because IEEE-754 defers to languages on this point:

A language standard should also define, and require implementations to provide, attributes that allow and disallow value-changing optimizations, separately or collectively, for a block. These optimizations might include, but are not limited to:

...

― Synthesis of a fusedMultiplyAdd operation from a multiplication and an addition.

In standard C, the STDC FP_CONTRACT pragma provides the means to control this value-changing optimization. So GCC is licensed to perform the fusion by default, so long as it allows you to disable the optimization by setting STDC FP_CONTRACT OFF. Not supporting that means not adhering to the C standard.