No posters have mentioned the contraction of floating expressions yet (ISO C standard, 6.5p8 and 7.12.2). If the FP_CONTRACT pragma is set to ON, the compiler is allowed to regard an expression such as a*a*a*a*a*a as a single operation, as if evaluated exactly with a single rounding. For instance, a compiler may replace it by an internal power function that is both faster and more accurate. This is particularly interesting as the behavior is partly controlled by the programmer directly in the source code, while compiler options provided by the end user may sometimes be used incorrectly.
The default state of the FP_CONTRACT pragma is implementation-defined, so that a compiler is allowed to do such optimizations by default. Thus portable code that needs to strictly follow the IEEE 754 rules should explicitly set it to OFF.
If a compiler doesn't support this pragma, it must be conservative by avoiding any such optimization, in case the developer has chosen to set it to OFF.
GCC doesn't support this pragma, but with the default options, it assumes it to be ON; thus for targets with a hardware FMA, if one wants to prevent the transformation a*b+c to fma(a,b,c), one needs to provide an option such as -ffp-contract=off (to explicitly set the pragma to OFF) or -std=c99 (to tell GCC to conform to some C standard version, here C99, thus follow the above paragraph). In the past, the latter option was not preventing the transformation, meaning that GCC was not conforming on this point: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=37845