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Signed zeros, Infinity, and NaN invalidate some optimizations by programmers and compilers that might otherwise have seemed obvious:
x + 0 and x - 0 are not the same as x when
x is zero, because the result depends on the rounding rule.
See Rounding, for more about rounding rules.
x * 0.0 is not the same as 0.0 when x is
Infinity, a NaN, or negative zero.
x / x is not the same as 1.0 when x is Infinity,
a NaN, or zero.
(x - y) is not the same as -(y - x) because when the
operands are finite and equal, one evaluates to +0 and the
other to -0.
x - x is not the same as 0.0 when x is Infinity or
a NaN.
x == x and x != x are not equivalent to 1 and
0 when x is a NaN.
x < y and isless (x, y) are not equivalent, because the
first sets a sticky exception flag (see Floating Arithmetic Exception Flags) when an
operand is a NaN, whereas the second does not affect that flag. The
same holds for the other isxxx functions that are companions to
relational operators. See FP Comparison Functions in The
GNU C Library Reference Manual.
The -funsafe-math-optimizations option enables these optimizations.