The libc-provided isnan/isinf/isfinite macro implementations are specifically designed to function correctly, even in the presence of -ffast-math (or, more specifically, -ffinite-math-only). As such, on most implementation, these either always turn into external function calls (e.g. glibc) or are specifically function calls when __FINITE_MATH_ONLY__ is defined (e.g. Darwin).

Our implementation of complex arithmetic make heavy use of isnan/isinf/isfinite to deal with corner cases involving non-finite quantities. This is problematic in two respects:

- On systems where these are always function calls (e.g. Linux/glibc), there is a performance penalty
- When compiling with -ffast-math, there is a significant performance penalty (in fact, on Darwin and systems with similar implementations, the code may in fact be slower than not using -ffast-math, because the inline definitions provided by libc become unavailable to prevent the checks from being optimized out).

Eliding these inf/nan checks in -ffast-math mode is consistent with what happens with libstdc++, and in my experience, what users expect. This is critical to getting high-performance code when using complex<T>. This patch replaces uses of those functions on basic floating-point types with calls to __builtin_isnan/isinf/isfinite, which Clang will always expand inline. When using -ffast-math (or -ffinite-math-only), the optimizer will remove the checks as expected.