7.25.2.6p12:

If the correct value overflows and default rounding is in effect (7.12.2), plus or minus HUGE_VAL, HUGE_VALF, or HUGE_VALL is returned (according to the return type and sign of the value); if the integer expression math_errhandling & MATH_ERRNO is nonzero, the integer expression errno acquires the value of ERANGE; if the integer expression math_errhandling & MATH_ERREXCEPT is nonzero, the "overflow" floating-point exception is raised.

If the result underflows (7.12.2), the functions return a value whose magnitude is no greater than the smallest normalized positive number in the return type; if the integer expression math_errhandling & MATH_ERRNO is nonzero, whether errno acquires the value ERANGE is implementation-defined; if the integer expression math_errhandling & MATH_ERREXCEPT is nonzero, whether the "underflow" floating-point exception is raised is implementation-defined.

the linux man pages for these functions literally don't mention this at all, and there actually is a reason why which i'll get to in a sec, but what the standard is saying is, if math_errhandling doesn't advertise support for errno (as is the case on musl, for instance), the string to float conversion functions don't set errno on error. furthermore, if the result underflows, the function isn't required to report an error at all.

keep in mind that the return value alone isn't enough to determine if an error occurred, so to test for overflow, you need to use one of the two error handling mechanisms.

here is my attempt at a standards-blessed way of portably checking for overflow/underflow errors in the string to float functions:

feclearexcept(FE_OVERFLOW | FE_UNDERFLOW);
errno = 0;
double x = strtod(s, nullptr);
bool errored = math_errhandling & MATH_ERRNO
    ? errno == ERANGE
    : fetestexcept(FE_OVERFLOW | FE_UNDERFLOW);

note that this still doesn't guarantee that underflow is detected, since reporting underflow is entirely optional for the implementation.

the reason you've never done this ever (and the reason the man pages don't mention this) is that posix specifies the functions differently:

If the correct value is outside the range of representable values, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL shall be returned (according to the sign of the value), and errno shall be set to [ERANGE].

If the correct value would cause an underflow, a value whose magnitude is no greater than the smallest normalized positive number in the return type shall be returned and errno set to [ERANGE].

so posix doesn't give a shit about math_errhandling; it always requires the implementation to set errno if overflow or underflow occurs. while it's not uncommon for posix to specify stricter requirements on functions than standard c, the fact that the man page never makes any note of this being an extension (neither strtod(3) nor the posix specification strtod(3p)) is really notable to me.

whether or not posix's behavior is even compatible with standard c is... unclear. at least for math.h functions, setting errno regardless of the value of math_errhandling is permitted:

7.12.2p8:

If a domain, pole, or range error occurs and the integer expression math_errhandling & MATH_ERRNO is zero, then errno shall either be set to the value corresponding to the error or left unmodified.

but earlier on, when specifying errno.h, the standard says this:

7.5p3:

[...] The value of errno may be set to nonzero by a library function call whether or not there is an error, provided the use of errno is not documented in the description of the function in this document.

errno is documented in the description for these functions, and that description makes no mention of setting errno when math_errhandling & MATH_ERRNO is zero. so that suggests that posix's behavior is non-conformant.

but hang on! everything i've talked about so far is only for overflow and underflow. but if the string is malformed and can't be parsed as a number, then the standard doesn't specify any error at all:

7.25.2.6p11:

The functions return the converted value, if any. If no conversion could be performed, positive or unsigned zero is returned.

instead, you're supposed to use the endptr parameter, and check afterward if endptr == nptr (i.e. the end pointer is the same as the start pointer, so no data was parsed):

7.25.2.6p8:

If the subject sequence is empty or does not have the expected form, no conversion is performed; the value of nptr is stored in the object pointed to by endptr, provided that endptr is not a null pointer.

the man page strtod(3) says something similar:

If no conversion is performed, zero is returned and (unless endptr is null) the value of nptr is stored in the location referenced by endptr.

but check out what posix says:

Upon successful completion, these functions shall return the converted value. If no conversion could be performed, 0 shall be returned, and errno may be set to [EINVAL].

the word "may" basically means that it's implementation-defined. but this is a big deal, because it's pretty common to check for errors by doing something like this:

errno = 0;
double x = strtod(s, nullptr);
if (errno != 0) {
    // ...
}

strtod(3) suggests doing exactly this:

Since 0 can be legitimately returned on both success and failure, the calling program should set errno to 0 before the call, and then determine if an error occurred by checking whether errno has a nonzero value after the call.

but even for posix-compatible libcs, this isn't portable! different conforming libcs may behave differently if no conversion can be performed. in fact...

errno = 0;
strtod("x", nullptr);
printf("%d\n", errno);

on glibc, this prints 0, because glibc's strtod never sets errno to EINVAL. musl, on the other hand, does set errno to EINVAL, so this prints "22". this is completely undocumented on the linux man page.

it's also, from my reading of the standard, not conformant to standard c, because it's setting errno to a nonzero value in a function with other documented error conditions (and as far as standard c is concerned, invalid input isn't an error condition). musl could defend itself by saying that, because it doesn't set errno in its math.h functions, the errno condition in strtod's description no longer applies, therefore there's no documented use for errno (since the use of errno is dependent on the value of math_errhandling). but that's clearly a stretch.

either way, it's clear to me that the standard needs clearer wording here.

conclusion

just for fun, i figured i'd conclude with a list of all the "correct" ways to check for errors in the string to float conversion functions, just to hammer the point home:

overflow

• if you're targeting posix, set errno to 0 before the call, and afterward

  check copysign(result, 1.0) == HUGE_VAL && errno == ERANGE.

• otherwise, set errno to 0 and call feclearexcept(FE_OVERFLOW) before the call, and, if copysign(result, 1.0) == HUGE_VAL, either check errno == ERANGE or fetestexcept(FE_OVERFLOW) after the call, depending on the value of math_errhandling.

  if you're targeting just one implementation, and you know which error-reporting methods it supports beforehand, you can skip the math_errhandling check and only support one of the two methods.

  if you're using feclearexcept/fetestexcept, make sure that the compiler knows you may be accessing the floating point environment: on gcc the relevant flag is -ftrapping-math, which is the default (unless you're using -ffast-math). there's also a standard pragma for this purpose: #pragma STDC FENV_ACCESS ON. this pragma isn't supported by gcc though.

underflow

• if you're targeting posix, set errno to 0 before the call, and afterward check result == 0.0 && errno == ERANGE.

  be sure to check specifically that errno is ERANGE, not just that it's nonzero. otherwise you'll end up with nonportable behavior.

• otherwise, if you're just targeting one implementation, check if it documents its behavior on underflow in math.h functions. the behavior is implementation-defined, so technically it's required to document it. but in practice, even clang doesn't bother documenting its implementation-defined shit, so don't hold your breath.

  but if it is documented, and it reports underflow errors, then, depending on the implementation's value of math_errhandling, either set errno to 0 before the call and check result == 0.0 && errno == ERANGE after the call, or call feclearexcept(FE_UNDERFLOW) before the call and check fetestexcept(FE_UNDERFLOW) after the call.

• otherwise you're SOL.

  if you reeally need to check for underflow, and you need to use the libc function for some reason, here's the only option i can think of: check if result == 0.0, and if so, check yourself if the input string contains any nonzero digits before the exponent. if so, underflow occurred. this is difficult to get right though; read the description of strtod et al from the standard and make sure you cover all edge-cases.

invalid input (no conversion)

• pass in &endptr as a second argument to the function, and then check if endptr == nptr. errno can't be relied on.