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A floating result overflows if the magnitude of the mathematical result is finite but so large that the mathematical result cannot be represented without extraordinary roundoff error in an object of the specified type. If a floating result overflows and default rounding is in effect, then the function returns the value of the macro HUGE_VAL, HUGE_VALF, or HUGE_VALL according to the return type, with the same sign as the correct value of the function; if the integer expression math_errhandling & MATH_ERRNO is nonzero, the integer expression errno acquires the value ERANGE; if the integer expression math_errhandling & MATH_ERREXCEPT is nonzero, the ‘‘overflow’’ floating-point exception is raised.

It is best preferable not to check for errors by comparing the returned value against HUGE_VAL or 0 for several reasons:

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It is also difficult to check for math errors using errno because an implementation might not set it. For real functions, the programmer can tell whether determine if the implementation sets errno by checking whether math_errhandling & MATH_ERRNO is nonzero. For complex functions, the C Standard, subclause 7.3.2, paragraph 1, simply states that "an implementation may set errno but is not required to" [ISO/IEC 9899:2011].

The System V Interface Definition (SVID3) [UNIX 1992] provides more control over the treatment of errors in the math library. The user can provide a function named matherr() that is invoked if errors occur in a math function. This function can print diagnostics, terminate the execution, or specify the desired return value. The matherr() function has not been adopted by C, so its use it is not generally portable.

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The result underflows if the magnitude of the mathematical result is so small that the mathematical result cannot be represented, without extraordinary roundoff error, in an object of the specified type. If the result underflows, the function returns an implementation-defined value whose magnitude is no greater than the smallest normalized positive number in the specified 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.

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Implementations that support floating point arithmetic but does not support subnormals, such as IBM S/360 hex floating point or sloppy IEEE-754 implementations that skip subnormals (or "support" them by flushing them to zero) can return a range error when calling one of the following family of functions with the following arguments:

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