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Section 7.12.1 of the C standard Standard [ISO/IEC 9899:2011] defines two types of errors that relate specifically to math functions in math.h [ISO/IEC 9899:2011]:

A domain error occurs if an input argument is outside the domain over which the mathematical function is defined.

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The following table lists standard mathematical functions, along with any checks that should be performed on their domain, and indicates if they also throw range errors, as reported by the C standardStandard. If a function has a specific domain over which it is defined, the programmer should check its input values, and if a function throws range errors, the programmer should detect if a range error occurs. The standard math functions not listed in this table, such as atan(), have no domain restrictions and do not throw range errors.

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The exact treatment of error conditions from math functions is quite complicated. C11, Section 7.12.1 , defines the following behavior for floating-point overflow of the C Standard [ISO/IEC 9899:2011] defines the following behavior for floating-point overflow:

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

• These are, in general, valid (albeit unlikely) data values.
• Making such tests requires detailed knowledge of the various error returns for each math function.
• There are three different possibilities, -HUGE_VAL, 0, and HUGE_VAL, and you must know which are possible in each case.
• Different versions of the library have differed in their error-return behavior.

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 the implementation sets errno by checking whether math_errhandling & MATH_ERRNO is nonzero. For complex functions, the C standardStandard, Section 7.3.2, simply states that "an implementation may set errno but is not required to" [ISO/IEC 9899:2011].

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The following error-handing template uses C standard Standard functions for floating-point errors when the C macro math_errhandling is defined and indicates that they should be used; otherwise, it examines errno.

#include <math.h>
#if defined(math_errhandling) \
  && (math_errhandling & MATH_ERREXCEPT)
#include <fenv.h>
#endif

/* ... */

#if defined(math_errhandling) \
  && (math_errhandling & MATH_ERREXCEPT)
  feclearexcept(FE_ALL_EXCEPT);
#endif
errno = 0;

/* call the function */

#if !defined(math_errhandling) \
  || (math_errhandling & MATH_ERRNO)
if (errno != 0) {
  /* handle range error */
}
#endif
#if defined(math_errhandling) \
  && (math_errhandling & MATH_ERREXCEPT)
if (fetestexcept(FE_INVALID
               | FE_DIVBYZERO
               | FE_OVERFLOW
               | FE_UNDERFLOW) != 0) {
  /* handle range error */
}
#endif

See FLP03-C. Detect and handle floating-point errors for more details on how to detect floating-point errors.

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Search for vulnerabilities resulting from the violation of this rule on the CERT website.

Related Guidelines

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Bibliography

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