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Prevent It is important to prevent or detect domain errors and range errors in the C99 math functions (as defined in math.h) math functions before using the results in further computations.

Most of the math functions can fail if they are given arguments that do not produce a proper result. For example, the square root of a negative number, such as sqrt(-1.0), has no meaning in real arithmetic. This is known as a domain error; the argument is outside the domain over which the function is defined. For another example, ten raised to the one-millionth power, pow(10., 1e6), likely cannot be represented in any (current) an implementation's floating point representation. This is known as a range error; the result cannot be represented as a proper double number. In all such error cases, the function will return some value, but the value returned is not the correct result of the computation.

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However, for some functions it is not practical to use bounds-checking to prevent all errors.  For In the above pow example, the above bounds check for pow() does not prevent the pow(10., 1e6) range error. In these cases detection must be used, either in addition to bounds checking or instead of bounds checking.

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Non-Compliant Code Example

The following non-compliant code computes the arc cosine of the variable x

double x, result;

/* Set the value for x */

result = acos(x);

ThisHowever, this code may produce a domain error if the argument {{x}} is not in the range \[-1, \+1\].

double x, result;

result = acos(x);

Compliant Solution

This code uses bounds checking to ensure that there is not a domain error.

double x, result;

/* Set the value for x */

if ( islessequal(x,-1) || isgreaterequal(x, 1) ){
     /* handle domain error */
}

result = acos(x);

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Non-Compliant Code Example

This code may produce a domain error if both The following non-compliant code computes the arc tangent of the two variables x and y are zero.

double x, y, result;

/* Set the value for x and y */

result = atan2(y, x);

However, this code may produce a domain error if both x and y are zero.

Compliant Solution

This code tests the arguments to ensure that there is not a domain error.

double x, y, result;

/* Set the value for x and y */

if ( (x == 0.f) && (y == 0.f) ) {
     /* handle domain error */
}

result = atan2(y, x);

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Non-Compliant Code Example

This code may produce a domain error if x is negative and a range error if x is zeroThe following non-compliant code determines the natural logarithm of x.

double result, x;

/* Set the value for x */

result = log(x);

However, this code may produce a domain error if x is negative and a range error if x is zero.

Compliant Solution

This code tests the suspect arguments to ensure that no domain or range errors are raised.

double result, x;

/* Set the value for x */

if (islessequal(x, 0)) {
  /* handle domain and range errors */
}

result = log(x);

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Non-Compliant Code Example

The following non-compliant code raises x to the {{y}}th power.

double x, y, result;

result = pow(x, y);

However, this This code may produce a domain error if x is negative and y is not an integer, or if x is zero and y is zero. A domain error or range error may occur if x is zero and y is negative, and a range error may occur if the result cannot be represented as a double.

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double x, y, result;

result = pow(x, y);

Non-Compliant Code Example

This code only performs bounds-checking on x and y. It prevents domain errors and some range errors, but does not prevent range errors where the result cannot be represented as a double.

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Non-Compliant Code Example

This code may produce a domain error if x is negative.The following non-compliant code determines the square root of x

double x, result;

result = sqrt(x);

However, this code may produce a domain error if x is negative.

Compliant Solution

This code tests the suspect argument to ensure that no domain error is raised.

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