Be careful when rearranging floating-point expressions to ensure the greatest accuracy of the result.
Subclause Wiki Markup
Rearrangement for floating-point expressions is often restricted because of limitations in precision as well as range. The implementation cannot generally apply the mathematical associative rules for addition or multiplication, nor the distributive rule, because of roundoff error, even in the absence of overflow and underflow. Likewise, implementations cannot generally replace decimal constants to rearrange expressions. In the following fragment, rearrangements suggested by mathematical rules for real numbers are often not valid.
Code Block double x, y, z; /* ... */ x = (x * y) * z; /* not equivalent to x *= y * z; */ z = (x - y) + y ; /* not equivalent to z = x; */ z = x + x * y; /* not equivalent to z = x * (1.0 + y); */ y = x / 5.0; /* not equivalent to y = x * 0.2; */
Therefore, care must be taken when rearranging floating point exceptions in order to ensure the greatest accuracy of the result.
Risk Assessment
Failing Failure to understand the limitations in precision of floating-point-represented numbers and the their implications of this on the arrangement of expressions can cause unexpected arithmetic results.
Recommendation | Severity | Likelihood | Remediation Cost | Priority | Level |
|---|---|---|---|---|---|
FLP01-A C | low Low | probable Probable | medium High | P4 P2 | L3 |
Related Vulnerabilities
Search for vulnerabilities resulting from the violation of this rule recommendation on the CERT website.
References
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Related Guidelines
| SEI CERT C++ Coding Standard | FLP01-CPP. Take care in rearranging floating-point expressions |
| ISO/IEC TR 24772:2013 | Floating-point Arithmetic [PLF] |
Bibliography
| [ISO/IEC 9899:2011] | Subclause |
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| 5.1.2.3, |
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| "Program |
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| Execution" |
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FFLP00-A. Understand the limitations of floating point numbers 05. Floating Point (FLP) FLP02-A. Understand the caveats of floating point exceptions