Be careful when rearranging floating-point expressions to ensure the greatest accuracy of the result.
According to C99, Section 5.1.2.3, "Program execution" [ISO/IEC 9899:1999]
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.
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; */
Risk Assessment
Failure to understand the limitations in precision of floating-point-represented numbers and the implications of this on the arrangement of expressions, can cause unexpected arithmetic results.
Recommendation |
Severity |
Likelihood |
Remediation Cost |
Priority |
Level |
|---|---|---|---|---|---|
FLP01-C |
low |
probable |
high |
P2 |
L3 |
Related Vulnerabilities
Search for vulnerabilities resulting from the violation of this recommendation on the CERT website.
Related Guidelines
CERT C++ Secure Coding Standard: FLP01-CPP. Take care in rearranging floating point expressions
ISO/IEC 9899:1999 Section 5.1.2.3, "Program execution"
ISO/IEC TR 24772 "PLF Floating Point Arithmetic"
Bibliography
FLP00-C. Understand the limitations of floating point numbers 05. Floating Point (FLP) FLP02-C. Avoid using floating point numbers when precise computation is needed