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Denormalized numbers can severely impair the precision of floating point numbers and should not be used.
Print Representation of Denormalized Numbers
Denormalized numbers can also be troublesome because their printed representation is unusual. Floats and normalized doubles, when formatted with the %a specifier begin with a leading nonzero digit. Denormalized doubles can begin with a leading zero to the left of the decimal point in the mantissa.
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| Code Block |
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normalized float with %e : 2.350989e-38 normalized float with %a : 0x1.0p-125 denormalized float with %e : 7.174648e-43 denormalized float with %a : 0x1.0p-140 normalized double with %e : 8.900295e-308 normalized double with %a : 0x1.0p-1020 denormalized double with %e : 8.289046e-317 denormalized double with %a : 0x0.0000001p-1022 |
Noncompliant Code Example
This code attempts to reduce a floating point number to a denormalized value and then restore the value.
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Original : 0.33333334 Denormalized? : 2.8E-45 Restored : 0.4 |
Compliant Solution
Do not use code that could use denormalized numbers. If calculations using float are producing denormalized numbers, use double instead.
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| Code Block |
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Original : 0.3333333333333333 Denormalized? : 2.333333333333333E-45 Restored : 0.3333333333333333 |
Risk Assessment
Floating point numbers are an approximation; using subnormal floating point number are a worse approximation.
Rule | Severity | Likelihood | Remediation Cost | Priority | Level |
|---|---|---|---|---|---|
FLP03-J | low | probable | high | P2 | L3 |
Related Guidelines
CERT C Secure Coding Standard FLP05-C. Don't use denormalized numbers
Bibliography
| Wiki Markup |
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\[[IEEE 754|AA. Bibliography#IEEE 754 2006]\] \[[Bryant 2003|AA. Bibliography#Bryant 03]\] Computer Systems: A Programmer's Perspective. Section 2.4 Floating Point |
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