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Using denormalized numbers can severely impair the precision of floating-point calculations; as a result, denormalized numbers must not be used.

Detecting Denormalized Numbers

The following code tests whether a float value is denormalized in strictfp mode, or for platforms that lack extended range support. Testing for denormalized numbers in the presence of extended range support is platform dependent; see rule "NUM09-J. Use the strictfp modifier for floating point calculation consistency across platforms" for additional information.

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Testing whether values of type double are denormalized is exactly analogous.

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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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. When calculations using float produce denormalized numbers, use of double can provide sufficient precision.

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Original      : 0.3333333333333333
Denormalized? : 2.333333333333333E-45
Restored      : 0.3333333333333333

Exceptions

NUM08-EX1: Denormalized numbers are acceptable when competent numerical analysis demonstrates that the computed values will meet all accuracy and behavioral requirements that are appropriate to the application. Note that "competent numerical analysis" generally requires a specialized professional numerical analyst; lesser levels of rigor fail to qualify for this exception.

Risk Assessment

Floating-point numbers are an approximation; denormalized floating-point numbers are a less precise approximation. Use of denormalized numbers can cause unexpected loss of precision, possibly leading to incorrect or unexpected results. Although the severity stated below for violations of this rule is low, applications that require accurate results should consider the severity of this violation to be high.

Related Guidelines

Bibliography

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