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A denormalized number is a nonzero number that does not use all of its precision bits ([IEEE 754)]. They can be used to represent values that are closer to 0 than the smallest normal number (one that uses all of its precision bits). However, certain functions may produce range errors specifically when applied with a denormalized number. These functions are: asin(), asinh(), atan(), atanh(), and erf(). When evaluated with a denormalized number, these functions can produce an inexact, denormalized value, which is an underflow error. Subclause 7.12.1, paragraph 6, of the C Standard [ISO/IEC 9899:2011] defines the following behavior for floating-point underflow:
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| [ISO/IEC 9899:2011] | Subclause 7.3.2, "Conventions" |
| [IEEE 754] | |
| [Plum 1985] | Rule 2-2 |
| [Plum 1989] | Topic 2.10, "conv—Conversions and Overflow" |
| [UNIX 1992] | System V Interface Definition (SVID3) |
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