Denormal number

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In computer science, denormal numbers (also called subnormal numbers) fill the gap around zero in floating point arithmetic: any non-zero number which is smaller than the smallest normal number is 'sub-normal'.

Producing a denormal is sometimes called gradual underflow because it allows the calculation to lose precision slowly, rather than all at once.

As implemented in the IEEE floating-point standard binary formats, denormal numbers are encoded with a biased exponent of 0, but are interpreted with the value of the smallest allowed exponent, which is one greater (i.e., as if it were encoded as a 1).

In the proposed IEEE 754 revision, denormal numbers are renamed subnormal numbers, and are supported in both binary and decimal formats. In the latter, they require no special encoding because the format support unnormalized numbers directly.

Background

Denormal numbers were implemented in the Intel 8087 while the IEEE 754 standard was being written. This implementation demonstrated that denormals could be supported in a practical implementation. Some implementations of floating point units do not directly support denormal numbers in hardware, but rather trap to some kind of software support. While this may be transparent to the user, it can result in calculations which produce or consume denormal numbers to be much slower than similar calculations on normal numbers.

Further reading

For an extensive discussion on known methods of implementing denormal numbers for binary floating-point numbers, see Hardware Implementations of Denormalized Numbers, Eric Schwarz, Martin Schmookler and Son Dao Trong, Proceedings 16th IEEE Symposium on Computer Arithmetic (Arith16), ISBN 0-7695-1894-X, pp104-111, IEEE Comp. Soc., June 2003 (PDF (http://www.ece.ucdavis.edu/acsel/arithmetic/arith16/papers/ARITH16_Schwarz.pdf))

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