Denormal Number
In computer science, denormal numbers or denormalized numbers (now often called subnormal numbers) fill the underflow gap around zero in floating point arithmetic. Any non-zero number with magnitude smaller than the smallest normal number is 'sub-normal'.
In a normal floating point value there are no leading zeros in the significand, instead leading zeros are moved to the exponent. So 0.0123 would be written as 1.23 * 10-2. Denormal numbers are numbers where this representation would result in an exponent that is too small (the exponent usually having a limited range). Such numbers are represented using leading zeros in the significand.
The significand (or mantissa) of an IEEE number is the part of a floating point number that represents the significant digits. For a positive normalised number it can be represented as m0.m1m2m3...mp-2mp-1 (where m represents a significant digit and p is the precision, and m0 is non-zero). Notice that for a binary radix, the leading binary digit is one. In a denormal number, since the exponent is the least that it can be, zero is the lead significand digit (0.m1m2m3...mp-2mp-1) in order to represent numbers closer to zero than the smallest normal number.
By filling the underflow gap like this, significant digits are lost, but not to the extent as when doing flush to zero on underflow (losing all significant digits all through the underflow gap). Hence the production of a denormal number is sometimes called gradual underflow because it allows a calculation to lose precision slowly when the result is small.
In IEEE 754-2008, denormal numbers are renamed subnormal numbers, and are supported in both binary and decimal formats. In binary interchange formats, subnormal 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 decimal interchange formats they require no special encoding because the format supports unnormalized numbers directly.
| Floating-point precisions |
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| IEEE 754 |
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Read more about Denormal Number: Background, Performance Issues
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