Arithmetic underflow

The term arithmetic underflow (also floating-point underflow, or just underflow) is a condition in a <a href="/facts/Computer_program/e38jH9N9">computer program</a> where the result of a calculation is a number of more precise absolute value than the computer can actually represent in <a href="/facts/Computer_memory/hQKVQ51J">memory</a> on its <a href="/facts/Central_processing_unit/Jxp1bqMV">central processing unit</a> (CPU).
Arithmetic underflow can occur when the true result of a <a href="/facts/Floating-point_arithmetic/eIckahxe">floating-point operation</a> is smaller in magnitude (that is, closer to zero) than the smallest value representable as a <a href="/facts/Normal_number_(computing)/5pvlHVvg">normal</a> floating-point number in the target <a href="/facts/Data_type/fcx5hgVL">datatype</a>. Underflow can in part be regarded as negative <a href="/facts/Arithmetic_overflow/sVNnSolT">overflow</a> of the <a href="/facts/Exponent/pac6QY2g">exponent</a> of the floating-point value. For example, if the exponent part can represent values from −128 to 127, then a result with a value less than −128 may cause underflow.
For integers, the term "integer underflow" typically refers to a special kind of <a href="/facts/Integer_overflow/sVNnSolT">integer overflow</a> or integer wraparound condition whereby the result of subtraction would result in a value less than the minimum allowed for a given integer type, i.e. the ideal result was closer to negative infinity than the output type's representable value closest to negative infinity.

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Arithmetic underflow