Underflow
TLDR: Underflow occurs when a numerical computation results in a value closer to zero than the smallest positive nonzero value that a data type or system can represent. Commonly associated with floating-point arithmetic, underflow results in the value being rounded to zero or a subnormal (denormalized) number. Defined in IEEE 754 in 1985, subnormal numbers help retain precision close to zero, but underflow can still lead to numerical inaccuracies in sensitive calculations.
https://en.wikipedia.org/wiki/Arithmetic_underflow
In floating-point arithmetic, underflow happens when a result is smaller in magnitude than the smallest positive normalized value for a given precision. For example, in single-precision IEEE 754, the smallest normalized positive value is approximately 1.175 × 10^-38. Values smaller than this are represented as subnormal numbers or are flushed to zero, depending on the floating-point unit's configuration. Subnormal numbers maintain a portion of the precision, but computations involving them may lose accuracy due to limited significant digits.
https://standards.ieee.org/standard/754-2019.html
The effects of underflow can be problematic in applications requiring high precision, such as scientific simulations, financial modeling, and cryptography. Developers can mitigate these issues by using data types with higher precision, employing scaling techniques, or relying on libraries that handle numerical stability. For instance, Java's `BigDecimal` provides greater precision for small values compared to primitive floating-point types. Recognizing and addressing underflow scenarios ensures reliable results in computations across various domains.
https://docs.oracle.com/javase/tutorial/java/nutsandbolts/datatypes.html