## Floating-point Exceptions and GPU Applications

A floating-point exception occurs when an attempted arithmetic operation produces an abnormal result. For example, an exception arises when a program attempts to compute the square root of a negative number or when a division by zero occurs. In traditional CPU-based programming languages and system software, several methods exist to...

## What can be Done About Floating-Point Cancellation

Scientific visualization of a very large simulation of a Rayleighâ€“Taylor instability problem. One of the difficulties of dealing with floating-point arithmetic arises when subtracting numbers. When we subtract nearby quantities, the most significant digits in the operands match and cancel each other. This is...

## Subnormal Numbers and Compiler Optimizations: A Dangerous Combination

Subnormal numbers (previously known as denormal numbers) fill the underflow gap in floating-point arithmetic. Traditionally, an underflow computation is said to occur when the exact result of the calculation is nonzero but is smaller than the smallest normalized floating-point number. Subnormal numbers represent the result of computations that produce very...