Liukulukulaskenta

Liukulukulaskenta, often translated as floating-point arithmetic, is a method for representing and computing with real numbers in a computer. It is necessary because computers can only store a finite number of bits, making it impossible to represent all real numbers exactly. Floating-point numbers are represented in a form similar to scientific notation, consisting of a sign, a significand (also known as the mantissa), and an exponent. The significand holds the significant digits of the number, and the exponent determines its magnitude.

The most common standard for floating-point arithmetic is IEEE 754. This standard defines various formats, such as single-precision (32-bit) and double-precision (64-bit), specifying how the bits are allocated for the sign, exponent, and significand. It also defines how arithmetic operations like addition, subtraction, multiplication, and division are performed on these numbers, as well as how to handle special values like infinity and Not-a-Number (NaN).

Due to the finite representation, floating-point arithmetic is inherently inexact. This means that not all real numbers can be represented precisely, and computations can introduce small errors. These errors can accumulate over many operations, potentially leading to significant deviations from the true mathematical result. Understanding these limitations is crucial for programmers and scientists to ensure the accuracy and reliability of their calculations. Rounding is a key aspect of floating-point arithmetic, as numbers that cannot be represented exactly must be rounded to the nearest representable value according to specific rules defined by the standard.