exp2

exp2 is a mathematical function that returns the value of 2 raised to a given exponent. In mathematical notation it is written as exp₂(x) = 2ˣ. The function closely resembles the natural exponential function exp(x), which returns e raised to the power of x, but uses a base of two instead of the base e ≈ 2.71828.

In computational contexts exp2 is provided as a standard library routine in many programming languages. For example, C and C++ offer exp2 in the <cmath> header, while Python provides the function under the math module as math.exp2. These implementations are typically optimized for speed and accuracy, with most modern CPUs offering hardware support for exponential operations. The function is commonly used in scientific computing, statistical modeling, and fields where logarithmic base 2 calculations are required, such as information theory, where logarithms base 2 measure entropy in bits.

The domain of exp2 is all real numbers. For negative exponents the function yields fractional values: exp2(−1) equals 0.5. For integer inputs it produces exact powers of two, e.g., exp2(4) equals 16. Graphically, the function grows exponentially, doubling its value each time the exponent increases by one. It is continuous, strictly increasing, and differentiable everywhere. The derivative of exp2(x) is exp2(x)·ln 2, analogous to the derivative of the natural exponential which is exp(x).

In information theory and computer science, exp2 often appears in formulas for calculating the number of states, code lengths, or in binary logarithm conversions. Because its base matches the binary number system, the function also enables efficient scaling of data structures and algorithms that depend on binary partitions. Knowledge of exp2’s properties and computational advantages makes it an essential tool for practitioners in fields ranging from cryptography to machine learning.