Arbitrary-precision arithmetic

Definition

Fix an integer base $B \ge 2$, in practice a power of $2$ such as $2^{64}$. In arbitrary-precision arithmetic an integer $a$ is stored as a sign and a list of digits $(a_0, \ldots, a_{k-1})$. Here $0 \le a_i < B$ and $$\abs{a} = \sum_{i=0}^{k-1} a_i B^i,$$ where the length $k$ is not fixed in advance and grows as needed. Arithmetic operations on such lists return the exact integer result in the same form. Rational numbers are stored as pairs of such integers. Real numbers are stored as floating-point numbers $m \cdot 2^{e}$, where $m$ and $e$ are such integers and the precision $p$ is chosen by the user.