enso/docs/semantics/numbers.md

layout	title	category	tags	order
developer-doc	Numbers	semantics	semantics runtime number	8

Numbers

In order to enhance the user experience, Enso provides a number hierarchy, encompassing both integers of unbound size and floating-point decimals.

• Number Types
• Internal Representation
• Type Conversions

Number Types

The base number type in Enso is Number. It includes both integers and floating-point numbers and is the basic type that should be used whenever numerical computations are performed. Any method defined on the type Number is automatically available on all types of numeric values.

The hierarchy is further split into the Integer and Decimal types. Integer is capable of representing values of unbound length. Decimal is capable of representing IEEE 64-bit (double precision) floating numbers.

Any method defined on Integer is available for all integers, while any method defined on Decimal is available on all floating-point numbers. Methods defined on Integer or Decimal take precedence over methods defined on Number, when name resolution is performed.

Internal Representation

Integers that can be represented in a 64-bit integer type are represented as such. When a 64-bit representation would overflow (either by the result of creating a large number literal or an arithmetic operation), it is represented in a Java BigInteger type, thus becoming significantly slower than the 64-bit representation.

Decimals are represented using the Java double type.

Type Conversions

Number literals that do not contain a decimal point, are treated as integers. Other literals are interpreted as decimals (even if the fractional part is 0).

Any arithmetic operation where at least one of the operands is a decimal will result in a decimal result.

Moreover, the default division operator / is implemented as floating-point division and always returns a decimal. If the desired behavior is integral division instead, the Integer.div method implements it.

Another operator worth noting is the exponentiation operator (^). It will always result in a decimal whenever either operand is decimal or the exponent is negative. It will also return a float result when the exponent is outside the 64-bit integer range.

There is a Number.to_decimal method, that allows converting any number to a decimal. This is useful in certain high-performance and polyglot applications.