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67 lines
2.5 KiB
Markdown
67 lines
2.5 KiB
Markdown
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---
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layout: developer-doc
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title: Numbers
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category: semantics
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tags: [semantics, runtime, number]
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order: 8
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---
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# Numbers
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In order to enhance the user experience, Enso provides a number hierarchy,
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encompassing both integers of unbound size and floating-point decimals.
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<!-- MarkdownTOC levels="2,3" autolink="true" -->
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- [Number Types](#number-types)
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- [Internal Representation](#internal-representation)
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- [Type Conversions](#type-conversions)
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<!-- /MarkdownTOC -->
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## Number Types
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The base number type in Enso is `Number`. It includes both integers and
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floating-point numbers and is the basic type that should be used whenever
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numerical computations are performed. Any method defined on the type `Number` is
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automatically available on all types of numeric values.
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The hierarchy is further split into the `Integer` and `Decimal` types. `Integer`
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is capable of representing values of unbound length. `Decimal` is capable of
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representing IEEE 64-bit (double precision) floating numbers.
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Any method defined on `Integer` is available for all integers, while any method
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defined on `Decimal` is available on all floating-point numbers. Methods defined
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on `Integer` or `Decimal` take precedence over methods defined on `Number`, when
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name resolution is performed.
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## Internal Representation
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Integers that can be represented in a 64-bit integer type are represented as
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such. When a 64-bit representation would overflow (either by the result of
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creating a large number literal or an arithmetic operation), it is represented
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in a Java `BigInteger` type, thus becoming significantly slower than the 64-bit
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representation.
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Decimals are represented using the Java `double` type.
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## Type Conversions
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Number literals that do not contain a decimal point, are treated as integers.
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Other literals are interpreted as decimals (even if the fractional part is 0).
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Any arithmetic operation where at least one of the operands is a decimal will
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result in a decimal result.
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Moreover, the default division operator `/` is implemented as floating-point
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division and always returns a decimal. If the desired behavior is integral
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division instead, the `Integer.div` method implements it.
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Another operator worth noting is the exponentiation operator (`^`). It will
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always result in a decimal whenever either operand is decimal or the exponent is
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negative. It will also return a float result when the exponent is outside the
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64-bit integer range.
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There is a `Number.to_decimal` method, that allows converting any number to a
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decimal. This is useful in certain high-performance and polyglot applications.
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