基本功能

介绍

Julia Base 中包含一系列适用于科学及数值计算的函数和宏，但也可以用于通用编程，其它功能则由 Julia 生态圈中的各种库来提供。函数按主题划分如下：

一些通用的提示：

• 可以通过 Import Module 导入想要使用的模块，并利用 Module.fn(x) 语句来实现对模块内函数的调用。
• 此外，using Module 语句会将名为 Module 的模块中的所有可调函数引入当前的命名空间。
• 按照约定，名字以感叹号（!）结尾的函数会改变其输入参数的内容。 一些函数同时拥有改变参数（例如 sort!）和不改变参数（sort）的版本

The behaviors of Base and standard libraries are stable as defined in SemVer only if they are documented; i.e., included in the Julia documentation and not marked as unstable. See API FAQ for more information.

Getting Around

Base.exit — Function

exit(code=0)

Stop the program with an exit code. The default exit code is zero, indicating that the program completed successfully. In an interactive session, exit() can be called with the keyboard shortcut ^D.

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Base.atexit — Function

atexit(f)

Register a zero-argument function f() to be called at process exit. atexit() hooks are called in last in first out (LIFO) order and run before object finalizers.

Exit hooks are allowed to call exit(n), in which case Julia will exit with exit code n (instead of the original exit code). If more than one exit hook calls exit(n), then Julia will exit with the exit code corresponding to the last called exit hook that calls exit(n). (Because exit hooks are called in LIFO order, “last called” is equivalent to “first registered”.)

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Base.isinteractive — Function

isinteractive() -> Bool

Determine whether Julia is running an interactive session.

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Base.summarysize — Function

Base.summarysize(obj; exclude=Union{...}, chargeall=Union{...}) -> Int

Compute the amount of memory, in bytes, used by all unique objects reachable from the argument.

Keyword Arguments

• exclude: specifies the types of objects to exclude from the traversal.
• chargeall: specifies the types of objects to always charge the size of all of their fields, even if those fields would normally be excluded.

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Base.require — Function

require(into::Module, module::Symbol)

This function is part of the implementation of using / import, if a module is not already defined in Main. It can also be called directly to force reloading a module, regardless of whether it has been loaded before (for example, when interactively developing libraries).

Loads a source file, in the context of the Main module, on every active node, searching standard locations for files. require is considered a top-level operation, so it sets the current include path but does not use it to search for files (see help for include). This function is typically used to load library code, and is implicitly called by using to load packages.

When searching for files, require first looks for package code in the global array LOAD_PATH. require is case-sensitive on all platforms, including those with case-insensitive filesystems like macOS and Windows.

For more details regarding code loading, see the manual sections on modules and parallel computing.

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Base.compilecache — Function

Base.compilecache(module::PkgId)

Creates a precompiled cache file for a module and all of its dependencies. This can be used to reduce package load times. Cache files are stored in DEPOT_PATH[1]/compiled. See Module initialization and precompilation for important notes.

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Base.__precompile__ — Function

__precompile__(isprecompilable::Bool)

Specify whether the file calling this function is precompilable, defaulting to true. If a module or file is not safely precompilable, it should call __precompile__(false) in order to throw an error if Julia attempts to precompile it.

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Base.include — Function

Base.include([mapexpr::Function,] [m::Module,] path::AbstractString)

Evaluate the contents of the input source file in the global scope of module m. Every module (except those defined with baremodule) has its own definition of include omitting the m argument, which evaluates the file in that module. Returns the result of the last evaluated expression of the input file. During including, a task-local include path is set to the directory containing the file. Nested calls to include will search relative to that path. This function is typically used to load source interactively, or to combine files in packages that are broken into multiple source files.

The optional first argument mapexpr can be used to transform the included code before it is evaluated: for each parsed expression expr in path, the include function actually evaluates mapexpr(expr). If it is omitted, mapexpr defaults to identity.

Julia 1.5

Julia 1.5 is required for passing the mapexpr argument.

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Base.MainInclude.include — Function

include([mapexpr::Function,] path::AbstractString)

Evaluate the contents of the input source file in the global scope of the containing module. Every module (except those defined with baremodule) has its own definition of include, which evaluates the file in that module. Returns the result of the last evaluated expression of the input file. During including, a task-local include path is set to the directory containing the file. Nested calls to include will search relative to that path. This function is typically used to load source interactively, or to combine files in packages that are broken into multiple source files.

The optional first argument mapexpr can be used to transform the included code before it is evaluated: for each parsed expression expr in path, the include function actually evaluates mapexpr(expr). If it is omitted, mapexpr defaults to identity.

Use Base.include to evaluate a file into another module.

Julia 1.5

Julia 1.5 is required for passing the mapexpr argument.

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Base.include_string — Function

include_string([mapexpr::Function,] m::Module, code::AbstractString, filename::AbstractString="string")

Like include, except reads code from the given string rather than from a file.

The optional first argument mapexpr can be used to transform the included code before it is evaluated: for each parsed expression expr in code, the include_string function actually evaluates mapexpr(expr). If it is omitted, mapexpr defaults to identity.

Julia 1.5

Julia 1.5 is required for passing the mapexpr argument.

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Base.include_dependency — Function

include_dependency(path::AbstractString)

In a module, declare that the file specified by path (relative or absolute) is a dependency for precompilation; that is, the module will need to be recompiled if this file changes.

This is only needed if your module depends on a file that is not used via include. It has no effect outside of compilation.

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Base.which — Method

which(f, types)

Returns the method of f (a Method object) that would be called for arguments of the given types.

If types is an abstract type, then the method that would be called by invoke is returned.

See also: parentmodule, and @which and @edit in InteractiveUtils.

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Base.methods — Function

methods(f, [types], [module])

Return the method table for f.

If types is specified, return an array of methods whose types match. If module is specified, return an array of methods defined in that module. A list of modules can also be specified as an array.

Julia 1.4

At least Julia 1.4 is required for specifying a module.

See also: which and @which.

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Base.@show — Macro

@show exs...

Prints one or more expressions, and their results, to stdout, and returns the last result.

See also: show, @info, println.

Examples

julia> x = @show 1+2
1 + 2 = 3
3
julia> @show x^2 x/2;
x ^ 2 = 9
x / 2 = 1.5

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ans — Keyword

ans

A variable referring to the last computed value, automatically set at the interactive prompt.

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Base.active_project — Function

active_project()

Return the path of the active Project.toml file.

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Keywords

This is the list of reserved keywords in Julia: baremodule, begin, break, catch, const, continue, do, else, elseif, end, export, false, finally, for, function, global, if, import, let, local, macro, module, quote, return, struct, true, try, using, while. Those keywords are not allowed to be used as variable names.

The following two-word sequences are reserved: abstract type, mutable struct, primitive type. However, you can create variables with names: abstract, mutable, primitive and type.

Finally: where is parsed as an infix operator for writing parametric method and type definitions; in and isa are parsed as infix operators; and outer is parsed as a keyword when used to modify the scope of a variable in an iteration specification of a for loop or generator expression. Creation of variables named where, in, isa or outer is allowed though.

module — Keyword

module

module declares a Module, which is a separate global variable workspace. Within a module, you can control which names from other modules are visible (via importing), and specify which of your names are intended to be public (via exporting). Modules allow you to create top-level definitions without worrying about name conflicts when your code is used together with somebody else’s. See the manual section about modules for more details.

Examples

module Foo
import Base.show
export MyType, foo
struct MyType
    x
end
bar(x) = 2x
foo(a::MyType) = bar(a.x) + 1
show(io::IO, a::MyType) = print(io, "MyType $(a.x)")
end

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export — Keyword

export

export is used within modules to tell Julia which functions should be made available to the user. For example: export foo makes the name foo available when using the module. See the manual section about modules for details.

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import — Keyword

import

import Foo will load the module or package Foo. Names from the imported Foo module can be accessed with dot syntax (e.g. Foo.foo to access the name foo). See the manual section about modules for details.

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using — Keyword

using

using Foo will load the module or package Foo and make its exported names available for direct use. Names can also be used via dot syntax (e.g. Foo.foo to access the name foo), whether they are exported or not. See the manual section about modules for details.

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baremodule — Keyword

baremodule

baremodule declares a module that does not contain using Base or local definitions of eval and include. It does still import Core. In other words,

module Mod
...
end

is equivalent to

baremodule Mod
using Base
eval(x) = Core.eval(Mod, x)
include(p) = Base.include(Mod, p)
...
end

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function — Keyword

function

Functions are defined with the function keyword:

function add(a, b)
    return a + b
end

Or the short form notation:

add(a, b) = a + b

The use of the return keyword is exactly the same as in other languages, but is often optional. A function without an explicit return statement will return the last expression in the function body.

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macro — Keyword

macro

macro defines a method for inserting generated code into a program. A macro maps a sequence of argument expressions to a returned expression, and the resulting expression is substituted directly into the program at the point where the macro is invoked. Macros are a way to run generated code without calling eval, since the generated code instead simply becomes part of the surrounding program. Macro arguments may include expressions, literal values, and symbols. Macros can be defined for variable number of arguments (varargs), but do not accept keyword arguments. Every macro also implicitly gets passed the arguments __source__, which contains the line number and file name the macro is called from, and __module__, which is the module the macro is expanded in.

Examples

julia> macro sayhello(name)
           return :( println("Hello, ", $name, "!") )
       end
@sayhello (macro with 1 method)
julia> @sayhello "Charlie"
Hello, Charlie!
julia> macro saylots(x...)
           return :( println("Say: ", $(x...)) )
       end
@saylots (macro with 1 method)
julia> @saylots "hey " "there " "friend"
Say: hey there friend

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return — Keyword

return

return x causes the enclosing function to exit early, passing the given value x back to its caller. return by itself with no value is equivalent to return nothing (see nothing).

function compare(a, b)
    a == b && return "equal to"
    a < b ? "less than" : "greater than"
end

In general you can place a return statement anywhere within a function body, including within deeply nested loops or conditionals, but be careful with do blocks. For example:

function test1(xs)
    for x in xs
        iseven(x) && return 2x
    end
end
function test2(xs)
    map(xs) do x
        iseven(x) && return 2x
        x
    end
end

In the first example, the return breaks out of test1 as soon as it hits an even number, so test1([5,6,7]) returns 12.

You might expect the second example to behave the same way, but in fact the return there only breaks out of the inner function (inside the do block) and gives a value back to map. test2([5,6,7]) then returns [5,12,7].

When used in a top-level expression (i.e. outside any function), return causes the entire current top-level expression to terminate early.

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do — Keyword

do

Create an anonymous function and pass it as the first argument to a function call. For example:

map(1:10) do x
    2x
end

is equivalent to map(x->2x, 1:10).

Use multiple arguments like so:

map(1:10, 11:20) do x, y
    x + y
end

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begin — Keyword

begin

begin...end denotes a block of code.

begin
    println("Hello, ")
    println("World!")
end

Usually begin will not be necessary, since keywords such as function and let implicitly begin blocks of code. See also ;.

begin may also be used when indexing to represent the first index of a collection or the first index of a dimension of an array.

Examples

julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
 1  2
 3  4
julia> A[begin, :]
2-element Array{Int64,1}:
 1
 2

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end — Keyword

end

end marks the conclusion of a block of expressions, for example module, struct, mutable struct, begin, let, for etc.

end may also be used when indexing to represent the last index of a collection or the last index of a dimension of an array.

Examples

julia> A = [1 2; 3 4]
2×2 Array{Int64, 2}:
 1  2
 3  4
julia> A[end, :]
2-element Array{Int64, 1}:
 3
 4

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let — Keyword

let

let statements create a new hard scope block and introduce new variable bindings each time they run. Whereas assignments might reassign a new value to an existing value location, let always creates a new location. This difference is only detectable in the case of variables that outlive their scope via closures. The let syntax accepts a comma-separated series of assignments and variable names:

let var1 = value1, var2, var3 = value3
    code
end

The assignments are evaluated in order, with each right-hand side evaluated in the scope before the new variable on the left-hand side has been introduced. Therefore it makes sense to write something like let x = x, since the two x variables are distinct and have separate storage.

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if — Keyword

if/elseif/else

if/elseif/else performs conditional evaluation, which allows portions of code to be evaluated or not evaluated depending on the value of a boolean expression. Here is the anatomy of the if/elseif/else conditional syntax:

if x < y
    println("x is less than y")
elseif x > y
    println("x is greater than y")
else
    println("x is equal to y")
end

If the condition expression x < y is true, then the corresponding block is evaluated; otherwise the condition expression x > y is evaluated, and if it is true, the corresponding block is evaluated; if neither expression is true, the else block is evaluated. The elseif and else blocks are optional, and as many elseif blocks as desired can be used.

In contrast to some other languages conditions must be of type Bool. It does not suffice for conditions to be convertible to Bool.

julia> if 1 end
ERROR: TypeError: non-boolean (Int64) used in boolean context

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for — Keyword

for

for loops repeatedly evaluate a block of statements while iterating over a sequence of values.

Examples

julia> for i in [1, 4, 0]
           println(i)
       end
1
4
0

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while — Keyword

while

while loops repeatedly evaluate a conditional expression, and continue evaluating the body of the while loop as long as the expression remains true. If the condition expression is false when the while loop is first reached, the body is never evaluated.

Examples

julia> i = 1
1
julia> while i < 5
           println(i)
           global i += 1
       end
1
2
3
4

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break — Keyword

break

Break out of a loop immediately.

Examples

julia> i = 0
0
julia> while true
           global i += 1
           i > 5 && break
           println(i)
       end
1
2
3
4
5

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continue — Keyword

continue

Skip the rest of the current loop iteration.

Examples

julia> for i = 1:6
           iseven(i) && continue
           println(i)
       end
1
3
5

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try — Keyword

try/catch

A try/catch statement allows intercepting errors (exceptions) thrown by throw so that program execution can continue. For example, the following code attempts to write a file, but warns the user and proceeds instead of terminating execution if the file cannot be written:

try
    open("/danger", "w") do f
        println(f, "Hello")
    end
catch
    @warn "Could not write file."
end

or, when the file cannot be read into a variable:

lines = try
    open("/danger", "r") do f
        readlines(f)
    end
catch
    @warn "File not found."
end

The syntax catch e (where e is any variable) assigns the thrown exception object to the given variable within the catch block.

The power of the try/catch construct lies in the ability to unwind a deeply nested computation immediately to a much higher level in the stack of calling functions.

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finally — Keyword

finally

Run some code when a given block of code exits, regardless of how it exits. For example, here is how we can guarantee that an opened file is closed:

f = open("file")
try
    operate_on_file(f)
finally
    close(f)
end

When control leaves the try block (for example, due to a return, or just finishing normally), close(f) will be executed. If the try block exits due to an exception, the exception will continue propagating. A catch block may be combined with try and finally as well. In this case the finally block will run after catch has handled the error.

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quote — Keyword

quote

quote creates multiple expression objects in a block without using the explicit Expr constructor. For example:

ex = quote
    x = 1
    y = 2
    x + y
end

Unlike the other means of quoting, :( ... ), this form introduces QuoteNode elements to the expression tree, which must be considered when directly manipulating the tree. For other purposes, :( ... ) and quote .. end blocks are treated identically.

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local — Keyword

local

local introduces a new local variable. See the manual section on variable scoping for more information.

Examples

julia> function foo(n)
           x = 0
           for i = 1:n
               local x # introduce a loop-local x
               x = i
           end
           x
       end
foo (generic function with 1 method)
julia> foo(10)
0

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global — Keyword

global

global x makes x in the current scope and its inner scopes refer to the global variable of that name. See the manual section on variable scoping for more information.

Examples

julia> z = 3
3
julia> function foo()
           global z = 6 # use the z variable defined outside foo
       end
foo (generic function with 1 method)
julia> foo()
6
julia> z
6

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const — Keyword

const

const is used to declare global variables whose values will not change. In almost all code (and particularly performance sensitive code) global variables should be declared constant in this way.

const x = 5

Multiple variables can be declared within a single const:

const y, z = 7, 11

Note that const only applies to one = operation, therefore const x = y = 1 declares x to be constant but not y. On the other hand, const x = const y = 1 declares both x and y constant.

Note that “constant-ness” does not extend into mutable containers; only the association between a variable and its value is constant. If x is an array or dictionary (for example) you can still modify, add, or remove elements.

In some cases changing the value of a const variable gives a warning instead of an error. However, this can produce unpredictable behavior or corrupt the state of your program, and so should be avoided. This feature is intended only for convenience during interactive use.

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struct — Keyword

struct

The most commonly used kind of type in Julia is a struct, specified as a name and a set of fields.

struct Point
    x
    y
end

Fields can have type restrictions, which may be parameterized:

struct Point{X}
    x::X
    y::Float64
end

A struct can also declare an abstract super type via <: syntax:

struct Point <: AbstractPoint
    x
    y
end

structs are immutable by default; an instance of one of these types cannot be modified after construction. Use mutable struct instead to declare a type whose instances can be modified.

See the manual section on Composite Types for more details, such as how to define constructors.

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mutable struct — Keyword

mutable struct

mutable struct is similar to struct, but additionally allows the fields of the type to be set after construction. See the manual section on Composite Types for more information.

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abstract type — Keyword

abstract type

abstract type declares a type that cannot be instantiated, and serves only as a node in the type graph, thereby describing sets of related concrete types: those concrete types which are their descendants. Abstract types form the conceptual hierarchy which makes Julia’s type system more than just a collection of object implementations. For example:

abstract type Number end
abstract type Real <: Number end

Number has no supertype, whereas Real is an abstract subtype of Number.

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primitive type — Keyword

primitive type

primitive type declares a concrete type whose data consists only of a series of bits. Classic examples of primitive types are integers and floating-point values. Some example built-in primitive type declarations:

primitive type Char 32 end
primitive type Bool <: Integer 8 end

The number after the name indicates how many bits of storage the type requires. Currently, only sizes that are multiples of 8 bits are supported. The Bool declaration shows how a primitive type can be optionally declared to be a subtype of some supertype.

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where — Keyword

where

The where keyword creates a type that is an iterated union of other types, over all values of some variable. For example Vector{T} where T<:Real includes all Vectors where the element type is some kind of Real number.

The variable bound defaults to Any if it is omitted:

Vector{T} where T    # short for `where T<:Any`

Variables can also have lower bounds:

Vector{T} where T>:Int
Vector{T} where Int<:T<:Real

There is also a concise syntax for nested where expressions. For example, this:

Pair{T, S} where S<:Array{T} where T<:Number

can be shortened to:

Pair{T, S} where {T<:Number, S<:Array{T}}

This form is often found on method signatures.

Note that in this form, the variables are listed outermost-first. This matches the order in which variables are substituted when a type is “applied” to parameter values using the syntax T{p1, p2, ...}.

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… — Keyword

...

The “splat” operator, ..., represents a sequence of arguments. ... can be used in function definitions, to indicate that the function accepts an arbitrary number of arguments. ... can also be used to apply a function to a sequence of arguments.

Examples

julia> add(xs...) = reduce(+, xs)
add (generic function with 1 method)
julia> add(1, 2, 3, 4, 5)
15
julia> add([1, 2, 3]...)
6
julia> add(7, 1:100..., 1000:1100...)
111107

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; — Keyword

;

; has a similar role in Julia as in many C-like languages, and is used to delimit the end of the previous statement. ; is not necessary after new lines, but can be used to separate statements on a single line or to join statements into a single expression. ; is also used to suppress output printing in the REPL and similar interfaces.

Examples

julia> function foo()
           x = "Hello, "; x *= "World!"
           return x
       end
foo (generic function with 1 method)
julia> bar() = (x = "Hello, Mars!"; return x)
bar (generic function with 1 method)
julia> foo();
julia> bar()
"Hello, Mars!"

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\= — Keyword

=

= is the assignment operator.

• For variable a and expression b, a = b makes a refer to the value of b.
• For functions f(x), f(x) = x defines a new function constant f, or adds a new method to f if f is already defined; this usage is equivalent to function f(x); x; end.
• a[i] = v calls setindex!(a,v,i).
• a.b = c calls setproperty!(a,:b,c).
• Inside a function call, f(a=b) passes b as the value of keyword argument a.
• Inside parentheses with commas, (a=1,) constructs a NamedTuple.

Examples

Assigning a to b does not create a copy of b; instead use copy or deepcopy.

julia> b = [1]; a = b; b[1] = 2; a
1-element Array{Int64, 1}:
 2
julia> b = [1]; a = copy(b); b[1] = 2; a
1-element Array{Int64, 1}:
 1

Collections passed to functions are also not copied. Functions can modify (mutate) the contents of the objects their arguments refer to. (The names of functions which do this are conventionally suffixed with ‘!’.)

julia> function f!(x); x[:] .+= 1; end
f! (generic function with 1 method)
julia> a = [1]; f!(a); a
1-element Array{Int64, 1}:
 2

Assignment can operate on multiple variables in parallel, taking values from an iterable:

julia> a, b = 4, 5
(4, 5)
julia> a, b = 1:3
1:3
julia> a, b
(1, 2)

Assignment can operate on multiple variables in series, and will return the value of the right-hand-most expression:

julia> a = [1]; b = [2]; c = [3]; a = b = c
1-element Array{Int64, 1}:
 3
julia> b[1] = 2; a, b, c
([2], [2], [2])

Assignment at out-of-bounds indices does not grow a collection. If the collection is a Vector it can instead be grown with push! or append!.

julia> a = [1, 1]; a[3] = 2
ERROR: BoundsError: attempt to access 2-element Array{Int64, 1} at index [3]
[...]
julia> push!(a, 2, 3)
4-element Array{Int64, 1}:
 1
 1
 2
 3

Assigning [] does not eliminate elements from a collection; instead use filter!.

julia> a = collect(1:3); a[a .<= 1] = []
ERROR: DimensionMismatch("tried to assign 0 elements to 1 destinations")
[...]
julia> filter!(x -> x > 1, a) # in-place & thus more efficient than a = a[a .> 1]
2-element Array{Int64, 1}:
 2
 3

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?: — Keyword

a ? b : c

Short form for conditionals; read “if a, evaluate b otherwise evaluate c“. Also known as the ternary operator.

This syntax is equivalent to if a; b else c end, but is often used to emphasize the value b-or-c which is being used as part of a larger expression, rather than the side effects that evaluating b or c may have.

See the manual section on control flow for more details.

Examples

julia> x = 1; y = 2;
julia> x > y ? println("x is larger") : println("y is larger")
y is larger

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Standard Modules

Missing docstring.

Missing docstring for Main. Check Documenter’s build log for details.

Core — Module

Core

Core is the module that contains all identifiers considered “built in” to the language, i.e. part of the core language and not libraries. Every module implicitly specifies using Core, since you can’t do anything without those definitions.

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Base — Module

Base

The base library of Julia. Base is a module that contains basic functionality (the contents of base/). All modules implicitly contain using Base, since this is needed in the vast majority of cases.

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Base Submodules

Base.Broadcast — Module

Base.Broadcast

Module containing the broadcasting implementation.

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Base.Docs — Module

Docs

The Docs module provides the @doc macro which can be used to set and retrieve documentation metadata for Julia objects.

Please see the manual section on documentation for more information.

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Base.Iterators — Module

Methods for working with Iterators.

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Base.Libc — Module

Interface to libc, the C standard library.

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Base.Meta — Module

Convenience functions for metaprogramming.

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Base.StackTraces — Module

Tools for collecting and manipulating stack traces. Mainly used for building errors.

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Base.Sys — Module

Provide methods for retrieving information about hardware and the operating system.

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Base.Threads — Module

Multithreading support.

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Base.GC — Module

Base.GC

Module with garbage collection utilities.

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All Objects

Core.:=== — Function

===(x,y) -> Bool
≡(x,y) -> Bool

Determine whether x and y are identical, in the sense that no program could distinguish them. First the types of x and y are compared. If those are identical, mutable objects are compared by address in memory and immutable objects (such as numbers) are compared by contents at the bit level. This function is sometimes called “egal”. It always returns a Bool value.

Examples

julia> a = [1, 2]; b = [1, 2];
julia> a == b
true
julia> a === b
false
julia> a === a
true

source

Core.isa — Function

isa(x, type) -> Bool

Determine whether x is of the given type. Can also be used as an infix operator, e.g. x isa type.

Examples

julia> isa(1, Int)
true
julia> isa(1, Matrix)
false
julia> isa(1, Char)
false
julia> isa(1, Number)
true
julia> 1 isa Number
true

source

Base.isequal — Function

isequal(x, y)

Similar to \==, except for the treatment of floating point numbers and of missing values. isequal treats all floating-point NaN values as equal to each other, treats -0.0 as unequal to 0.0, and missing as equal to missing. Always returns a Bool value.

isequal is an equivalence relation - it is reflexive (=== implies isequal), symmetric (isequal(a, b) implies isequal(b, a)) and transitive (isequal(a, b) and isequal(b, c) implies isequal(a, c)).

Implementation

The default implementation of isequal calls ==, so a type that does not involve floating-point values generally only needs to define ==.

isequal is the comparison function used by hash tables (Dict). isequal(x,y) must imply that hash(x) == hash(y).

This typically means that types for which a custom == or isequal method exists must implement a corresponding hash method (and vice versa). Collections typically implement isequal by calling isequal recursively on all contents.

Furthermore, isequal is linked with isless, and they work together to define a fixed total ordering, where exactly one of isequal(x, y), isless(x, y), or isless(y, x) must be true (and the other two false).

Scalar types generally do not need to implement isequal separate from ==, unless they represent floating-point numbers amenable to a more efficient implementation than that provided as a generic fallback (based on isnan, signbit, and ==).

Examples

julia> isequal([1., NaN], [1., NaN])
true
julia> [1., NaN] == [1., NaN]
false
julia> 0.0 == -0.0
true
julia> isequal(0.0, -0.0)
false
julia> missing == missing
missing
julia> isequal(missing, missing)
true

source

isequal(x)

Create a function that compares its argument to x using isequal, i.e. a function equivalent to y -> isequal(y, x).

The returned function is of type Base.Fix2{typeof(isequal)}, which can be used to implement specialized methods.

source

Base.isless — Function

isless(x, y)

Test whether x is less than y, according to a fixed total order (defined together with isequal). isless is not defined on all pairs of values (x, y). However, if it is defined, it is expected to satisfy the following:

• If isless(x, y) is defined, then so is isless(y, x) and isequal(x, y), and exactly one of those three yields true.
• The relation defined by isless is transitive, i.e., isless(x, y) && isless(y, z) implies isless(x, z).

Values that are normally unordered, such as NaN, are ordered after regular values. missing values are ordered last.

This is the default comparison used by sort.

Implementation

Non-numeric types with a total order should implement this function. Numeric types only need to implement it if they have special values such as NaN. Types with a partial order should implement <. See the documentation on Alternate orderings for how to define alternate ordering methods that can be used in sorting and related functions.

Examples

julia> isless(1, 3)
true
julia> isless("Red", "Blue")
false

source

Core.ifelse — Function

ifelse(condition::Bool, x, y)

Return x if condition is true, otherwise return y. This differs from ? or if in that it is an ordinary function, so all the arguments are evaluated first. In some cases, using ifelse instead of an if statement can eliminate the branch in generated code and provide higher performance in tight loops.

Examples

julia> ifelse(1 > 2, 1, 2)
2

source

Core.typeassert — Function

typeassert(x, type)

Throw a TypeError unless x isa type. The syntax x::type calls this function.

Examples

julia> typeassert(2.5, Int)
ERROR: TypeError: in typeassert, expected Int64, got a value of type Float64
Stacktrace:
[...]

source

Core.typeof — Function

typeof(x)

Get the concrete type of x.

See also eltype.

Examples

julia> a = 1//2;
julia> typeof(a)
Rational{Int64}
julia> M = [1 2; 3.5 4];
julia> typeof(M)
Matrix{Float64} (alias for Array{Float64, 2})

source

Core.tuple — Function

tuple(xs...)

Construct a tuple of the given objects.

See also Tuple, NamedTuple.

Examples

julia> tuple(1, 'b', pi)
(1, 'b', π)
julia> ans === (1, 'b', π)
true
julia> Tuple(Real[1, 2, pi])  # takes a collection
(1, 2, π)

source

Base.ntuple — Function

ntuple(f::Function, n::Integer)

Create a tuple of length n, computing each element as f(i), where i is the index of the element.

Examples

julia> ntuple(i -> 2*i, 4)
(2, 4, 6, 8)

source

ntuple(f, ::Val{N})

Create a tuple of length N, computing each element as f(i), where i is the index of the element. By taking a Val(N) argument, it is possible that this version of ntuple may generate more efficient code than the version taking the length as an integer. But ntuple(f, N) is preferable to ntuple(f, Val(N)) in cases where N cannot be determined at compile time.

Examples

julia> ntuple(i -> 2*i, Val(4))
(2, 4, 6, 8)

source

Base.objectid — Function

objectid(x) -> UInt

Get a hash value for x based on object identity. objectid(x)==objectid(y) if x === y.

See also hash, IdDict.

source

Base.hash — Function

hash(x[, h::UInt]) -> UInt

Compute an integer hash code such that isequal(x,y) implies hash(x)==hash(y). The optional second argument h is a hash code to be mixed with the result.

New types should implement the 2-argument form, typically by calling the 2-argument hash method recursively in order to mix hashes of the contents with each other (and with h). Typically, any type that implements hash should also implement its own \== (hence isequal) to guarantee the property mentioned above. Types supporting subtraction (operator -) should also implement widen, which is required to hash values inside heterogeneous arrays.

See also: objectid, Dict, Set.

source

Base.finalizer — Function

finalizer(f, x)

Register a function f(x) to be called when there are no program-accessible references to x, and return x. The type of x must be a mutable struct, otherwise the behavior of this function is unpredictable.

f must not cause a task switch, which excludes most I/O operations such as println. Using the @async macro (to defer context switching to outside of the finalizer) or ccall to directly invoke IO functions in C may be helpful for debugging purposes.

Examples

finalizer(my_mutable_struct) do x
    @async println("Finalizing $x.")
end
finalizer(my_mutable_struct) do x
    ccall(:jl_safe_printf, Cvoid, (Cstring, Cstring), "Finalizing %s.", repr(x))
end

A finalizer may be registered at object construction. In the following example note that we implicitly rely on the finalizer returning the newly created mutable struct x.

Example

mutable struct MyMutableStruct
    bar
    function MyMutableStruct(bar)
        x = new(bar)
        f(t) = @async println("Finalizing $t.")
        finalizer(f, x)
    end
end

source

Base.finalize — Function

finalize(x)

Immediately run finalizers registered for object x.

source

Base.copy — Function

copy(x)

Create a shallow copy of x: the outer structure is copied, but not all internal values. For example, copying an array produces a new array with identically-same elements as the original.

See also copy!, copyto!.

source

Base.deepcopy — Function

deepcopy(x)

Create a deep copy of x: everything is copied recursively, resulting in a fully independent object. For example, deep-copying an array produces a new array whose elements are deep copies of the original elements. Calling deepcopy on an object should generally have the same effect as serializing and then deserializing it.

While it isn’t normally necessary, user-defined types can override the default deepcopy behavior by defining a specialized version of the function deepcopy_internal(x::T, dict::IdDict) (which shouldn’t otherwise be used), where T is the type to be specialized for, and dict keeps track of objects copied so far within the recursion. Within the definition, deepcopy_internal should be used in place of deepcopy, and the dict variable should be updated as appropriate before returning.

source

Base.getproperty — Function

getproperty(value, name::Symbol)
getproperty(value, name::Symbol, order::Symbol)

The syntax a.b calls getproperty(a, :b). The syntax @atomic order a.b calls getproperty(a, :b, :order) and the syntax @atomic a.b calls getproperty(a, :b, :sequentially_consistent).

Examples

julia> struct MyType
           x
       end
julia> function Base.getproperty(obj::MyType, sym::Symbol)
           if sym === :special
               return obj.x + 1
           else # fallback to getfield
               return getfield(obj, sym)
           end
       end
julia> obj = MyType(1);
julia> obj.special
2
julia> obj.x
1

See also getfield, propertynames and setproperty!.

source

Base.setproperty! — Function

setproperty!(value, name::Symbol, x)
setproperty!(value, name::Symbol, x, order::Symbol)

The syntax a.b = c calls setproperty!(a, :b, c). The syntax @atomic order a.b = c calls setproperty!(a, :b, c, :order) and the syntax @atomic a.b = c calls getproperty(a, :b, :sequentially_consistent).

See also setfield!, propertynames and getproperty.

source

Base.propertynames — Function

propertynames(x, private=false)

Get a tuple or a vector of the properties (x.property) of an object x. This is typically the same as fieldnames(typeof(x)), but types that overload getproperty should generally overload propertynames as well to get the properties of an instance of the type.

propertynames(x) may return only “public” property names that are part of the documented interface of x. If you want it to also return “private” fieldnames intended for internal use, pass true for the optional second argument. REPL tab completion on x. shows only the private=false properties.

See also: hasproperty, hasfield.

source

Base.hasproperty — Function

hasproperty(x, s::Symbol)

Return a boolean indicating whether the object x has s as one of its own properties.

Julia 1.2

This function requires at least Julia 1.2.

See also: propertynames, hasfield.

source

Core.getfield — Function

getfield(value, name::Symbol, [order::Symbol])
getfield(value, i::Int, [order::Symbol])

Extract a field from a composite value by name or position. Optionally, an ordering can be defined for the operation. If the field was declared @atomic, the specification is strongly recommended to be compatible with the stores to that location. Otherwise, if not declared as @atomic, this parameter must be :not_atomic if specified. See also getproperty and fieldnames.

Examples

julia> a = 1//2
1//2
julia> getfield(a, :num)
1
julia> a.num
1
julia> getfield(a, 1)
1

source

Core.setfield! — Function

setfield!(value, name::Symbol, x, [order::Symbol])
setfield!(value, i::Int, x, [order::Symbol])

Assign x to a named field in value of composite type. The value must be mutable and x must be a subtype of fieldtype(typeof(value), name). Additionally, an ordering can be specified for this operation. If the field was declared @atomic, this specification is mandatory. Otherwise, if not declared as @atomic, it must be :not_atomic if specified. See also setproperty!.

Examples

julia> mutable struct MyMutableStruct
           field::Int
       end
julia> a = MyMutableStruct(1);
julia> setfield!(a, :field, 2);
julia> getfield(a, :field)
2
julia> a = 1//2
1//2
julia> setfield!(a, :num, 3);
ERROR: setfield!: immutable struct of type Rational cannot be changed

source

Core.isdefined — Function

isdefined(m::Module, s::Symbol, [order::Symbol])
isdefined(object, s::Symbol, [order::Symbol])
isdefined(object, index::Int, [order::Symbol])

Tests whether a global variable or object field is defined. The arguments can be a module and a symbol or a composite object and field name (as a symbol) or index. Optionally, an ordering can be defined for the operation. If the field was declared @atomic, the specification is strongly recommended to be compatible with the stores to that location. Otherwise, if not declared as @atomic, this parameter must be :not_atomic if specified.

To test whether an array element is defined, use isassigned instead.

See also @isdefined.

Examples

julia> isdefined(Base, :sum)
true
julia> isdefined(Base, :NonExistentMethod)
false
julia> a = 1//2;
julia> isdefined(a, 2)
true
julia> isdefined(a, 3)
false
julia> isdefined(a, :num)
true
julia> isdefined(a, :numerator)
false

source

Base.@isdefined — Macro

@isdefined s -> Bool

Tests whether variable s is defined in the current scope.

See also isdefined for field properties and isassigned for array indexes or haskey for other mappings.

Examples

julia> @isdefined newvar
false
julia> newvar = 1
1
julia> @isdefined newvar
true
julia> function f()
           println(@isdefined x)
           x = 3
           println(@isdefined x)
       end
f (generic function with 1 method)
julia> f()
false
true

source

Base.convert — Function

convert(T, x)

Convert x to a value of type T.

If T is an Integer type, an InexactError will be raised if x is not representable by T, for example if x is not integer-valued, or is outside the range supported by T.

Examples

julia> convert(Int, 3.0)
3
julia> convert(Int, 3.5)
ERROR: InexactError: Int64(3.5)
Stacktrace:
[...]

If T is a AbstractFloat or Rational type, then it will return the closest value to x representable by T.

julia> x = 1/3
0.3333333333333333
julia> convert(Float32, x)
0.33333334f0
julia> convert(Rational{Int32}, x)
1//3
julia> convert(Rational{Int64}, x)
6004799503160661//18014398509481984

If T is a collection type and x a collection, the result of convert(T, x) may alias all or part of x.

julia> x = Int[1, 2, 3];
julia> y = convert(Vector{Int}, x);
julia> y === x
true

See also: round, trunc, oftype, reinterpret.

source

Base.promote — Function

promote(xs...)

Convert all arguments to a common type, and return them all (as a tuple). If no arguments can be converted, an error is raised.

See also: [promote_type], [promote_rule].

Examples

julia> promote(Int8(1), Float16(4.5), Float32(4.1))
(1.0f0, 4.5f0, 4.1f0)

source

Base.oftype — Function

oftype(x, y)

Convert y to the type of x (convert(typeof(x), y)).

Examples

julia> x = 4;
julia> y = 3.;
julia> oftype(x, y)
3
julia> oftype(y, x)
4.0

source

Base.widen — Function

widen(x)

If x is a type, return a “larger” type, defined so that arithmetic operations + and - are guaranteed not to overflow nor lose precision for any combination of values that type x can hold.

For fixed-size integer types less than 128 bits, widen will return a type with twice the number of bits.

If x is a value, it is converted to widen(typeof(x)).

Examples

julia> widen(Int32)
Int64
julia> widen(1.5f0)
1.5

source

Base.identity — Function

identity(x)

The identity function. Returns its argument.

See also: one, oneunit, and LinearAlgebra‘s I.

Examples

julia> identity("Well, what did you expect?")
"Well, what did you expect?"

source

Properties of Types

Type relations

Base.supertype — Function

supertype(T::DataType)

Return the supertype of DataType T.

Examples

julia> supertype(Int32)
Signed

source

Core.Type — Type

Core.Type{T}

Core.Type is an abstract type which has all type objects as its instances. The only instance of the singleton type Core.Type{T} is the object T.

Examples

julia> isa(Type{Float64}, Type)
true
julia> isa(Float64, Type)
true
julia> isa(Real, Type{Float64})
false
julia> isa(Real, Type{Real})
true

source

Core.DataType — Type

DataType <: Type{T}

DataType represents explicitly declared types that have names, explicitly declared supertypes, and, optionally, parameters. Every concrete value in the system is an instance of some DataType.

Examples

julia> typeof(Real)
DataType
julia> typeof(Int)
DataType
julia> struct Point
           x::Int
           y
       end
julia> typeof(Point)
DataType

source

Core.:<: — Function

<:(T1, T2)

Subtype operator: returns true if and only if all values of type T1 are also of type T2.

Examples

julia> Float64 <: AbstractFloat
true
julia> Vector{Int} <: AbstractArray
true
julia> Matrix{Float64} <: Matrix{AbstractFloat}
false

source

Base.:>: — Function

>:(T1, T2)

Supertype operator, equivalent to T2 <: T1.

source

Base.typejoin — Function

typejoin(T, S)

Return the closest common ancestor of T and S, i.e. the narrowest type from which they both inherit.

source

Base.typeintersect — Function

typeintersect(T, S)

Compute a type that contains the intersection of T and S. Usually this will be the smallest such type or one close to it.

source

Base.promote_type — Function

promote_type(type1, type2)

Promotion refers to converting values of mixed types to a single common type. promote_type represents the default promotion behavior in Julia when operators (usually mathematical) are given arguments of differing types. promote_type generally tries to return a type which can at least approximate most values of either input type without excessively widening. Some loss is tolerated; for example, promote_type(Int64, Float64) returns Float64 even though strictly, not all Int64 values can be represented exactly as Float64 values.

See also: promote, promote_typejoin, promote_rule.

Examples

julia> promote_type(Int64, Float64)
Float64
julia> promote_type(Int32, Int64)
Int64
julia> promote_type(Float32, BigInt)
BigFloat
julia> promote_type(Int16, Float16)
Float16
julia> promote_type(Int64, Float16)
Float16
julia> promote_type(Int8, UInt16)
UInt16

source

Base.promote_rule — Function

promote_rule(type1, type2)

Specifies what type should be used by promote when given values of types type1 and type2. This function should not be called directly, but should have definitions added to it for new types as appropriate.

source

Base.promote_typejoin — Function

promote_typejoin(T, S)

Compute a type that contains both T and S, which could be either a parent of both types, or a Union if appropriate. Falls back to typejoin.

See instead promote, promote_type.

Examples

julia> Base.promote_typejoin(Int, Float64)
Real
julia> Base.promote_type(Int, Float64)
Float64

source

Base.isdispatchtuple — Function

isdispatchtuple(T)

Determine whether type T is a tuple “leaf type”, meaning it could appear as a type signature in dispatch and has no subtypes (or supertypes) which could appear in a call.

source

Declared structure

Base.ismutable — Function

ismutable(v) -> Bool

Return true iff value v is mutable. See Mutable Composite Types for a discussion of immutability. Note that this function works on values, so if you give it a type, it will tell you that a value of DataType is mutable.

See also isbits, isstructtype.

Examples

julia> ismutable(1)
false
julia> ismutable([1,2])
true

Julia 1.5

This function requires at least Julia 1.5.

source

Base.isimmutable — Function

isimmutable(v) -> Bool

Warning

Consider using !ismutable(v) instead, as isimmutable(v) will be replaced by !ismutable(v) in a future release. (Since Julia 1.5)

Return true iff value v is immutable. See Mutable Composite Types for a discussion of immutability. Note that this function works on values, so if you give it a type, it will tell you that a value of DataType is mutable.

Examples

julia> isimmutable(1)
true
julia> isimmutable([1,2])
false

source

Base.isabstracttype — Function

isabstracttype(T)

Determine whether type T was declared as an abstract type (i.e. using the abstract keyword).

Examples

julia> isabstracttype(AbstractArray)
true
julia> isabstracttype(Vector)
false

source

Base.isprimitivetype — Function

isprimitivetype(T) -> Bool

Determine whether type T was declared as a primitive type (i.e. using the primitive keyword).

source

Base.issingletontype — Function

Base.issingletontype(T)

Determine whether type T has exactly one possible instance; for example, a struct type with no fields.

source

Base.isstructtype — Function

isstructtype(T) -> Bool

Determine whether type T was declared as a struct type (i.e. using the struct or mutable struct keyword).

source

Base.nameof — Method

nameof(t::DataType) -> Symbol

Get the name of a (potentially UnionAll-wrapped) DataType (without its parent module) as a symbol.

Examples

julia> module Foo
           struct S{T}
           end
       end
Foo
julia> nameof(Foo.S{T} where T)
:S

source

Base.fieldnames — Function

fieldnames(x::DataType)

Get a tuple with the names of the fields of a DataType.

See also propertynames, hasfield.

Examples

julia> fieldnames(Rational)
(:num, :den)
julia> fieldnames(typeof(1+im))
(:re, :im)

source

Base.fieldname — Function

fieldname(x::DataType, i::Integer)

Get the name of field i of a DataType.

Examples

julia> fieldname(Rational, 1)
:num
julia> fieldname(Rational, 2)
:den

source

Base.hasfield — Function

hasfield(T::Type, name::Symbol)

Return a boolean indicating whether T has name as one of its own fields.

Julia 1.2

This function requires at least Julia 1.2.

source

Memory layout

Base.sizeof — Method

sizeof(T::DataType)
sizeof(obj)

Size, in bytes, of the canonical binary representation of the given DataType T, if any. Size, in bytes, of object obj if it is not DataType.

Examples

julia> sizeof(Float32)
4
julia> sizeof(ComplexF64)
16
julia> sizeof(1.0)
8
julia> sizeof([1.0:10.0;])
80

If DataType T does not have a specific size, an error is thrown.

julia> sizeof(AbstractArray)
ERROR: Abstract type AbstractArray does not have a definite size.
Stacktrace:
[...]

source

Base.isconcretetype — Function

isconcretetype(T)

Determine whether type T is a concrete type, meaning it could have direct instances (values x such that typeof(x) === T).

See also: isbits, isabstracttype, issingletontype.

Examples

julia> isconcretetype(Complex)
false
julia> isconcretetype(Complex{Float32})
true
julia> isconcretetype(Vector{Complex})
true
julia> isconcretetype(Vector{Complex{Float32}})
true
julia> isconcretetype(Union{})
false
julia> isconcretetype(Union{Int,String})
false

source

Base.isbits — Function

isbits(x)

Return true if x is an instance of an isbitstype type.

source

Base.isbitstype — Function

isbitstype(T)

Return true if type T is a “plain data” type, meaning it is immutable and contains no references to other values, only primitive types and other isbitstype types. Typical examples are numeric types such as UInt8, Float64, and Complex{Float64}. This category of types is significant since they are valid as type parameters, may not track isdefined / isassigned status, and have a defined layout that is compatible with C.

See also isbits, isprimitivetype, ismutable.

Examples

julia> isbitstype(Complex{Float64})
true
julia> isbitstype(Complex)
false

source

Core.fieldtype — Function

fieldtype(T, name::Symbol | index::Int)

Determine the declared type of a field (specified by name or index) in a composite DataType T.

Examples

julia> struct Foo
           x::Int64
           y::String
       end
julia> fieldtype(Foo, :x)
Int64
julia> fieldtype(Foo, 2)
String

source

Base.fieldtypes — Function

fieldtypes(T::Type)

The declared types of all fields in a composite DataType T as a tuple.

Julia 1.1

This function requires at least Julia 1.1.

Examples

julia> struct Foo
           x::Int64
           y::String
       end
julia> fieldtypes(Foo)
(Int64, String)

source

Base.fieldcount — Function

fieldcount(t::Type)

Get the number of fields that an instance of the given type would have. An error is thrown if the type is too abstract to determine this.

source

Base.fieldoffset — Function

fieldoffset(type, i)

The byte offset of field i of a type relative to the data start. For example, we could use it in the following manner to summarize information about a struct:

julia> structinfo(T) = [(fieldoffset(T,i), fieldname(T,i), fieldtype(T,i)) for i = 1:fieldcount(T)];
julia> structinfo(Base.Filesystem.StatStruct)
13-element Vector{Tuple{UInt64, Symbol, Type}}:
 (0x0000000000000000, :desc, Union{RawFD, String})
 (0x0000000000000008, :device, UInt64)
 (0x0000000000000010, :inode, UInt64)
 (0x0000000000000018, :mode, UInt64)
 (0x0000000000000020, :nlink, Int64)
 (0x0000000000000028, :uid, UInt64)
 (0x0000000000000030, :gid, UInt64)
 (0x0000000000000038, :rdev, UInt64)
 (0x0000000000000040, :size, Int64)
 (0x0000000000000048, :blksize, Int64)
 (0x0000000000000050, :blocks, Int64)
 (0x0000000000000058, :mtime, Float64)
 (0x0000000000000060, :ctime, Float64)

source

Base.datatype_alignment — Function

Base.datatype_alignment(dt::DataType) -> Int

Memory allocation minimum alignment for instances of this type. Can be called on any isconcretetype.

source

Base.datatype_haspadding — Function

Base.datatype_haspadding(dt::DataType) -> Bool

Return whether the fields of instances of this type are packed in memory, with no intervening padding bytes. Can be called on any isconcretetype.

source

Base.datatype_pointerfree — Function

Base.datatype_pointerfree(dt::DataType) -> Bool

Return whether instances of this type can contain references to gc-managed memory. Can be called on any isconcretetype.

source

Special values

Base.typemin — Function

typemin(T)

The lowest value representable by the given (real) numeric DataType T.

Examples

julia> typemin(Float16)
-Inf16
julia> typemin(Float32)
-Inf32

source

Base.typemax — Function

typemax(T)

The highest value representable by the given (real) numeric DataType.

See also: floatmax, typemin, eps.

Examples

julia> typemax(Int8)
127
julia> typemax(UInt32)
0xffffffff
julia> typemax(Float64)
Inf
julia> floatmax(Float32)  # largest finite floating point number
3.4028235f38

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Base.floatmin — Function

floatmin(T = Float64)

Return the smallest positive normal number representable by the floating-point type T.

Examples

julia> floatmin(Float16)
Float16(6.104e-5)
julia> floatmin(Float32)
1.1754944f-38
julia> floatmin()
2.2250738585072014e-308

source

Base.floatmax — Function

floatmax(T = Float64)

Return the largest finite number representable by the floating-point type T.

See also: typemax, floatmin, eps.

Examples

julia> floatmax(Float16)
Float16(6.55e4)
julia> floatmax(Float32)
3.4028235f38
julia> floatmax()
1.7976931348623157e308
julia> typemax(Float64)
Inf

source

Base.maxintfloat — Function

maxintfloat(T=Float64)

The largest consecutive integer-valued floating-point number that is exactly represented in the given floating-point type T (which defaults to Float64).

That is, maxintfloat returns the smallest positive integer-valued floating-point number n such that n+1 is not exactly representable in the type T.

When an Integer-type value is needed, use Integer(maxintfloat(T)).

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maxintfloat(T, S)

The largest consecutive integer representable in the given floating-point type T that also does not exceed the maximum integer representable by the integer type S. Equivalently, it is the minimum of maxintfloat(T) and typemax(S).

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Base.eps — Method

eps(::Type{T}) where T<:AbstractFloat
eps()

Return the machine epsilon of the floating point type T (T = Float64 by default). This is defined as the gap between 1 and the next largest value representable by typeof(one(T)), and is equivalent to eps(one(T)). (Since eps(T) is a bound on the relative error of T, it is a “dimensionless” quantity like one.)

Examples

julia> eps()
2.220446049250313e-16
julia> eps(Float32)
1.1920929f-7
julia> 1.0 + eps()
1.0000000000000002
julia> 1.0 + eps()/2
1.0

source

Base.eps — Method

eps(x::AbstractFloat)

Return the unit in last place (ulp) of x. This is the distance between consecutive representable floating point values at x. In most cases, if the distance on either side of x is different, then the larger of the two is taken, that is

eps(x) == max(x-prevfloat(x), nextfloat(x)-x)