The Julia Language 1.12.5

Contents....2

Manual....16

Julia 1.12 Documentation....17

Introduction....17

Julia Compared to Other Languages....17

Important Links....19

Getting Started....20

Resources....21

Installation....22

Windows....22

Mac and Linux....22

Alternative installation methods....23

Variables....25

Allowed Variable Names....27

Assignment expressions and assignment versus mutation....28

Stylistic Conventions....29

Integers and Floating-Point Numbers....30

Integers....31

Floating-Point Numbers....35

Arbitrary Precision Arithmetic....40

Numeric Literal Coefficients....42

Literal zero and one....44

Mathematical Operations and Elementary Functions....45

Arithmetic Operators....45

Boolean Operators....46

Bitwise Operators....46

Updating operators....47

Vectorized "dot" operators....48

Numeric Comparisons....49

Operator Precedence and Associativity....52

Numerical Conversions....53

Complex and Rational Numbers....57

Complex Numbers....57

Rational Numbers....60

Strings....64

Characters....65

String Basics....67

Unicode and UTF-8....68

Concatenation....72

Interpolation....73

Triple-Quoted String Literals....74

Common Operations....76

Non-Standard String Literals....77

Regular Expressions....77

Byte Array Literals....82

Version Number Literals....84

Raw String Literals....84

Annotated Strings....85

Functions....87

Argument Passing Behavior....88

Argument-type declarations....89

The return Keyword....90

Operators Are Functions....92

Operators With Special Names....92

Anonymous Functions....92

Tuples....93

Named Tuples....94

Destructuring Assignment and Multiple Return Values....94

Property destructuring....97

Argument destructuring....98

Varargs Functions....98

Optional Arguments....100

Keyword Arguments....101

Evaluation Scope of Default Values....103

Do-Block Syntax for Function Arguments....103

Function composition and piping....104

Dot Syntax for Vectorizing Functions....105

Further Reading....107

Control Flow....108

Compound Expressions....108

Conditional Evaluation....109

Short-Circuit Evaluation....112

Repeated Evaluation: Loops....115

Exception Handling....118

Tasks (aka Coroutines)....124

Scope of Variables....125

Global Scope....127

Local Scope....127

Constants....138

Typed Globals....139

Types....140

Type Declarations....141

Abstract Types....143

Primitive Types....144

Composite Types....145

Mutable Composite Types....147

Declared Types....149

Type Unions....149

Parametric Types....150

UnionAll Types....158

Singleton types....159

Types of functions....160

Type{T} type selectors....161

Type Aliases....163

Operations on Types....163

Custom pretty-printing....164

"Value types"....168

Methods....170

Defining Methods....171

Method specializations....175

Method Ambiguities....175

Parametric Methods....176

Redefining Methods....179

Design Patterns with Parametric Methods....180

Parametrically-constrained Varargs methods....184

Note on Optional and keyword Arguments....185

Function-like objects....186

Empty generic functions....186

Method design and the avoidance of ambiguities....186

Defining methods in local scope....189

Constructors....191

Outer Constructor Methods....192

Inner Constructor Methods....192

Incomplete Initialization....194

Parametric Constructors....196

Case Study: Rational....198

Outer-only constructors....200

Constructors are just callable objects....201

Conversion and Promotion....203

Conversion....204

Promotion....206

Interfaces....210

Iteration....210

Indexing....213

Abstract Arrays....214

Strided Arrays....217

Customizing broadcasting....217

Instance Properties....222

Rounding....224

Modules....228

Namespace management....229

Submodules and relative paths....236

Module initialization and precompilation....237

Documentation....242

Accessing Documentation....242

Writing Documentation....242

Functions & Methods....246

Advanced Usage....247

Syntax Guide....248

Metaprogramming....255

Program representation....255

Expressions and evaluation....258

Macros....263

Code Generation....271

Non-Standard String Literals....272

Generated functions....274

Single- and multi-dimensional Arrays....282

Basic Functions....282

Construction and Initialization....282

Array literals....283

Comprehensions....288

Generator Expressions....289

Indexing....290

Indexed Assignment....292

Supported index types....293

Iteration....299

Array traits....300

Array and Vectorized Operators and Functions....300

Broadcasting....300

Implementation....302

Missing Values....304

Propagation of Missing Values....304

Equality and Comparison Operators....305

Logical operators....306

Control Flow and Short-Circuiting Operators....307

Arrays With Missing Values....308

Skipping Missing Values....309

Logical Operations on Arrays....310

Networking and Streams....312

Basic Stream IO....312

Text IO....313

IO Output Contextual Properties....314

Working with Files....314

A simple TCP example....316

Resolving IP Addresses....318

Asynchronous IO....318

Multicast....319

Parallel Computing....321

Asynchronous Programming....322

Basic Task operations....322

Communicating with Channels....323

More task operations....327

Tasks and events....328

Multi-Threading....329

Starting Julia with multiple threads....329

Threadpools....331

The threads Macro....332

Communication and data-races between threads....334

Side effects and mutable function arguments....337

threadcall....337

Caveats....338

Task Migration....338

Safe use of Finalizers....338

Multi-processing and Distributed Computing....340

Code Availability and Loading Packages....342

Starting and managing worker processes....344

Data Movement....345

Global variables....345

Parallel Map and Loops....347

Remote References and AbstractChannels....349

Channels and RemoteChannels....350

Local invocations....352

Shared Arrays....354

ClusterManagers....357

Specifying Network Topology (Experimental)....363

Noteworthy external packages....364

Running External Programs....367

Interpolation....368

Quoting....370

Pipelines....371

Cmd Objects....373

Calling C and Fortran Code....375

Creating C-Compatible Julia Function Pointers....377

Mapping C Types to Julia....379

Mapping C Functions to Julia....385

C Wrapper Examples....388

Fortran Wrapper Example....389

Garbage Collection Safety....389

Non-constant Function Specifications....390

Indirect Calls....390

Closure cfunctions....391

Closing a Library....391

Variadic function calls....392

ccall interface....392

Calling Convention....392

Accessing Global Variables....393

Accessing Data through a Pointer....393

Thread-safety....394

More About Callbacks....394

C....395

Handling Operating System Variation....398

Environment Variables....399

File locations....399

Pkg.jl....402

Network transport....404

External applications....405

Parallelization....405

Garbage Collection....407

REPL formatting....407

System and Package Image Building....408

Debugging and profiling....409

Embedding Julia....411

High-Level Embedding....411

High-Level Embedding on Windows with Visual Studio....413

Converting Types....414

Calling Julia Functions....415

Memory Management....415

Working with Arrays....419

Exceptions....420

Code Loading....424

Definitions....424

Federation of packages....425

Environments....426

Conclusion....436

Profiling....438

Basic usage....438

Accumulation and clearing....442

Options for controlling the display of profile results....442

Configuration....443

Wall-time Profiler....443

Memory allocation analysis....449

External Profiling....452

Stack Traces....454

Viewing a stack trace....454

Extracting useful information....455

Error handling....456

Exception stacks and current_exceptions....457

Comparison with backtrace....458

Memory Management and Garbage Collection....460

Garbage Collection Overview....460

Memory Architecture....460

System Memory Requirements....461

Multithreaded Garbage Collection....461

Monitoring and Debugging....462

Performance Considerations....463

Advanced Configuration....463

Troubleshooting Memory Issues....463

Performance Tips....465

Table of contents....465

General advice....466

Type inference....470

Memory management and arrays....485

Execution latency, package loading and package precompiling time....491

Miscellaneous....494

Workflow Tips....501

REPL-based workflow....501

Browser-based workflow....502

Revise-based workflows....502

Style Guide....504

Indentation....504

Write functions, not just scripts....504

Avoid writing overly-specific types....504

Handle excess argument diversity in the caller....505

Append ! to names of functions that modify their arguments....505

Avoid strange type Unions....506

Avoid elaborate container types....506

Prefer exported methods over direct field access....506

Use naming conventions consistent with Julia base....507

Write functions with argument ordering similar to Julia Base....507

Don't overuse try-catch....508

Don't parenthesize conditions....508

Don't overuse .......508

Ensure constructors return an instance of their own type....508

Don't use unnecessary static parameters....509

Avoid confusion about whether something is an instance or a type....509

Don't overuse macros....509

Don't expose unsafe operations at the interface level....510

Don't overload methods of base container types....510

Avoid type piracy....510

Be careful with type equality....511

Don't write a trivial anonymous function x->f(x) for a named function f....511

Avoid using floats for numeric literals in generic code when possible....511

Frequently Asked Questions....513

General....513

Public API....514

Sessions and the REPL....514

Scripting....515

Variables and Assignments....516

Functions....516

Types, type declarations, and constructors....520

Troubleshooting "method not matched": parametric type invariance and MethodErrors....527

Packages and Modules....528

Nothingness and missing values....528

Memory....529

Asynchronous IO and concurrent synchronous writes....529

Arrays....530

Computing cluster....532

Julia Releases....532

Noteworthy Differences from other Languages....534

Noteworthy differences from MATLAB....534

Noteworthy differences from R....536

Noteworthy differences from Python....539

Noteworthy differences from CC....542

Noteworthy differences from Common Lisp....546

Unicode Input....548

Command-line Interface....549

Using arguments inside scripts....549

The Main.main entry point....550

Parallel mode....551

Startup file....551

Command-line switches for Julia....551

The World Age mechanism....554

World age in general....554

Temporarily raising the world age using invokelatest....556

World age and const struct redefinitions....557

World age and usingimport....558

World age capture....559

Base....562

Essentials....563

Introduction....563

Getting Around....563

Keywords....570

Standard Modules....592

Base Submodules....593

All Objects....594

Properties of Types....610

Special Types....627

Generic Functions....638

Syntax....647

Managing deprecations....666

Missing Values....667

System....670

Versioning....690

Errors....692

Events....702

Reflection....704

Documentation....714

Code loading....716

Internals....717

Meta....724

Collections and Data Structures....727

Iteration....727

Constructors and Types....729

General Collections....731

Iterable Collections....733

Indexable Collections....782

Dictionaries....784

Set-Like Collections....798

Dequeues....807

Utility Collections....816

Mathematics....818

Mathematical Operators....818

Mathematical Functions....851

Customizable binary operators....896

Numbers....897

Standard Numeric Types....897

Data Formats....904

General Number Functions and Constants....911

BigFloats and BigInts....925

Strings....929

AnnotatedStrings....974

Arrays....978

Constructors and Types....978

Basic functions....993

Broadcast and vectorization....999

Indexing and assignment....1004

Views (SubArrays and other view types)....1015

Concatenation and permutation....1024

Array functions....1047

Combinatorics....1060

Tasks....1065

Scheduling....1070

Synchronization....1072

Channels....1080

Low-level synchronization using schedule and wait....1086

Multi-Threading....1089

Atomic operations....1095

ccall using a libuv threadpool (Experimental)....1106

Low-level synchronization primitives....1107

Task metrics (Experimental)....1107

Scoped Values....1109

Example....1112

Idioms....1113

API docs....1114

Implementation notes and performance....1117

Design inspiration....1117

Constants....1118

Filesystem....1122

IO and Network....1146

General IO....1146

Text IO....1170

Multimedia IO....1178

Network IO....1183

Punctuation....1185

Sorting and Related Functions....1187

Sorting Functions....1189

Order-Related Functions....1198

Sorting Algorithms....1204

Alternate Orderings....1205

Iteration utilities....1207

Reflection and introspection....1219

Module bindings....1219

DataType fields....1219

Subtypes....1220

DataType layout....1220

Function methods....1220

Expansion and lowering....1220

Intermediate and compiled representations....1221

C Interface....1222

LLVM Interface....1237

C Standard Library....1238

StackTraces....1243

SIMD Support....1245

Standard Library....1246

ArgTools....1247

Argument Handling....1247

Function Testing....1248

Artifacts....1251

Base64....1254

CRC32c....1257

Dates....1258

Constructors....1258

DurationsComparisons....1261

Accessor Functions....1262

Query Functions....1263

TimeType-Period Arithmetic....1264

Adjuster Functions....1266

Period Types....1267

Rounding....1268

API reference....1270

Delimited Files....1295

Distributed Computing....1300

Cluster Manager Interface....1316

Downloads....1320

Dynamic Linker....1324

File Events....1327

Pidfile....1331

Primary Functions....1331

Helper Functions....1332

Future....1334

Interactive Utilities....1335

Julia Syntax Highlighting....1344

Functions....1344

Faces....1345

Lazy Artifacts....1348

LibCURL....1349

LibGit2....1350

Linear Algebra....1391

Special matrices....1394

Matrix factorizations....1396

Orthogonal matrices (AbstractQ)....1396

Pivoting Strategies....1398

Standard functions....1399

Low-level matrix operations....1500

BLAS functions....1506

LAPACK functions....1517

Developer Documentation....1532

Logging....1534

Log event structure....1535

Processing log events....1536

Testing log events....1537

Environment variables....1537

Examples....1538

Reference....1539

Markdown....1545

Inline elements....1545

Toplevel elements....1547

Markdown String Literals....1552

Markdown Syntax Extensions....1552

API reference....1552

Memory-mapped IO....1555

Network Options....1558

Pkg....1562

Printf....1566

Profiling....1569

CPU Profiling....1569

Via profile....1569

Triggered During Execution....1569

Reference....1570

Memory profiling....1573

Heap Snapshots....1574

Random Numbers....1576

Random numbers module....1577

Random generation functions....1577

Subsequences, permutations and shuffling....1581

Generators (creation and seeding)....1585

Hooking into the Random API....1588

Reproducibility....1595

The Julia REPL....1596

The different prompt modes....1596

Key bindings....1600

Tab completion....1601

Customizing Colors....1605

Changing the contextual module which is active at the REPL....1605

Numbered prompt....1606

TerminalMenus....1607

References....1610

Serialization....1616

SHA....1618

SHA functions....1618

Working with context....1622

HMAC functions....1625

Shared Arrays....1629

Sockets....1631

Sparse Arrays....1639

Compressed Sparse Column (CSC) Sparse Matrix Storage....1639

Sparse Vector Storage....1640

Sparse Vector and Matrix Constructors....1640

Sparse matrix operations....1642

Correspondence of dense and sparse methods....1642

SparseArrays API....1643

Noteworthy External Sparse Packages....1657

Statistics....1659

StyledStrings....1668

Styling....1668

Annotated Strings....1669

Styling via AnnotatedStrings....1669

Faces....1669

Styled String Literals....1672

API reference....1673

Tar....1678

TOML....1683

Parsing TOML data....1683

Exporting data to TOML file....1684

References....1685

Unicode....1687

Unit Testing....1692

Testing Base Julia....1692

Basic Unit Tests....1692

Working with Test Sets....1695

Testing Log Statements....1700

Other Test Macros....1702

Broken Tests....1704

Test result types....1705

Creating Custom AbstractTestSet Types....1706

Test utilities....1709

Workflow for Testing Packages....1710

UUIDs....1714

Developer Documentation....1716

Documentation of Julia's Internals....1717

Initialization of the Julia runtime....1717

Julia ASTs....1720

More about types....1735

Memory layout of Julia Objects....1744

Eval of Julia code....1747

Calling Conventions....1751

High-level Overview of the Native-Code Generation Process....1752

Julia Functions....1754

Base.Cartesian....1758

Talking to the compiler (the :meta mechanism)....1763

SubArrays....1764

isbits Union Optimizations....1768

System Image Building....1769

Package Images....1773

Custom LLVM Passes....1774

Working with LLVM....1779

printf() and stdio in the Julia runtime....1787

Bounds checking....1789

Proper maintenance and care of multi-threading locks....1791

Arrays with custom indices....1795

Module loading....1798

Inference....1799

Julia SSA-form IR....1801

EscapeAnalysis....1806

Ahead of Time Compilation....1821

Static analyzer annotations for GC correctness in C code....1824

Garbage Collection in Julia....1830

JIT Design and Implementation....1832

Core.Builtins....1837

Fixing precompilation hangs due to open tasks or IO....1841

Developingdebugging Julia's C code....1844

Reporting and analyzing crashes (segfaults)....1844

gdb debugging tips....1847

Using Valgrind with Julia....1851

External Profiler Support....1853

Sanitizer support....1856

Instrumenting Julia with DTrace, and bpftrace....1858

Building Julia....1865

Building Julia (Detailed)....1865

Linux....1874

macOS....1874

Windows....1874

FreeBSD....1880

ARM (Linux)....1880

RISC-V (Linux)....1881

Binary distributions....1883

Point releasing 101....1885

Julia v1.12 Release Notes....1892

New language features....1892

Language changes....1893

CompilerRuntime improvements....1893

Command-line option changes....1894

Multi-threading changes....1894

Build system changes....1894

New library functions....1894

New library features....1895

Standard library changes....1895

External dependencies....1897

Tooling Improvements....1897

Scientific computing has traditionally required the highest performance, yet domain experts have largely moved to slower dynamic languages for daily work. We believe there are many good reasons to prefer dynamic languages for these applications, and we do not expect their use to diminish. Fortunately, modern language design and compiler techniques make it possible to mostly eliminate the performance trade-off and provide a single environment productive enough for prototyping and efficient enough for deploying performance-intensive applications. The Julia programming language fills this role: it is a flexible dynamic language, appropriate for scientific and numerical computing, with performance comparable to traditional statically-typed languages.

Because Julia's compiler is different from the interpreters used for languages like Python or R, you may find that Julia's performance is unintuitive at first. If you find that something is slow, we highly recommend reading through the Performance Tips section before trying anything else. Once you understand how Julia works, it is easy to write code that is nearly as fast as C.

--

March 14, 2026

As a patch release, 1.12.5 contains no new features or breaking changes, only bug fixes, documentation improvements, and performance improvements. You can see the list of commits included since 1.12.4:

discourse.julialang.org/t/julia-v1-12-5-has-been-released/135566