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import() Function Complexity

__import__() is the function the import statement calls. The compiler emits one IMPORT_NAME for each module a statement names, and that instruction looks the name __import__ up in the executing frame's builtins and calls what it finds - so rebinding builtins.__import__ changes every subsequent import run with the usual builtins, and deleting it makes import raise ImportError. The function itself is the C implementation of the import protocol: a probe of sys.modules first, and only on a miss the search along sys.meta_path and the path entries, then reading, compiling and running the module.

The search and the module body happen once per name that imports successfully and stays in sys.modules; a later call with an empty fromlist is the probe alone. That is why the cost of an import is a property of the program's first run through a line rather than of the line - and why removing the entry, or reloading, runs the body again. What the function does not do is return what its name suggests: for a dotted name it hands back the head of the name, and only a non-empty fromlist makes it return the module named. That is the reason importlib.import_module() exists, and the reason direct use of this function is rare.

t is the finders on sys.meta_path, p is the entries on the path being searched (sys.path, or a package's __path__), s is the registered file suffixes, e is the directory entries listed during one search, summed over the path entries whose listing is not cached yet, n is the bytes in a module's source or bytecode, m is the time and space the module's body itself takes, c is the components of a dotted name, f is the names in fromlist, a is the names in a module's __all__, and g is the names in its namespace. Module names are treated as O(1) to split, hash and join, and one attribute check or one find_spec() call as O(1) - a module __getattr__ or a finder of your own costs whatever you wrote. Space in the first table below is what a call leaves in sys.modules, and in the second what the statement binds in the importing namespace; the directory listings a first search caches belong to the path entry finders either way, and are priced on the importlib page.

Complexity Reference

import

Operation	Time	Space	Notes
__import__(name, globals=None, locals=None, fromlist=(), level=0), resolved name in sys.modules, empty fromlist	O(1)	O(1)	Cached lookups only, and no finder is consulted. A None entry raises ModuleNotFoundError rather than returning it. A module another thread is still executing is waited for instead, which this bound does not cover: the wait is that module's body
__import__(name), name not loaded	O(c·(t + p·s + e) + n + m)	O(n + m)	A find and a load for every component of the dotted name that is missing, top down; each find walks sys.meta_path and then the path entries, listing any directory whose contents are not cached yet. n and m are summed over the modules actually run
Return value of a dotted name with an empty fromlist	O(1)	O(1)	The head of name, not the module it asks for: the top-level package for an absolute import, and for level > 0 the first component of name under the anchor. Reaching it costs no search. An undotted name returns the module itself
__import__(name, fromlist=names) on a package	O(f), plus an import per missing name	O(1), plus O(n + m) per name loaded	One attribute check per name, and an import of each name the package lacks - a probe when that submodule is already in sys.modules, the row above when it is not, and a full search every call for a name that is neither, whose ModuleNotFoundError is swallowed. The module named by name is returned instead of the head of the name
__import__(name, fromlist=names) on a non-package	O(1)	O(1)	No name in the list is checked: only a module with __path__ reaches the fromlist handling
__import__(name, fromlist=["*"])	O(a), plus an import per missing name	O(1), plus O(n + m) per name loaded	Expands to the package's __all__ and checks those names on the same terms as the row above; a package without __all__ costs one check and nothing else
__import__(name, globals, level=k)	O(1)	O(1)	Resolves name against globals: __package__ if set, else __spec__.parent, else __name__ behind an ImportWarning. TypeError unless globals is a dict - the default None and any other mapping are refused - so a positive level needs a dict that names the anchor, not a call from inside a module
locals	O(1)	O(1)	Never used; the statement passes the frame's locals and the implementation ignores them
builtins.__import__	O(1)	O(1)	An ordinary module attribute. IMPORT_NAME reads it from the frame's builtins every time, so a replacement takes effect at once and is called again on every subsequent import statement

The import statement

Every form below names one module and so compiles to one IMPORT_NAME, which is the call above. The costs here are what the statement adds to it.

Operation	Time	Space	Notes
import pkg.mod	O(1)	O(1)	An empty fromlist, so the call returns pkg, which is the name bound
import pkg.mod as name	O(1)	O(1)	Also an empty fromlist, then one attribute load for mod, which falls back to sys.modules['pkg.mod'] when the attribute is not there yet
from pkg.mod import x, y	O(f)	O(1)	fromlist is the names, so the call returns pkg.mod; then one attribute load per name, with the same sys.modules fallback
from . import x	O(1)	O(1)	level is the number of leading dots and name is what follows, so the module's own globals resolve it
from pkg import *	O(a), or O(g) with no __all__	O(a), or O(g) with no __all__	fromlist is ('*',), then every name in __all__ - or, with no __all__, every name in the namespace that does not start with _ - is bound in the importing namespace

A Probe Before a Search

The first import of a name pays for the search; a later one with an empty fromlist is a dictionary lookup that consults no finder at all. A finder on sys.meta_path that records what it is asked separates the two without a stopwatch.

import sys

class Recorder:
    """A meta path finder that answers nothing and remembers what it was asked."""

    def __init__(self):
        self.asked = []

    def find_spec(self, fullname, path=None, target=None):
        self.asked.append(fullname)
        return None

recorder = Recorder()
sys.meta_path.insert(0, recorder)
try:
    import base64  # the first import may search
    recorder.asked.clear()

    again = __import__("base64")  # O(1) - a sys.modules probe
    assert again is base64
    assert again is sys.modules["base64"]
    assert recorder.asked == []  # no finder was consulted

    try:
        __import__("no_such_module_anywhere")  # a full search before it fails
    except ModuleNotFoundError as error:
        assert error.name == "no_such_module_anywhere"
    else:
        raise AssertionError("a missing module was imported")
    assert recorder.asked == ["no_such_module_anywhere"]
finally:
    sys.meta_path.remove(recorder)

A None left in sys.modules is not a cached module: the probe finds it and raises instead of searching, which is how an import is blocked outright.

import sys

sys.modules["blocked_module"] = None
try:
    __import__("blocked_module")  # O(1) - the probe finds None
except ModuleNotFoundError as error:
    assert "None in sys.modules" in str(error)
else:
    raise AssertionError("a blocked module was imported")
finally:
    del sys.modules["blocked_module"]

The Return Value Depends on fromlist

For a dotted name the function returns the head of that name - for an absolute import, the top-level package - because that is the name import pkg.mod binds. A non-empty fromlist switches it to the module the name asks for. This is the difference that makes importlib.import_module() the right tool for importing a module whose name is computed.

import importlib

top = __import__("json.decoder")  # O(1) once loaded
assert top.__name__ == "json"  # not json.decoder

named = __import__("json.decoder", fromlist=["JSONDecoder"])  # O(f) on top of the import
assert named.__name__ == "json.decoder"

assert importlib.import_module("json.decoder") is named  # what you usually want
assert top.decoder is named  # the submodule is an attribute of its package

What fromlist Costs

Each name in the list is one attribute check. Only the names the package does not already have are imported, and a name whose module is already in sys.modules costs a probe rather than a search - so a second call over a list whose names have all become attributes touches no finder. A name that is neither an attribute nor an importable submodule is the exception: it is searched for on every call, and the failure is swallowed. A module that is not a package skips the list entirely, because the handling is reached only through __path__.

import sys

assert "email.utils" not in sys.modules

package = __import__("email", fromlist=["utils"])  # one check, then one import
assert package.__name__ == "email"
assert "email.utils" in sys.modules
assert package.utils is sys.modules["email.utils"]

# The second call finds the attribute and imports nothing
before = set(sys.modules)
assert __import__("email", fromlist=["utils"]) is package  # O(f) checks, no import
assert set(sys.modules) == before

# A name that is neither an attribute nor a submodule is searched for every call,
# and says nothing about it
assert __import__("email", fromlist=["no_such_submodule"]) is package
assert not hasattr(package, "no_such_submodule")

# A module without __path__ never reaches the list
import base64

assert not hasattr(base64, "__path__")
assert __import__("base64", fromlist=["no_such_name"]) is base64

'*' is the same loop over the package's __all__. Whether that costs anything depends on what the names already are: submodules get imported, everything else is already an attribute.

import json
import sys

# json.__all__ is functions and classes, so every name is already an attribute
loaded = set(sys.modules)
assert __import__("json", fromlist=["*"]).__name__ == "json"  # O(a) checks, no import
assert set(sys.modules) == loaded

xml_package = __import__("xml", fromlist=["*"])  # O(a) checks, and four imports
assert xml_package.__all__ == ["dom", "parsers", "sax", "etree"]
assert {"xml.dom", "xml.parsers", "xml.sax", "xml.etree"} <= set(sys.modules)

# A package with no __all__ has nothing to expand
import urllib

assert not hasattr(urllib, "__all__")
assert __import__("urllib", fromlist=["*"]) is urllib  # O(1)

Relative Imports Read globals

level counts the leading dots of a relative import, and the anchor comes from the globals passed in - __package__ when it is set, then __spec__.parent, and __name__ only as a fallback that warns. It has to be a dict: the default None, and any other mapping, are refused before any search happens. Where the dict comes from does not matter, so a hand-built one works as well as a module's own.

import json.decoder
import sys
import warnings

try:
    __import__("decoder", None, None, ("JSONDecoder",), 1)  # O(1) - no search
except TypeError as error:
    assert "globals must be a dict" in str(error)
else:
    raise AssertionError("a relative import without globals resolved")

# What a module's own globals supply
inside = {"__name__": "json", "__package__": "json", "__spec__": json.__spec__}
assert __import__("decoder", inside, None, ("JSONDecoder",), 1) is json.decoder

# Without __package__ or __spec__, __name__ is used and the fallback warns
with warnings.catch_warnings(record=True) as caught:
    warnings.simplefilter("always")
    resolved = __import__("scanner", {"__name__": "json.decoder"}, None, ("x",), 1)

assert resolved is sys.modules["json.scanner"]
assert any(issubclass(w.category, ImportWarning) for w in caught)

Replacing the Function

IMPORT_NAME reads __import__ out of the frame's builtins on every execution, so a replacement is live immediately and needs no import hook - and a frame given its own __builtins__ mapping never sees it. importlib.__import__ is a separate object, a pure-Python implementation of the same protocol: the call itself goes nowhere near the builtins entry, though import statements in a module it loads still read it like any other.

import builtins
import importlib

assert importlib.__import__ is not builtins.__import__

seen = []
original = builtins.__import__

def recording(name, globals=None, locals=None, fromlist=(), level=0):
    seen.append(name)
    return original(name, globals, locals, fromlist, level)

builtins.__import__ = recording  # O(1) - and the next statement uses it
try:
    import sys  # goes through the replacement, already loaded so nothing nests
    importlib.__import__("sys")  # does not
finally:
    builtins.__import__ = original

assert seen == ["sys"]

Removing the name entirely leaves the statement with nothing to call.

import builtins

original = builtins.__import__
del builtins.__import__
try:
    import base64
except ImportError as error:
    assert "__import__ not found" in str(error)
else:
    raise AssertionError("import worked without the builtin")
finally:
    builtins.__import__ = original

Common Patterns

Importing a Computed Name

import importlib

name = "json.decoder"

# Wrong: returns the top-level package
assert __import__(name).__name__ == "json"

# Works, but the fromlist is only there to change the return value
assert __import__(name, fromlist=["JSONDecoder"]).__name__ == name

# What to write instead - O(1) once loaded
assert importlib.import_module(name).__name__ == name

Performance Best Practices

✅ Do:

• Call importlib.import_module() for a computed name; it returns the module you named rather than the head of the name
• Let repeated imports hit sys.modules instead of caching modules yourself - the probe is a dict lookup and it is what the statement already does
• Import inside a function when a heavy dependency is used on one rare path; the module body runs once, on the first call that reaches it

❌ Avoid:

• __import__(name) for a dotted name: it hands back the head of the name, not the module the name asks for, and raises nothing to say so
• A fromlist used only to force the return value - that is import_module() spelled awkwardly
• from pkg import *, which binds every name in __all__ on each execution and, for a package of submodules, imports all of them
• Replacing builtins.__import__ to change import behaviour; a sys.meta_path finder usually reaches the same goal without putting a Python call on every IMPORT_NAME

Version Notes

• Python 3.12+: a globals whose __package__ disagrees with __spec__.parent raises DeprecationWarning on a relative import; 3.10 and 3.11 raise ImportWarning. __package__ wins either way
• All Python 3: locals is ignored, and globals is read only when level is positive
• All Python 3: a dotted name with an empty fromlist returns the head of the name - the top-level package for an absolute import, and the first component under the anchor for a relative one

Related Functions

• importlib - import_module(), the search along sys.meta_path and sys.path, and the loaders behind the O(n + m) term
• exec() and eval() - The other builtins that run code supplied at run time
• compile() - Where the IMPORT_NAME instruction comes from
• globals() - The mapping a relative import resolves its anchor against