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Notes on Inlining

There are occasions where it is useful to be able to inline a function at its call site, at the Numba IR level of representation. The decorators such as numba.jit(), numba.extending.overload() and register_jitable() support the keyword argument inline, to facilitate this behaviour.

When attempting to inline at this level, it is important to understand what purpose this serves and what effect this will have. In contrast to the inlining performed by LLVM, which is aimed at improving performance, the main reason to inline at the Numba IR level is to allow type inference to cross function boundaries.

As an example, consider the following snippet:

from numba import njit


@njit
def bar(a):
    a.append(10)


@njit
def foo():
    z = []
    bar(z)


foo()

This will fail to compile and run, because the type of z can not be inferred as it will only be refined within bar. If we now add inline=True to the decorator for bar the snippet will compile and run. This is because inlining the call to a.append(10) will mean that z will be refined to hold integers and so type inference will succeed.

So, to recap, inlining at the Numba IR level is unlikely to have a performance benefit. Whereas inlining at the LLVM level stands a better chance.

The inline keyword argument can be one of three values:

  • The string 'never', this is the default and results in the function not being inlined under any circumstances.

  • The string 'always', this results in the function being inlined at all call sites.

  • A python function that takes three arguments. The first argument is always the ir.Expr node that is the call requesting the inline, this is present to allow the function to make call contextually aware decisions. The second and third arguments are:

    • In the case of an untyped inline, i.e. that which occurs when using the numba.jit() family of decorators, both arguments are numba.ir.FunctionIR instances. The second argument corresponding to the IR of the caller, the third argument corresponding to the IR of the callee.

    • In the case of a typed inline, i.e. that which occurs when using numba.extending.overload(), both arguments are instances of a namedtuple with fields (corresponding to their standard use in the compiler internals):

      • func_ir - the function’s Numba IR.

      • typemap - the function’s type map.

      • calltypes - the call types of any calls in the function.

      • signature - the function’s signature.

      The second argument holds the information from the caller, the third holds the information from the callee.

    In all cases the function should return True to inline and return False to not inline, this essentially permitting custom inlining rules (typical use might be cost models).

  • Recursive functions with inline='always' will result in a non-terminating compilation. If you wish to avoid this, supply a function to limit the recursion depth (see below).

Note

No guarantee is made about the order in which functions are assessed for inlining or about the order in which they are inlined.

Example using numba.jit()

An example of using all three options to inline in the numba.njit() decorator:

from numba import njit
import numba
from numba.core import ir


@njit(inline='never')
def never_inline():
    return 100


@njit(inline='always')
def always_inline():
    return 200


def sentinel_cost_model(expr, caller_info, callee_info):
    # this cost model will return True (i.e. do inlining) if either:
    # a) the callee IR contains an `ir.Const(37)`
    # b) the caller IR contains an `ir.Const(13)` logically prior to the call
    #    site

    # check the callee
    for blk in callee_info.blocks.values():
        for stmt in blk.body:
            if isinstance(stmt, ir.Assign):
                if isinstance(stmt.value, ir.Const):
                    if stmt.value.value == 37:
                        return True

    # check the caller
    before_expr = True
    for blk in caller_info.blocks.values():
        for stmt in blk.body:
            if isinstance(stmt, ir.Assign):
                if isinstance(stmt.value, ir.Expr):
                    if stmt.value == expr:
                        before_expr = False
                if isinstance(stmt.value, ir.Const):
                    if stmt.value.value == 13:
                        return True & before_expr
    return False


@njit(inline=sentinel_cost_model)
def maybe_inline1():
    # Will not inline based on the callee IR with the declared cost model
    # The following is ir.Const(300).
    return 300


@njit(inline=sentinel_cost_model)
def maybe_inline2():
    # Will inline based on the callee IR with the declared cost model
    # The following is ir.Const(37).
    return 37


@njit
def foo():
    a = never_inline()  # will never inline
    b = always_inline()  # will always inline

    # will not inline as the function does not contain a magic constant known to
    # the cost model, and the IR up to the call site does not contain a magic
    # constant either
    d = maybe_inline1()

    # declare this magic constant to trigger inlining of maybe_inline1 in a
    # subsequent call
    magic_const = 13

    # will inline due to above constant declaration
    e = maybe_inline1()

    # will inline as the maybe_inline2 function contains a magic constant known
    # to the cost model
    c = maybe_inline2()

    return a + b + c + d + e + magic_const


foo()

which produces the following when executed (with a print of the IR after the legalization pass, enabled via the environment variable NUMBA_DEBUG_PRINT_AFTER="ir_legalization"):

label 0:
    $0.1 = global(never_inline: CPUDispatcher(<function never_inline at 0x7f890ccf9048>)) ['$0.1']
    $0.2 = call $0.1(func=$0.1, args=[], kws=(), vararg=None) ['$0.1', '$0.2']
    del $0.1                                 []
    a = $0.2                                 ['$0.2', 'a']
    del $0.2                                 []
    $0.3 = global(always_inline: CPUDispatcher(<function always_inline at 0x7f890ccf9598>)) ['$0.3']
    del $0.3                                 []
    $const0.1.0 = const(int, 200)            ['$const0.1.0']
    $0.2.1 = $const0.1.0                     ['$0.2.1', '$const0.1.0']
    del $const0.1.0                          []
    $0.4 = $0.2.1                            ['$0.2.1', '$0.4']
    del $0.2.1                               []
    b = $0.4                                 ['$0.4', 'b']
    del $0.4                                 []
    $0.5 = global(maybe_inline1: CPUDispatcher(<function maybe_inline1 at 0x7f890ccf9ae8>)) ['$0.5']
    $0.6 = call $0.5(func=$0.5, args=[], kws=(), vararg=None) ['$0.5', '$0.6']
    del $0.5                                 []
    d = $0.6                                 ['$0.6', 'd']
    del $0.6                                 []
    $const0.7 = const(int, 13)               ['$const0.7']
    magic_const = $const0.7                  ['$const0.7', 'magic_const']
    del $const0.7                            []
    $0.8 = global(maybe_inline1: CPUDispatcher(<function maybe_inline1 at 0x7f890ccf9ae8>)) ['$0.8']
    del $0.8                                 []
    $const0.1.2 = const(int, 300)            ['$const0.1.2']
    $0.2.3 = $const0.1.2                     ['$0.2.3', '$const0.1.2']
    del $const0.1.2                          []
    $0.9 = $0.2.3                            ['$0.2.3', '$0.9']
    del $0.2.3                               []
    e = $0.9                                 ['$0.9', 'e']
    del $0.9                                 []
    $0.10 = global(maybe_inline2: CPUDispatcher(<function maybe_inline2 at 0x7f890ccf9b70>)) ['$0.10']
    del $0.10                                []
    $const0.1.4 = const(int, 37)             ['$const0.1.4']
    $0.2.5 = $const0.1.4                     ['$0.2.5', '$const0.1.4']
    del $const0.1.4                          []
    $0.11 = $0.2.5                           ['$0.11', '$0.2.5']
    del $0.2.5                               []
    c = $0.11                                ['$0.11', 'c']
    del $0.11                                []
    $0.14 = a + b                            ['$0.14', 'a', 'b']
    del b                                    []
    del a                                    []
    $0.16 = $0.14 + c                        ['$0.14', '$0.16', 'c']
    del c                                    []
    del $0.14                                []
    $0.18 = $0.16 + d                        ['$0.16', '$0.18', 'd']
    del d                                    []
    del $0.16                                []
    $0.20 = $0.18 + e                        ['$0.18', '$0.20', 'e']
    del e                                    []
    del $0.18                                []
    $0.22 = $0.20 + magic_const              ['$0.20', '$0.22', 'magic_const']
    del magic_const                          []
    del $0.20                                []
    $0.23 = cast(value=$0.22)                ['$0.22', '$0.23']
    del $0.22                                []
    return $0.23                             ['$0.23']

Things to note in the above:

  1. The call to the function never_inline remains as a call.

  2. The always_inline function has been inlined, note its const(int, 200) in the caller body.

  3. There is a call to maybe_inline1 before the const(int, 13) declaration, the cost model prevented this from being inlined.

  4. After the const(int, 13) the subsequent call to maybe_inline1 has been inlined as shown by the const(int, 300) in the caller body.

  5. The function maybe_inline2 has been inlined as demonstrated by const(int, 37) in the caller body.

  6. That dead code elimination has not been performed and as a result there are superfluous statements present in the IR.

Example using numba.extending.overload()

An example of using inlining with the numba.extending.overload() decorator. It is most interesting to note that if a function is supplied as the argument to inline a lot more information is available via the supplied function arguments for use in decision making. Also that different @overload s can have different inlining behaviours, with multiple ways to achieve this:

import numba
from numba.extending import overload
from numba import njit, types


def bar(x):
    """A function stub to overload"""
    pass


@overload(bar, inline='always')
def ol_bar_tuple(x):
    # An overload that will always inline, there is a type guard so that this
    # only applies to UniTuples.
    if isinstance(x, types.UniTuple):
        def impl(x):
            return x[0]
        return impl


def cost_model(expr, caller, callee):
    # Only inline if the type of the argument is an Integer
    return isinstance(caller.typemap[expr.args[0].name], types.Integer)


@overload(bar, inline=cost_model)
def ol_bar_scalar(x):
    # An overload that will inline based on a cost model, it only applies to
    # scalar values in the numerical domain as per the type guard on Number
    if isinstance(x, types.Number):
        def impl(x):
            return x + 1
        return impl


@njit
def foo():

    # This will resolve via `ol_bar_tuple` as the argument is a types.UniTuple
    # instance. It will always be inlined as specified in the decorator for this
    # overload.
    a = bar((1, 2, 3))

    # This will resolve via `ol_bar_scalar` as the argument is a types.Number
    # instance, hence the cost_model will be used to determine whether to
    # inline.
    # The function will be inlined as the value 100 is an IntegerLiteral which
    # is an instance of a types.Integer as required by the cost_model function.
    b = bar(100)

    # This will also resolve via `ol_bar_scalar` as the argument is a
    # types.Number instance, again the cost_model will be used to determine
    # whether to inline.
    # The function will not be inlined as the complex value is not an instance
    # of a types.Integer as required by the cost_model function.
    c = bar(300j)

    return a + b + c


foo()

which produces the following when executed (with a print of the IR after the legalization pass, enabled via the environment variable NUMBA_DEBUG_PRINT_AFTER="ir_legalization"):

label 0:
    $const0.2 = const(tuple, (1, 2, 3))      ['$const0.2']
    x.0 = $const0.2                          ['$const0.2', 'x.0']
    del $const0.2                            []
    $const0.2.2 = const(int, 0)              ['$const0.2.2']
    $0.3.3 = getitem(value=x.0, index=$const0.2.2) ['$0.3.3', '$const0.2.2', 'x.0']
    del x.0                                  []
    del $const0.2.2                          []
    $0.4.4 = $0.3.3                          ['$0.3.3', '$0.4.4']
    del $0.3.3                               []
    $0.3 = $0.4.4                            ['$0.3', '$0.4.4']
    del $0.4.4                               []
    a = $0.3                                 ['$0.3', 'a']
    del $0.3                                 []
    $const0.5 = const(int, 100)              ['$const0.5']
    x.5 = $const0.5                          ['$const0.5', 'x.5']
    del $const0.5                            []
    $const0.2.7 = const(int, 1)              ['$const0.2.7']
    $0.3.8 = x.5 + $const0.2.7               ['$0.3.8', '$const0.2.7', 'x.5']
    del x.5                                  []
    del $const0.2.7                          []
    $0.4.9 = $0.3.8                          ['$0.3.8', '$0.4.9']
    del $0.3.8                               []
    $0.6 = $0.4.9                            ['$0.4.9', '$0.6']
    del $0.4.9                               []
    b = $0.6                                 ['$0.6', 'b']
    del $0.6                                 []
    $0.7 = global(bar: <function bar at 0x7f6c3710d268>) ['$0.7']
    $const0.8 = const(complex, 300j)         ['$const0.8']
    $0.9 = call $0.7($const0.8, func=$0.7, args=[Var($const0.8, inline_overload_example.py (56))], kws=(), vararg=None) ['$0.7', '$0.9', '$const0.8']
    del $const0.8                            []
    del $0.7                                 []
    c = $0.9                                 ['$0.9', 'c']
    del $0.9                                 []
    $0.12 = a + b                            ['$0.12', 'a', 'b']
    del b                                    []
    del a                                    []
    $0.14 = $0.12 + c                        ['$0.12', '$0.14', 'c']
    del c                                    []
    del $0.12                                []
    $0.15 = cast(value=$0.14)                ['$0.14', '$0.15']
    del $0.14                                []
    return $0.15                             ['$0.15']

Things to note in the above:

  1. The first highlighted section is the always inlined overload for the UniTuple argument type.

  2. The second highlighted section is the overload for the Number argument type that has been inlined as the cost model function decided to do so as the argument was an Integer type instance.

  3. The third highlighted section is the overload for the Number argument type that has not inlined as the cost model function decided to reject it as the argument was an Complex type instance.

  4. That dead code elimination has not been performed and as a result there are superfluous statements present in the IR.

Using a function to limit the inlining depth of a recursive function

When using recursive inlines, you can terminate the compilation by using a cost model.

from numba import njit
import numpy as np

class CostModel(object):
    def __init__(self, max_inlines):
        self._count = 0
        self._max_inlines = max_inlines

    def __call__(self, expr, caller, callee):
        ret = self._count < self._max_inlines
        self._count += 1
        return ret

@njit(inline=CostModel(3))
def factorial(n):
    if n <= 0:
        return 1
    return n * factorial(n - 1)

factorial(5)