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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:

inline_example.py

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:

inline_overload_example.py

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)