Functions compiled using
are open-ended: they can be called with many different input types and
have to select (possibly compile on-the-fly) the right low-level
specialization. We hereby explain how this mechanism is implemented.
JIT-compiled functions can take several arguments and each of them is taken into account when selecting a specialization. Thus it is a form of multiple dispatch, more complex than single dispatch.
Each argument weighs in the selection based on its Numba type. Numba types are often more granular than Python types: for example, Numba types Numpy arrays differently depending on their dimensionality and their layout (C-contiguous, etc.).
Once a Numba type is inferred for each argument, a specialization must
be chosen amongst the available ones; or, if not suitable specialization
is found, a new one must be compiled. This is not a trivial decision:
there can be multiple specializations compatible with a given concrete
signature (for example, say a two-argument function has compiled
(float64, float64) and
and it is called with
Therefore, there are two crucial steps in the dispatch mechanism:
infer the Numba types of the concrete arguments
select the best available specialization (or choose to compile a new one) for the inferred Numba types
Compile-time vs. run-time
This document discusses dispatching when it is done at runtime, i.e. when a JIT-compiled function is called from pure Python. In that context, performance is important. To stay in the realm of normal function call overhead in Python, the overhead of dispatching should stay under a microsecond. Of course, the faster the better…
When a JIT-compiled function is called from another JIT-compiled function (in nopython mode), the polymorphism is resolved at compile-time, using a non-performance critical mechanism, bearing zero runtime performance overhead.
In practice, the performance-critical parts described here are coded in C.
The first step is therefore to infer, at call-time, a Numba type for each of the function’s concrete arguments. Given the finer granularity of Numba types compared to Python types, one cannot simply lookup an object’s class and key a dictionary with it to obtain the corresponding Numba type.
Instead, there is a machinery to inspect the object and, based on its
Python type, query various properties to infer the appropriate Numba
type. This can be more or less complex: for example, a Python
argument will always infer to a Numba
intp (a pointer-sized integer),
but a Python
tuple argument can infer to multiple Numba types (depending
on the tuple’s size and the concrete type of each of its elements).
The Numba type system is high-level and written in pure Python; there is
a pure Python machinery, based on a generic function, to do said inference
numba.typing.typeof). That machinery is used for compile-time
inference, e.g. on constants. Unfortunately, it is too slow for run-time
value-based dispatching. It is only used as a fallback for rarely used
(or difficult to infer) types, and exhibits multiple-microsecond overhead.
The Numba type system is really too high-level to be manipulated efficiently from C code. Therefore, the C dispatching layer uses another representation based on integer typecodes. Each Numba type gets a unique integer typecode when constructed; also, an interning system ensure no two instances of same type are created. The dispatching layer is therefore able to eschew the overhead of the Numba type system by working with simple integer typecodes, amenable to well-known optimizations (fast hash tables, etc.).
The goal of the type resolution step becomes: infer a Numba typecode for each of the function’s concrete arguments. Ideally, it doesn’t deal with Numba types anymore…
Hard-coded fast paths
While eschewing the abstraction and object-orientation overhead of the type system, the integer typecodes still have the same conceptual complexity. Therefore, an important technique to speed up inference is to first go through checks for the most important types, and hard-code a fast resolution for each of them.
Several types benefit from such an optimization, notably:
basic Python scalars (
basic Numpy scalars (the various kinds of integer, floating-point, complex numbers);
Numpy arrays of certain dimensionalities and basic element types.
Each of those fast paths ideally uses a hard-coded result value or a direct table lookup after a few simple checks.
However, we can’t apply that technique to all argument types; there would be an explosion of ad-hoc internal caches, and it would become difficult to maintain. Besides, the recursive application of hard-coded fast paths would not necessarily combine into a low overhead (in the nested tuple case, for example).
Fingerprint-based typecode cache
For non-so-trivial types (imagine a tuple, or a Numpy
for example), the hard-coded fast paths don’t match. Another mechanism
then kicks in, more generic.
The principle here is to examine each argument value, as the pure Python machinery would do, and to describe its Numba type unambiguously. The difference is that we don’t actually compute a Numba type. Instead, we compute a simple bytestring, a low-level possible denotation of that Numba type: a fingerprint. The fingerprint format is designed to be short and extremely simple to compute from C code (in practice, it has a bytecode-like format).
Once the fingerprint is computed, it is looked up in a cache mapping fingerprints to typecodes. The cache is a hash table, and the lookup is fast thanks to the fingerprints being generally very short (rarely more than 20 bytes).
If the cache lookup fails, the typecode must first be computed using the slow pure Python machinery. Luckily, this would only happen once: on subsequent calls, the cached typecode would be returned for the given fingerprint.
In rare cases, a fingerprint cannot be computed efficiently. This is
the case for some types which cannot be easily inspected from C: for
cffi function pointers. Then, the slow Pure Python machinery
is invoked at each function call with such an argument.
Two fingerprints may denote a single Numba type. This does not make the mechanism incorrect; it only creates more cache entries.
Type resolution of a function argument involves the following mechanisms in order:
Try a few hard-coded fast paths, for common simple types.
If the above failed, compute a fingerprint for the argument and lookup its typecode in a cache.
If all the above failed, invoke the pure Python machinery which will determine a Numba type for the argument (and look up its typecode).
At the previous step, an integer typecode has been determined for each concrete argument to the JIT-compiled function. Now it remains to match that concrete signature against each of the available specializations for the function. There can be three outcomes:
There is a satisfying best match: the corresponding specialization is then invoked (it will handle argument unboxing and other details).
There is a tie between two or more “best matches”: an exception is raised, refusing to solve the ambiguity.
There is no satisfying match: a new specialization is compiled tailored for the concrete argument types that were inferred.
The selection works by looping over all available specializations, and computing the compatibility of each concrete argument type with the corresponding type in the specialization’s intended signature. Specifically, we are interested in:
Whether the concrete argument type is allowed to convert implicitly to the specialization’s argument type;
If so, at what semantic (user-visible) cost the conversion comes.
Implicit conversion rules
There are five possible kinds of implicit conversion from a source type to a destination type (note this is an asymmetric relationship):
exact match: the two types are identical; this is the ideal case, since the specialization would behave exactly as intended;
same-kind promotion: the two types belong to the same “kind” (for example
int64are two integer types), and the source type can be converted losslessly to the destination type (e.g. from
int64, but not the reverse);
safe conversion: the two types belong to different kinds, but the source type can be reasonably converted to the destination type (e.g. from
float64, but not the reverse);
unsafe conversion: a conversion is available from the source type to the destination type, but it may lose precision, magnitude, or another desirable quality.
no conversion: there is no correct or reasonably efficient way to convert between the two types (for example between an
datetime64, or a C-contiguous array and a Fortran-contiguous array).
When a specialization is examined, the latter two cases eliminate it from the final choice: i.e. when at least one argument has no conversion or only an unsafe conversion to the signature’s argument type.
However, if the function is compiled with explicit signatures
jit() call (and therefore it is not allowed to compile
new specializations), unsafe conversion is allowed.
Candidates and best match
If a specialization is not eliminated by the rule above, it enters the
list of candidates for the final choice. Those candidates are ranked
by an ordered 4-uple of integers:
(number of unsafe conversions,
number of safe conversions, number of same-kind promotions, number of
exact matches) (note the sum of the tuple’s elements is equal to the
number of arguments). The best match is then the #1 result in sorted
ascending order, thereby preferring exact matches over promotions,
promotions over safe conversions, safe conversions over unsafe conversions.
The above-described mechanism works on integer typecodes, not on Numba
types. It uses an internal hash table storing the possible conversion
kind for each pair of compatible types. The internal hash table is in part
built at startup (for built-in trivial types such as
etc.), in part filled dynamically (for arbitrarily complex types such
as array types: for example to allow using a C-contiguous 2D array where
a function expects a non-contiguous 2D array).
Selecting the right specialization involves the following steps:
Examine each available specialization and match it against the concrete argument types.
Eliminate any specialization where at least one argument doesn’t offer sufficient compatibility.
If there are remaining candidates, choose the best one in terms of preserving the types’ semantics.