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NBEP 5: Type Inference

Author:Siu Kwan Lam
Date:Sept 2016

This document describes the current type inference implementation in numba.


Numba uses type information to ensure that every variable in the user code can be correctly lowered (translated into a low-level representation). The type of a variable describes the set of valid operations and available attributes. Resolving this information during compilation avoids the overhead of type checking and dispatching at runtime. However, Python is dynamically typed and the user does not declare variable types. Since type information is absent, we use type inference to reconstruct the missing information.

Numba Type Semantic

Type inference operates on Numba IR, a mostly static-single-assignment (SSA) encoding of the Python bytecode. Conceptually, all intermediate values in the Python code are explicitly assigned to a variable in the IR. Numba enforces that each IR variable to have one type only. A user variable (from the Python source code) can be mapped to multiple variables in the IR. They are versions of a variable. Each time a user variable is assigned to, a new version is created. From that point, all subsequent references will use the new version. The user variable evolves as the function logic updates its type. Merge points (e.g. subsequent block to an if-else, the loop body, etc..) in the control flow need extra care. At each merge point, a new version is implicitly created to merge the different variable versions from the incoming paths. The merging of the variable versions may translate into an implicit cast.

Numba uses function overloading to emulate Python duck-typing. The type of a function can contain multiple call signatures that accept different argument types and yield different return types. The process to decide the best signature for an overloaded function is called overload resolution. Numba partially implements the C++ overload resolution scheme (ISOCPP 13.3 Overload Resolution). The scheme uses a “best fit” algorithm by ranking each argument symmetrically. The five possible rankings in increasing order of penalty are:

  • Exact: the expected type is the same as the actual type.
  • Promotion: the actual type can be upcast to the expected type by extending the precision without changing the behavior.
  • Safe conversion: the actual type can be cast to the expected type by changing the type without losing information.
  • Unsafe conversion: the actual type can be cast to the expected type by changing the type or downcasting the type even if it is imprecise.
  • No match: no valid operation can convert the actual type to the expected type.

It is possible to have an ambiguous resolution. For example, a function with signatures (int16, int32) and (int32, int16) can become ambiguous if presented with the argument types (int32, int32), because demoting either argument to int16 is equally “fit”. Fortunately, numba can usually resolve such ambiguity by compiling a new version with the exact signature (int32, int32). When compilation is disabled and there are multiple signatures with equal fit, an exception is raised.

Type Inference

The type inference in numba has three important components—type variable, constraint network, and typing context.

  • The typing context provides all the type information and typing related operations, including the logic for type unification, and the logic for typing of global and constant values. It defines the semantic of the language that can be compiled by numba.
  • A type variable holds the type of each variable (in the Numba IR). Conceptually, it is initialized to the universal type and, as it is re-assigned, it stores a common type by unifying the new type with the existing type. The common type must be able to represent values of the new type and the existing type. Type conversion is applied as necessary and precision loss is accepted for usability reason.
  • The constraint network is a dependency graph built from the IR. Each node represents an operation in the Numba IR and updates at least one type variable. There may be cycles due to loops in user code.

The type inference process starts by seeding the argument types. These initial types are propagated in the constraint network, which eventually fills all the type variables. Due to cycles in the network, the process repeats until all type variables converge or it fails with undecidable types.

Type unification always returns a more “general” (quoted because unsafe conversion is allowed) type. Types will converge to the least “general” type that can represent all possible values that the variable can hold. Since unification will never move down the type hierarchy and there is a single top type, the universal type—object, the type inference is guaranteed to converge.

A failure in type inference can be caused by two reasons. The first reason is user error due to incorrect use of a type. This type of error will also trigger an exception in regular python execution. The second reason is due to the use of an unsupported feature, but the code is otherwise valid in regular python execution. Upon an error, the type inference will set all types to the object type. As a result, numba will fallback to object-mode.

Since functions can be overloaded, the type inference needs to decide the type signature used at each call site. The overload resolution is applied to all known overload versions of the callee function described in call-templates. A call-template can either be concrete or abstract. A concrete call-template defines a fixed list of all possible signatures. An abstract call-template defines the logic to compute the accepted signature and it is used to implement generic functions.

Numba-compiled functions are generic functions due to their ability to compile new versions. When it sees a new set of argument types, it triggers type inference to validate and determine the return type. When there are nested calls for numba-compiled functions, each call-site triggers type inference. This poses a problem to recursive functions because the type inference will also be triggered recursively. Currently, simple single recursion is supported if the signature is user-annotated by the user, which avoids unbound recursion in type inference that will never terminate.