Continuum Analytics: Documentation

# NBEP 1: Changes in integer typing

Author: | Antoine Pitrou
Date: | July 2015
Status: | Final

## Current semantics

Type inference of integers in Numba currently has some subtleties and some corner cases. The simple case is when some variable has an obvious Numba type (for example because it is the result of a constructor call to a Numpy scalar type such as `np.int64`). That case suffers no ambiguity.

The less simple case is when a variable doesn’t bear such explicit information. This can happen because it is inferred from a built-in Python `int` value, or from an arithmetic operation between two integers, or other cases yet. Then Numba has a number of rules to infer the resulting Numba type, especially its signedness and bitwidth.

Currently, the generic case could be summarized as: start small, grow bigger as required. Concretely:

1. Each constant or pseudo-constant is inferred using the smallest signed integer type that can correctly represent it (or, possibly, `uint64` for positive integers between `2**63` and `2**64 - 1`).
2. The result of an operation is typed so as to ensure safe representation in the face of overflow and other magnitude increases (for example, `int32 + int32` would be typed `int64`).
3. As an exception, a Python `int` used as function argument is always typed `intp`, a pointer-size integer. This is to avoid the proliferation of compiled specializations, as otherwise various integer bitwidths in input arguments may produce multiple signatures.

Note

The second rule above (the “respect magnitude increases” rule) reproduces Numpy’s behaviour with arithmetic on scalar values. Numba, however, has different implementation and performance constraints than Numpy scalars.

It is worth nothing, by the way, that Numpy arrays do not implement said rule (i.e. `array(int32) + array(int32)` is typed `array(int32)`, not `array(int64)`). Probably because this makes performance more controllable.

This has several non-obvious side-effects:

1. It is difficult to predict the precise type of a value inside a function, after several operations. The basic operands in an expression tree may for example be `int8` but the end result may be `int64`. Whether this is desirable or not is an open question; it is good for correctness, but potentially bad for performance.

2. In trying to follow the correctness over predictability rule, some values can actually leave the integer realm. For example, `int64 + uint64` is typed `float64` in order to avoid magnitude losses (but incidentally will lose precision on large integer values...), again following Numpy’s semantics for scalars. This is usually not intended by the user.

3. More complicated scenarios can produce unexpected errors at the type unification stage. An example is at Github issue 1299, the gist of which is reproduced here:

       @jit(nopython=True)
       def f():
           variable = 0
           for i in range(1):
               variable = variable + 1
           return np.arange(variable)

   At the time of this writing, this fails compiling, on a 64-bit system, with the error:

       numba.errors.TypingError: Failed at nopython (nopython frontend)
       Can't unify types of variable '$48.4': $48.4 := {array(int32, 1d, C), array(int64, 1d, C)}

   People expert with Numba’s type unification system can understand why. But the user is caught in mystery.

## Proposal: predictable width-conserving typing

We propose to turn the current typing philosophy on its head. Instead of “start small and grow as required”, we propose “start big and keep the width unchanged”.

Concretely:

1. The typing of Python `int` values used as function arguments doesn’t change, as it works satisfyingly and doesn’t surprise the user.
2. The typing of integer constants (and pseudo-constants) changes to match the typing of integer arguments. That is, every non-explicitly typed integer constant is typed `intp`, the pointer-sized integer; except for the rare cases where `int64` (on 32-bit systems) or `uint64` is required.
3. Operations on integers promote bitwidth to `intp`, if smaller, otherwise they don’t promote. For example, on a 32-bit machine, `int8 + int8` is typed `int32`, as is `int32 + int32`. However, `int64 + int64` is typed `int64`.
4. Furthermore, mixed operations between signed and unsigned fall back to signed, while following the same bitwidth rule. For example, on a 32-bit machine, `int8 + uint16` is typed `int32`, as is `uint32 + int32`.

## Proposal impact

### Semantics

With this proposal, the semantics become clearer. Regardless of whether the arguments and constants of a function were explicitly typed or not, the results of various expressions at any point in the function have easily predictable types.

When using built-in Python `int`, the user gets acceptable magnitude (32 or 64 bits depending on the system’s bitness), and the type remains the same accross all computations.

When explicitly using smaller bitwidths, intermediate results don’t suffer from magnitude loss, since their bitwidth is promoted to `intp`.

There is also less potential for annoyances with the type unification system as demonstrated above. The user would have to force several different types to be faced with such an error.

One potential cause for concern is the discrepancy with Numpy’s scalar semantics; but at the same time this brings Numba scalar semantics closer to array semantics (both Numba’s and Numpy’s), which seems a desirable outcome as well.

It is worth pointing out that some sources of integer numbers, such as the `range()` built-in, always yield 32-bit integers or larger. This proposal could be an opportunity to standardize them on `intp`.

### Performance

Except in trivial cases, it seems unlikely that the current “best fit” behaviour for integer constants really brings a performance benefit. After all, most integers in Numba code would either be stored in arrays (with well-known types, chosen by the user) or be used as indices, where a `int8` is highly unlikely to fare better than a `intp` (actually, it may be worse, if LLVM isn’t able to optimize away the required sign-extension).

As a side note, the default use of `intp` rather than `int64` ensures that 32-bit systems won’t suffer from poor arithmetic performance.

### Implementation

Optimistically, this proposal may simplify some Numba internals a bit. Or, at least, it doesn’t threaten to make them significantly more complicated.

### Limitations

This proposal doesn’t really solve the combination of signed and unsigned integers. It is geared mostly at solving the bitwidth issues, which are a somewhat common cause of pain for users. Unsigned integers are in practice very uncommon in Numba-compiled code, except when explicitly asked for, and therefore much less of a pain point.

On the bitwidth front, 32-bit systems could still show discrepancies based on the values of constants: if a constant is too large to fit in 32 bits, it is typed `int64`, which propagates through other computations. This would be a reminiscence of the current behaviour, but rarer and much more controlled still.

### Long-term horizon

While we believe this proposal makes Numba’s behaviour more regular and more predictable, it also pulls it further from general compatibility with pure Python semantics, where users can assume arbitrary-precision integers without any truncation issues.