# Example: An Interval Type

In this example, we will extend the Numba frontend to add support for a user-defined class that it does not internally support. This will allow:

- Passing an instance of the class to a Numba function

- Accessing attributes of the class in a Numba function

- Constructing and returning a new instance of the class from a Numba function

(all the above in nopython mode)

We will mix APIs from the high-level extension API and the low-level extension API, depending on what is available for a given task.

The starting point for our example is the following pure Python class:

    class Interval(object):
        """
        A half-open interval on the real number line.
        """
        def __init__(self, lo, hi):
            self.lo = lo
            self.hi = hi

        def __repr__(self):
            return 'Interval(%f, %f)' % (self.lo, self.hi)

        @property
        def width(self):
            return self.hi - self.lo

## Extending the typing layer

### Creating a new Numba type

As the `Interval` class is not known to Numba, we must create a new Numba type to represent instances of it. Numba does not deal with Python types directly: it has its own type system that allows a different level of granularity as well as various meta-information not available with regular Python types.

We first create a type class `IntervalType` and, since we don’t need the type to be parametric, we instantiate a single type instance `interval_type`:

    from numba import types

    class IntervalType(types.Type):
        def __init__(self):
            super(IntervalType, self).__init__(name='Interval')

    interval_type = IntervalType()

### Type inference for Python values

In itself, creating a Numba type doesn’t do anything. We must teach Numba how to infer some Python values as instances of that type. In this example, it is trivial: any instance of the `Interval` class should be treated as belonging to the type `interval_type`:

    from numba.extending import typeof_impl

    @typeof_impl.register(Interval)
    def typeof_index(val, c):
        return interval_type

Function arguments and global values will thusly be recognized as belonging to `interval_type` whenever they are instances of `Interval`.

### Type inference for Python types

While `typeof` is used to infer the Numba type of Python objects, `as_numba_type` is used to infer the Numba type of Python types. For simple cases, we can simply register that the Python type `Interval` corresponds with the Numba type `interval_type`:

    from numba.extending import as_numba_type

    as_numba_type.register(Interval, interval_type)

Note that `as_numba_type` is only used at compile time to infer types from type annotations on jitclass fields, and the `classinfo` argument to the `isinstance()` function. The `typeof` registry above is used to infer the type of objects at runtime.

### Type inference for operations

We want to be able to construct interval objects from Numba functions, so we must teach Numba to recognize the two-argument `Interval(lo, hi)` constructor. The arguments should be floating-point numbers:

    from numba.extending import type_callable

    @type_callable(Interval)
    def type_interval(context):
        def typer(lo, hi):
            if isinstance(lo, types.Float) and isinstance(hi, types.Float):
                return interval_type
        return typer

The `type_callable()` decorator specifies that the decorated function should be invoked when running type inference for the given callable object (here the `Interval` class itself). The decorated function must simply return a typer function that will be called with the argument types. The reason for this seemingly convoluted setup is for the typer function to have exactly the same signature as the typed callable. This allows handling keyword arguments correctly.

The context argument received by the decorated function is useful in more sophisticated cases where computing the callable’s return type requires resolving other types.

## Extending the lowering layer

We have finished teaching Numba about our type inference additions. We must now teach Numba how to actually generate code and data for the new operations.

### Defining the data model for native intervals

As a general rule, nopython mode does not work on Python objects as they are generated by the CPython interpreter. The representations used by the interpreter are far too inefficient for fast native code. Each type supported in nopython mode therefore has to define a tailored native representation, also called a data model.

A common case of data model is an immutable struct-like data model, that is akin to a C `struct`. Our interval datatype conveniently falls in that category, and here is a possible data model for it:

    from numba.extending import models, register_model

    @register_model(IntervalType)
    class IntervalModel(models.StructModel):
        def __init__(self, dmm, fe_type):
            members = [('lo', types.float64),
                       ('hi', types.float64),]
            models.StructModel.__init__(self, dmm, fe_type, members)

This instructs Numba that values of type `IntervalType` (or any instance thereof) are represented as a structure of two fields `lo` and `hi`, each of them a double-precision floating-point number (`types.float64`).

Note

Mutable types need more sophisticated data models to be able to persist their values after modification. They typically cannot be stored and passed on the stack or in registers like immutable types do.

### Exposing data model attributes

We want the data model attributes `lo` and `hi` to be exposed under the same names for use in Numba functions. Numba provides a convenience function to do exactly that:

    from numba.extending import make_attribute_wrapper

    make_attribute_wrapper(IntervalType, 'lo', 'lo')
    make_attribute_wrapper(IntervalType, 'hi', 'hi')

This will expose the attributes in read-only mode. As mentioned above, writable attributes don’t fit in this model.

### Exposing a property

As the `width` property is computed rather than stored in the structure, we cannot simply expose it like we did for `lo` and `hi`. We have to re-implement it explicitly:

    from numba.extending import overload_attribute

    @overload_attribute(IntervalType, "width")
    def get_width(interval):
        def getter(interval):
            return interval.hi - interval.lo
        return getter

You might ask why we didn’t need to expose a type inference hook for this attribute? The answer is that `@overload_attribute` is part of the high-level API: it combines type inference and code generation in a single API.

### Implementing the constructor

Now we want to implement the two-argument `Interval` constructor:

    from numba.extending import lower_builtin
    from numba.core import cgutils

    @lower_builtin(Interval, types.Float, types.Float)
    def impl_interval(context, builder, sig, args):
        typ = sig.return_type
        lo, hi = args
        interval = cgutils.create_struct_proxy(typ)(context, builder)
        interval.lo = lo
        interval.hi = hi
        return interval._getvalue()

There is a bit more going on here. `@lower_builtin` decorates the implementation of the given callable or operation (here the `Interval` constructor) for some specific argument types. This allows defining type-specific implementations of a given operation, which is important for heavily overloaded functions such as `len()`.

`types.Float` is the class of all floating-point types (`types.float64` is an instance of `types.Float`). It is generally more future-proof to match argument types on their class rather than on specific instances (however, when returning a type – chiefly during the type inference phase –, you must usually return a type instance).

`cgutils.create_struct_proxy()` and `interval._getvalue()` are a bit of boilerplate due to how Numba passes values around. Values are passed as instances of `llvmlite.ir.Value`, which can be too limited: LLVM structure values especially are quite low-level. A struct proxy is a temporary wrapper around a LLVM structure value allowing to easily get or set members of the structure. The `_getvalue()` call simply gets the LLVM value out of the wrapper.

### Boxing and unboxing

If you try to use an `Interval` instance at this point, you’ll certainly get the error “cannot convert Interval to native value”. This is because Numba doesn’t yet know how to make a native interval value from a Python `Interval` instance. Let’s teach it how to do it:

    from numba.extending import unbox, NativeValue
    from contextlib import ExitStack

    @unbox(IntervalType)
    def unbox_interval(typ, obj, c):
        """
        Convert a Interval object to a native interval structure.
        """
        is_error_ptr = cgutils.alloca_once_value(c.builder, cgutils.false_bit)
        interval = cgutils.create_struct_proxy(typ)(c.context, c.builder)

        with ExitStack() as stack:
            lo_obj = c.pyapi.object_getattr_string(obj, "lo")
            with cgutils.early_exit_if_null(c.builder, stack, lo_obj):
                c.builder.store(cgutils.true_bit, is_error_ptr)
            lo_native = c.unbox(types.float64, lo_obj)
            c.pyapi.decref(lo_obj)
            with cgutils.early_exit_if(c.builder, stack, lo_native.is_error):
                c.builder.store(cgutils.true_bit, is_error_ptr)

            hi_obj = c.pyapi.object_getattr_string(obj, "hi")
            with cgutils.early_exit_if_null(c.builder, stack, hi_obj):
                c.builder.store(cgutils.true_bit, is_error_ptr)
            hi_native = c.unbox(types.float64, hi_obj)
            c.pyapi.decref(hi_obj)
            with cgutils.early_exit_if(c.builder, stack, hi_native.is_error):
                c.builder.store(cgutils.true_bit, is_error_ptr)

            interval.lo = lo_native.value
            interval.hi = hi_native.value

        return NativeValue(interval._getvalue(), is_error=c.builder.load(is_error_ptr))

Unbox is the other name for “convert a Python object to a native value” (it fits the idea of a Python object as a sophisticated box containing a simple native value). The function returns a `NativeValue` object which gives its caller access to the computed native value, the error bit and possibly other information.

The snippet above makes abundant use of the `c.pyapi` object, which gives access to a subset of the Python interpreter’s C API. Note the use of `early_exit_if_null` to detect and handle any errors that may have happened when unboxing the object (try passing `Interval('a', 'b')` for example).

We also want to do the reverse operation, called boxing, so as to return interval values from Numba functions:

    from numba.extending import box

    @box(IntervalType)
    def box_interval(typ, val, c):
        """
        Convert a native interval structure to an Interval object.
        """
        ret_ptr = cgutils.alloca_once(c.builder, c.pyapi.pyobj)
        fail_obj = c.pyapi.get_null_object()

        with ExitStack() as stack:
            interval = cgutils.create_struct_proxy(typ)(c.context, c.builder, value=val)
            lo_obj = c.box(types.float64, interval.lo)
            with cgutils.early_exit_if_null(c.builder, stack, lo_obj):
                c.builder.store(fail_obj, ret_ptr)

            hi_obj = c.box(types.float64, interval.hi)
            with cgutils.early_exit_if_null(c.builder, stack, hi_obj):
                c.pyapi.decref(lo_obj)
                c.builder.store(fail_obj, ret_ptr)

            class_obj = c.pyapi.unserialize(c.pyapi.serialize_object(Interval))
            with cgutils.early_exit_if_null(c.builder, stack, class_obj):
                c.pyapi.decref(lo_obj)
                c.pyapi.decref(hi_obj)
                c.builder.store(fail_obj, ret_ptr)

            # NOTE: The result of this call is not checked as the clean up
            # has to occur regardless of whether it is successful. If it
            # fails `res` is set to NULL and a Python exception is set.
            res = c.pyapi.call_function_objargs(class_obj, (lo_obj, hi_obj))
            c.pyapi.decref(lo_obj)
            c.pyapi.decref(hi_obj)
            c.pyapi.decref(class_obj)
            c.builder.store(res, ret_ptr)

        return c.builder.load(ret_ptr)

## Using it

nopython mode functions are now able to make use of Interval objects and the various operations you have defined on them. You can try for example the following functions:

    from numba import njit

    @njit
    def inside_interval(interval, x):
        return interval.lo <= x < interval.hi

    @njit
    def interval_width(interval):
        return interval.width

    @njit
    def sum_intervals(i, j):
        return Interval(i.lo + j.lo, i.hi + j.hi)

## Conclusion

We have shown how to do the following tasks:

- Define a new Numba type class by subclassing the `Type` class

- Define a singleton Numba type instance for a non-parametric type

- Teach Numba how to infer the Numba type of Python values of a certain class, using `typeof_impl.register`

- Teach Numba how to infer the Numba type of the Python type itself, using `as_numba_type.register`

- Define the data model for a Numba type using `StructModel` and `register_model`

- Implementing a boxing function for a Numba type using the `@box` decorator

- Implementing an unboxing function for a Numba type using the `@unbox` decorator and the `NativeValue` class

- Type and implement a callable using the `@type_callable` and `@lower_builtin` decorators

- Expose a read-only structure attribute using the `make_attribute_wrapper` convenience function

- Implement a read-only property using the `@overload_attribute` decorator