Data structures

The amaranth.lib.data module provides a way to describe the bitwise layout of values and a proxy class for accessing fields of values using the attribute access and indexing syntax.

Introduction

Overview

This module provides four related facilities:

1. Low-level bitwise layout description via Field and Layout. These classes are rarely used directly, but are the foundation on which all other functionality is built. They are also useful for introspection.

2. High-level bitwise layout description via StructLayout, UnionLayout, ArrayLayout, and FlexibleLayout. These classes are the ones most often used directly, in particular StructLayout and ArrayLayout.

3. Data views via View or its user-defined subclasses. This class is used to apply a layout description to a plain Value, enabling structured access to its bits.

4. Data classes Struct and Union. These classes are data views with a layout that is defined using Python variable annotations (also known as type annotations).

To use this module, add the following imports to the beginning of the file:

from amaranth.lib import data

Motivation

The fundamental Amaranth type is a Value: a sequence of bits that can also be used as a number. Manipulating values directly is sufficient for simple applications, but in more complex ones, values are often more than just a sequence of bits; they have well-defined internal structure.

For example, consider a module that processes pixels, converting them from RGB to grayscale. The color pixel format is RGB565:

This module could be implemented (using a fast but very approximate method) as follows:

i_color = Signal(16)
o_gray  = Signal(8)

m.d.comb += o_gray.eq((i_color[0:5] + i_color[5:11] + i_color[11:16]) << 1)

While this implementation works, it is repetitive, error-prone, hard to read, and laborous to change; all because the color components are referenced using bit offsets. To improve it, the structure can be described with a Layout so that the components can be referenced by name:

from amaranth.lib import data, enum

rgb565_layout = data.StructLayout({
    "red":   5,
    "green": 6,
    "blue":  5
})

i_color = Signal(rgb565_layout)
o_gray  = Signal(8)

m.d.comb += o_gray.eq((i_color.red + i_color.green + i_color.blue) << 1)

The View is value-like and can be used anywhere a plain value can be used. For example, it can be assigned to in the usual way:

m.d.comb += i_color.eq(0) # everything is black

Composing layouts

Layouts are composable: a Layout is a shape and can be used as a part of another layout. In this case, an attribute access through a view returns a view as well.

For example, consider a module that processes RGB pixels in groups of up to four at a time, provided by another module, and accumulates their average intensity:

input_layout = data.StructLayout({
    "pixels": data.ArrayLayout(rgb565_layout, 4),
    "valid":  4
})

i_stream = Signal(input_layout)
r_accum  = Signal(32)

m.d.sync += r_accum.eq(
    r_accum + sum((i_stream.pixels[n].red +
                   i_stream.pixels[n].green +
                   i_stream.pixels[n].blue)
                  * i_stream.valid[n]
                  for n in range(len(i_stream.valid))))

Note how the width of i_stream is never defined explicitly; it is instead inferred from the shapes of its fields.

In the previous section, the precise bitwise layout was important, since RGB565 is an interchange format. In this section however the exact bit positions do not matter, since the layout is only used internally to communicate between two modules in the same design. It is sufficient that both of them use the same layout.

Defining layouts

Data layouts can be defined in a few different ways depending on the use case.

In case the data format is defined using a family of layouts instead of a single specific one, a function can be used:

def rgb_layout(r_bits, g_bits, b_bits):
    return data.StructLayout({
        "red":   unsigned(r_bits),
        "green": unsigned(g_bits),
        "blue":  unsigned(b_bits)
    })

rgb565_layout = rgb_layout(5, 6, 5)
rgb24_layout  = rgb_layout(8, 8, 8)

In case the data has related operations or transformations, View can be subclassed to define methods implementing them:

class RGBLayout(data.StructLayout):
    def __init__(self, r_bits, g_bits, b_bits):
        super().__init__({
            "red":   unsigned(r_bits),
            "green": unsigned(g_bits),
            "blue":  unsigned(b_bits)
        })

    def __call__(self, value):
        return RGBView(self, value)

class RGBView(data.View):
    def brightness(self):
        return (self.red + self.green + self.blue)[-8:]

Here, the RGBLayout class itself is shape-like and can be used anywhere a shape is accepted. When a Signal is constructed with this layout, the returned value is wrapped in an RGBView:

>>> pixel = Signal(RGBLayout(5, 6, 5))
>>> len(pixel.as_value())
16
>>> pixel.red
(slice (sig pixel) 0:5)

In case the data format is static, Struct (or Union) can be subclassed instead of View, to reduce the amount of boilerplate needed:

class IEEE754Single(data.Struct):
    fraction: 23
    exponent:  8 = 0x7f
    sign:      1

    def is_subnormal(self):
        return self.exponent == 0

Discriminated unions

This module provides a UnionLayout, which is rarely needed by itself, but is very useful in combination with a discriminant: a enumeration indicating which field of the union contains valid data.

For example, consider a module that can direct another module to perform one of a few operations, each of which requires its own parameters. The two modules could communicate through a channel with a layout like this:

class Command(data.Struct):
    class Kind(enum.Enum):
        SET_ADDR  = 0
        SEND_DATA = 1

    valid  : 1
    kind   : Kind
    params : data.UnionLayout({
        "set_addr": data.StructLayout({
            "addr": unsigned(32)
        }),
        "send_data": data.StructLayout({
            "byte": unsigned(8)
        })
    })

Here, the shape of the Command is inferred, being large enough to accommodate the biggest of all defined parameter structures, and it is not necessary to manage it manually.

One module could submit a command with:

cmd = Signal(Command)

m.d.comb += [
    cmd.valid.eq(1),
    cmd.kind.eq(Command.Kind.SET_ADDR),
    cmd.params.set_addr.addr.eq(0x00001234)
]

The other would react to commands as follows:

addr = Signal(32)

with m.If(cmd.valid):
    with m.Switch(cmd.kind):
        with m.Case(Command.Kind.SET_ADDR):
            m.d.sync += addr.eq(cmd.params.set_addr.addr)
        with m.Case(Command.Kind.SEND_DATA):
           ...

Modeling structured data

class amaranth.lib.data.Field(shape, offset)

Description of a data field.

The Field class specifies the signedness and bit positions of a field in an Amaranth value.

Field objects are immutable.

Attributes:

• shape (ShapeLike) – Shape of the field. When initialized or assigned, the object is stored as-is.

• offset (int, >=0) – Index of the least significant bit of the field.

property width

Width of the field.

This property should be used over self.shape.width because self.shape can be an arbitrary shape-like object, which may not have a width property.

Returns:

Shape.cast(self.shape).width

Return type:

int

__eq__(other)

Compare fields.

Two fields are equal if they have the same shape and offset.

class amaranth.lib.data.Layout

Description of a data layout.

The shape-like Layout interface associates keys (string names or integer indexes) with fields, giving identifiers to spans of bits in an Amaranth value.

It is an abstract base class; StructLayout, UnionLayout, ArrayLayout, and FlexibleLayout implement concrete layout rules. New layout rules can be defined by inheriting from this class.

Like all other shape-castable objects, all layouts are immutable. New classes deriving from Layout must preserve this invariant.

static cast(obj)

Cast a shape-like object to a layout.

This method performs a subset of the operations done by Shape.cast(); it will recursively call .as_shape(), but only until a layout is returned.

Raises:

• TypeError – If obj cannot be converted to a Layout instance.

• RecursionError – If obj.as_shape() returns obj.

abstract __iter__()

Iterate fields in the layout.

Yields:

• str or int – Key (either name or index) for accessing the field.

• Field – Description of the field.

abstract __getitem__(key)

Retrieve a field from the layout.

Returns:

The field associated with key.

Return type:

Field

Raises:

KeyError – If there is no field associated with key.

abstract property size

Size of the layout.

Returns:

The amount of bits required to store every field in the layout.

Return type:

int

as_shape()

Shape of the layout.

Returns:

unsigned(self.size)

Return type:

Shape

__eq__(other)

Compare layouts.

Two layouts are equal if they have the same size and the same fields under the same names. The order of the fields is not considered.

__call__(target)

Create a view into a target.

When a Layout is used as the shape of a Field and accessed through a View, this method is used to wrap the slice of the underlying value into another view with this layout.

Returns:

View(self, target)

Return type:

View

const(init)

Convert a constant initializer to a constant.

Converts init, which may be a sequence or a mapping of field values, to a constant.

Returns:

A constant that has the same value as a view with this layout that was initialized with an all-zero value and had every field assigned to the corresponding value in the order in which they appear in init.

Return type:

Const

from_bits(raw)

Convert a bit pattern to a constant.

Converts raw, which is an int, to a constant.

Returns:

Const(self, raw)

Return type:

Const

format(value, format_spec)

Format a value.

This method is called by the Amaranth language to implement formatting for custom shapes. Whenever "{obj:spec}" is encountered by Format, and obj has a custom shape that has a format() method, obj.shape().format(obj, "spec") is called, and the format specifier is replaced with the result.

The default format() implementation is:

def format(self, obj, spec):
    return Format(f"{{:{spec}}}", Value.cast(obj))

Return type:

Format

Common data layouts

class amaranth.lib.data.StructLayout(members)

Description of a structure layout.

The fields of a structure layout follow one another without any gaps, and the size of a structure layout is the sum of the sizes of its members.

For example, the following layout of a 16-bit value:

can be described with:

data.StructLayout({
    "first":  3,
    "second": 7,
    "third":  6
})

Note

Structures that have padding can be described with a FlexibleLayout. Alternately, padding can be added to the layout as fields called _1, _2, and so on. These fields won’t be accessible as attributes or by using indexing.

Attributes:

members (mapping of str to ShapeLike) – Dictionary of structure members.

property size

Size of the structure layout.

Returns:

Index of the most significant bit of the last field plus one; or zero if there are no fields.

Return type:

int

class amaranth.lib.data.UnionLayout(members)

Description of a union layout.

The fields of a union layout all start from bit 0, and the size of a union layout is the size of the largest of its members.

For example, the following layout of a 7-bit value:

can be described with:

data.UnionLayout({
    "first":  3,
    "second": 7,
    "third":  6
})

Attributes:

members (mapping of str to ShapeLike) – Dictionary of union members.

property size

Size of the union layout.

Returns:

Index of the most significant bit of the largest field plus one; or zero if there are no fields.

Return type:

int

const(init)

Convert a constant initializer to a constant.

Converts init, which may be a sequence or a mapping of field values, to a constant.

Returns:

A constant that has the same value as a view with this layout that was initialized with an all-zero value and had every field assigned to the corresponding value in the order in which they appear in init.

Return type:

Const

class amaranth.lib.data.ArrayLayout(elem_shape, length)

Description of an array layout.

The fields of an array layout follow one another without any gaps, and the size of an array layout is the size of its element multiplied by its length.

For example, the following layout of a 16-bit value:

can be described with:

data.ArrayLayout(unsigned(4), 4)

Note

Arrays that have padding can be described with a FlexibleLayout.

Attributes:

• elem_shape (ShapeLike) – Shape of an individual element.

• length (int) – Amount of elements.

property size

Size of the array layout.

Returns:

Size of an individual element multiplied by their amount.

Return type:

int

format(value, format_spec)

Format a value.

This method is called by the Amaranth language to implement formatting for custom shapes. Whenever "{obj:spec}" is encountered by Format, and obj has a custom shape that has a format() method, obj.shape().format(obj, "spec") is called, and the format specifier is replaced with the result.

The default format() implementation is:

def format(self, obj, spec):
    return Format(f"{{:{spec}}}", Value.cast(obj))

Return type:

Format

class amaranth.lib.data.FlexibleLayout(size, fields)

Description of a flexible layout.

A flexible layout is similar to a structure layout; while fields in StructLayout are defined contiguously, the fields in a flexible layout can overlap and have gaps between them.

Because the size and field boundaries in a flexible layout can be defined arbitrarily, it may also be more convenient to use a flexible layout when the layout information is derived from an external data file rather than defined in Python code.

For example, the following layout of a 16-bit value:

can be described with:

data.FlexibleLayout(16, {
    "first":  data.Field(unsigned(3), 1),
    "second": data.Field(unsigned(7), 0),
    "third":  data.Field(unsigned(6), 10),
    0:        data.Field(unsigned(1), 14)
})

Both strings and integers can be used as names of flexible layout fields, so flexible layouts can be used to describe structures with arbitrary padding and arrays with arbitrary stride.

If another data structure is used as the source of truth for creating flexible layouts, consider instead inheriting from the base Layout class, which may be more convenient.

Attributes:

• size (int) – Size of the layout.

• fields (mapping of str or int to Field) – Fields defined in the layout.

Data views

class amaranth.lib.data.View(layout, target)

A value viewed through the lens of a layout.

The value-like class View provides access to the fields of an underlying Amaranth value via the names or indexes defined in the provided layout.

Creating a view

A view must be created using an explicitly provided layout and target. To create a new Signal that is wrapped in a View with a given layout, use Signal(layout, ...), which for a Layout is equivalent to View(layout, Signal(...)).

Accessing a view

Slicing a view or accessing its attributes returns a part of the underlying value corresponding to the field with that index or name, which is itself either a value or a value-castable object. If the shape of the field is a Layout, it will be a View; if it is a class deriving from Struct or Union, it will be an instance of that data class; if it is another shape-like object implementing __call__(), it will be the result of calling that method.

Slicing a view whose layout is an ArrayLayout can be done with an index that is an Amaranth value rather than a constant integer. The returned element is chosen dynamically in that case.

A view can only be compared for equality with another view or constant with the same layout, returning a single-bit Value. No other operators are supported. A view can be lowered to a Value using as_value().

Custom view classes

The View class can be inherited from to define additional properties or methods on a view. The only three names that are reserved on instances of View and Const are as_value(), Const.as_bits(), and eq(), leaving the rest to the developer. The Struct and Union classes provided in this module are subclasses of View that also provide a concise way to define a layout.

shape()

Get layout of this view.

Returns:

The layout provided when constructing the view.

Return type:

Layout

as_value()

Get underlying value.

Returns:

The target provided when constructing the view, or the Signal that was created.

Return type:

Value

eq(other)

Assign to the underlying value.

Returns:

self.as_value().eq(other)

Return type:

Assign

__getitem__(key)

Slice the underlying value.

A field corresponding to key is looked up in the layout. If the field’s shape is a shape-castable object that has a __call__() method, it is called and the result is returned. Otherwise, as_shape() is called repeatedly on the shape until either an object with a __call__() method is reached, or a Shape is returned. In the latter case, returns an unspecified Amaranth expression with the right shape.

Parameters:

key (str or int or ValueCastable) – Name or index of a field.

Returns:

A slice of the underlying value defined by the field.

Return type:

Value or ValueCastable, assignable

Raises:

• KeyError – If the layout does not define a field corresponding to key.

• TypeError – If key is a value-castable object, but the layout of the view is not an ArrayLayout.

• TypeError – If ShapeCastable.__call__() does not return a value or a value-castable object.

__getattr__(name)

Access a field of the underlying value.

Returns self[name].

Raises:

AttributeError – If the layout does not define a field called name, or if name starts with an underscore.

class amaranth.lib.data.Const(layout, target)

A constant value viewed through the lens of a layout.

The Const class is similar to the View class, except that its target is a specific bit pattern and operations on it return constants.

Creating a constant

A constant can be created from a dict or list of field values using Layout.const(), or from a bit pattern using Layout.from_bits().

Accessing a constant

Slicing a constant or accessing its attributes returns a part of the underlying value corresponding to the field with that index or name. If the shape of the field is a Layout, the returned value is a Const; if it is a different shape-like object implementing from_bits(), it will be the result of calling that method; otherwise, it is an int.

Slicing a constant whose layout is an ArrayLayout can be done with an index that is an Amaranth value rather than a constant integer. The returned element is chosen dynamically in that case, and the resulting value will be a View instead of a Const.

A Const can only be compared for equality with another constant or view that has the same layout. When compared with another constant, the result will be a bool. When compared with a view, the result will be a single-bit Value. No other operators are supported. A constant can be lowered to a Value using as_value(), or to its underlying bit pattern using as_bits().

shape()

Get layout of this constant.

Returns:

The layout provided when constructing the constant.

Return type:

Layout

as_bits()

Get underlying bit pattern.

Returns:

The target provided when constructing the constant.

Return type:

int

as_value()

Convert to a value.

Returns:

The bit pattern of this constant, as a Value.

Return type:

Const

__getitem__(key)

Slice the underlying value.

A field corresponding to key is looked up in the layout. If the field’s shape is a shape-castable object that has a from_bits() method, returns the result of calling that method. Otherwise, returns an int.

Parameters:

key (str or int or ValueCastable) – Name or index of a field.

Returns:

A slice of the underlying value defined by the field.

Return type:

unspecified type or int

Raises:

• KeyError – If the layout does not define a field corresponding to key.

• TypeError – If key is a value-castable object, but the layout of the constant is not an ArrayLayout.

• Exception – If the bit pattern of the field is not valid according to ShapeCastable.from_bits(). Usually this will be a ValueError.

__getattr__(name)

Access a field of the underlying value.

Returns self[name].

Raises:

• AttributeError – If the layout does not define a field called name, or if name starts with an underscore.

• Exception – If the bit pattern of the field is not valid according to ShapeCastable.from_bits(). Usually this will be a ValueError.

Data classes

class amaranth.lib.data.Struct(target)

Structures defined with annotations.

The Struct base class is a subclass of View that provides a concise way to describe the structure layout and initial values for the fields using Python variable annotations.

Any annotations containing shape-like objects are used, in the order in which they appear in the source code, to construct a StructLayout. The values assigned to such annotations are used to populate the initial value of the signal created by the view. Any other annotations are kept as-is.

As an example, a structure for IEEE 754 single-precision floating-point format can be defined as:

class IEEE754Single(Struct):
    fraction: 23
    exponent:  8 = 0x7f
    sign:      1

    def is_subnormal(self):
        return self.exponent == 0

The IEEE754Single class itself can be used where a shape is expected:

>>> IEEE754Single.as_shape()
StructLayout({'fraction': 23, 'exponent': 8, 'sign': 1})
>>> Signal(IEEE754Single).as_value().width
32

Instances of this class can be used where values are expected:

>>> flt = Signal(IEEE754Single)
>>> Signal(32).eq(flt)
(eq (sig $signal) (sig flt))

Accessing shape-castable properties returns slices of the underlying value:

>>> flt.fraction
(slice (sig flt) 0:23)
>>> flt.is_subnormal()
(== (slice (sig flt) 23:31) (const 1'd0))

The initial values for individual fields can be overridden during instantiation:

>>> hex(Signal(IEEE754Single).as_value().init)
'0x3f800000'
>>> hex(Signal(IEEE754Single, init={'sign': 1}).as_value().init)
'0xbf800000'
>>> hex(Signal(IEEE754Single, init={'exponent': 0}).as_value().init)
'0x0'

Classes inheriting from Struct can be used as base classes. The only restrictions are that:

• Classes that do not define a layout cannot be instantiated or converted to a shape;

• A layout can be defined exactly once in the inheritance hierarchy.

Behavior can be shared through inheritance:

class HasChecksum(Struct):
    def checksum(self):
        bits = Value.cast(self)
        return sum(bits[n:n+8] for n in range(0, len(bits), 8))

class BareHeader(HasChecksum):
    address: 16
    length:   8

class HeaderWithParam(HasChecksum):
    address: 16
    length:   8
    param:    8

>>> HasChecksum.as_shape()
Traceback (most recent call last):
  ...
TypeError: Aggregate class 'HasChecksum' does not have a defined shape
>>> bare = Signal(BareHeader); bare.checksum()
(+ (+ (+ (const 1'd0) (slice (sig bare) 0:8)) (slice (sig bare) 8:16)) (slice (sig bare) 16:24))
>>> param = Signal(HeaderWithParam); param.checksum()
(+ (+ (+ (+ (const 1'd0) (slice (sig param) 0:8)) (slice (sig param) 8:16)) (slice (sig param) 16:24)) (slice (sig param) 24:32))

class amaranth.lib.data.Union(target)

Unions defined with annotations.

The Union base class is a subclass of View that provides a concise way to describe the union layout using Python variable annotations. It is very similar to the Struct class, except that its layout is a UnionLayout.

A Union can have only one field with a specified initial value. If an initial value is explicitly provided during instantiation, it overrides the initial value specified with an annotation:

class VarInt(Union):
    int8:  8
    int16: 16 = 0x100

>>> Signal(VarInt).as_value().init
256
>>> Signal(VarInt, init={'int8': 10}).as_value().init
10