Language reference

Warning

This reference is a work in progress and is seriously incomplete!

While the wording below states that anything not described in this document isn’t covered by the backwards compatibility guarantee, this should be ignored until the document is complete and this warning is removed.

This reference describes the Python classes that underlie the Amaranth language’s syntax. It assumes familiarity with the language guide.

Backwards compatibility

As part of the Amaranth backwards compatibility guarantee, any behaviors described in this document will not change from a version to another without at least one version including a warning about the impending change. Any nontrivial change to these behaviors must also go through the public review as a part of the Amaranth Request for Comments process.

Conversely, any behavior not documented here is subject to change at any time with or without notice, and any names under the amaranth.hdl module that are not explicitly included in this document, even if they do not begin with an underscore, are internal to the implementation of the language.

Importing syntax

There are two ways to import the Amaranth syntax into a Python file: by importing the prelude or by importing individual names from the amaranth.hdl module. Since the prelude is kept small and rarely extended to avoid breaking downstream code that uses a glob import, there are some names that are only exported from the amaranth.hdl module. The following three snippets are equivalent:

from amaranth import *

m = Module()

import amaranth as am

m = am.Module()

from amaranth.hdl import Module

m = Module()

The prelude exports exactly the following names:

  • Shape

  • unsigned()

  • signed()

  • Value

  • Const

  • C()

  • Mux()

  • Cat

  • Array

  • Signal

  • ClockSignal

  • ResetSignal

  • Module

  • ClockDomain

  • Elaboratable

  • Fragment

  • Instance

  • Memory

  • Record (deprecated)

  • DomainRenamer

  • ResetInserter

  • EnableInserter

Source locations

Many functions and methods in Amaranth take the src_loc_at=0 keyword argument. These language constructs may inspect the call stack to determine the file and line of its call site, which will be used to annotate generated code when a netlist is generated or to improve diagnostic messages.

Some call sites are not relevant for an Amaranth designer; e.g. when an Amaranth language construct is called from a user-defined utility function, the source location of the call site within this utility function is usually not interesting to the designer. In these cases, one or more levels of function calls can be removed from consideration using the src_loc_at argument as follows (using Shape.cast() to demonstrate the concept):

def my_shape_cast(obj, *, src_loc_at=0):
    ... # additionally process `obj`...
    return Shape.cast(obj, src_loc_at=1 + src_loc_at)

The number 1 corresponds to the number of call stack frames that should be skipped.

Shapes

See also the introduction to shapes and casting from shape-like objects in the language guide.

class amaranth.hdl.Shape(width=1, signed=False)

Bit width and signedness of a Value.

A Shape can be obtained by:

  • constructing with explicit bit width and signedness;

  • using the signed() and unsigned() aliases if the signedness is known upfront;

  • casting from a variety of objects using the cast() method.

Parameters:

  • width (int) – The number of bits in the representation of a value. This includes the sign bit for signed values. Cannot be zero if the value is signed.

  • signed (bool) – Whether the value is signed. Signed values use the two’s complement representation.

static cast(obj, *, src_loc_at=0)

Cast obj to a shape.

Many shape-like objects can be cast to a shape:

  • a Shape, where the result is itself;

  • an int, where the result is unsigned(obj);

  • a range, where the result has minimal width required to represent all elements of the range, and is signed if any element of the range is signed;

  • an enum.Enum whose members are all constant-castable or enum.IntEnum, where the result is wide enough to represent any member of the enumeration, and is signed if any member of the enumeration is signed;

  • a ShapeCastable object, where the result is obtained by repeatedly calling obj.as_shape().

Raises:
__repr__()

Python code that creates this shape.

Returns f"signed({self.width})" or f"unsigned({self.width})".

amaranth.hdl.unsigned(width)

Returns Shape(width, signed=False).

amaranth.hdl.signed(width)

Returns Shape(width, signed=True).

class amaranth.hdl.ShapeCastable

Interface class for objects that can be cast to a Shape.

Shapes of values in the Amaranth language are specified using shape-like objects. Inheriting a class from ShapeCastable and implementing all of the methods described below adds instances of that class to the list of shape-like objects recognized by the Shape.cast() method. This is a part of the mechanism for seamlessly extending the Amaranth language in third-party code.

To illustrate their purpose, consider constructing a signal from a shape-castable object shape_castable:

value_like = Signal(shape_castable, reset=initializer)

The code above is equivalent to:

value_like = shape_castable(Signal(
    shape_castable.as_shape(),
    reset=shape_castable.const(initializer)
))

Note that the shape_castable(x) syntax performs shape_castable.__call__(x).

Tip

The source code of the amaranth.lib.data module can be used as a reference for implementing a fully featured shape-castable object.

as_shape()

Convert self to a shape-like object.

This method is called by the Amaranth language to convert self to a concrete Shape. It will usually return a Shape object, but it may also return another shape-like object to delegate its functionality.

This method must be idempotent: when called twice on the same object, the result must be exactly the same.

This method may also be called by code that is not a part of the Amaranth language.

Return type:

Any other object recognized by Shape.cast().

Raises:

Exception – When the conversion cannot be done. This exception must be propagated by callers (except when checking whether an object is shape-castable or not), either directly or as a cause of another exception.

const(obj)

Convert a constant initializer obj to its value representation.

This method is called by the Amaranth language to convert obj, which may be an arbitrary Python object, to a concrete value-like object. The object obj will usually be a Python literal that can conveniently represent a constant value whose shape is described by self. While not constrained here, the result will usually be an instance of the return type of __call__().

For any obj, the following condition must hold:

Shape.cast(self) == Const.cast(self.const(obj)).shape()

This method may also be called by code that is not a part of the Amaranth language.

Return type:

A value-like object that is constant-castable.

Raises:

Exception – When the conversion cannot be done. This exception must be propagated by callers, either directly or as a cause of another exception. While not constrained here, usually the exception class will be TypeError or ValueError.

__call__(obj)

Lift a value-like object to a higher-level representation.

This method is called by the Amaranth language to lift obj, which may be any value-like object whose shape equals Shape.cast(self), to a higher-level representation, which may be any value-like object with the same shape. While not constrained here, usually a ShapeCastable implementation will be paired with a ValueCastable implementation, and this method will return an instance of the latter.

If obj is not as described above, this interface does not constrain the behavior of this method. This may be used to implement another call-based protocol at the same time.

For any compliant obj, the following condition must hold:

Value.cast(self(obj)) == Value.cast(obj)

This method may also be called by code that is not a part of the Amaranth language.

Return type:

A value-like object.

class amaranth.hdl.ShapeLike

Abstract class representing all objects that can be cast to a Shape.

issubclass(cls, ShapeLike) returns True for:

isinstance(obj, ShapeLike) returns True for:

This class cannot be instantiated or subclassed. It can only be used for checking types of objects.

Values

See also the introduction to values and casting from value-like objects in the language guide.

class amaranth.hdl.Value(*, src_loc_at=0)

Abstract representation of a bit pattern computed in a circuit.

The Amaranth language gives Python code the ability to create a circuit netlist by manipulating objects representing the computations within that circuit. The Value class represents the bit pattern of a constant, or of a circuit input or output, or within a storage element; or the result of an arithmetic, logical, or bit container operation.

Operations on this class interpret this bit pattern either as an integer, which can be signed or unsigned depending on the value’s shape(), or as a bit container. In either case, the semantics of operations that implement Python’s syntax, like + (also known as __add__()), are identical to the corresponding operation on a Python int (or on a Python sequence container). The bitwise inversion ~ (also known as __invert__()) is the sole exception to this rule.

Data that is not conveniently representable by a single integer or a bit container can be represented by wrapping a Value in a ValueCastable subclass that provides domain-specific operations. It is possible to extend Amaranth in third-party code using value-castable objects, and the Amaranth standard library provides several built-in ones:

  • amaranth.lib.enum classes are a drop-in replacement for the standard Python enum classes that can be defined with an Amaranth shape;

  • amaranth.lib.data classes allow defining complex data structures such as structures and unions.

Operations on Value instances return another Value instance. Unless the exact type and value of the result is explicitly specified below, it should be considered opaque, and may change without notice between Amaranth releases as long as the semantics remains the same.

Note

In each of the descriptions below, you will see a line similar to:

Return type: Value, unsigned(1), assignable

The first part (Value) indicates that the returned object’s type is a subclass of Value. The second part (unsigned(1)) describes the shape of that value. The third part, if present, indicates that the value is assignable if self is assignable.

static cast(obj)

Cast obj to an Amaranth value.

Many value-like objects can be cast to a value:

  • a Value instance, where the result is itself;

  • a bool or int instance, where the result is Const(obj);

  • an enum.IntEnum instance, or a enum.Enum instance whose members are all integers, where the result is a Const(obj, enum_shape) where enum_shape is a shape that can represent every member of the enumeration;

  • a ValueCastable instance, where the result is obtained by repeatedly calling obj.as_value().

Raises:
abstract shape()

Shape of self.

Returns:

  • shape-like object

  • .. – TODO: while this is documented as returning a shape-like object, in practice we guarantee that this is a concrete Shape. it’s unclear whether we will ever want to return a shape-catable object here, but there is not much harm in stating a relaxed contract, as it can always be tightened later, but not vice-versa

as_unsigned()

Reinterpretation as an unsigned value.

Return type:

Value, unsigned(len(self)), assignable

as_signed()

Reinterpretation as a signed value.

Return type:

Value, signed(len(self)), assignable

__bool__()

Forbidden conversion to boolean.

Python uses this operator for its built-in semantics, e.g. if, and requires it to return a bool. Since this is not possible for Amaranth values, this operator always raises an exception.

Raises:

TypeError – Always.

bool()

Conversion to boolean.

Performs the same operation as any().

Return type:

Value, unsigned(1)

__pos__()

Unary position, +self.

Returns:

self

Return type:

Value, self.shape()

__neg__()

Unary negation, -self.

Return type:

Value, signed(len(self) + 1)

__add__(other)

Addition, self + other.

Returns:

  • Value, unsigned(max(self.width(), other.width()) + 1) – If both self and other are unsigned.

  • Value, signed(max(self.width() + 1, other.width()) + 1) – If self is unsigned and other is signed.

  • Value, signed(max(self.width(), other.width() + 1) + 1) – If self is signed and other is unsigned.

  • Value, signed(max(self.width(), other.width()) + 1) – If both self and other are unsigned.

__radd__(other)

Addition, other + self (reflected).

Like __add__(), with operands swapped.

__sub__(other)

Subtraction, self - other.

Returns:

  • Value, signed(max(self.width(), other.width()) + 1) – If both self and other are unsigned.

  • Value, signed(max(self.width() + 1, other.width()) + 1) – If self is unsigned and other is signed.

  • Value, signed(max(self.width(), other.width() + 1) + 1) – If self is signed and other is unsigned.

  • Value, signed(max(self.width(), other.width()) + 1) – If both self and other are unsigned.

Return type:

Value

__rsub__(other)

Subtraction, other - self (reflected).

Like __sub__(), with operands swapped.

__mul__(other)

Multiplication, self * other.

Returns:

  • Value, unsigned(len(self) + len(other)) – If both self and other are unsigned.

  • Value, signed(len(self) + len(other)) – If either self or other are signed.

__rmul__(other)

Multiplication, other * self (reflected).

Like __mul__(), with operands swapped.

__floordiv__(other)

Flooring division, self // other.

If other is zero, the result of this operation is zero.

Returns:

  • Value, unsigned(len(self)) – If both self and other are unsigned.

  • Value, signed(len(self) + 1) – If self is unsigned and other is signed.

  • Value, signed(len(self)) – If self is signed and other is unsigned.

  • Value, signed(len(self) + 1) – If both self and other are signed.

__rfloordiv__(other)

Flooring division, other // self (reflected).

If self is zero, the result of this operation is zero.

Like __floordiv__(), with operands swapped.

__mod__(other)

Flooring modulo or remainder, self % other.

If other is zero, the result of this operation is zero.

Return type:

Value, other.shape()

__rmod__(other)

Flooring modulo or remainder, other % self (reflected).

Like __mod__(), with operands swapped.

__eq__(other)

Equality comparison, self == other.

Return type:

Value, unsigned(1)

__ne__(other)

Inequality comparison, self != other.

Return type:

Value, unsigned(1)

__lt__(other)

Less than comparison, self < other.

Return type:

Value, unsigned(1)

__le__(other)

Less than or equals comparison, self <= other.

Return type:

Value, unsigned(1)

__gt__(other)

Greater than comparison, self > other.

Return type:

Value, unsigned(1)

__ge__(other)

Greater than or equals comparison, self >= other.

Return type:

Value, unsigned(1)

__abs__()

Absolute value, abs(self).

Return type:

Value, unsigned(len(self))

__invert__()

Bitwise NOT, ~self.

The shape of the result is the same as the shape of self, even for unsigned values.

Important

In Python, ~0 equals -1. In Amaranth, ~C(0) equals C(1). This is the only case where an Amaranth operator deviates from the Python operator with the same name.

This deviation is necessary because Python does not allow overriding the logical and, or, and not operators. Amaranth uses &, |, and ~ instead; if it wasn’t the case that ~C(0) == C(1), that would have been impossible.

Return type:

Value, self.shape()

__and__(other)

Bitwise AND, self & other.

Returns:

  • Value, unsigned(max(self.width(), other.width())) – If both self and other are unsigned.

  • Value, signed(max(self.width() + 1, other.width())) – If self is unsigned and other is signed.

  • Value, signed(max(self.width(), other.width() + 1)) – If self is signed and other is unsigned.

  • Value, signed(max(self.width(), other.width())) – If both self and other are unsigned.

__rand__(other)

Bitwise AND, other & self.

Like __and__(), with operands swapped.

all()

Reduction AND; are all bits 1?

Return type:

Value, unsigned(1)

__or__(other)

Bitwise OR, self | other.

Returns:

  • Value, unsigned(max(self.width(), other.width())) – If both self and other are unsigned.

  • Value, signed(max(self.width() + 1, other.width())) – If self is unsigned and other is signed.

  • Value, signed(max(self.width(), other.width() + 1)) – If self is signed and other is unsigned.

  • Value, signed(max(self.width(), other.width())) – If both self and other are unsigned.

__ror__(other)

Bitwise OR, other | self.

Like __or__(), with operands swapped.

any()

Reduction OR; is any bit 1?

Return type:

Value, unsigned(1)

__xor__(other)

Bitwise XOR, self ^ other.

Returns:

  • Value, unsigned(max(self.width(), other.width())) – If both self and other are unsigned.

  • Value, signed(max(self.width() + 1, other.width())) – If self is unsigned and other is signed.

  • Value, signed(max(self.width(), other.width() + 1)) – If self is signed and other is unsigned.

  • Value, signed(max(self.width(), other.width())) – If both self and other are unsigned.

__rxor__(other)

Bitwise XOR, other ^ self.

Like __xor__(), with operands swapped.

xor()

Reduction XOR; is an odd amount of bits 1?

Return type:

Value, unsigned(1)

__lshift__(other)

Left shift by variable amount, self << other.

Returns:

  • Value, unsigned(len(self) + 2 ** len(other) - 1) – If self is unsigned.

  • Value, signed(len(self) + 2 ** len(other) - 1) – If self is signed.

Raises:

TypeError – If other is signed.

__rlshift__(other)

Left shift by variable amount, other << self.

Like __lshift__(), with operands swapped.

shift_left(amount)

Left shift by constant amount.

If amount < 0, performs the same operation as self.shift_right(-amount).

Returns:

  • Value, unsigned(len(self) + amount) – If self is unsigned.

  • Value, signed(len(self) + amount) – If self is signed.

rotate_left(amount)

Left rotate by constant amount.

If amount < 0, performs the same operation as self.rotate_right(-amount).

Return type:

Value, unsigned(len(self)), assignable

__rshift__(other)

Right shift by variable amount, self >> other.

Returns:

  • Value, unsigned(len(self)) – If self is unsigned.

  • Value, signed(len(self)) – If self is signed.

Raises:

TypeError – If other is signed.

__rrshift__(other)

Right shift by variable amount, other >> self.

Like __rshift__(), with operands swapped.

shift_right(amount)

Right shift by constant amount.

If amount < 0, performs the same operation as self.left_right(-amount).

Returns:

  • Value, unsigned(max(len(self) - amount, 0)) – If self is unsigned.

  • Value, signed(max(len(self) - amount, 1)) – If self is signed.

rotate_right(amount)

Right rotate by constant amount.

If amount < 0, performs the same operation as self.rotate_right(-amount).

Return type:

Value, unsigned(len(self)), assignable

__len__()

Bit width of self.

Returns:

self.shape().width

Return type:

int

__getitem__(key)

Bit slicing.

Todo

Describe this operation.

__contains__(other)

Forbidden membership test operator.

Python requires this operator to return a bool. Since this is not possible for Amaranth values, this operator always raises an exception.

To check membership in a set of constant integer values, use matches() instead.

Raises:

TypeError – Always.

bit_select(offset, width)

Part-select with bit granularity.

Selects a constant width, variable offset part of self, where parts with successive offsets overlap by width - 1 bits. When offset is a constant integer, this operation is equivalent to self[offset:offset + width].

Parameters:

  • offset (value-like) – Index of the first selected bit.

  • width (int) – Amount of bits to select.

Return type:

Value, unsigned(width), assignable

Raises:
word_select(offset, width)

Part-select with word granularity.

Selects a constant width, variable offset part of self, where parts with successive offsets are adjacent but do not overlap. When offset is a constant integer, this operation is equivalent to self[offset * width:(offset + 1) * width].

Parameters:

  • offset (value-like) – Index of the first selected word.

  • width (int) – Amount of bits to select.

Return type:

Value, unsigned(width), assignable

Raises:
replicate(count)

Replication.

Equivalent to Cat(self for _ in range(count)), but not assignable.

Return type:

Value, unsigned(len(self) * count)

Raises:

TypeError – If count is negative.

matches(*patterns)

Pattern matching.

Matches against a set of patterns, recognizing the same grammar as with m.Case().

Todo

Describe the pattern language in detail.

Return type:

Value, unsigned(1)

eq(value, *, src_loc_at=0)

Assignment.

Once it is placed in a domain, an assignment changes the bit pattern of self to equal value. If the bit width of value is less than that of self, it is zero-extended (for unsigned values) or sign-extended (for signed values). If the bit width of value is greater than that of self, it is truncated.

Return type:

Statement

__hash__ = None

Forbidden hashing.

Python objects are hashable if they provide a __hash__ method that returns an int and an __eq__ method that returns a bool. Amaranth values define __eq__() to return a Value, which precludes them from being hashable.

To use a Value as a key in a dict, use the following pattern:

value = Signal()
assoc = {}
assoc[id(value)] = value, "a signal"
_, info = assoc[id(value)]
assert info == "a signal"
class amaranth.hdl.ValueCastable

Interface class for objects that can be cast to a Value.

Computations in the Amaranth language are described by combining value-like objects. Inheriting a class from ValueCastable and implementing all of the methods described below adds instances of that class to the list of value-like objects recognized by the Value.cast() method. This is a part of the mechanism for seamlessly extending the Amaranth language in third-party code.

Note

All methods and operators defined by the Value class will implicitly cast a ValueCastable object to a Value, with the exception of arithmetic operators, which will prefer calling a reflected arithmetic operation on the ValueCastable argument if it defines one.

For example, if value_castable implements __radd__, then C(1) + value_castable will perform value_castable.__radd__(C(1)), and otherwise it will perform C(1).__add__(value_castable.as_value()).

as_value()

Convert self to a value-like object.

This method is called by the Amaranth language to convert self to a concrete Value. It will usually return a Value object, but it may also return another value-like object to delegate its functionality.

This method must be idempotent: when called twice on the same object, the result must be exactly the same.

This method may also be called by code that is not a part of the Amaranth language.

Return type:

Any other object recognized by Value.cast().

Raises:

Exception – When the conversion cannot be done. This exception must be propagated by callers, either directly or as a cause of another exception. It is recommended that, in cases where this method raises an exception, the shape() method also raises an exception.

shape()

Compute the shape of self.

This method is not called by the Amaranth language itself; whenever it needs to discover the shape of a value-castable object, it calls self.as_value().shape(). However, that method must return a Shape, and ValueCastable subclasses may have a richer representation of their shape provided by an instance of a ShapeCastable subclass. This method may return such a representation.

This method must be idempotent: when called twice on the same object, the result must be exactly the same.

The following condition must hold:

Shape.cast(self.shape()) == Value.cast(self).shape()
Return type:

A shape-like object.

Raises:

Exception – When the conversion cannot be done. This exception must be propagated by callers, either directly or as a cause of another exception. It is recommended that, in cases where this method raises an exception, the as_value() method also raises an exception.

static lowermethod(func)

Decorator to memoize lowering methods.

Ensures the decorated method is called only once, with subsequent method calls returning the object returned by the first first method call.

This decorator is required to decorate the as_value method of ValueCastable subclasses. This is to ensure that Amaranth’s view of representation of all values stays internally consistent.

class amaranth.hdl.ValueLike

Abstract class representing all objects that can be cast to a Value.

issubclass(cls, ValueLike) returns True for:

isinstance(obj, ValueLike) returns the same value as issubclass(type(obj), ValueLike).

This class cannot be instantiated or subclassed. It can only be used for checking types of objects.

Note

It is possible to define an enumeration with a member that is value-like but not constant-castable, meaning that issubclass(BadEnum, ValueLike) returns True, but Value.cast(BadEnum.MEMBER) raises an exception.

The amaranth.lib.enum module prevents such enumerations from being defined when the shape is specified explicitly. Using amaranth.lib.enum and specifying the shape ensures that all of your enumeration members are constant-castable and fit in the provided shape.