HDL21

Analog Hardware Description Library in Python

Hdl21 is a hardware description library embedded in Python. It is targeted for analog and custom integrated circuits, and for maximum productivity with minimum fancy-programming skill.

Installation

pip install hdl21

That's it. No crazy build step, no crazy dependencies, no crazy EDA stuff, no "clone and just modify these 300 things", no sourceing, none of that. Hdl21 is pure Python, and is designed to be as easy to install as any other Python package.

Modules

Hdl21's primary unit of hardware reuse is the Module. Think of it as Verilog's module, or VHDL's entity, or SPICE's subckt. Better yet if you are used to graphical schematics, think of it as the content of a schematic. Hdl21 Modules are containers of a handful of hdl21 types. Think of them as including:

Instances of other Modules
Connections between them, defined by Signals and Ports
Fancy combinations thereof, covered later

An example Module:

import hdl21 as h

m = h.Module(name="MyModule")
m.i = h.Input()
m.o = h.Output(width=8)
m.s = h.Signal()
m.a = AnotherModule()

In addition to the procedural-syntax shown above, Modules can also be defined through a class-based syntax by applying the hdl21.module decorator to a class-definition.

import hdl21 as h

@h.module
class MyModule:
    i = h.Input()
    o = h.Output(width=8)
    s = h.Signal()
    a = AnotherModule()

This class-based syntax produces identical results to the procedural code-block above. Its declarative style can be much more natural and expressive in many contexts, especially for designers familiar with popular HDLs.

Creation of Module signal-attributes is generally performed by the built-in Signal, Port, Input, and Output constructors. Each comes with a "plural version" (Input*s* etc.) which creates several identical objects at once:

import hdl21 as h

@h.module
class MyModule:
    a, b = h.Inputs(2)
    c, d, e = h.Outputs(3, width=16)
    z, y, x, w = h.Signals(4)

Signals

Hdl21's primary connection type is Signal. Think of it as Verilog's wire, or a node in that schematic. Each Signal has an integer-valued bus width field, and can be connected to any other equal-width Port.

A subset of Signals are exposed outside their parent Module. These externally-connectable signals are referred to as Ports. Hdl21 provides four port constructors: Input, Output, Inout, and Port. The last creates a directionless (or direction unspecified) port akin to those of common spice-level languages.

Connections

Popular HDLs generally feature one of two forms of connection semantics. Verilog, VHDL, and most dedicated HDLs use "connect by call" semantics, in which signal-objects are first declared, then passed as function-call-style arguments to instances of other modules.

module my_module();
  logic a, b, c;                              // Declare signals
  another_module i1 (a, b, c);                // Create an instance
  another_module i2 (.a(a), .b(b), .c(c));    // Another instance, connected by-name
endmodule

Chisel, in contrast, uses "connection by assignment" - more literally using the walrus := operator. Instances of child modules are created first, and their ports are directly walrus-connected to one another. No local-signal objects ever need be declared in the instantiating parent module.

class MyModule extends Module {
  // Create Module Instances
  val i1 = Module(new AnotherModule)
  val i2 = Module(new AnotherModule)
  // Wire them directly to one another
  i1.io.a := i2.io.a
  i1.io.b := i2.io.b
  i1.io.c := i2.io.c
}

Each can be more concise and expressive depending on context. Hdl21 Modules support both connect-by-call and connect-by-assignment forms.

Connections by assignment are performed by assigning either a Signal or another instance's Port to an attribute of a Module-Instance.

# Create a module
m = h.Module()
# Create its internal Signals
m.a, m.b, m.c = h.Signals(3)
# Create an Instance
m.i1 = AnotherModule()
# And wire them up
m.i1.a = m.a
m.i1.b = m.b
m.i1.c = m.c

This also works without the parent-module Signals:

# Create a module
m = h.Module()
# Create the Instances
m.i1 = AnotherModule()
m.i2 = AnotherModule()
# And wire them up
m.i1.a = m.i2.a
m.i1.b = m.i2.b
m.i1.c = m.i2.c

Instances can instead be connected by call:

# Create a module
m = h.Module()
# Create the Instances
m.i1 = AnotherModule()
m.i2 = AnotherModule()
# Call one to connect them
m.i1(a=m.i2.a, b=m.i2.b, c=m.i2.c)

These connection-calls can also be performed inline, as the instances are being created.

# Create a module
m = h.Module()
# Create the Instance `i1`
m.i1 = AnotherModule()
# Create another Instance `i2`, and connect to `i1`
m.i2 = AnotherModule(a=m.i1.a, b=m.i1.b, c=m.i1.c)

These methods hides some of what happens under the hood of HDL21 for ease-of-use. A more thorough method of defining objects, especially in Generators seen below, leverage endpoints in the Module and Instance APIs:

h.Module.add is used to add either Signal or Instances instantiated in the usual way and also allows the use of an optional name keyword argument which names the newly added object so it can be accessed using the methods we've already described above.

h.Module.get is used to get the Signal or Instance with a given name from a module via a single argument in string form.

h.Instance.connect takes two arguments, the first a string referring to an Instance's available ports and the second refers to any "connectable" object which can be of the type Signal, PortRef, Slice or Concat.

Slicing

Signal objects are equipped with a width keyword argument, which determines the width of a signal bus. This creates a 1D array that can accessed using Python's usual slicing syntax used with lists:

sig1 = h.Signal(width=12)
sig2 = h.Input(width=6)
# Map sig2 signals to even numbered sig1 signals
sig2 = sig1[::2]

NOTE: the slicing provided works by creating a reference to the underlying signals to be mapped, so at this time can't be used to set connections but only get connections. That is, the following will raise an error:

sig1 = h.Signal(width=12)
sig2 = h.Input(width=6)
# Map sig2 signals to even numbered sig1 signals
sig1[::2] = sig2

Concatenation

Signal's can be concatenated to make wider signal buses that you can use to interface with between buses of variable width. This is done using the Concat command:

a = h.Signal()
b = h.Signal(width=2)

# This is a Concat with two parts
# that is resolved into signal bus
# with a width of 3.
c = h.Concat(a,b)

The Concat command can be used with an arbitrary number of Signals, as well as recursively to create heirarchical Concat structures:

a = h.Signal()
b = h.Signal(width=2)
c = h.Signal(width=3)

# This is a Concat with three parts
# it is resolved to a width-6 bus
d = h.Concat(a,b,c)

# This is a Concat with two parts
# with objects 2-part Concat and c
# it is flattened to the same width-6 bus
d = h.Concat(h.Concat(a,b),c)

Debugging Tips

Each Module has an attribute called ports and signals which store what they are labelled respectively. Taking either of these, you can examine individual Signals to see if they've been correctly connected by checking their individual _slices, _concats and _connected_ports attributes.

Whereas, Instances contain attributes conns which list what objects an Instance's ports are connected to and _refs which keeps track of where PortRefs for a given Instance are being distributed to other Modules and Instances in your program.

Generators

Hdl21 Modules are "plain old data". They require no runtime or execution environment. They can be (and are!) fully represented in markup languages such as ProtoBuf, JSON, and YAML. The power of embedding Modules in a general-purpose programming language lies in allowing code to create and manipulate them. Hdl21's Generators are functions which produce Modules, and have a number of built-in features to aid embedding in a hierarchical hardware tree.

In other words:

Modules are "structs". Generators are functions which return Modules.
Generators are code. Modules are data.
Generators require a runtime environment. Modules do not.

Creating a generator just requires applying the @hdl21.generator decorator to a Python function:

import hdl21 as h

@h.generator
def MyFirstGenerator(params: MyParams) -> h.Module:
    # A very exciting first generator function
    m = h.Module()
    m.i = h.Input(width=params.w)
    return m

The generator-function body can define a Module however it likes - procedurally or via the class-style syntax.

@h.generator
def MySecondGenerator(params: MyParams) -> h.Module:
    # A very exciting (second) generator function
    @h.module
    class MySecondGen:
        i = h.Input(width=params.w)
    return MySecondGen

Or any combination of the two:

@h.generator
def MyThirdGenerator(params: MyParams) -> h.Module:
    # Create an internal Module
    @h.module
    class Inner:
        i = h.Input(width=params.w)

    # Manipulate it a bit
    Inner.o = h.Output(width=2 * Inner.i.width)

    # Instantiate that in another Module
    @h.module
    class Outer:
        inner = Inner()

    # And manipulate that some more too
    Outer.inp = h.Input(width=params.w)
    return Outer

Debugging Tips

Generators when they're called return GeneratorCalls, which are sufficient to validate them with respect to the rest of circuit, but don't contain the resolved Module that you might intuitively expect from the type-hinting. To get at this module the usual procedure is as follows:

MyGen = MyGenerator(params)
#  Explicitly elaborate your generator
h.elaborate(MyGen)
# Extract the resolved Module within
MyGen = MyGen.result

You can then manipulate this Module using the debugging tips provided above at the end of the Signal section.

Parameters

Generators must take a single argument params which is a collection of hdl21.Params. Generator parameters are strongly type-checked at runtime. Each requires a data-type dtype and description-string desc. Optional parameters include a default-value, which must be an instance of dtype.

# Example parameter:
nf = h.Param(dtype=int, desc="Number of parallel fingers", default=1)

The collections of these parameters used by Generators are called param-classes, and are typically formed by applying the hdl21.paramclass decorator to a class-body-full of hdl21.Params:

import hdl21 as h

@h.paramclass
class MyParams:
    # Required
    width = h.Param(dtype=int, desc="Width. Required")
    # Optional - including a default value
    text = h.Param(dtype=str, desc="Optional string", default="My Favorite Module")

Each param-class is defined similarly to the Python standard-library's dataclass. The paramclass decorator converts these class-definitions into type-checked dataclasses, with fields using the dtype of each parameter.

p = MyParams(width=8, text="Your Favorite Module")
assert p.width == 8  # Passes. Note this is an `int`, not a `Param`
assert p.text == "Your Favorite Module"  # Also passes

Similar to dataclasses, param-class constructors use the field-order defined in the class body. Note Python's function-argument rules dictate that all required arguments be declared first, and all optional arguments come last.

Param-classes can be nested, and can be converted to (potentially nested) dictionaries via dataclasses.asdict. The same conversion applies in reverse - (potentially nested) dictionaries can be expanded to serve as param-class constructor arguments:

import hdl21 as h
from dataclasses import asdict

@h.paramclass
class Inner:
    i = h.Param(dtype=int, desc="Inner int-field")

@h.paramclass
class Outer:
    inner = h.Param(dtype=Inner, desc="Inner fields")
    f = h.Param(dtype=float, desc="A float", default=3.14159)

# Create from a (nested) dictionary literal
d1 = {"inner": {"i": 11}, "f": 22.2}
o = Outer(**d1)
# Convert back to another dictionary
d2 = asdict(o)
# And check they line up
assert d1 == d2

Generators include the capability to construct their param-classes inline, if provided a set of compatible keyword arguments. For example, defining a generator using the MyParams parameters above:

@h.generator
def MyGen(params: MyParams) -> h.Module:
    ... # Create a `Module` & return it

This typical invocation:

p = MyParams(width=8, text="My Favorite Module")
MyGen(p)

is the same as calling:

MyParams(width=8, text="My Favorite Module")

Parameters may be provided as keywords, or as a single positional argument which is an instance of the generator's param-class. Combinations of the two are not supported.

Names of Generated Modules

Using Params with a Generator will generally produce a module with a name in the form of {Module_Name}_{long_string}, e.g. NmosIdac_46b3842dc8718a80a86891e28bc798e5_. This 32-character hex-string is a hash of the parameters. This rule applies when parameters are "compound", i.e. not a simple scalar.

In constrast, when the Params are all-scalar, exported modules are named with a suffixed string of the directly concatenated values, e.g. NmosIdac_nbits_5.

A Note on Parametrization

Hdl21 Generators have parameters. Modules do not.

This is a deliberate decision, which in this sense makes hdl21.Module less feature-rich than the analogous module concepts in existing HDLs (Verilog, VHDL, and even SPICE). These languages support what might be called "static parameters" - relatively simple relationships between parent and child-module parameterization. Setting, for example, the width of a signal or number of instances in an array is straightforward. But more elaborate parametrization-cases are either highly cumbersome or altogether impossible to create. (As an example, try using Verilog parametrization to make a programmable-depth binary tree.) Hdl21, in contrast, exposes all parametrization to the full Python-power of its generators.

Numeric Parameters

`Prefixed` Numbers

Hdl21 provides an SI prefixed numeric type Prefixed, which is especially common for physical generator parameters. Each Prefixed value is a combination of the Python standard library's Decimal and an enumerated SI Prefix:

@dataclass
class Prefixed:
    number: Decimal  # Numeric Portion
    prefix: Prefix   # Enumerated SI Prefix

Most of Hdl21's built-in Generators and Primitives use Prefixed extensively, for a key reason: floating-point rounding. It is commonplace for physical parameter values - e.g. the physical width of a transistor - to have allowed and disallowed values. And those values do not necessarily land on IEEE floating-point values! Hdl21 generators are often used to produce legacy-HDL netlists and other code, which must convert these values to strings. Prefixed ensures a way to do this at arbitrary scale without the possibility of rounding error.

Prefixed values rarely need to be instantiated directly. Instead Hdl21 exposes a set of common prefixes via their typical single-character names:

f = FEMTO = Prefix.FEMTO
p = PICO = Prefix.PICO
n = NANO = Prefix.NANO
µ = u = MICRO = Prefix.MICRO # Note both `u` and `µ` are valid
m = MILLI = Prefix.MILLI
K = KILO = Prefix.KILO
M = MEGA = Prefix.MEGA
G = GIGA = Prefix.GIGA
T = TERA = Prefix.TERA
P = PETA = Prefix.PETA
UNIT = Prefix.UNIT

Multiplying by these values produces a Prefixed value.

from hdl21.prefix import µ, n, f

# Create a few parameter values using them
Mos.Params(
    w=1 * µ,
    l=20 * n,
)
Capacitor.Params(
    c=1 * f,
)

These multiplications are the easiest and most common way to create Prefixed parameter values. Note the single-character identifiers µ, n, f, et al are not exported by star-exports (from hdl21 import *). They must be imported explicitly from hdl21.prefix.

hdl21.prefix also exposes an e() function which returns an Exponent type, which produces a prefix from an integer exponent value:

from hdl21.prefix import e, µ

11 * e(-6) == 11 * µ  # True

These e() values are also most common in multiplication expressions, to create Prefixed values in "floating point" style such as 11 * e(-9).

Exponent Arithmetic

The Prefix has its own arithmetic which can be accessed with *, / and **, this allows users to chain together rescaling parameters. Behind the scenes, this is done by converting the Prefix's into an Exponent type (the default type returned by the e function). For example, the following test passes:

def test_prefix_arithmetic:

    assert 1 * m * m == 1 * u
    assert 1 * (K / D) == 0.1 * K
    assert 1 * (K ** 2) == 1 * M

Exponent types support floats and also have arithmetic with *, / and ** which works using rules relating power arithmetic to these operators:

def test_exponent_arithmetic:

    assert 1 * e(0.5) * e(0.5) == 1 * e(1)
    assert 1 * e(0.5) / e(0.5) == 1 * e(0)
    assert 1 * e(0.2) ** 5 == 1 * e(1)

Mathematical Tricks

Comparison and Equality

Prefixed determines if two values are the same by comparing their difference up to 20 decimal places in their SI unit, this means that a yottameter + yoctometer is indistinguishable from a plain yottameter in Prefixed comparison logic. It's assumed this is safe because numerical errors at this scale difference compound very quickly with routine mathematics like square-roots, even with arbitrary precision arithmetic.

At this time, comparison and equality operators are not supported for the Prefix or Exponent, since these types describe scale rather than encode actual quantities, a Kilomilliwatt is just a Watt, after all.

Scale Agnostic

Prefixed in general is scale agnostic and can safely move across scales without any issue, with the prefix serving more as an indication of where the user would like to treat as units than explicit declaration of scale where no comparison can happen.

Linear Algebra

numpy supports Prefixed arrays out of the box, meaning that arrays can be used with Prefix arithmetic and used for simple linear algebra and any operations where a np.float dtype is required.

Zero Division

Dividing a Prefixed instance by 0 will return float('inf') regardless of sign.

`Scalar`

Many Hdl21 primitive parameters can be either numbers or string-literals.
The combination is so common that Hdl21 defines a Scalar type which is (roughly):

Scalar = Union[Prefixed, Literal]

With automatic conversions from each of str, int, float, and Decimal.

Scalar is particularly designed for parameter-values of Primitives and of simulations. Most such parameters "want" to be the Prefixed type, for reasons outlined above. They often also need a string-valued escape hatch, e.g. when referring to out-of-Hdl21 quantities such as parameters in external netlists or simulation decks. These out-of-Hdl21 expressions are represented by the Literal type, a simple wrapper around str.

Where possible Scalar prefers to use the Prefixed variant. Built-in numbers (int, float, Decimal) are converted to Prefixed inline. Strings are attempted to be converted to Prefixed, and fall back to Literal if unsuccessful. This conversion process is also available as the free-standing to_scalar() function.

Example:

import hdl21 as h
from hdl21.prefix import NANO, µ
from decimal import Decimal

@h.paramclass
class MyMosParams:
    w = h.Param(dtype=h.Scalar, desc="Width", default=1e-6) # Default `float` converts to a `Prefixed`
    l = h.Param(dtype=h.Scalar, desc="Length", default="w/5") # Default `str` converts to a `Literal`

# Example instantiations
MyMosParams() # Default values
MyMosParams(w=Decimal(1e-6), l=3*µ)
MyMosParams(w=h.Literal("sim_param_width"), l=h.Prefixed.new(20, NANO))
MyMosParams(w="11*l", l=11)

When defining "primitive level" parameters - e.g. those that will be used in PDK-level devices - Scalar is generally the best datatype to use.

Primitives and External Modules

The leaf-nodes of each hierarchical Hdl21 circuit are generally defined in one of two places:

Primitive elements, defined in the hdl21.primitives package. Each is designed to be a technology-independent representation of an irreducible component.
ExternalModules, defined outside Hdl21. Such "module wrappers", which might alternately be called "black boxes", are common for including circuits from other HDLs.

`Primitives`

Hdl21's library of generic primitive elements is defined in the hdl21.primitives package. Its content is roughly equivalent to that built into a typical SPICE simulator.

A summary of hdl21.primitives:

Name	Description	Type	Aliases	Ports
Mos	Mos Transistor	PHYSICAL	MOS	d, g, s, b
IdealResistor	Ideal Resistor	IDEAL	R, Res, Resistor, IdealR, IdealRes	p, n
PhysicalResistor	Physical Resistor	PHYSICAL	PhyR, PhyRes, ResPhy, PhyResistor	p, n
ThreeTerminalResistor	Three Terminal Resistor	PHYSICAL	Res3, PhyRes3, ResPhy3, PhyResistor3	p, n, b
IdealCapacitor	Ideal Capacitor	IDEAL	C, Cap, Capacitor, IdealC, IdealCap	p, n
PhysicalCapacitor	Physical Capacitor	PHYSICAL	PhyC, PhyCap, CapPhy, PhyCapacitor	p, n
ThreeTerminalCapacitor	Three Terminal Capacitor	PHYSICAL	Cap3, PhyCap3, CapPhy3, PhyCapacitor3	p, n, b
IdealInductor	Ideal Inductor	IDEAL	L, Ind, Inductor, IdealL, IdealInd	p, n
PhysicalInductor	Physical Inductor	PHYSICAL	PhyL, PhyInd, IndPhy, PhyInductor	p, n
ThreeTerminalInductor	Three Terminal Inductor	PHYSICAL	Ind3, PhyInd3, IndPhy3, PhyInductor3	p, n, b
PhysicalShort	Short-Circuit/Net-Tie	PHYSICAL	Short	p, n
DcVoltageSource	DC Voltage Source	IDEAL	V, Vdc, Vsrc	p, n
PulseVoltageSource	Pulse Voltage Source	IDEAL	Vpu, Vpulse	p, n
CurrentSource	Ideal DC Current Source	IDEAL	I, Idc, Isrc	p, n
VoltageControlledVoltageSource	Voltage Controlled Voltage Source	IDEAL	Vcvs, VCVS	p, n, cp, cn
CurrentControlledVoltageSource	Current Controlled Voltage Source	IDEAL	Ccvs, CCVS	p, n, cp, cn
VoltageControlledCurrentSource	Voltage Controlled Current Source	IDEAL	Vccs, VCCS	p, n, cp, cn
CurrentControlledCurrentSource	Current Controlled Current Source	IDEAL	Cccs, CCCS	p, n, cp, cn
Bipolar	Bipolar Transistor	PHYSICAL	Bjt, BJT	c, b, e
Diode	Diode	PHYSICAL	D	p, n

Each primitive is available in the hdl21.primitives namespace, either through its full name or any of its aliases. Most primitives have fairly verbose names (e.g. VoltageControlledCurrentSource, IdealResistor), but also expose short-form aliases (e.g. Vcvs, R). Each of the aliases in Table 1 above refer to the same Python object, i.e.

from hdl21.primitives import R, Res, IdealResistor

R is Res            # evaluates to True
R is IdealResistor  # also evaluates to True

Hdl21 Primitives come in ideal and physical flavors. The difference is most frequently relevant for passive elements, which can for example represent either

(a) technology-specific passives, e.g. a MIM or MOS capacitor, or
(b) an ideal capacitor

Some element-types have solely physical implementations, some are solely ideal, and others include both.

`ExternalModules`

Alternately Hdl21 includes an ExternalModule type which defines the interface to a module-implementation outside Hdl21. These external definitions are common for instantiating technology-specific modules and libraries. Think of them as a module "function header"; other popular modern HDLs refer to them as module black boxes.

An example ExternalModule:

import hdl21 as h
from hdl21.prefix import µ
from hdl21.primitives import Diode

@h.paramclass
class BandGapParams:
    self_destruct = h.Param(
        dtype=bool,
        desc="Whether to include the self-destruction feature",
        default=True,
    )

BandGap = h.ExternalModule(
    name="BandGap",
    desc="Example ExternalModule, defined outside Hdl21",
    port_list=[h.Port(name="vref"), h.Port(name="enable")],
    paramtype=BandGapParams,
)

Both Primitives and ExternalModules have names, ordered Ports, and a few other pieces of metadata, but no internal implementation: no internal signals, and no instances of other modules. Unlike Modules, both do have parameters. Primitives each have an associated paramclass, while ExternalModules can optionally declare one via their paramtype attribute. Their parameter-types are limited to a small subset of those possible for Generators - generally "scalar" types such as numbers, strings, and Scalar - primarily limited by the need to need to provide them to legacy HDLs. Parameters are applied in the same style as for Generators, by calling the Primitive or ExternalModule. Parameter-applications can either be an instance of the module's paramtype or a set of keyword arguments which validly construct one inline.

# Continuing from the snippet above:
params = BandGapParams(self_destruct=False)  # Watch out there!

Primitives and ExternalModules can be instantiated and connected in all the same styles as Modules:

@h.module
class BandGapPlus:
    vref, enable = h.Signals(2)
    # Instantiate the `ExternalModule` defined above
    bg = BandGap(params)(vref=vref, enable=enable)
    # ...Anything else...

@h.module
class DiodePlus:
    p, n = h.Signals(2)
    # Parameterize, instantiate, and connect a `primitives.Diode`
    d = Diode(w=1 * µ, l=1 * µ)(p=p, n=n)
    # ... Everything else ...

Exporting and Importing

Hdl21 generates hardware databases in the VLSIR interchange formats, defined through Google Protocol Buffers. Through VLSIR's Python tools Hdl21 also includes drivers for popular industry-standard data formats and popular spice-class simulation engines.

The hdl21.to_proto() function converts an Hdl21 Module or group of Modules into a VLSIR Package. The hdl21.from_proto() function similarly imports a VLSIR Package into a Python namespace of Hdl21 Modules.

Exporting to industry-standard netlist formats is a particularly common operation for Hdl21 users. The hdl21.netlist() function uses VLSIR to export any of its supported netlist formats.

import sys
import hdl21 as h

@h.module
class Rlc:
    p, n = h.Ports(2)

    res = h.Res(r=1e3)(p=p, n=n)
    cap = h.Cap(c=1e3)(p=p, n=n)
    ind = h.Ind(l=1e-9)(p=p, n=n)

# Write a spice-format netlist to stdout
h.netlist(Rlc, sys.stdout, fmt="spice")

hdl21.netlist takes a second destination argument dest, which is commonly either an open file-handle or sys.stdout.

Each Module includes a list of Literal contents, designed to be included directly in exported netlists. These are commonly used to refer to out-of-Hdl21 quantities, or to include netlist-language features not first-class supported by Hdl21. Example:

@h.module
class HasLiterals:
    a, b, c = h.Ports(3)

# Add some literal content
HasLiterals.literals.extend([
    h.Literal("generate some_verilog_code"),
    h.Literal(".some_spice_attribute what=ever"),
    h.Literal("PRAGMA: some_pragma"),
])

Module.literals is a Python built-in list and can be manipulated with any of its typical methods (append, extend, etc.). Literals are written to netlists in the order they appear in the list. Order between Literals and other Module content is not preserved.

Spice-Class Simulation

Hdl21 includes drivers for popular spice-class simulation engines commonly used to evaluate analog circuits. The hdl21.sim package includes a wide variety of spice-class simulation constructs, including:

DC, AC, Transient, Operating-Point, Noise, Monte-Carlo, Parameter-Sweep and Custom (per netlist language) Analyses
Control elements for saving signals (Save), simulation options (Options), including external files and contents (Include, Lib), measurements (Meas), simulation parameters (Param), and literal netlist commands (Literal)

The entrypoint to Hdl21-driven simulation is the simulation-input type hdl21.sim.Sim. Each Sim includes:

A testbench Module tb, and
A list of simulation attributes (attrs), including any and all of the analyses, controls, and related elements listed above.

Example:

import hdl21 as h
from hdl21.sim import *

@h.module
class MyModulesTestbench:
    # ... Testbench content ...

# Create simulation input
s = Sim(
    tb=MyModulesTestbench,
    attrs=[
        Param(name="x", val=5),
        Dc(var="x", sweep=PointSweep([1]), name="mydc"),
        Ac(sweep=LogSweep(1e1, 1e10, 10), name="myac"),
        Tran(tstop=11 * h.prefix.p, name="mytran"),
        SweepAnalysis(
            inner=[Tran(tstop=1, name="swptran")],
            var="x",
            sweep=LinearSweep(0, 1, 2),
            name="mysweep",
        ),
        MonteCarlo(
            inner=[Dc(var="y", sweep=PointSweep([1]), name="swpdc")],
            npts=11,
            name="mymc",
        ),
        Save(SaveMode.ALL),
        Meas(analysis="mytr", name="a_delay", expr="trig_targ_something"),
        Include("/home/models"),
        Lib(path="/home/models", section="fast"),
        Options(reltol=1e-9),
    ],
)

# And run it!
s.run()

Sim also includes a class-based syntax similar to Module and Bundle. This also allows for inline definition of a testbench module, which can be named either tb or Tb:

import hdl21 as h
from hdl21.sim import *

@sim
class MySim:

    @h.module
    class Tb:
        # ... Testbench content ...

    x = Param(5)
    y = Param(6)
    mydc = Dc(var=x, sweep=PointSweep([1]))
    myac = Ac(sweep=LogSweep(1e1, 1e10, 10))
    mytran = Tran(tstop=11 * h.prefix.PICO)
    mysweep = SweepAnalysis(
        inner=[mytran],
        var=x,
        sweep=LinearSweep(0, 1, 2),
    )
    mymc = MonteCarlo(inner=[Dc(var="y", sweep=PointSweep([1]), name="swpdc")], npts=11)
    delay = Meas(analysis=mytran, expr="trig_targ_something")
    opts = Options(reltol=1e-9)

    save_all = Save(SaveMode.ALL)
    a_path = "/home/models"
    include_that_path = Include(a_path)
    fast_lib = Lib(path=a_path, section="fast")

MySim.run()

Note that in these class-based definitions, attributes whose names don't really matter such as save_all above can be named anything, but must be assigned into the class, not just constructed.

Class-based Sim definitions retain all class members which are SimAttrs and drop all others. Non-SimAttr-valued fields can nonetheless be handy for defining intermediate values upon which the ultimate SimAttrs depend, such as the a_path field in the example above.

Classes decorated by @sim have a single special required field: a testbench attribute, named either tb or Tb, which sets the simulation testbench. A handful of names are disallowed in sim class-definitions, generally corresponding to the names of the Sim class's fields and methods such as attrs and run.

Each sim also includes a set of methods to add simulation attributes from their keyword constructor arguments. These methods use the same names as the simulation attributes (Dc, Meas, etc.) but incorporating the python language convention that functions and methods be lowercase (dc, meas, etc.). Example:

# Create a `Sim`
s = Sim(tb=MyTb)

# Add all the same attributes as above
p = s.param(name="x", val=5)
dc = s.dc(var=p, sweep=PointSweep([1]), name="mydc")
ac = s.ac(sweep=LogSweep(1e1, 1e10, 10), name="myac")
tr = s.tran(tstop=11 * h.prefix.p, name="mytran")
noise = s.noise(
    output=MyTb.p,
    input_source=MyTb.v,
    sweep=LogSweep(1e1, 1e10, 10),
    name="mynoise",
)
sw = s.sweepanalysis(inner=[tr], var=p, sweep=LinearSweep(0, 1, 2), name="mysweep")
mc = s.montecarlo(
    inner=[Dc(var="y", sweep=PointSweep([1]), name="swpdc"),], npts=11, name="mymc",
)
s.save(SaveMode.ALL)
s.meas(analysis=tr, name="a_delay", expr="trig_targ_something")
s.include("/home/models")
s.lib(path="/home/models", section="fast")
s.options(reltol=1e-9)

# And run it!
s.run()

Process Technologies

Designing for a specific implementation technology (or "process development kit", or PDK) with Hdl21 can use either of (or a combination of) two routes:

Instantiate ExternalModules corresponding to the target technology. These would commonly include its process-specific transistor and passive modules, and potentially larger cells, for example from a cell library. Such external modules are frequently defined as part of a PDK (python) package, but can also be defined anywhere else, including inline among Hdl21 generator code.
Use hdl21.Primitives, each of which is designed to be a technology-independent representation of a primitive component. Moving to a particular technology then generally requires passing the design through an hdl21.pdk's compile function.

Hdl21 PDKs are Python packages which generally include two primary elements:

(a) A library ExternalModules describing the technology's cells, and
(b) A compile conversion-method which transforms a hierarchical Hdl21 tree, mapping generic hdl21.Primitives into the tech-specific ExternalModules.

Since PDKs are python packages, using them is as simple as importing them. Hdl21 includes a built-in sample PDK available via hdl21.pdk.sample_pdk which includes simulatable NMOS and PMOS transistors. Hdl21's source tree includes three additional PDK packages:

	PyPi	Source
ASAP7 Predictive/Academic PDK	https://pypi.org/project/asap7-hdl21/	pdks/Asap7
SkyWater 130nm Open-Source PDK	https://pypi.org/project/sky130-hdl21/	pdks/Sky130
GlobalFoundries 180nm Open-Source PDK	https://pypi.org/project/gf180-hdl21/	pdks/Gf180

Each contain much more detail documentation on their specific installation and use.

import hdl21 as h
import sky130_hdl21

@h.module
class SkyInv:
    """ An inverter, demonstrating using PDK modules """

    # Create some IO
    i, o, VDD, VSS = h.Ports(4)

    p = sky130_hdl21.Sky130MosParams(w=1,l=1)

    # And create some transistors!
    ps = sky130_hdl21.primitives.PMOS_1p8V_STD(p)(d=o, g=i, s=VDD, b=VDD)
    ns = sky130_hdl21.primitives.NMOS_1p8V_STD(p)(d=o, g=i, s=VSS, b=VSS)

Process-portable modules instead use Hdl21 Primitives, which can be compiled to a target technology:

import hdl21 as h
from hdl21.prefix import µ
from hdl21.primitives import Nmos, Pmos, MosVth

@h.module
class Inv:
    """ An inverter, demonstrating instantiating PDK modules """

    # Create some IO
    i, o, VDD, VSS = h.Ports(4)

    # And now create some generic transistors!
    ps = Pmos(w=1*µ, l=1*µ, vth=MosVth.STD)(d=o, g=i, s=VDD, b=VDD)
    ns = Nmos(w=1*µ, l=1*µ, vth=MosVth.STD)(d=o, g=i, s=VSS, b=VSS)

Compiling the generic devices to a target PDK then just requires a pass through the PDK's compile() method:

import hdl21 as h
import sky130_hdl21

sky130_hdl21.compile(Inv) # Produces the same content as `SkyInv` above

Hdl21 includes an hdl21.pdk subpackage which tracks the available in-memory PDKs. If there is a single PDK available, it need not be explicitly imported: hdl21.pdk.compile() will use it by default.

import hdl21 as h
import sky130  # Note this import can be elsewhere in the program, i.e. in a configuration layer.

h.pdk.compile(Inv)  # With `sky130` in memory, this does the same thing as above.

PDK Corners

The hdl21.pdk package inclues a three-valued Corner enumerated type and related classes for describing common process-corner variations. In pseudo type-union code:

Corner = TYP | SLOW | FAST

Typical technologies includes several quantities which undergo such variations. Values of the Corner enum can mean either the variations in a particular quantity, e.g. the "slow" versus "fast" variations of a poly resistor, or can just as oftern refer to a set of such variations within a given technology. In the latter case Corner values are often expanded by PDK-level code to include each constituent device variation. For example my.pdk.corner(Corner.FAST) may expand to definitions of "fast" Cmos transistors, resistors, and capacitors.

Quantities which can be varied are often keyed by a CornerType. In similar pseudo-code:

CornerType = MOS | CMOS | RES | CAP | ...

A particularly common such use case pairs NMOS and PMOS transistors into a CmosCornerPair. CMOS circuits are then commonly evauated at its four extremes, plus their typical case. These five conditions are enumerated in the CmosCorner type:

@dataclass
class CmosCornerPair:
    nmos: Corner
    pmos: Corner

CmosCorner = TT | FF | SS | SF | FS

Hdl21 exposes each of these corner-types as Python enumerations and combinations thereof. Each PDK package then defines its mapping from these Corner types to the content they include, typically in the form of external files.

PDK Installations and Sites

Much of the content of a typical process technology - even the subset that Hdl21 cares about - is not defined in Python. Transistor models and SPICE "library" files, such as those defining the PMOS and NMOS above, are common examples pertinent to Hdl21. Tech-files, layout libraries, and the like are similarly necessary for related pieces of EDA software. These PDK contents are commonly stored in a technology-specific arrangement of interdependent files. Hdl21 PDK packages structure this external content as a PdkInstallation type.

Each PdkInstallation is a runtime type-checked Python dataclass which extends the base hdl21.pdk.PdkInstallation type. Installations are free to define arbitrary fields and methods, which will be type-validated for each Install instance. Example:

""" A sample PDK package with an `Install` type """

from pydantic.dataclasses import dataclass
from hdl21.pdk import PdkInstallation

@dataclass
class Install(PdkInstallation):
    """Sample Pdk Installation Data"""

    model_lib: Path  # Filesystem `Path` to transistor models

The name of each PDK's installation-type is by convention Install with a capital I. PDK packages which include an installation-type also conventionally include an Install instance named install, with a lower-case i. Code using the PDK package can then refer to the PDK's install attribute. Extending the example above:

""" A sample PDK package with an `Install` type """

@dataclass
class Install(PdkInstallation):
    """Sample Pdk Installation Data"""

    model_lib: Path  # Filesystem `Path` to transistor models

install: Optional[Install] = None  # The active installation, if any

The content of this installation data varies from site to site. To enable "site-portable" code to use the PDK installation, Hdl21 PDK users conventionally define a "site-specific" module or package which:

Imports the target PDK module
Creates an instance of its PdkInstallation subtype
Affixes that instance to the PDK package's install attribute

For example:

# In "sitepdks.py" or similar
import mypdk

mypdk.install = mypdk.Install(
    models = "/path/to/models",
    path2 = "/path/2",
    # etc.
)

These "site packages" are named sitepdks by convention. They can often be shared among several PDKs on a given filesystem. Hdl21 includes one built-in example such site-package, SampleSitePdks, which demonstrates setting up both built-in PDKs, Sky130 and ASAP7:

# The built-in sample `sitepdks` package
from pathlib import Path

import sky130_hdl21
sky130_hdl21.install = sky130_hdl21.Install(model_lib=Path("pdks") / "sky130" / ... / "sky130.lib.spice")

import asap7_hdl21
asap7_hdl21.install = asap7_hdl21.Install(model_lib=Path("pdks") / "asap7" / ... / "TT.pm")

"Site-portable" code requiring external PDK content can then refer to the PDK package's install, without being directly aware of its contents. An example simulation using mypdk's models with the sitepdks defined above:

# sim_my_pdk.py
import hdl21 as h
from hdl21.sim import Lib
import sitepdks as _ # <= This sets up `mypdk.install`
import mypdk

@h.sim
class SimMyPdk:
    # A set of simulation input using `mypdk`'s installation
    tb = MyTestBench()
    models = Lib(
        path=mypdk.install.models, # <- Here
        section="ss"
    )

# And run it!
SimMyPdk.run()

Note that sim_my_pdk.py need not necessarily import or directly depend upon sitepdks itself. So long as sitepdks is imported and configures the PDK installation anywhere in the Python program, further code will be able to refer to the PDK's install fields.

Creating PDK Packages

Hdl21's source tree includes a cookiecutter template for creating a new PDK package, available at pdks/PdkTemplate.

Bundles

Hdl21 Bundles are structured connection types which can include Signals and instances of other Bundles. Think of them as "connection structs". Similar ideas are implemented by Chisel's Bundles and SystemVerilog's interfaces.

@h.bundle
class Diff:
    p = h.Signal()
    n = h.Signal()

@h.bundle
class Quadrature:
    i = Diff()
    q = Diff()

Like Modules, Bundles can be defined either procedurally or as a class decorated by the hdl21.bundle function.

# This creates the same stuff as the class-based definitions above:

Diff = h.Bundle(name="Diff")
Diff.add(h.Signal(name="p"))
Diff.add(h.Signal(name="n"))

Quadrature = h.Bundle(name="Quadrature")
Quadrature.add(Diff(name="i"))
Quadrature.add(Diff(name="q"))

Calling a Bundle as in the calls to Diff() and Diff(name=q) creates an instance of that Bundle.

Bundle Ports

Bundles are commonly most valuable for shipping collections of related Signals between Modules. Modules can accordingly have Bundle-valued ports. To create a Bundle-port, set the port argument to either the boolean True or the hdl21.Visibility.PORT value.

@h.module
class HasDiffs:
    d1 = Diff(port=True)
    d2 = Diff(port=h.Visbility.PORT)

Port directions on bundle-ports can be set by either of two methods. The first is to set the directions directly on the Bundle's constituent Signals. To swap directions, pass the bundle-instances through the hdl21.flipped function, or set the flipped argument to the instance-constructor.

@h.bundle
class Inner:
    i = h.Input()
    o = h.Output()

@h.bundle
class Outer:
    b1 = Inner()
    b2 = h.flipped(Inner())
    b3 = Inner(flipped=True)

Here:

An Inner bundle defines an Input and an Output
An Outer bundle instantiates three of them
- Instance b1 is not flipped; its i is an input, and its o is an output
- Instance b2 is flipped; its i is an output, and its o is an input
- Instance b3 is also flipped, via its constructor argument

These "flipping based" bundles require that all constituent signals, including nested ones, have port-visibility. The rules for flipping port directions are:

Inputs become Outputs
Outputs become Inputs
Inouts and undirected ports (direction=NONE) retain their directions

@h.bundle
class B:
    clk = h.Output()
    data = h.Input()

@h.module
class X: # Module with a `clk` output and `data` input
    b = B(port=True)

@h.module
class Y: # Module with a `clk` input and `data` output
    b = B(flipped=True, port=True)

@h.module
class Z:
    b = B() # Internal instance of the `B` bundle
    x = X(b=b)
    y = Y(b=b)

The second method for setting bundle-port directions is with Roles. Each Hdl21 bundle either explicitly or implicitly defines a set of Roles, which might alternately be called "endpoints". These are the expected "end users" of the Bundle. Signal directions are then defined on each signal's src (source) and dest (destination) arguments, which can be set to any of the bundle's roles.

@h.roles
class HostDevice(Enum):
    HOST = auto()
    DEVICE = auto()

@h.bundle
class Jtag:
    roles = HostDevice # Set the bundle's roles
    # Note each signal sets one of the roles as `src` and another as `dest`
    tck, tdi, tms = h.Signals(3, src=roles.HOST, dest=roles.DEVICE)
    tdo = h.Signal(src=roles.DEVICE, dest=roles.HOST)

Bundle-valued ports are then assigned a role and associated signal-port directions via their role constructor argument.

@h.module
class Widget: # with a Jtag Device port
    jtag = Jtag(port=True, role=Jtag.roles.DEVICE)

@h.module
class Debugger: # with a Jtag Host port
    jtag = Jtag(port=True, role=Jtag.roles.HOST)

@h.module
class System: # combining the two
    widget = Widget()
    debugger = Debugger(jtag=widget.jtag)

The rules for port-directions of role-based bundles are:

If the bundle's role is the signal's source, the signal is an Output
If the bundle's role is the signal's destination, the signal is an Input
Otherwise the signal is assigned no direction, i.e. direction=NONE

Collecting Bundles

It is often helpful or necessary to collect existing signals into a bundle, or to "re-arrange" signals from one bundle into another. The primary mechanism for doing so is the hdl21.bundlize function which creates them. Each call to bundlize creates an "anonymous" bundle which lacks a backing bundle-definition type.

@h.bundle
class Uart:
    tx = h.Output()
    rx = h.Input()

@h.module
class HasUart:
    # Module with a `Uart` port
    uart = Uart(port=True)

@h.module
class ConnectTwo:
    # Connect two `HasUart`s, swapping `tx` and `rx`.
    uart = Uart()
    m1 = HasUart(uart=uart)
    m2 = HasUart(uart=h.bundlize(tx=uart.rx, rx=uart.tx))

Examples

Built-In Examples Library

Hdl21's source tree includes a built-in examples library. Each is designed to be a straightforward but realistic use-case, and is a self-contained Python program which can be run directly, e.g. with:

python examples/rdac.py

The built-in examples include:

Reading, copying, or cloning these example programs is generally among the best ways to get started.
And adding an example is a highly encouraged form of pull request!

Featured Community Examples

Continuous-Time Delta-Sigma ADC Generators
USB 2.0 PHY
VCO-Based ADC Generators (Coming soon!)

Related Projects

Why Use Python?

Custom IC design is a complicated field. Its practitioners have to know a | lot | of | stuff, independent of any programming background. Many have little or no programming experience at all. Python is renowned for its accessibility to new programmers, largely attributable to its concise syntax, prototyping-friendly execution model, and thriving community. Moreover, Python has also become a hotbed for many of the tasks hardware designers otherwise learn programming for: numerical analysis, data visualization, machine learning, and the like.

Hdl21 exposes the ideas they're used to - Modules, Ports, Signals - via as simple of a Python interface as it can. Generators are just functions. For many, this fact alone is enough to create powerfully reusable hardware.

Why Not Use {X}?

We know you have plenty of choice when you fly, and appreciate you choosing Hdl21.
A few alternatives and how they compare:

Schematics

Graphical schematics have been the lingua franca of the custom-circuit field for, well, as long as it's been around. Most practitioners are most comfortable in this graphical form. (For plenty of circuits, so are Hdl21's authors.) Their most obvious limitation is the lack of capacity for programmable manipulation via something like Hdl21 Generators. Some schematic-GUI programs attempt to include "embedded scripting", perhaps even in Hdl21's own language (Python). We see those GUIs as entombing your programs in their badness. Hdl21 is instead a library, designed to be used by any Python program you like, sharable and runnable by anyone who has Python. (Which is everyone.)

Netlists (Spice et al)

Take all of the shortcomings listed for schematics above, and add to them an under-expressive, under-specified, ill-formed, incomplete suite of "programming languages", and you've got netlists. Their primary redeeming quality: existing EDA CAD tools take them as direct input. So Hdl21 Modules export netlists of most popular formats instead.

(System)Verilog, VHDL, other Existing Dedicated HDLs

The industry's primary, 80s-born digital HDLs Verilog and VHDL have more of the good stuff we want here - notably an open, text-based format, and a more reasonable level of parametrization. And they have the desirable trait of being primary input to the EDA industry's core tools. They nonetheless lack the levels of programmability present here. And they generally require one of those EDA tools to execute and do, well, much of anything. Parsing and manipulating them is well-reknowned for requiring a high pain tolerance. Again Hdl21 sees these as export formats.

Chisel

Explicitly designed for digital-circuit generators at the same home as Hdl21 (UC Berkeley), Chisel encodes RTL-level hardware in Scala-language classes. It's the closest of the alternatives in spirit to Hdl21. (And it's aways more mature.) If you want big, custom, RTL-level circuits - processors, full SoCs, and the like - you should probably turn to Chisel instead. Chisel makes a number of decisions that make it less desirable for custom circuits, and have accordingly kept their designers' hands-off.

The Chisel library's primary goal is producing a compiler-style intermediate representation (FIRRTL) to be manipulated by a series of compiler-style passes. We like the compiler-style IR (and may some day output FIRRTL). But custom circuits really don't want that compiler. The point of designing custom circuits is dictating exactly what comes out - the compiler output. The compiler is, at best, in the way.

Next, Chisel targets RTL-level hardware. This includes lots of things that would need something like a logic-synthesis tool to resolve to the structural circuits targeted by Hdl21. For example in Chisel (as well as Verilog and VHDL), it's semantically valid to perform an operation like Signal + Signal. In custom-circuit-land, it's much harder to say what that addition-operator would mean. Should it infer a digital adder? Short two currents together? Stick two capacitors in series? Many custom-circuit primitives such as individual transistors actively fight the signal-flow/RTL modeling style assumed by the Chisel semantics and compiler. Again, it's in the way. Perhaps more important, many of Chisel's abstractions actively hide much of the detail custom circuits are designed to explicitly create. Implicit clock and reset signals serve as prominent examples.

Above all - Chisel is embedded in Scala. It's niche, it's complicated, it's subtle, it requires dragging around a JVM. It's not a language anyone would recommend to expert-designer/novice-programmers for any reason other than using Chisel. For Hdl21's goals, Scala itself is Chisel's biggest burden.

Other Fancy Modern HDLs

There are lots of other very cool hardware-description projects out there which take Hdl21's big-picture approach - embedding hardware idioms as a library in a modern programming language. All focus on logical and/or RTL-level descriptions, unlike Hdl21's structural/custom/analog focus. We recommend checking them out:

Development

Clone this repository & navigate to it.
bash scripts/install-dev.sh. See the note below.
pytest -s should yield something like:

$ pytest -s
============================ test session starts =============================
collected 126 items

hdl21/pdk/test_pdk.py ...
hdl21/pdk/sample_pdk/test_sample_pdk.py ...
hdl21/sim/tests/test_sim.py .........s
hdl21/tests/test_builtin_generators.py ..
hdl21/tests/test_bundles.py ............
hdl21/tests/test_conns.py ..............
hdl21/tests/test_exports.py x............
hdl21/tests/test_hdl21.py ...............x..............x...x........x...
hdl21/tests/test_params.py .....x
hdl21/tests/test_prefix.py ..........
hdl21/tests/test_source_info.py .
pdks/Asap7/asap7/test_asap7.py .
pdks/Sky130/sky130/test_sky130.py ....

================= 119 passed, 1 skipped, 6 xfailed in 0.55s ==================

Note: Hdl21 is commonly co-developed with the VLSIR interchange formats. The scripts folder includes two short installation scripts which install VLSIR from either PyPi or GitHub. Tweaks to PyPi-released versions Hdl21 may be able to use the PyPi versions of VLSIR. Most Hdl21 development cannot, and should clone VLSIR from GitHub. The install-dev script will install VLSIR alongside Hdl21/, i.e. in the parent directory of the Hdl21 clone.

Name		Name	Last commit message	Last commit date
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.github/workflows		.github/workflows
.vscode		.vscode
SampleSitePdks		SampleSitePdks
examples		examples
hdl21		hdl21
pdks		pdks
scratch		scratch
scripts		scripts
.gitignore		.gitignore
.pre-commit-config.yaml		.pre-commit-config.yaml
Cargo.toml		Cargo.toml
LICENSE		LICENSE
conftest.py		conftest.py
pyproject.toml		pyproject.toml
readme.md		readme.md

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HDL21

Analog Hardware Description Library in Python

Contents

Installation

Modules

Signals

Connections

Slicing

Concatenation

Debugging Tips

Generators

Debugging Tips

Parameters

Names of Generated Modules

A Note on Parametrization

Numeric Parameters

Prefixed Numbers

Exponent Arithmetic

Mathematical Tricks

Comparison and Equality

Scale Agnostic

Linear Algebra

Zero Division

Scalar

Primitives and External Modules

Primitives

ExternalModules

Exporting and Importing

Spice-Class Simulation

Process Technologies

PDK Corners

PDK Installations and Sites

Creating PDK Packages

Bundles

Bundle Ports

Collecting Bundles

Examples

Built-In Examples Library

Featured Community Examples

Related Projects

Why Use Python?

Why Not Use {X}?

Schematics

Netlists (Spice et al)

(System)Verilog, VHDL, other Existing Dedicated HDLs

Chisel

Other Fancy Modern HDLs

Development

About

Resources

License

Stars

Watchers

Forks

Releases

Packages 0

Contributors 9

Languages

`Prefixed` Numbers

`Scalar`

`Primitives`

`ExternalModules`

Packages