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AIFloats.jl

The internal constructive model for MicroFloats. A Julia package for modeling and working with abstract and concrete floating point types, supporting both signed/unsigned and finite/extended (Inf-supporting) variants.

Table of Contents

Overview

AIFloats.jl provides a flexible and extensible framework for defining and working with floating-point types. This includes support for various encodings, bit widths, signedness, and finite or extended (Inf-supporting) domains. It is intended for research, experimentation, or custom numerical types.

Installation

import Pkg
Pkg.add(url="https://github.com/JeffreySarnoff/AIFloats.jl.git")

Module Exports

The main exports from the AIFloats module are:

Abstract Types

  • AbstractAIFloat
  • AbstractUnsigned / AbstractUnsignedFinite / AbstractUnsignedExtended
  • AbstractSigned / AbstractSignedFinite / AbstractSignedExtended

Concrete Types & Constructors

  • floats, codes
  • AIFloat — generalized constructor
  • UnsignedFinite, UnsignedExtended
  • SignedFinite, SignedExtended

Typed Predicates

  • is_aifloat, is_unsigned, is_signed, is_finite, is_extended

Functions Over Types

  • encoding_sequence, value_sequence
  • foundation_magnitudes

Bit/Value Counts

  • nBits, nSigBits, nFracBits, nSignBits, nExpBits
  • nNaNs, nZeros, nInfs, nPosInfs, nNegInfs
  • nPrenormalMagnitudes, nSubnormalMagnitudes, nNormalMagnitudes, nMagnitudes
  • nValues, nNumericValues, nNonzeroNumericValues
  • nMagnitudes, nNonzeroMagnitudes
  • nExpValues, nNonzeroExpValues
  • nFiniteValues, nNonzeroFiniteValues

Exponent Utilities

  • expBias, expUnbiasedValues, expMinValue, expMaxValue, expValues

Julia Support Functions

  • index1, value_to_index, index_to_value, floatleast
  • ulp_distance

Core Concepts

  • AbstractAIFloat: Root for all AI float types.
  • Signedness: Support for both signed and unsigned floats.
  • Finiteness: Both finite (no infinities) and extended (with ±Inf) types.
  • Bit Layout: Customizable bit widths, exponent, and significand size.

Type Hierarchy

AbstractAIFloat
 ├─ AbstractUnsigned
 │   ├─ AbstractUnsignedFinite
 │   └─ AbstractUnsignedExtended
 └─ AbstractSigned
     ├─ AbstractSignedFinite
     └─ AbstractSignedExtended

Concrete types are constructed via the AIFloat function and specialized subtypes, parameterized by bit width, significand bits, signedness, and extension.

Key Functions

Generalized Constructor

AIFloat(bits::Int, sigbits::Int; signed::Bool, extended::Bool)
  • Instantiates the appropriate AI float concrete type depending on the parameters.

Typed Predicates

  • is_aifloat(x): True if x is an AI float type.
  • is_unsigned(x), is_signed(x), is_finite(x), is_extended(x): Type properties.

Bit/Value Analysis

  • Functions such as nBits, nSigBits, nExpBits, nMagnitudes, nValues, etc., return details about the bit structure and value set for a given type.

Sequences

  • encoding_sequence, value_sequence, foundation_magnitudes: Enumerate underlying representations and corresponding values.

Julia Support

  • Indexing and conversion helpers: index1, value_to_index, index_to_value, floatleast, ulp_distance.

Usage Examples

Constructing a Custom Float Type

using AIFloats

# Create a 16-bit signed, extended (Inf-supporting) float type
T = AIFloat(16, 11; signed=true, extended=true)

# Query some properties
nBits(T)            # Number of bits
nFiniteValues(T)    # Number of finite representable values

Checking Type Properties

is_signed(T)   # true
is_extended(T) # true

Dependencies

Development

The main module includes and organizes its logic across several source files:

  • type/constants.jl — type-level constants
  • type/abstract.jl — abstract type definitions
  • support/indices.jl — helper functions for indexing
  • concrete/encodings.jl — concrete encoding definitions
  • concrete/foundation.jl — foundation logic for concrete types
  • concrete/unsigned.jl and concrete/signed.jl — unsigned/signed types
  • support/julialang.jl — Julia language support and integration

License

[Specify your license here.]

Note: For further details, please refer to the individual source files and Julia docstrings as implemented in the codebase.