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float16 package - github.com/zerfoo/float16 - Go Packages

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float16

package module
v1.0.0 Latest Latest

This package is not in the latest version of its module.

 Go to latest Published: Mar 30, 2026 License: Apache-2.0 Imports: 6 Imported by: 12
Main Versions Licenses Imports Imported By

Details

Repository

github.com/zerfoo/float16

Links

README

README

float16

IEEE 754-2008 half-precision (Float16) and BFloat16 arithmetic library for Go.

Part of the Zerfoo ML ecosystem.

Features

  • Full IEEE 754-2008 compliance for 16-bit floating-point arithmetic
  • BFloat16 support — Google Brain format for ML training and inference
  • Special value handling — ±0, ±Inf, NaN (with payload), normalized and subnormal numbers
  • Multiple rounding modes — nearest-even, toward zero, toward ±Inf, nearest-away
  • Vectorized operations — batch add, multiply, and dot product
  • Fast math mode — optional lookup-table acceleration for performance-critical paths
  • Zero dependencies — pure Go, no CGo

Installation

go get github.com/zerfoo/float16

Requires Go 1.26+.

Quick Start

package main

import (
    "fmt"
    "github.com/zerfoo/float16"
)

func main() {
    a := float16.FromFloat32(3.14159)
    b := float16.FromFloat32(2.71828)

    sum := a.Add(b)
    product := a.Mul(b)

    fmt.Printf("Sum: %f\n", sum.ToFloat32())
    fmt.Printf("Product: %f\n", product.ToFloat32())

    // Special values
    inf := float16.Inf(1)
    fmt.Printf("Inf: %v, IsInf: %v\n", inf, inf.IsInf(0))
}

Conversion

// From float32/float64
f16 := float16.FromFloat32(3.14)
f16 := float16.FromFloat64(2.718)

// From bit representation
f16 := float16.FromBits(0x4200) // 3.0

// Back to native types
f32 := f16.ToFloat32()
f64 := f16.ToFloat64()

Rounding Modes

config := float16.GetConfig()
config.DefaultRoundingMode = float16.RoundTowardZero
float16.Configure(config)

// RoundNearestEven (default), RoundTowardZero, RoundTowardPositive,
// RoundTowardNegative, RoundNearestAway

Range and Precision

Property Value
Range ±65,504
Precision ~3-4 decimal digits
Smallest normal ~6.10 × 10⁻⁵
Smallest subnormal ~5.96 × 10⁻⁸
Machine epsilon ~9.77 × 10⁻⁴

Used By

  • ztensor — GPU-accelerated tensor library

License

Apache 2.0

Documentation

Overview

Package float16 implements both 16-bit floating point data types: - Float16: IEEE 754-2008 half-precision (1 sign, 5 exponent, 10 mantissa bits) - BFloat16: "Brain Floating Point" format (1 sign, 8 exponent, 7 mantissa bits)

This implementation provides conversion between both types and other floating-point types (float32 and float64) with support for various rounding modes and error handling.

Special Values

The float16 type supports all IEEE 754-2008 special values:

  • Positive and negative zero
  • Positive and negative infinity
  • Not-a-Number (NaN) values with payload
  • Normalized numbers
  • Subnormal (denormal) numbers

Subnormal Numbers

When converting to higher-precision types (float32/float64), subnormal float16 values are preserved. However, when converting back from higher-precision types to float16, subnormal values may be rounded to the nearest representable normal float16 value. This behavior is consistent with many hardware implementations that handle subnormals in a similar way for performance reasons.

Rounding Modes

The following rounding modes are supported for conversions:

  • RoundNearestEven: Round to nearest, ties to even (default)
  • RoundTowardZero: Round toward zero (truncate)
  • RoundTowardPositive: Round toward positive infinity
  • RoundTowardNegative: Round toward negative infinity
  • RoundNearestAway: Round to nearest, ties away from zero

Error Handling

Conversion functions with a ConversionMode parameter can return errors for:

  • Overflow: When a value is too large to be represented
  • Underflow: When a value is too small to be represented (in strict mode)
  • Inexact: When rounding occurs (in strict mode)

See: http://en.wikipedia.org/wiki/Half-precision_floating-point_format

Index

Constants

View Source 
const (
	BFloat16SignMask     = 0x8000 // 0b1000000000000000 - Sign bit mask
	BFloat16ExponentMask = 0x7F80 // 0b0111111110000000 - Exponent bits mask
	BFloat16MantissaMask = 0x007F // 0b0000000001111111 - Mantissa bits mask
	BFloat16MantissaLen  = 7      // Number of mantissa bits
	BFloat16ExponentLen  = 8      // Number of exponent bits

	// Exponent bias and limits for BFloat16
	// bias = 2^(exponent_bits-1) - 1 = 2^7 - 1 = 127 (same as Float32)
	BFloat16ExponentBias = 127 // Bias for 8-bit exponent
	BFloat16ExponentMax  = 255 // Maximum exponent value
	BFloat16ExponentMin  = 0   // Minimum exponent value

	// Normalized exponent range
	BFloat16ExponentNormalMin = 1   // Minimum normalized exponent
	BFloat16ExponentNormalMax = 254 // Maximum normalized exponent (infinity at 255)

	// Special exponent values
	BFloat16ExponentZero     = 0   // Zero and subnormal numbers
	BFloat16ExponentInfinity = 255 // Infinity and NaN
)

BFloat16 format constants

View Source 
const (
	Version      = "1.0.0"
	VersionMajor = 1
	VersionMinor = 0
	VersionPatch = 0
)

Package version information

View Source 
const (
	SignMask     = 0x8000 // 0b1000000000000000 - Sign bit mask
	ExponentMask = 0x7C00 // 0b0111110000000000 - Exponent bits mask
	MantissaMask = 0x03FF // 0b0000001111111111 - Mantissa bits mask
	MantissaLen  = 10     // Number of mantissa bits
	ExponentLen  = 5      // Number of exponent bits

	// Exponent bias and limits for IEEE 754 half-precision
	// bias = 2^(exponent_bits-1) - 1 = 2^4 - 1 = 15
	ExponentBias = 15 // Bias for 5-bit exponent
	ExponentMax  = 31 // Maximum exponent value (11111 binary)
	ExponentMin  = 0  // Minimum exponent value

	// Normalized exponent range
	ExponentNormalMin = 1  // Minimum normalized exponent
	ExponentNormalMax = 30 // Maximum normalized exponent (infinity at 31)

	// Float32 constants for conversion
	Float32ExponentBias = 127 // IEEE 754 single precision bias
	Float32ExponentLen  = 8   // Float32 exponent bits
	Float32MantissaLen  = 23  // Float32 mantissa bits

	// Special exponent values
	ExponentZero     = 0  // Zero and subnormal numbers
	ExponentInfinity = 31 // Infinity and NaN
)

IEEE 754 half-precision format constants

Variables

View Source 
var (
	DefaultArithmeticMode = ModeIEEEArithmetic
	DefaultRounding       = DefaultRoundingMode
)

Global arithmetic settings

View Source 
var (
	BFloat16Zero  = BFloat16PositiveZero
	BFloat16One   = BFloat16FromFloat32(1.0)
	BFloat16Two   = BFloat16FromFloat32(2.0)
	BFloat16Half  = BFloat16FromFloat32(0.5)
	BFloat16E     = BFloat16FromFloat32(float32(math.E))
	BFloat16Pi    = BFloat16FromFloat32(float32(math.Pi))
	BFloat16Sqrt2 = BFloat16FromFloat32(float32(math.Sqrt2))
)

Convenience constants for common BFloat16 values

View Source 
var (
	DefaultConversionMode ConversionMode = ModeIEEE
	DefaultRoundingMode   RoundingMode   = RoundNearestEven
)
View Source 
var (
	// Common integer values
	Zero16  = PositiveZero
	One16   = FromFloat32(1.0)
	Two16   = FromFloat32(2.0)
	Three16 = FromFloat32(3.0)
	Four16  = FromFloat32(4.0)
	Five16  = FromFloat32(5.0)
	Ten16   = FromFloat32(10.0)

	// Common fractional values
	Half16    = FromFloat32(0.5)
	Quarter16 = FromFloat32(0.25)
	Third16   = FromFloat32(1.0 / 3.0)

	// Special mathematical values
	NaN16  = QuietNaN
	PosInf = PositiveInfinity
	NegInf = NegativeInfinity

	// Commonly used constants
	Deg2Rad = FromFloat32(float32(math.Pi / 180.0)) // Degrees to radians
	Rad2Deg = FromFloat32(float32(180.0 / math.Pi)) // Radians to degrees
)

Constants for common values

View Source 
var (
	E       = FromFloat32(float32(math.E))       // Euler's number
	Pi      = FromFloat32(float32(math.Pi))      // Pi
	Phi     = FromFloat32(float32(math.Phi))     // Golden ratio
	Sqrt2   = FromFloat32(float32(math.Sqrt2))   // Square root of 2
	SqrtE   = FromFloat32(float32(math.SqrtE))   // Square root of E
	SqrtPi  = FromFloat32(float32(math.SqrtPi))  // Square root of Pi
	SqrtPhi = FromFloat32(float32(math.SqrtPhi)) // Square root of Phi
	Ln2     = FromFloat32(float32(math.Ln2))     // Natural logarithm of 2
	Log2E   = FromFloat32(float32(math.Log2E))   // Base-2 logarithm of E
	Ln10    = FromFloat32(float32(math.Ln10))    // Natural logarithm of 10
	Log10E  = FromFloat32(float32(math.Log10E))  // Base-10 logarithm of E
)

Mathematical constants as Float16 values

Functions

func BFloat16Equal added in v0.2.0 

func BFloat16Equal(a, b BFloat16) bool

BFloat16Equal returns true if a equals b

func BFloat16Greater added in v0.2.0 

func BFloat16Greater(a, b BFloat16) bool

BFloat16Greater returns true if a > b

func BFloat16GreaterEqual added in v0.2.0 

func BFloat16GreaterEqual(a, b BFloat16) bool

BFloat16GreaterEqual returns true if a >= b

func BFloat16Less added in v0.2.0 

func BFloat16Less(a, b BFloat16) bool

BFloat16Less returns true if a < b

func BFloat16LessEqual added in v0.2.0 

func BFloat16LessEqual(a, b BFloat16) bool

BFloat16LessEqual returns true if a <= b

func BFloat16ToSlice32 added in v1.0.0 

func BFloat16ToSlice32(s []BFloat16) []float32

BFloat16ToSlice32 converts a slice of BFloat16 values to float32

func BFloat16ToSlice64 added in v1.0.0 

func BFloat16ToSlice64(s []BFloat16) []float64

BFloat16ToSlice64 converts a slice of BFloat16 values to float64

func Configure 

func Configure(cfg *Config)

Configure applies the given configuration to the package

func DebugInfo 

func DebugInfo() map[string]interface{}

DebugInfo returns debugging information about the package state

func Equal 

func Equal(a, b Float16) bool

Equal returns true if two Float16 values are equal

func GetBenchmarkOperations 

func GetBenchmarkOperations() map[string]BenchmarkOperation

GetBenchmarkOperations returns a map of operations suitable for benchmarking

func GetMemoryUsage 

func GetMemoryUsage() int

GetMemoryUsage returns the current memory usage of the package in bytes

func GetVersion 

func GetVersion() string

GetVersion returns the package version string

func Greater 

func Greater(a, b Float16) bool

Greater returns true if a > b

func GreaterEqual 

func GreaterEqual(a, b Float16) bool

GreaterEqual returns true if a >= b

func IsFinite 

func IsFinite(f Float16) bool

IsFinite reports whether f is neither infinite nor NaN

func IsInf 

func IsInf(f Float16, sign int) bool

IsInf reports whether f is an infinity, according to sign If sign > 0, IsInf reports whether f is positive infinity If sign < 0, IsInf reports whether f is negative infinity If sign == 0, IsInf reports whether f is either infinity

func IsNaN 

func IsNaN(f Float16) bool

IsNaN reports whether f is an IEEE 754 "not-a-number" value

func IsNormal 

func IsNormal(f Float16) bool

IsNormal reports whether f is a normal number (not zero, subnormal, infinite, or NaN)

func IsSubnormal 

func IsSubnormal(f Float16) bool

IsSubnormal reports whether f is a subnormal number

func Less 

func Less(a, b Float16) bool

Less returns true if a < b

func LessEqual 

func LessEqual(a, b Float16) bool

LessEqual returns true if a <= b

func Signbit 

func Signbit(f Float16) bool

Signbit reports whether f is negative or negative zero

func ToSlice32 

func ToSlice32(s []Float16) []float32

ToSlice32 converts a slice of Float16 to a slice of float32

func ToSlice64 

func ToSlice64(s []Float16) []float64

ToSlice64 converts a slice of Float16 to a slice of float64

func ValidateSliceLength 

func ValidateSliceLength(a, b []Float16) error

ValidateSliceLength checks if two slices have the same length

Types

type ArithmeticMode 

type ArithmeticMode int

ArithmeticMode defines the precision/performance trade-off for arithmetic operations 

const (
	// ModeIEEE provides full IEEE 754 compliance with proper rounding
	ModeIEEEArithmetic ArithmeticMode = iota
	// ModeFastArithmetic optimizes for speed, may sacrifice some precision
	ModeFastArithmetic
	// ModeExactArithmetic provides exact results when possible, errors on precision loss
	ModeExactArithmetic
)

type BFloat16 added in v0.2.0 

type BFloat16 uint16

BFloat16 represents a 16-bit "Brain Floating Point" format value Used by Google Brain, TensorFlow, and various ML frameworks Format: 1 sign bit, 8 exponent bits, 7 mantissa bits 

const (
	BFloat16PositiveZero     BFloat16 = 0x0000 // +0.0
	BFloat16NegativeZero     BFloat16 = 0x8000 // -0.0
	BFloat16PositiveInfinity BFloat16 = 0x7F80 // +∞
	BFloat16NegativeInfinity BFloat16 = 0xFF80 // -∞
	BFloat16QuietNaN         BFloat16 = 0x7FC0 // Quiet NaN
	BFloat16SignalingNaN     BFloat16 = 0x7F81 // Signaling NaN

	// Largest finite values
	BFloat16MaxValue    BFloat16 = 0x7F7F // Largest positive normal
	BFloat16MinValue    BFloat16 = 0xFF7F // Largest negative normal (most negative)
	BFloat16SmallestPos BFloat16 = 0x0080 // Smallest positive normal
	BFloat16SmallestNeg BFloat16 = 0x8080 // Smallest negative normal

	// Smallest subnormal values
	BFloat16SmallestPosSubnormal BFloat16 = 0x0001 // Smallest positive subnormal
	BFloat16SmallestNegSubnormal BFloat16 = 0x8001 // Smallest negative subnormal
)

Special BFloat16 values

func BFloat16Abs added in v0.2.0 

func BFloat16Abs(b BFloat16) BFloat16

BFloat16Abs returns the absolute value of b

func BFloat16Add added in v0.2.0 

func BFloat16Add(a, b BFloat16) BFloat16

BFloat16Add adds two BFloat16 values

func BFloat16AddSlice added in v1.0.0 

func BFloat16AddSlice(a, b []BFloat16) []BFloat16

BFloat16AddSlice performs element-wise addition of two BFloat16 slices

func BFloat16AddWithMode added in v1.0.0 

func BFloat16AddWithMode(a, b BFloat16, mode ArithmeticMode, rounding RoundingMode) (BFloat16, error)

BFloat16AddWithMode performs addition with specified arithmetic and rounding modes.

func BFloat16Cos added in v1.0.0 

func BFloat16Cos(b BFloat16) BFloat16

BFloat16Cos returns the cosine of b (in radians).

func BFloat16Div added in v0.2.0 

func BFloat16Div(a, b BFloat16) BFloat16

BFloat16Div divides two BFloat16 values

func BFloat16DivSlice added in v1.0.0 

func BFloat16DivSlice(a, b []BFloat16) []BFloat16

BFloat16DivSlice performs element-wise division of two BFloat16 slices

func BFloat16DivWithMode added in v1.0.0 

func BFloat16DivWithMode(a, b BFloat16, mode ArithmeticMode, rounding RoundingMode) (BFloat16, error)

BFloat16DivWithMode performs division with specified arithmetic and rounding modes.

func BFloat16Exp added in v1.0.0 

func BFloat16Exp(b BFloat16) BFloat16

BFloat16Exp returns e^b.

func BFloat16FMA added in v1.0.0 

func BFloat16FMA(a, b, c BFloat16) (BFloat16, error)

BFloat16FMA computes a fused multiply-add (a*b + c) for BFloat16 values. This is a stub that returns an error; a full implementation is planned for a future phase.

func BFloat16FastSigmoid added in v1.0.0 

func BFloat16FastSigmoid(b BFloat16) BFloat16

BFloat16FastSigmoid computes an approximate sigmoid using a rational polynomial. Uses the approximation: sigmoid(x) ≈ 0.5 + 0.5 * x / (1 + |x|) which avoids exp() entirely.

func BFloat16FastTanh added in v1.0.0 

func BFloat16FastTanh(b BFloat16) BFloat16

BFloat16FastTanh computes an approximate tanh using a rational polynomial. Uses the approximation: tanh(x) ≈ x*(27 + x*x) / (27 + 9*x*x) which is a Padé approximant accurate to within ~0.004 for |x| < 3.

func BFloat16FromBits added in v0.2.0 

func BFloat16FromBits(bits uint16) BFloat16

FromBits creates a BFloat16 from its bit representation

func BFloat16FromFloat16 added in v0.2.0 

func BFloat16FromFloat16(f Float16) BFloat16

BFloat16FromFloat16 converts a Float16 to BFloat16

func BFloat16FromFloat32 added in v0.2.0 

func BFloat16FromFloat32(f float32) BFloat16

FromFloat32 converts a float32 to BFloat16 using round-to-nearest-even BFloat16 is essentially a truncated float32, so conversion is straightforward

func BFloat16FromFloat32WithMode added in v0.2.0 

func BFloat16FromFloat32WithMode(f32 float32, convMode ConversionMode, roundMode RoundingMode) (BFloat16, error)

BFloat16FromFloat32WithMode converts a float32 to BFloat16 with specified conversion and rounding modes.

func BFloat16FromFloat32WithRounding added in v0.2.0 

func BFloat16FromFloat32WithRounding(f float32, mode RoundingMode) BFloat16

BFloat16FromFloat32WithRounding converts a float32 to BFloat16 with the specified rounding mode.

func BFloat16FromFloat64 added in v0.2.0 

func BFloat16FromFloat64(f float64) BFloat16

FromFloat64 converts a float64 to BFloat16

func BFloat16FromFloat64WithMode added in v0.2.0 

func BFloat16FromFloat64WithMode(f64 float64, convMode ConversionMode, roundMode RoundingMode) (BFloat16, error)

BFloat16FromFloat64WithMode converts a float64 to BFloat16 with specified conversion and rounding modes.

func BFloat16FromFloat64WithRounding added in v0.2.0 

func BFloat16FromFloat64WithRounding(f float64, mode RoundingMode) BFloat16

BFloat16FromFloat64WithRounding converts a float64 to BFloat16 with the specified rounding mode.

func BFloat16FromSlice32 added in v1.0.0 

func BFloat16FromSlice32(s []float32) []BFloat16

BFloat16FromSlice32 converts a slice of float32 values to BFloat16

func BFloat16FromSlice64 added in v1.0.0 

func BFloat16FromSlice64(s []float64) []BFloat16

BFloat16FromSlice64 converts a slice of float64 values to BFloat16

func BFloat16FromString added in v1.0.0 

func BFloat16FromString(s string) (BFloat16, error)

BFloat16FromString parses a string into a BFloat16 value. It handles special values (NaN, Inf) and numeric strings.

func BFloat16Log added in v1.0.0 

func BFloat16Log(b BFloat16) BFloat16

BFloat16Log returns the natural logarithm of b.

func BFloat16Log2 added in v1.0.0 

func BFloat16Log2(b BFloat16) BFloat16

BFloat16Log2 returns the base-2 logarithm of b.

func BFloat16Max added in v0.2.0 

func BFloat16Max(a, b BFloat16) BFloat16

BFloat16Max returns the larger of a or b

func BFloat16Min added in v0.2.0 

func BFloat16Min(a, b BFloat16) BFloat16

BFloat16Min returns the smaller of a or b

func BFloat16Mul added in v0.2.0 

func BFloat16Mul(a, b BFloat16) BFloat16

BFloat16Mul multiplies two BFloat16 values

func BFloat16MulSlice added in v1.0.0 

func BFloat16MulSlice(a, b []BFloat16) []BFloat16

BFloat16MulSlice performs element-wise multiplication of two BFloat16 slices

func BFloat16MulWithMode added in v1.0.0 

func BFloat16MulWithMode(a, b BFloat16, mode ArithmeticMode, rounding RoundingMode) (BFloat16, error)

BFloat16MulWithMode performs multiplication with specified arithmetic and rounding modes.

func BFloat16Neg added in v0.2.0 

func BFloat16Neg(b BFloat16) BFloat16

BFloat16Neg returns the negation of b

func BFloat16ScaleSlice added in v1.0.0 

func BFloat16ScaleSlice(s []BFloat16, scalar BFloat16) []BFloat16

BFloat16ScaleSlice multiplies each element in the slice by a scalar

func BFloat16Sigmoid added in v1.0.0 

func BFloat16Sigmoid(b BFloat16) BFloat16

BFloat16Sigmoid returns 1 / (1 + exp(-b)).

func BFloat16Sin added in v1.0.0 

func BFloat16Sin(b BFloat16) BFloat16

BFloat16Sin returns the sine of b (in radians).

func BFloat16Sqrt added in v1.0.0 

func BFloat16Sqrt(b BFloat16) BFloat16

BFloat16Sqrt returns the square root of the BFloat16 value.

func BFloat16Sub added in v0.2.0 

func BFloat16Sub(a, b BFloat16) BFloat16

BFloat16Sub subtracts two BFloat16 values

func BFloat16SubSlice added in v1.0.0 

func BFloat16SubSlice(a, b []BFloat16) []BFloat16

BFloat16SubSlice performs element-wise subtraction of two BFloat16 slices

func BFloat16SubWithMode added in v1.0.0 

func BFloat16SubWithMode(a, b BFloat16, mode ArithmeticMode, rounding RoundingMode) (BFloat16, error)

BFloat16SubWithMode performs subtraction with specified arithmetic and rounding modes.

func BFloat16SumSlice added in v1.0.0 

func BFloat16SumSlice(s []BFloat16) BFloat16

BFloat16SumSlice returns the sum of all elements in the slice

func BFloat16Tanh added in v1.0.0 

func BFloat16Tanh(b BFloat16) BFloat16

BFloat16Tanh returns the hyperbolic tangent of b.

func (BFloat16) Bits added in v0.2.0 

func (b BFloat16) Bits() uint16

Bits returns the bit representation of the BFloat16

func (BFloat16) Class added in v0.2.0 

func (b BFloat16) Class() FloatClass

Class returns the IEEE 754 classification of the BFloat16 value

func (BFloat16) CopySign added in v0.2.0 

func (b BFloat16) CopySign(s BFloat16) BFloat16

CopySign returns a value with the magnitude of f and the sign of s

func (BFloat16) Format added in v1.0.0 

func (b BFloat16) Format(s fmt.State, verb rune)

Format implements fmt.Formatter, supporting %e, %f, %g, %E, %F, %G, %v, and %s verbs.

func (BFloat16) GoString added in v1.0.0 

func (b BFloat16) GoString() string

GoString returns a Go syntax representation of the BFloat16 value.

func (BFloat16) IsFinite added in v0.2.0 

func (b BFloat16) IsFinite() bool

IsFinite reports whether b is neither infinite nor NaN

func (BFloat16) IsInf added in v0.2.0 

func (b BFloat16) IsInf(sign int) bool

IsInf reports whether b is an infinity, according to sign

func (BFloat16) IsNaN added in v0.2.0 

func (b BFloat16) IsNaN() bool

IsNaN reports whether b is an IEEE 754 "not-a-number" value

func (BFloat16) IsNormal added in v0.2.0 

func (b BFloat16) IsNormal() bool

IsNormal reports whether b is a normal number

func (BFloat16) IsSubnormal added in v0.2.0 

func (b BFloat16) IsSubnormal() bool

IsSubnormal reports whether b is a subnormal number

func (BFloat16) IsZero added in v0.2.0 

func (b BFloat16) IsZero() bool

IsZero returns true if the BFloat16 is zero (positive or negative)

func (BFloat16) MarshalBinary added in v1.0.0 

func (b BFloat16) MarshalBinary() ([]byte, error)

MarshalBinary implements encoding.BinaryMarshaler. The encoding is 2 bytes in little-endian order.

func (BFloat16) MarshalJSON added in v1.0.0 

func (b BFloat16) MarshalJSON() ([]byte, error)

MarshalJSON implements json.Marshaler.

func (BFloat16) Signbit added in v0.2.0 

func (b BFloat16) Signbit() bool

Signbit reports whether b is negative or negative zero

func (BFloat16) String added in v0.2.0 

func (b BFloat16) String() string

String returns a string representation of the BFloat16

func (BFloat16) ToFloat16 added in v0.2.0 

func (b BFloat16) ToFloat16() Float16

ToFloat16 converts a BFloat16 to Float16

func (BFloat16) ToFloat32 added in v0.2.0 

func (b BFloat16) ToFloat32() float32

ToFloat32 converts BFloat16 to float32

func (*BFloat16) UnmarshalBinary added in v1.0.0 

func (b *BFloat16) UnmarshalBinary(data []byte) error

UnmarshalBinary implements encoding.BinaryUnmarshaler. The encoding is 2 bytes in little-endian order.

func (*BFloat16) UnmarshalJSON added in v1.0.0 

func (b *BFloat16) UnmarshalJSON(data []byte) error

UnmarshalJSON implements json.Unmarshaler.

type BFloat16Error added in v1.0.0 

type BFloat16Error struct {
	Op   string
	Msg  string
	Code ErrorCode
}

BFloat16Error provides detailed error information for bfloat16 operations

func (*BFloat16Error) Error added in v1.0.0 

func (e *BFloat16Error) Error() string

type BenchmarkOperation 

type BenchmarkOperation func(Float16, Float16) Float16

BenchmarkOperation represents a benchmarkable operation

type Config 

type Config struct {
	DefaultConversionMode ConversionMode
	DefaultRoundingMode   RoundingMode
	DefaultArithmeticMode ArithmeticMode
	EnableFastMath        bool // Package float16 implements the 16-bit floating point data type (IEEE 754-2008).

}

Package configuration

func DefaultConfig 

func DefaultConfig() *Config

DefaultConfig returns the default package configuration

func GetConfig 

func GetConfig() *Config

GetConfig returns the current package configuration

type ConversionMode 

type ConversionMode int

ConversionMode controls error reporting behavior for conversions 

const (
	// ModeIEEE performs IEEE-style conversion, saturating to Inf/0 with no errors
	ModeIEEE ConversionMode = iota
	// ModeStrict reports errors for NaN, Inf, overflow, and underflow
	ModeStrict
)

type ErrorCode 

type ErrorCode int

ErrorCode represents specific error categories for float16 operations 

const (
	ErrInvalidOperation ErrorCode = iota
	ErrNaN
	ErrInfinity
	ErrOverflow
	ErrUnderflow
	ErrDivisionByZero
	ErrNotImplemented
)

type Float16 

type Float16 uint16

Float16 represents a 16-bit IEEE 754 half-precision floating-point value 

const (
	PositiveZero     Float16 = 0x0000 // +0.0
	NegativeZero     Float16 = 0x8000 // -0.0
	PositiveInfinity Float16 = 0x7C00 // +∞
	NegativeInfinity Float16 = 0xFC00 // -∞

	// Largest finite values
	MaxValue Float16 = 0x7BFF // Largest positive finite value (~65504)
	MinValue Float16 = 0xFBFF // Largest negative finite value (~-65504)

	// Smallest normalized positive value
	SmallestNormal Float16 = 0x0400 // 2^-14 ≈ 6.103515625e-05

	// Largest subnormal value
	LargestSubnormal Float16 = 0x03FF // (1023/1024) * 2^-14 ≈ 6.097555161e-05

	// Smallest positive subnormal value
	SmallestSubnormal Float16 = 0x0001 // 2^-24 ≈ 5.960464478e-08

	// Common NaN representations
	QuietNaN     Float16 = 0x7E00 // Quiet NaN (most significant mantissa bit set)
	SignalingNaN Float16 = 0x7D00 // Signaling NaN
	NegativeQNaN Float16 = 0xFE00 // Negative quiet NaN
)

Special values following IEEE 754 half-precision standard

func Abs 

func Abs(f Float16) Float16

Abs returns the absolute value of f

func Acos 

func Acos(f Float16) Float16

Acos returns the arccosine of f

func Add 

func Add(a, b Float16) Float16

Add performs addition of two Float16 values

func AddSlice 

func AddSlice(a, b []Float16) []Float16

AddSlice performs element-wise addition of two Float16 slices

func AddWithMode 

func AddWithMode(a, b Float16, mode ArithmeticMode, rounding RoundingMode) (Float16, error)

AddWithMode performs addition with specified arithmetic and rounding modes

func Asin 

func Asin(f Float16) Float16

Asin returns the arcsine of f

func Atan 

func Atan(f Float16) Float16

Atan returns the arctangent of f

func Atan2 

func Atan2(y, x Float16) Float16

Atan2 returns the arctangent of y/x

func Cbrt 

func Cbrt(f Float16) Float16

Cbrt returns the cube root of the Float16 value

func Ceil 

func Ceil(f Float16) Float16

Ceil returns the smallest integer value greater than or equal to f

func Clamp 

func Clamp(f, min, max Float16) Float16

Clamp restricts f to the range [min, max]

func CopySign 

func CopySign(f, sign Float16) Float16

CopySign returns a Float16 with the magnitude of f and the sign of sign

func Cos 

func Cos(f Float16) Float16

Cos returns the cosine of f (in radians)

func Cosh 

func Cosh(f Float16) Float16

Cosh returns the hyperbolic cosine of f

func Dim 

func Dim(f, g Float16) Float16

Dim returns the positive difference between f and g: max(f-g, 0)

func Div 

func Div(a, b Float16) Float16

Div performs division of two Float16 values

func DivSlice 

func DivSlice(a, b []Float16) []Float16

DivSlice performs element-wise division of two Float16 slices

func DivWithMode 

func DivWithMode(a, b Float16, mode ArithmeticMode, rounding RoundingMode) (Float16, error)

DivWithMode performs division with specified arithmetic and rounding modes

func DotProduct 

func DotProduct(a, b []Float16) Float16

DotProduct computes the dot product of two Float16 slices

func Erf 

func Erf(f Float16) Float16

Erf returns the error function of f

func Erfc 

func Erfc(f Float16) Float16

Erfc returns the complementary error function of f

func Exp 

func Exp(f Float16) Float16

Exp returns e^f

func Exp2 

func Exp2(f Float16) Float16

Exp2 returns 2^f

func Exp10 

func Exp10(f Float16) Float16

Exp10 returns 10^f

func FastAdd 

func FastAdd(a, b Float16) Float16

FastAdd performs addition optimized for speed (may sacrifice precision)

func FastMul 

func FastMul(a, b Float16) Float16

FastMul performs multiplication optimized for speed (may sacrifice precision)

func Float16FromBFloat16 added in v0.2.0 

func Float16FromBFloat16(b BFloat16) Float16

Float16FromBFloat16 converts a BFloat16 to Float16

func Floor 

func Floor(f Float16) Float16

Floor returns the largest integer value less than or equal to f

func Frexp 

func Frexp(f Float16) (frac Float16, exp int)

Frexp breaks f into a normalized fraction and an integral power of two It returns frac and exp satisfying f == frac × 2^exp, with the absolute value of frac in the interval [0.5, 1) or zero

func FromBits 

func FromBits(b uint16) Float16

FromBits constructs a Float16 from its IEEE 754 half-precision bit pattern

func FromFloat32 

func FromFloat32(f32 float32) Float16

FromFloat32 converts a float32 value to a Float16 value. It handles special cases like NaN, infinities, and zeros. The conversion follows IEEE 754-2008 rules for half-precision.

func FromFloat32WithRounding added in v0.2.0 

func FromFloat32WithRounding(f32 float32, mode RoundingMode) Float16

FromFloat32WithRounding converts a float32 to Float16 using the provided rounding mode. It mirrors fromFloat32New but respects the explicit rounding mode instead of always rounding to nearest-even.

func FromFloat64 

func FromFloat64(f64 float64) Float16

FromFloat64 converts a float64 value to a Float16 value. It handles special cases like NaN, infinities, and zeros.

func FromFloat64WithMode 

func FromFloat64WithMode(f64 float64, convMode ConversionMode, roundMode RoundingMode) (Float16, error)

FromFloat64WithMode converts a float64 to Float16 with specified conversion and rounding modes

func FromInt 

func FromInt(i int) Float16

FromInt converts an integer to Float16

func FromInt32 

func FromInt32(i int32) Float16

FromInt32 converts an int32 to Float16

func FromInt64 

func FromInt64(i int64) Float16

FromInt64 converts an int64 to Float16

func FromSlice64 

func FromSlice64(s []float64) []Float16

FromSlice64 converts a slice of float64 to a slice of Float16

func Gamma 

func Gamma(f Float16) Float16

Gamma returns the Gamma function of f

func Hypot 

func Hypot(f, g Float16) Float16

Hypot returns sqrt(f*f + g*g), taking care to avoid overflow and underflow

func Inf 

func Inf(sign int) Float16

Inf returns a Float16 infinity value If sign >= 0, returns positive infinity If sign < 0, returns negative infinity

func J0 

func J0(f Float16) Float16

J0 returns the order-zero Bessel function of the first kind

func J1 

func J1(f Float16) Float16

J1 returns the order-one Bessel function of the first kind

func Ldexp 

func Ldexp(frac Float16, exp int) Float16

Ldexp returns frac × 2^exp

func Lerp 

func Lerp(a, b, t Float16) Float16

Lerp performs linear interpolation between a and b by factor t

func Lgamma 

func Lgamma(f Float16) (Float16, int)

Lgamma returns the natural logarithm and sign of Gamma(f)

func Log 

func Log(f Float16) Float16

Log returns the natural logarithm of f

func Log2 

func Log2(f Float16) Float16

Log2 returns the base-2 logarithm of f

func Log10 

func Log10(f Float16) Float16

Log10 returns the base-10 logarithm of f

func Max 

func Max(a, b Float16) Float16

Max returns the larger of two Float16 values

func Min 

func Min(a, b Float16) Float16

Min returns the smaller of two Float16 values

func Mod 

func Mod(f, divisor Float16) Float16

Mod returns the floating-point remainder of f/divisor

func Modf 

func Modf(f Float16) (integer, frac Float16)

Modf returns integer and fractional floating-point numbers that sum to f Both values have the same sign as f

func Mul 

func Mul(a, b Float16) Float16

Mul performs multiplication of two Float16 values

func MulSlice 

func MulSlice(a, b []Float16) []Float16

MulSlice performs element-wise multiplication of two Float16 slices

func MulWithMode 

func MulWithMode(a, b Float16, mode ArithmeticMode, rounding RoundingMode) (Float16, error)

MulWithMode performs multiplication with specified arithmetic and rounding modes

func NaN 

func NaN() Float16

NaN returns a Float16 quiet NaN value

func NextAfter 

func NextAfter(f, g Float16) Float16

NextAfter returns the next representable Float16 value after f in the direction of g

func Norm2 

func Norm2(s []Float16) Float16

Norm2 computes the L2 norm (Euclidean norm) of a Float16 slice

func One 

func One() Float16

One returns a Float16 value representing 1.0

func Parse 

func Parse(s string) (Float16, error)

Parse converts a string to a Float16 value This is a simplified implementation for testing

func ParseFloat added in v0.2.0 

func ParseFloat(s string, precision int) (Float16, error)

ParseFloat converts a string to a Float16 value. The precision parameter is ignored for Float16. It returns the Float16 value and an error if the string cannot be parsed.

func Pow 

func Pow(f, exp Float16) Float16

Pow returns f raised to the power of exp

func Remainder 

func Remainder(f, divisor Float16) Float16

Remainder returns the IEEE 754 floating-point remainder of f/divisor

func Round 

func Round(f Float16) Float16

Round returns the nearest integer value to f

func RoundToEven 

func RoundToEven(f Float16) Float16

RoundToEven returns the nearest integer value to f, rounding ties to even

func ScaleSlice 

func ScaleSlice(s []Float16, scalar Float16) []Float16

ScaleSlice multiplies each element in the slice by a scalar

func Sign 

func Sign(f Float16) Float16

Sign returns -1, 0, or 1 depending on the sign of f

func Sin 

func Sin(f Float16) Float16

Sin returns the sine of f (in radians)

func Sinh 

func Sinh(f Float16) Float16

Sinh returns the hyperbolic sine of f

func Sqrt 

func Sqrt(f Float16) Float16

Sqrt returns the square root of the Float16 value

func Sub 

func Sub(a, b Float16) Float16

Sub performs subtraction of two Float16 values

func SubSlice 

func SubSlice(a, b []Float16) []Float16

SubSlice performs element-wise subtraction of two Float16 slices

func SubWithMode 

func SubWithMode(a, b Float16, mode ArithmeticMode, rounding RoundingMode) (Float16, error)

SubWithMode performs subtraction with specified arithmetic and rounding modes

func SumSlice 

func SumSlice(s []Float16) Float16

SumSlice returns the sum of all elements in the slice

func Tan 

func Tan(f Float16) Float16

Tan returns the tangent of f (in radians)

func Tanh 

func Tanh(f Float16) Float16

Tanh returns the hyperbolic tangent of f

func ToFloat16 

func ToFloat16(f64 float64) Float16

ToFloat16 converts a float64 to a Float16 value. This is a convenience wrapper used in tests and utilities.

func ToSlice16 

func ToSlice16(s []float32) []Float16

ToSlice16 converts a slice of float32 to a slice of Float16. This is a convenience wrapper used in tests and utilities.

func ToSlice16WithMode 

func ToSlice16WithMode(s []float32, convMode ConversionMode, roundMode RoundingMode) ([]Float16, []error)

ToSlice16WithMode converts a slice of float32 to Float16 with specified modes

func Trunc 

func Trunc(f Float16) Float16

Trunc returns the integer part of f (truncated towards zero)

func VectorAdd 

func VectorAdd(a, b []Float16) []Float16

VectorAdd performs vectorized addition (placeholder for future SIMD implementation)

func VectorMul 

func VectorMul(a, b []Float16) []Float16

VectorMul performs vectorized multiplication (placeholder for future SIMD implementation)

func Y0 

func Y0(f Float16) Float16

Y0 returns the order-zero Bessel function of the second kind

func Y1 

func Y1(f Float16) Float16

Y1 returns the order-one Bessel function of the second kind

func Zero 

func Zero() Float16

Zero returns a Float16 zero value

func (Float16) Abs 

func (f Float16) Abs() Float16

Abs returns the absolute value of the Float16

func (Float16) Bits 

func (f Float16) Bits() uint16

Bits returns the IEEE 754 half-precision bit pattern of f

func (Float16) Class 

func (f Float16) Class() FloatClass

Class returns the IEEE 754 classification of the value

func (Float16) CopySign 

func (f Float16) CopySign(s Float16) Float16

CopySign returns a value with the magnitude of f and the sign of s

func (Float16) GoString 

func (f Float16) GoString() string

GoString returns a Go syntax representation of the Float16 value

func (Float16) IsFinite 

func (f Float16) IsFinite() bool

IsFinite returns true if the Float16 value is finite (not infinity or NaN)

func (Float16) IsInf 

func (f Float16) IsInf(sign int) bool

IsInf returns true if the Float16 value represents infinity If sign > 0, returns true only for positive infinity If sign < 0, returns true only for negative infinity If sign == 0, returns true for either infinity

func (Float16) IsNaN 

func (f Float16) IsNaN() bool

IsNaN returns true if the Float16 value represents NaN (Not a Number)

func (Float16) IsNormal 

func (f Float16) IsNormal() bool

IsNormal returns true if the Float16 value is normalized (not zero, subnormal, infinite, or NaN)

func (Float16) IsSubnormal 

func (f Float16) IsSubnormal() bool

IsSubnormal returns true if the Float16 value is subnormal (denormalized)

func (Float16) IsZero 

func (f Float16) IsZero() bool

IsZero returns true if the Float16 value represents zero (positive or negative)

func (Float16) Neg 

func (f Float16) Neg() Float16

Neg returns the negation of the Float16

func (Float16) Sign 

func (f Float16) Sign() int

Sign returns the sign of the Float16 value: 1 for positive, -1 for negative, 0 for zero

func (Float16) Signbit 

func (f Float16) Signbit() bool

Signbit returns true if the Float16 value has a negative sign bit

func (Float16) String 

func (f Float16) String() string

String returns a string representation of the Float16 value

func (Float16) ToBFloat16 added in v0.2.0 

func (f Float16) ToBFloat16() BFloat16

ToBFloat16 converts a Float16 to BFloat16

func (Float16) ToFloat32 

func (f Float16) ToFloat32() float32

ToFloat32 converts a Float16 value to a float32 value. It handles special cases like NaN, infinities, and zeros.

func (Float16) ToFloat64 

func (f Float16) ToFloat64() float64

ToFloat64 converts a Float16 value to a float64 value. It handles special cases like NaN, infinities, and zeros.

func (Float16) ToInt 

func (f Float16) ToInt() int

ToInt converts Float16 to int (truncates toward zero)

func (Float16) ToInt32 

func (f Float16) ToInt32() int32

func (Float16) ToInt64 

func (f Float16) ToInt64() int64

ToInt64 converts Float16 to int64 (truncates toward zero)

type Float16Error 

type Float16Error struct {
	Op   string
	Msg  string
	Code ErrorCode
}

Float16Error provides detailed error information for float16 operations

func (*Float16Error) Error 

func (e *Float16Error) Error() string

type FloatClass 

type FloatClass int

FloatClass enumerates the IEEE 754 classification of a Float16 value 

const (
	ClassPositiveZero FloatClass = iota
	ClassNegativeZero
	ClassPositiveSubnormal
	ClassNegativeSubnormal
	ClassPositiveNormal
	ClassNegativeNormal
	ClassPositiveInfinity
	ClassNegativeInfinity
	ClassQuietNaN
	ClassSignalingNaN
)

func FpClassify 

func FpClassify(f Float16) FloatClass

FpClassify returns the IEEE 754 class of f

type RoundingMode 

type RoundingMode int

RoundingMode controls how results are rounded during conversion/arithmetic 

const (
	// Round to nearest, ties to even
	RoundNearestEven RoundingMode = iota
	// Round toward zero (truncate)
	RoundTowardZero
	// Round toward +Inf
	RoundTowardPositive
	// Round toward -Inf
	RoundTowardNegative
	// Round to nearest, ties away from zero
	RoundNearestAway
)

type SliceStats 

type SliceStats struct {
	Min    Float16
	Max    Float16
	Sum    Float16
	Mean   Float16
	Length int
}

SliceStats computes basic statistics for a Float16 slice

func ComputeSliceStats 

func ComputeSliceStats(s []Float16) SliceStats

ComputeSliceStats calculates statistics for a Float16 slice

Source Files

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