float16/types.go at v1.0.0 · zerfoo/float16 · GitHub

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package float16

import (

"fmt"

)

// ErrorCode represents specific error categories for float16 operations

type ErrorCode int

const (

ErrInvalidOperation ErrorCode = iota

ErrNaN

ErrInfinity

ErrOverflow

ErrUnderflow

ErrDivisionByZero

ErrNotImplemented

)

// Float16Error provides detailed error information for float16 operations

type Float16Error struct {

Op string

Msg string

Code ErrorCode

}

func (e *Float16Error) Error() string {

if e == nil {

return "<nil>"

}

if e.Op != "" {

return fmt.Sprintf("float16 %s: %s", e.Op, e.Msg)

}

return "float16: " + e.Msg

}

// BFloat16Error provides detailed error information for bfloat16 operations

type BFloat16Error struct {

Op string

Msg string

Code ErrorCode

}

func (e *BFloat16Error) Error() string {

if e == nil {

return "<nil>"

}

if e.Op != "" {

return fmt.Sprintf("bfloat16 %s: %s", e.Op, e.Msg)

}

return "bfloat16: " + e.Msg

}

// RoundingMode controls how results are rounded during conversion/arithmetic

type RoundingMode int

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

)

// ConversionMode controls error reporting behavior for conversions

type ConversionMode int

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

)

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

type Float16 uint16

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

func (f Float16) Bits() uint16 { return uint16(f) }

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

func FromBits(b uint16) Float16 { return Float16(b) }

// IEEE 754 half-precision format constants

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

)

// Special values following IEEE 754 half-precision standard

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

)

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

func (f Float16) IsZero() bool {

return (f & 0x7FFF) == 0

}

// 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 (f Float16) IsInf(sign int) bool {

if (f & 0x7FFF) != PositiveInfinity {

return false

}

if sign == 0 {

return true

}

return (sign > 0) == ((f & SignMask) == 0)

}

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

func (f Float16) IsNaN() bool {

exp := (f & ExponentMask) >> MantissaLen

mant := f & MantissaMask

return exp == ExponentInfinity && mant != 0

}

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

func (f Float16) IsFinite() bool {

exp := (f & ExponentMask) >> MantissaLen

return exp != ExponentInfinity

}

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

func (f Float16) IsNormal() bool {

exp := (f & ExponentMask) >> MantissaLen

return exp != ExponentZero && exp != ExponentInfinity

}

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

func (f Float16) IsSubnormal() bool {

exp := (f & ExponentMask) >> MantissaLen

mant := f & MantissaMask

return exp == ExponentZero && mant != 0

}

// FloatClass enumerates the IEEE 754 classification of a Float16 value

type FloatClass int

const (

ClassPositiveZero FloatClass = iota

ClassNegativeZero

ClassPositiveSubnormal

ClassNegativeSubnormal

ClassPositiveNormal

ClassNegativeNormal

ClassPositiveInfinity

ClassNegativeInfinity

ClassQuietNaN

ClassSignalingNaN

)

// Class returns the IEEE 754 classification of the value

func (f Float16) Class() FloatClass {

bits := uint16(f)

sign := (bits & SignMask) != 0

exp := (bits & ExponentMask) >> MantissaLen

mant := bits & MantissaMask

switch exp {

case ExponentZero:

if mant == 0 {

if sign {

return ClassNegativeZero

}

return ClassPositiveZero

}

if sign {

return ClassNegativeSubnormal

}

return ClassPositiveSubnormal

case ExponentInfinity:

if mant == 0 {

if sign {

return ClassNegativeInfinity

}

return ClassPositiveInfinity

}

// NaN: distinguish quiet vs signaling by top mantissa bit (bit 9)

if (mant & (1 << (MantissaLen - 1))) != 0 {

return ClassQuietNaN

}

return ClassSignalingNaN

default:

if sign {

return ClassNegativeNormal

}

return ClassPositiveNormal

}

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

func (f Float16) Sign() int {

if f.IsZero() {

return 0

}

if (f & SignMask) != 0 {

return -1

}

return 1

}

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

func (f Float16) Signbit() bool {

return (f & SignMask) != 0

}

// Abs returns the absolute value of the Float16

func (f Float16) Abs() Float16 {

return f & 0x7FFF // Clear sign bit

}

// Neg returns the negation of the Float16

func (f Float16) Neg() Float16 {

return f ^ SignMask // Flip sign bit

}

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

func (f Float16) CopySign(s Float16) Float16 {

// Clear sign bit of f, then OR with sign bit of s

return (f & ^Float16(SignMask)) | (s & Float16(SignMask))

}

// ToInt converts Float16 to int (truncates toward zero)

func (f Float16) ToInt() int {

return int(f.ToFloat32())

}

// String returns a string representation of the Float16 value

func (f Float16) String() string {

if f.IsNaN() {

if f.Signbit() {

return "-NaN"

}

return "NaN"

}

if f.IsInf(0) {

if f.Signbit() {

return "-Inf"

}

return "+Inf"

}

return fmt.Sprintf("%.6g", f.ToFloat32())

}

// GoString returns a Go syntax representation of the Float16 value

func (f Float16) GoString() string {

return fmt.Sprintf("float16.FromBits(0x%04x)", uint16(f))

}

func (f Float16) ToInt32() int32 {

return int32(f.ToFloat32())

}

// ToInt64 converts Float16 to int64 (truncates toward zero)

func (f Float16) ToInt64() int64 {

return int64(f.ToFloat32())

}

float16/types.go at v1.0.0 · zerfoo/float16 · GitHub

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