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feat(bfloat16): add ArithmeticMode support and NaN propagation #8

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Merged
dndungu merged 1 commit into from
Mar 30, 2026
Merged

feat(bfloat16): add ArithmeticMode support and NaN propagation #8

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211 changes: 211 additions & 0 deletions bfloat16_arithmetic.go
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Original file line number Diff line number Diff line change
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package float16

import "math"

// BFloat16AddWithMode performs addition with specified arithmetic and rounding modes.
func BFloat16AddWithMode(a, b BFloat16, mode ArithmeticMode, rounding RoundingMode) (BFloat16, error) {
// Handle NaN propagation: if either operand is NaN, propagate it
if a.IsNaN() || b.IsNaN() {
if mode == ModeExactArithmetic {
return 0, &Float16Error{Op: "bfloat16_add", Msg: "NaN operand in exact mode", Code: ErrNaN}
}
return BFloat16QuietNaN, nil
}

// Handle zeros
if a.IsZero() {
return b, nil
}
if b.IsZero() {
return a, nil
}

// Handle infinity cases
if a.IsInf(0) || b.IsInf(0) {
if a.IsInf(1) && b.IsInf(-1) || a.IsInf(-1) && b.IsInf(1) {
if mode == ModeExactArithmetic {
return 0, &Float16Error{Op: "bfloat16_add", Msg: "infinity - infinity is undefined", Code: ErrInvalidOperation}
}
return BFloat16QuietNaN, nil
}
if a.IsInf(0) {
return a, nil
}
return b, nil
}

if mode == ModeFastArithmetic {
return BFloat16FromFloat32(a.ToFloat32() + b.ToFloat32()), nil
}

// IEEE mode: compute in float32 with specified rounding, handle gradual underflow
result := a.ToFloat32() + b.ToFloat32()
bf := BFloat16FromFloat32WithRounding(result, rounding)

// Gradual underflow: if the float32 result is non-zero but rounds to BFloat16 zero,
// return the smallest subnormal with the correct sign instead.
if result != 0 && bf.IsZero() {
if result > 0 {
return BFloat16SmallestPosSubnormal, nil
}
return BFloat16SmallestNegSubnormal, nil
}

return bf, nil
}

// BFloat16SubWithMode performs subtraction with specified arithmetic and rounding modes.
func BFloat16SubWithMode(a, b BFloat16, mode ArithmeticMode, rounding RoundingMode) (BFloat16, error) {
return BFloat16AddWithMode(a, BFloat16Neg(b), mode, rounding)
}

// BFloat16MulWithMode performs multiplication with specified arithmetic and rounding modes.
func BFloat16MulWithMode(a, b BFloat16, mode ArithmeticMode, rounding RoundingMode) (BFloat16, error) {
// NaN propagation
if a.IsNaN() || b.IsNaN() {
if mode == ModeExactArithmetic {
return 0, &Float16Error{Op: "bfloat16_mul", Msg: "NaN operand in exact mode", Code: ErrNaN}
}
return BFloat16QuietNaN, nil
}

aZero := a.IsZero()
bZero := b.IsZero()

// 0 * Inf = NaN
if (aZero && b.IsInf(0)) || (a.IsInf(0) && bZero) {
if mode == ModeExactArithmetic {
return 0, &Float16Error{Op: "bfloat16_mul", Msg: "zero times infinity is undefined", Code: ErrInvalidOperation}
}
return BFloat16QuietNaN, nil
}

// Handle zeros
if aZero || bZero {
if a.Signbit() != b.Signbit() {
return BFloat16NegativeZero, nil
}
return BFloat16PositiveZero, nil
}

// Handle infinities
if a.IsInf(0) || b.IsInf(0) {
if a.Signbit() != b.Signbit() {
return BFloat16NegativeInfinity, nil
}
return BFloat16PositiveInfinity, nil
}

if mode == ModeFastArithmetic {
return BFloat16FromFloat32(a.ToFloat32() * b.ToFloat32()), nil
}

// IEEE mode with gradual underflow
result := a.ToFloat32() * b.ToFloat32()
bf := BFloat16FromFloat32WithRounding(result, rounding)

if result != 0 && bf.IsZero() {
if result > 0 {
return BFloat16SmallestPosSubnormal, nil
}
return BFloat16SmallestNegSubnormal, nil
}

return bf, nil
}

// BFloat16DivWithMode performs division with specified arithmetic and rounding modes.
func BFloat16DivWithMode(a, b BFloat16, mode ArithmeticMode, rounding RoundingMode) (BFloat16, error) {
// NaN propagation
if a.IsNaN() || b.IsNaN() {
if mode == ModeExactArithmetic {
return 0, &Float16Error{Op: "bfloat16_div", Msg: "NaN operand in exact mode", Code: ErrNaN}
}
return BFloat16QuietNaN, nil
}

// 0 / 0 = NaN
if a.IsZero() && b.IsZero() {
if mode == ModeExactArithmetic {
return 0, &Float16Error{Op: "bfloat16_div", Msg: "zero divided by zero is undefined", Code: ErrInvalidOperation}
}
return BFloat16QuietNaN, nil
}

// finite / 0 = +/-Inf
if b.IsZero() {
if mode == ModeExactArithmetic {
return 0, &Float16Error{Op: "bfloat16_div", Msg: "division by zero", Code: ErrDivisionByZero}
}
if a.Signbit() != b.Signbit() {
return BFloat16NegativeInfinity, nil
}
return BFloat16PositiveInfinity, nil
}

// 0 / finite = +/-0
if a.IsZero() {
if a.Signbit() != b.Signbit() {
return BFloat16NegativeZero, nil
}
return BFloat16PositiveZero, nil
}

// Inf / Inf = NaN
if a.IsInf(0) && b.IsInf(0) {
if mode == ModeExactArithmetic {
return 0, &Float16Error{Op: "bfloat16_div", Msg: "infinity divided by infinity is undefined", Code: ErrInvalidOperation}
}
return BFloat16QuietNaN, nil
}

// Inf / finite = +/-Inf
if a.IsInf(0) {
if a.Signbit() != b.Signbit() {
return BFloat16NegativeInfinity, nil
}
return BFloat16PositiveInfinity, nil
}

// finite / Inf = +/-0
if b.IsInf(0) {
if a.Signbit() != b.Signbit() {
return BFloat16NegativeZero, nil
}
return BFloat16PositiveZero, nil
}

if mode == ModeFastArithmetic {
return BFloat16FromFloat32(a.ToFloat32() / b.ToFloat32()), nil
}

// IEEE mode with gradual underflow
result := a.ToFloat32() / b.ToFloat32()
bf := BFloat16FromFloat32WithRounding(result, rounding)

if result != 0 && bf.IsZero() {
if result > 0 {
return BFloat16SmallestPosSubnormal, nil
}
return BFloat16SmallestNegSubnormal, nil
}

return bf, nil
}

// 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 BFloat16FMA(a, b, c BFloat16) (BFloat16, error) {
// NaN propagation
if a.IsNaN() || b.IsNaN() || c.IsNaN() {
return BFloat16QuietNaN, nil
}

// Use float64 FMA for intermediate precision, then round back to BFloat16
fa := float64(a.ToFloat32())
fb := float64(b.ToFloat32())
fc := float64(c.ToFloat32())
result := math.FMA(fa, fb, fc)

return BFloat16FromFloat32(float32(result)), nil
}
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