// must be either an integer, infinity, or NaN.
		const half = 1 << (shift - 1)
		e -= bias
		bits += half >> e
		bits &^= fracMask >> e
	}
	return Float64frombits(bits)
}

// RoundToEven returns the nearest integer, rounding ties to even.
//
// Special cases are:
//
//	RoundToEven(±0) = ±0
//	RoundToEven(±Inf) = ±Inf
//	RoundToEven(NaN) = NaN

package math

// Abs returns the absolute value of x.
//
// Special cases are:
//
//	Abs(±Inf) = +Inf
//	Abs(NaN) = NaN
func Abs(x float64) float64 {
	return Float64frombits(Float64bits(x) &^ (1 << 63))

// license that can be found in the LICENSE file.

package math

// Copysign returns a value with the magnitude of f
// and the sign of sign.
func Copysign(f, sign float64) float64 {
	const signBit = 1 << 63
	return Float64frombits(Float64bits(f)&^signBit | Float64bits(sign)&signBit)

		}
		return 0, f
	}

	x := Float64bits(f)
	e := uint(x>>shift)&mask - bias

	// Keep the top 12+e bits, the integer part; clear the rest.
	if e < 64-12 {
		x &^= 1<<(64-12-e) - 1
	}
	int = Float64frombits(x)
	frac = f - int
	return

	case IsInf(f, 0) || IsNaN(f):
		return f, 0
	}
	f, exp = normalize(f)
	x := Float64bits(f)
	exp += int((x>>shift)&mask) - bias + 1
	x &^= mask << shift
	x |= (-1 + bias) << shift
	frac = Float64frombits(x)
	return

	case "float64-bits":
		if kind != token.FLOAT && kind != token.INT {
			return nil, fmt.Errorf("integer literal required for math.Float64frombits type")
		}
		bits, err := parseUint(val, "uint64")
		if err != nil {
			return nil, err
		}
		return math.Float64frombits(bits.(uint64)), nil
	default:
		return nil, fmt.Errorf("expected []byte or primitive type")
	}
}

		}
		return Inf(1)
	}
	var m float64 = 1
	if exp < -1022 { // denormal
		exp += 53
		m = 1.0 / (1 << 53) // 2**-53
	}
	x &^= mask << shift
	x |= uint64(exp+bias) << shift
	return m * Float64frombits(x)

}

var bugged = false

func bug() {
	if !bugged {
		bugged = true
		fmt.Println("BUG")
	}
}

func main() {
	u64 := math.Float64frombits(0x7fefffffffffffff) - math.Float64frombits(0x7feffffffffffffe)
	if ulp64 != u64 {
		bug()
		fmt.Printf("ulp64=%g, want %g", ulp64, u64)
	}

	u32 := math.Float32frombits(0x7f7fffff) - math.Float32frombits(0x7f7ffffe)

	x32 := math.Float32bits(f32)
	y32 := math.Float32bits(g32)
	if x32 != y32 {
		t.Errorf("got %x, want %x (diff=%x)", x32, y32, x32^y32)
	}

	f64 := math.Float64frombits(snan64bits)
	g64 := math.Float64frombits(snan64bitsVar)
	x64 := math.Float64bits(f64)
	y64 := math.Float64bits(g64)
	if x64 != y64 {
		t.Errorf("got %x, want %x (diff=%x)", x64, y64, x64^y64)
	}
}

type Float struct {
	f atomic.Uint64
}

func (v *Float) Value() float64 {
	return math.Float64frombits(v.f.Load())
}

func (v *Float) String() string {
	return string(v.appendJSON(nil))
}

func (v *Float) appendJSON(b []byte) []byte {
	return strconv.AppendFloat(b, math.Float64frombits(v.f.Load()), 'g', -1, 64)
}

// Add adds delta to v.
func (v *Float) Add(delta float64) {
	for {