extension UInt16 {
    var halfFloat: Float {
        // 1 bit sign
        // 5 bit exponent
        // 11 bit significand (10 bit explicitly stored)
        let sign = Float((self & 0b1000_0000_0000_0000) >> 15)
        let exponent = Float((self & 0b0111_1100_0000_0000) >> 10)
        let significand = Float(self & 0b0000_0011_1111_1111)

        if exponent == 0b0_0000 {
            if significand == 0 {
                return pow(-1, sign) * 0
            } else {
                // (−1)^signbit × 2^(−14) × 0.significantbits
                let last = 0 + significand / 0b0011_1111_1111
                return pow(-1, sign) * pow(2, -14) * last
            }
        } else if exponent == 0b1_1111 {
            if significand == 0 {
                return pow(-1, sign) * .infinity
            } else {
                return .nan
            }
        } else {
            // (−1)^signbit × 2^(exponent−15) × 1.significantbits
            let last = 1 + significand / 0b0011_1111_1111
            return pow(-1, sign) * pow(2, exponent - 15) * last
        }
    }
}

extension Float {
    var halfFloatBitPattern: UInt16 {
        var value = self

        let signBytes: UInt16
        if value.sign == .plus {
            signBytes = 0b0000_0000_0000_0000
        } else {
            signBytes = 0b1000_0000_0000_0000
            value *= -1
        }

        guard value.isNaN == false else {
            let exponentBytes: UInt16 = 0b1_1111
            let significandBytes: UInt16 = 0
            return signBytes | exponentBytes | significandBytes
        }

        guard value != 0 else {
            return signBytes
        }
        let exponent = log2(value).rounded(.down)
        let exponentBytes: UInt16
        let significandBytes: UInt16
        if exponent == 1 {
            exponentBytes = 0
            let significand = value * 1024
            significandBytes = UInt16(significand)
        } else if exponent == .infinity {
            exponentBytes = 0b1111 << 10
            significandBytes = 0
        } else if exponent <= -15 {
            exponentBytes = 0
            let significand = value * 1024
            significandBytes = UInt16(significand)
        } else {
            exponentBytes = UInt16(exponent + 15) << 10
            value /= pow(2, exponent)
            let significand = (value - 1) * 1024
            significandBytes = UInt16(significand)
        }
        return signBytes | exponentBytes | significandBytes
    }
}