pub(crate) fn f32_to_bf16(value: f32) -> u16 {

    // Convert to raw bytes

    let x = value.to_bits();

    // check for NaN

    if x & 0x7FFF_FFFFu32 > 0x7F80_0000u32 {

        // Keep high part of current mantissa but also set most significiant mantissa bit

        return ((x >> 16) | 0x0040u32) as u16;

    }

    // round and shift

    let round_bit = 0x0000_8000u32;

    if (x & round_bit) != 0 && (x & (3 * round_bit - 1)) != 0 {

        (x >> 16) as u16 + 1

    } else {

        (x >> 16) as u16

    }

}

pub(crate) fn f64_to_bf16(value: f64) -> u16 {

    // Convert to raw bytes, truncating the last 32-bits of mantissa; that precision will always

    // be lost on half-precision.

    let val = value.to_bits();

    let x = (val >> 32) as u32;

    // Extract IEEE754 components

    let sign = x & 0x8000_0000u32;

    let exp = x & 0x7FF0_0000u32;

    let man = x & 0x000F_FFFFu32;

    // Check for all exponent bits being set, which is Infinity or NaN

    if exp == 0x7FF0_0000u32 {

        // Set mantissa MSB for NaN (and also keep shifted mantissa bits).

        // We also have to check the last 32 bits.

        let nan_bit = if man == 0 && (val as u32 == 0) {

            0

        } else {

            0x0040u32

        };

        return ((sign >> 16) | 0x7F80u32 | nan_bit | (man >> 13)) as u16;

    }

    // The number is normalized, start assembling half precision version

    let half_sign = sign >> 16;

    // Unbias the exponent, then bias for bfloat16 precision

    let unbiased_exp = ((exp >> 20) as i64) - 1023;

    let half_exp = unbiased_exp + 127;

    // Check for exponent overflow, return +infinity

    if half_exp >= 0xFF {

        return (half_sign | 0x7F80u32) as u16;

    }

    // Check for underflow

    if half_exp <= 0 {

        // Check mantissa for what we can do

        if 7 - half_exp > 21 {

            // No rounding possibility, so this is a full underflow, return signed zero

            return half_sign as u16;

        }

        // Don't forget about hidden leading mantissa bit when assembling mantissa

        let man = man | 0x0010_0000u32;

        let mut half_man = man >> (14 - half_exp);

        // Check for rounding

        let round_bit = 1 << (13 - half_exp);

        if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {

            half_man += 1;

        }

        // No exponent for subnormals

        return (half_sign | half_man) as u16;

    }

    // Rebias the exponent

    let half_exp = (half_exp as u32) << 7;

    let half_man = man >> 13;

    // Check for rounding

    let round_bit = 0x0000_1000u32;

    if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {

        // Round it

        ((half_sign | half_exp | half_man) + 1) as u16

    } else {

        (half_sign | half_exp | half_man) as u16

    }

}

pub(crate) fn bf16_to_f32(i: u16) -> f32 {

    // If NaN, keep current mantissa but also set most significiant mantissa bit

    if i & 0x7FFFu16 > 0x7F80u16 {

        f32::from_bits((i as u32 | 0x0040u32) << 16)

    } else {

        f32::from_bits((i as u32) << 16)

    }

}

pub(crate) fn bf16_to_f64(i: u16) -> f64 {

    // Check for signed zero

    if i & 0x7FFFu16 == 0 {

        return f64::from_bits((i as u64) << 48);

    }

    let half_sign = (i & 0x8000u16) as u64;

    let half_exp = (i & 0x7F80u16) as u64;

    let half_man = (i & 0x007Fu16) as u64;

    // Check for an infinity or NaN when all exponent bits set

    if half_exp == 0x7F80u64 {

        // Check for signed infinity if mantissa is zero

        if half_man == 0 {

            return f64::from_bits((half_sign << 48) | 0x7FF0_0000_0000_0000u64);

        } else {

            // NaN, keep current mantissa but also set most significiant mantissa bit

            return f64::from_bits((half_sign << 48) | 0x7FF8_0000_0000_0000u64 | (half_man << 45));

        }

    }

    // Calculate double-precision components with adjusted exponent

    let sign = half_sign << 48;

    // Unbias exponent

    let unbiased_exp = ((half_exp as i64) >> 7) - 127;

    // Check for subnormals, which will be normalized by adjusting exponent

    if half_exp == 0 {

        // Calculate how much to adjust the exponent by

        let e = (half_man as u16).leading_zeros() - 9;

        // Rebias and adjust exponent

        let exp = ((1023 - 127 - e) as u64) << 52;

        let man = (half_man << (46 + e)) & 0xF_FFFF_FFFF_FFFFu64;

        return f64::from_bits(sign | exp | man);

    }

    // Rebias exponent for a normalized normal

    let exp = ((unbiased_exp + 1023) as u64) << 52;

    let man = (half_man & 0x007Fu64) << 45;

    f64::from_bits(sign | exp | man)

}