How would frexp work for ABDKMathQuad in solidity

[yashnaman]

I need a function that converts ABDKMathQuad number into mantissa and exponent where quad = mantissa * 2**exponent. The mantissa lies in the open interval(-1, 1), while the twos exponent is a signed integer. It isn't as straightforward as I thought. The function I have constructed is shown below. But it is obvious that it isn't correct. Can anyone help me with this?

I expect the output to be equivalent to what numpy.frexp would return for a float.

function frexp(
        bytes16 quad
    ) public pure returns (uint256 mantissa, int256 exponent) {
        uint256 exponent1 = (uint128(quad) >> 112) & 0x7FFF;
        mantissa = uint128(quad) & 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF;

        mantissa = mantissa * 2 ** 63;
        exponent = -int256(exponent1);
        if (exponent == 0) {
            //it's a subnormal number
            exponent += 63;
        } else {
            //substract one from the whole number
            quad = quad.sub(ABDKMathQuad.fromUInt(1));
            //mantissat = mantissa of the original number 2**63
            //exponent = exponent of the substracted number - 16383 - 63
            exponent += 16383 + 63;
        }
    }