An apparatus and method are provided for estimating a shift amount when employing processing circuitry to perform a subtraction operation to subtract a second significand value of a second floating-point operand from a first significand value of a first floating-point operand in order to generate a difference value. Shift estimation circuitry then determines an estimated shift amount to be applied to the difference value. The shift estimation circuitry comprises significand analysis circuitry to generate, from analysis of the significand values of the two floating-point operands, a first bit string identifying a most significant bit position within the difference value that is predicted to have its bit set to a determined value. In parallel, shift limiting circuitry generates from an exponent value a second bit string identifying a shift limit bit position. The shift limiting circuitry has computation circuitry to perform, for each bit position in at least a subset of bit positions of the second bit string, an associated computation using bits of the exponent value to determine a value for that bit position within the second bit string. The associated computation is different for different bit positions. Combining circuitry then generates a combined bit string from the first and second bit strings, and shift determination circuitry determines the estimated shift amount from the combined bit string.