A processing apparatus is provided with processing circuitry 6, 8 and decoder circuitry 10 responsive to a received argument reduction instruction FREDUCE4, FDOT3R to generate control signals 16 for controlling the processing circuitry 6, 8. The action of the argument reduction instruction is to subject each component of an input vector to a scaling which adds or subtracts an exponent shift value C to the exponent of the input vector component. The exponent shift value C is selected such that a sum of this exponent shift value C with the maximum exponent value B of any of the input vector components lies within a range between a first predetermined value and a second predetermined value. A consequence of execution of this argument reduction instruction is that the result vector when subject to a dot-product operation will be resistant to floating point underflows or overflows.