An FFT conversion instruction based on a single instruction multiple data (“SIMD”) technique is executed to reduce the number of cycles for software to perform conversion processing used in an FFT computation. In an embodiment, the FFT conversion instruction implements two instances of a conversion operation, i.e., 2-way SIMD, over two sets of complex points at once. A control register or variant opcode controls an inverse flag to control the behavior of the conversion process. In an embodiment, the control register contains a control bit to select between forward and inverse FFT context.