A method and apparatus, especially suited for computers that can execute fused multiply-add instructions, for performing a fast Fourier transform (FFT) are disclosed. Divisions by zero that create a risk of error in other methods are avoided. In a first example embodiment, a zero divisor is detected and the division circumvented by performing an alternate computation. In a second example embodiment, a zero divisor is detected replaced by a safe finite value. In a third example embodiment, two optimized FFT kernels are used, one avoiding division by a zero real part of a root of unity and one avoiding division by a zero imaginary part. In a fourth example embodiment, a first kernel computes some kernel iterations without multiplication, and a second, optimized kernel computes the remaining iterations without risk of division by zero.