Complex vector dot product

I need to compute the dot product of two complex vectors x and y, i.e, the transpose of the complex conjugate of x times y,

(x,y) = sum(x_real[n] * y_real[n] + x_imag[n] * y_imag[n]) + j * sum(x_real[n] * y_real[n] - x_imag[n] * y_imag[n]) .         (1)

I was  trying to use the function DSPF_sp_dotp_cplx in C67xdsplib. But I found that this function compute the dot product in a different way. Its definition of dot product of two complex vectors x and y is the product of the transpose of x times y, i.e.,

(x,y) = sum(x_real[n] * y_real[n] - x_imag[n] * y_imag[n]) + j * sum(x_real[n] * y_real[n] + x_imag[n] * y_imag[n]) .          (2)

See below for definition of this function from TMS320C67X DSP Library Programmer’s Reference Guide. Anyway I suggestion on what I can do to compute the dot product in (1)?

This is the C equivalent for the assembly code. Note that the assembly code

is hand optimized and restrictions may apply.

− x[2*i+1]*y[2*i+1]);

imag+=(x[2*i]*y[2*i+1] + x[2*i+1]*y[2*i]);

}

*re=real;

*im=imag;