  In this paper we introduce the algorithm and the fixed point hardware to
calculate the normalized singular value decomposition of a non-symmetric
matrices using Givens fast (approximate) rotations. This algorithm only uses
the basic combinational logic modules such as adders, multiplexers, encoders,
Barrel shifters (B-shifters), and comparators and does not use any lookup
table. This method in fact combines the iterative properties of singular value
decomposition method and CORDIC method in one single iteration. The introduced
architecture is a systolic architecture that uses two different types of
processors, diagonal and non-diagonal processors. The diagonal processor
calculates, transmits and applies the horizontal and vertical rotations, while
the non-diagonal processor uses a fully combinational architecture to receive,
and apply the rotations. The diagonal processor uses priority encoders, Barrel
shifters, and comparators to calculate the rotation angles. Both processors use
a series of adders to apply the rotation angles. The design presented in this
work provides $2.83\sim649$ times better energy per matrix performance compared
to the state of the art designs. This performance achieved without the
employment of pipelining; a better performance advantage is expected to be
achieved employing pipelining.
