the present invention comprises a direct digital frequency synthesizer . a phase accumulator provides a normalized angle θ to a sine / cosine generator that outputs the value of the sine / cosine function at the provided angle . the she / cosine generator in a preferred embodiment comprises a plurality of multiplierless butterfly and carry - save stages in cascade that perform angle rotations on a phasor on the unit circle whose x and y coordinates correspond to cosine and sine values . to calculate the sine and cosine values at a particular angle θ = b 1 θ 1 + b 2 θ 2 +. . . + b n θ n where b k ε are the binary bits and the θ k = 2 - k are the associated positional weights , each of the butterfly and carry - save stages rotate the phasor by an amount θ k = 2 - k . the direction of the rotation , clockwise or counter - clockwise , depends upon the value of the binary bits b k . after undergoing all of the rotations , the phasor has x and y coordinates that approximate the desired cosine and sine values to a specified accuracy . in a preferred embodiment , the datapath of the present invention is multiplierless . the stages for angles where the approximation tan θ k = θ k is acceptable are multiplierless while for angles where this approximation does not hold , the x and y phasor coordinates are transformed through a multiplexer or a rom .