1. A direct digital frequency synthesizer circuit, comprising: a phase accumulator responsive to a frequency control word input to produce a sequence of truncated, normalized rotation angles; and a mapping function circuit responsive to the phase accumulator circuit for producing one or more digital output signals including a sequence of values representing sine and/or cosine functions of the sequence of rotation angles related to the frequency control word input, the mapping function circuit comprising: a phase mapper and phase multiplier circuit responsive to the sequence of normalized rotation angles for producing a series of subangles in a fixed angular range; a minority-bit detector circuit responsive to the series of subangles to determine whether positive rotation operations or no rotation operations are in the minority in a subset of the series of subangles; and a series of circuit stages in cascade for performing transformation operations responsive to the series of subangles to produce angle rotations corresponding to the series of subangles, the series of circuit stages including at least one minority-select rotation circuit stage for performing a positive, negative, or zero rotation for a subset of transformation operations in response to the minority-bit detector circuit.