1. A direct digital frequency synthesizer circuit, comprising: a phase accumulator responsive to a frequency control input to produce a sequence of 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 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 generate a minority-bit signal based on whether positive rotation operations or no-rotation operations are in the minority in a subset of the series of subangles; and at least one minority-select rotation circuit stage for performing a positive, negative, or zero rotation on the subset of the series of subangles in response to the minority-bit detector circuit.