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A low-power, area-efficient 4-way 32-bit unified vector and transcendental function unit has been developed for programmable shaders for handheld 3-D graphics systems. It adopts the logarithmic number system (LNS) at the arithmetic core for the small-size, low-power unification and single cycle throughput with maximum 4-cycle latency of various vector and transcendental functions. A novel logarithmic conversion scheme is proposed with 0.41% of maximum conversion error. A test chip is implemented by 0.18-mum CMOS technology with 91 K gates. It operates at 210 MHz and consumes 15 mW at 1.8 V.