A 231-MHz, 2.18-mW 32-bit Logarithmic Arithmetic Unit for Fixed-Point 3-D Graphics System

A logarithmic approach to energy-efficient GPU arithmetic for mobile devices

“…Kim et al [6] implemented an energy-efficient 32-bit fixed-point logarithmic arithmetic unit suitable for GPUs in mobile devices. The 32-bit word consists of 6 whole bits and 26 fractional bits.…”

“…The logarithmic converter of Kim et al [6] uses 8-way partitioning of the interval [0, 1] for piecewise linear approximation to improve upon the very simple linear method of Mitchell [9] and a somewhat more accurate, but still crude, method of Juang et al [5], introducing the relative errors of 5.9% and 2.9%, respectively. The 8 intervals are associated with the linear approximations…”

“…The antilogarithmic converter of Kim et al [6] computes the function 2 Table 4 shows the implementation parameters. As evident from Fig.…”

“…3. Error plot for the antilogarithmic converter [6]. ) from the fifth and sixth d values in Table 4 would shift the curves downward by too large an amount, so that they then dictate the maximum negative error.…”

“…In Section 2, we referred to the energy-efficient 32-bit logarithmic arithmetic unit implemented by Kim et al [6]. In this appendix, we provide a brief overview of what causes logarithmic representation to have lower energy requirements compared with standard 2's-complement binary arithmetic.…”