| Summary: | 碩士 === 國立中山大學 === 資訊工程學系研究所 === 100 === A multi-precision function interpolator, which is fitted in with the IEEE-754 single precision floating point standard, is proposed in this paper. It provides logarithms, exponentials, reciprocal and square root reciprocal operations. Each operation is able to dynamically select four different precision modes in demand. The hardware architecture is designed with fully pipeline in order to comply with hardware architectures of general digital signal processors (DSPs) and graphics processors (GPUs).
When considering the usefulness of each precision mode, it is designed to minimize the error among various modes as far as possible in the beginning. According to the precision from high to low, function interpolator can provide 23, 18, 13 and 8-bit accuracy respectively in spite of the rounding effect. This function interpolator is designed based on the look-up table method. It can get the approximation value of target function through the calculation of quadratic polynomial. The coefficient of quadratic polynomial is obtained by piecewise minimax approximation. Before implementing the hardware, we use the Maple algebra software to generate the quadratic polynomial coefficients of aforementioned four operations, and estimate whether these coefficients can meet IEEE-754 single precision floating point standard. In addition, we take the exhaustive search to check the results generated by our implementation to make sure that it can meet the requirements for various operations and precision modes.
When performing one of the above four operations, only the tables of the operation are used to obtain the quadratic polynomial coefficient. Therefore, we can take the advantage of the tri-state buffer as a switch to reduce dynamic power consumption of tables for the other three operations. In addition, when performing lower precision modes, we can turn off a part of hardwares, which are used to calculate the quadratic polynomial, to save the power consumption more effectively. By providing multi-precision hardware, we hope users or developers, those who use the battery device, can choose a lower precision mode within the permissible error range to extend the battery life.
|
|---|
