Accelerated computational schemes for symbolic and numeric algorithms

该研究项目的目标是开发一套算法和软硬件工具，用于加速一些标准的符号和数值算法。我们的目标符号算法是在符号求和领域。目标数值算法侧重于初等函数和特殊函数的高精度计算。我们的加速方法是基于计算问题的符号预处理，包括选择适当的表示，例如，闭合形式公式、零化线性微分或差分算符、递归链、组合和的积分表示以及基于所选表示的代码生成；-使用用于高精度计算的替代算法，例如具有特殊模数选择的任意精度有理数的模表示、自适应精度浮点运算；-在工作站网络上或通过网络分布计算困难的问题；--用于加速特定计算任务的专用硬件的VHDL化原型，包括基于多维递归链和自适应精度浮点运算技术的专用浮点单元的原型设计。

The objective of this research program is to develop a set of algorithms, software and hardware tools for acceleration of some standard symbolic and numeric algorithms. Our target symbolic algorithms are in the area of symbolic summation. The target numeric algorithms focus on high precision evaluation of elementary and special functions. Our approach to the acceleration is based on -- symbolic preprocessing of computational problems, including the choice of an appropriate representation, for example, closed form formula, annihilating linear differential or difference operator, chains of recurrences, integral representation of combinatorial sums and code generation based on chosen representation; -- use of alternative arithmetics for high precision computations such as modular representation of arbitrary precision rational numbers with special choice of moduli, adaptive precision floating-point arithmetic; -- distributing computationally hard problems over a network of workstations or through the web; -- VHDL prototyping of specialized hardware for acceleration of a particular computational task, including prototyping of specialized floating point units based on the technique of multidimensional chains of recurrences and adaptive precision floating-point arithmetic.