一个浮点数学函数库测试平台

Testing Platform for Floating Mathematical Function Libraries

数学函数库作为CPU软件的重要组成部分,对于高性能计算机平台上的科学计算、工程数值计算起着极为关键的作用.现有的测试工具只能片面地对函数库进行测试,没有从正确性、精度和函数性能这3方面加以考虑,而且往往只针对一类目标体系结构,适用性有限.针对现有测试工具的缺陷,提出了面向多目标体系结构、全面可复用的一体化测试平台BMltest(basic math library test).测试平台结合函数特征值、IEEE-754特殊数以及利用浮点数生成规则实现的全浮点域指数分布的IEEE-754规范数构造了测试集,有效提高了测试集浮点数的覆盖率;提出了基于多精度库MPFR(multiple-precision floating-point reliable library)的精度测试方法,提高了精度测试的可靠性;提出了基于代码隔离的性能测试方法,最大限度地降低了外部环境对性能测试的干扰.针对大量的浮点测试结果,给出了合理的结果评价方案.测试平台使用的测试集数据与函数做到了相关性的极大分离,保证了测试方法的普适性.通过对包括GNU,Open64及Mlib函数库内所有855个函数的测试结果表明:BMltest平台的测试数据集更全面、有效,精度测试方法更可靠;与其他测试平台相比,性能测试结果更准确、稳定.

As one of the most important essentials of CPU, mathematical function libraries play a key role in scientific and engineering computing with high performance computers. Existing testing techniques and platforms can only evaluate function libraries from one or two aspects, therefore are unable to provide an evaluation result as a whole picture. Consequently, they are applicable for a specific targeting architecture and the scalability is restricted. To address this problem, this study proposes a novel testing platform BMltest （Basic math library test）. It constructs the testing suite, which is composed of eigenvalues, IEEE-754 special values and IEEE-754 normalized values, to improve the cover rate of the floating numbers. A MPFR （multiple-precision floating-point reliable library） based precision test is introduced, and as a result, the reliability is improved. A code isolation based performance test is also described, so as to further eliminate the impact from enclosing circumstance. Some practical evaluating strategies are proposed to evaluate the test result. Such design makes the testing suite not correlated to mathematical functions, thereby ensuring the applicability. The experimental results show that, by testing 855 functions from various libraries, including GNU, Open64 and Mlib, the testing suite provided by BMltest is more efficient and the precision test is more reliable. At the same time, compared with those of other testing platforms, the performance test is more stable.