Research on Algorithms of Number Theory

在符号代数程序设计中，初等占优函数的计算速度比FORTRAN和C语言要慢，所以我们需要快速计算初等占优函数。我们使用连分式和整数计算。在计算中，我们只使用一个除法。误差由Stirling公式得到。我们的计算量超过了著名的快速计算语言PanGP。例如，在30000位数中，Expornetian和Tangent快10个Pines，而ancTangent快30%或40%。但日志是相同的或稍慢一些。我们将改进连分式的计算方法。

In Symbolic Algebraic Manuplation, time of caluclating elementary trancendental functions are slow than Fortran and C.So we want to fast computing the functions. We used continued fraction and integer computing. In the computing we use only one division. The error is got by Stirling formula. Our computing are firster than Pan GP which is well-known as fast computing language. For example expornetian and tangent are 10 Pines faster and anctangent is 30 or 40 percent faster in 30000 digits. But log is same or a little slower. We will improve the method on computing of continued fraction.