When the ratio of the execution time of point additions to that of point doublings is 3 during computing scalar multiplication, the parallel efficiency of the proposed algorithm could be best, 90 % 当计算标量乘的点加时间是点倍数时间的3倍时,其并行效率最高可达到90%。
The second algorithm compute 2k p directly from p, where p is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings 该算法从p直接计算2~kp,不需要计算中介点,因此较k次倍乘快,其实现效率与投射坐标下的算法相当。
When the nonlinear action of slope itself is equivalent to the action of outside environment, the evolution process of slope is of chaos phenomenon and its road to chaos is realized with bifurcation of period doublings 并且通过对边坡位移历史数据序列进行特征分析,计算出饱和嵌入维数和最大lyapunov指数,给出了边坡位移的最大可预报时间尺度。
Ray kurzweil, in his book the age of spiritual machines, calculates that there have been 32 doublings since world war ii and that the singularity point ? the point at which total computational power will rise to levels so far beyond anything that we can imagine that it will appear nearly infinite and thus be indistinguishable from omniscience ? may be upon us as early as 2050 科兹威尔在他《心灵机器时代》一书中计算,从第二次世界大战以来,已经有了32次的倍增,而奇异点的来临(意指所有电脑运算能力都提升到一个超越想像的水准,因而彷佛具有无穷的能力,已经无异于无所不知)可能就近在2050年。