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Elementary Functions

Hardware algorithms have been introduced into Maple 17 that greatly speed up operations on complex floating-point numbers. Compared to Maple 16, the Maple 17 is almost 2000 times faster in some cases.

To demonstrate this, the following commands create a random vector, V, containing 10,000 complex floating-point numbers. The time (in seconds) needed to perform operations on all 10,000 elements is found using various functions

 > $V:=\mathrm{LinearAlgebra}:-\mathrm{RandomVector}\left({10}^{4},\mathrm{datatype}={\mathrm{complex}}_{8}\right):$
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{ln}~\left(V\right)\right);$
 ${0.002}$ (1)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{log}~\left(V\right)\right);$
 ${0.002}$ (2)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{log10}~\left(V\right)\right);$
 ${0.005}$ (3)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{sqrt}~\left(V\right)\right);$
 ${0.001}$ (4)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{arcsin}~\left(V\right)\right);$
 ${0.003}$ (5)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{arcsinh}~\left(V\right)\right);$
 ${0.027}$ (6)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{arctan}~\left(V\right)\right);$
 ${0.003}$ (7)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{arctanh}~\left(V\right)\right);$
 ${0.003}$ (8)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{arccos}~\left(V\right)\right);$
 ${0.003}$ (9)
 > $\mathrm{time}\left[\mathrm{real}\right]\left(\mathrm{arccosh}~\left(V\right)\right);$
 ${0.003}$ (10)

The following lists, m16 and m17, contain the measured times to compute these operations using Maple 16 and 17, respectively. The column graph plots these lists to show the speed up between the two versions.

 > $\mathrm{m16}:=\left[2.557,2.914,3.162,2.020,5.193,5.417,2.810,2.972,5.655,6.300\right]:$
 > $\mathrm{m17}:=\left[0.002,0.002,0.005,0.001,0.003,0.0027,0.003,0.003,0.003,0.003\right]:$
 >
 >



*Benchmarks computed on an Intel Q8200 2.33GHz Quad-Core CPU running Linux.



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