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Question: Exponentiation by Squaring Issue

Question:Exponentiation by Squaring Issue

Adam Ledger 360 Maple 2016
performance programming
November 06 2019
0

My problem is explained with sufficient detail in the below worksheet:

 

> 

restart
> 

Digits := 100:
> 

with(StringTools); with(FileTools); with(ListTools)
> 

``
> 

currentdir("H:\\MAIN DIRECTORY\\ESD-USB\\my_maple_library")
> 

L[1] := ListDirectory(currentdir()):
> 

L[2] := [seq([k, L[1][k]], k = 1 .. nops(L[1]))]:
> 

read L[1][15]:
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currentdir("H:\\MAIN DIRECTORY\\ESD-USB\\Computer Science\\MAPLE\\Exponentiation by Squaring"):

 

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B := proc (n) options operator, arrow; [seq(d(n, 2, j), j = 0 .. floor(ln(n)/ln(2)))] end proc:

 

 

> 

Identity0 := proc (x, n) options operator, arrow; x^n = piecewise(`mod`(x, 2) = 1, x*(x^2)^((1/2)*n-1/2), `mod`(x, 2) = 0, (x^2)^((1/2)*n)) end proc
> 

NULL
> 

Generate_Equations_List := proc (n) global EquationsList, r, B_n, T; B_n := B(n); T := nops(B_n); r[T] := 1; return [seq(r[u-1] = r[u]^2*x^B_n[u], u = 1 .. T)] end proc:
> 

Exp_by_squares := proc (M, Y) global R; Generate_Equations_List(M); R[1] := max([allvalues(rhs(isolate(F[0](Y, M)[1], r[1])))]); return 'x^n' = R[1]^2*X^B_n[1] end proc:

 

> 

N := (rand(25 .. 33))():

n = 31

  

x = 34

  

x^n = 299120672332806228664106719451209941853702979584

  

x^n = 299120672332806228664106719451209941853702979584

 (1)
> 

NULL
> 

st := time[real]():

x^n = 299120672332806228664106719451209941853702979584

  

0.40e-1

 (2)
> 

st := time[real]():

x^n = 299120672332806228664106719451209941853702979584

  

0.74e-1

 (3)
> 

is(t2 < t1)

false

 (4)
> 

``


 

Download slow.mw

 

  

So I know I have obviously done something wrong, but it has proven very difficult to establish where given how little i know about the solve function

 
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