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loda-lang / loda-cpp

Runtime and miner for the LODA language written in C++
https://loda-lang.org/
Apache License 2.0
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Use local variables in generated PARI code #230

Closed ckrause closed 1 year ago

ckrause commented 1 year ago

To improve the performance of generated PARI code, we should use local variables if sequences terms are computed more than once. Here is an example:

A036211:

OLD VERSION:
(a(n) = truncate(A019520(n+50)/A178500(2*n+100))-10*truncate(truncate(A019520(n+50)/A178500(2*n+100))/10));
(b(n) = if(n==4,100,if(n==3,10,if(n==2,10,if(n==1,10,if(n==0,10,9*b(n-1)*truncate((2*n+2)/b(n-1))+b(n-1)))))));
(c(n) = if(n==4,12,if(n==3,10,if(n==2,8,if(n==1,6,if(n==0,4,2*n+4))))));
(A019520(n) = if(n==4,246810,if(n==3,2468,if(n==2,246,if(n==1,24,if(n==0,2,A019520(n-1)*(9*(9*b(n-2)*truncate(c(n-2)/b(n-2))+b(n-2))*truncate((2*n+2)/(9*b(n-2)*truncate(c(n-2)/b(n-2))+b(n-2)))+9*b(n-2)*truncate(c(n-2)/b(n-2))+b(n-2))+2*n+2))))));
(A178500(n) = (10^n)%(10^n+n))

NEW VERSION:
(a(n) = local(a1 = A019520(n+50)); local(a2 = A178500(2*n+100)); truncate(a1/a2)-10*truncate(truncate(a1/a2)/10));
(b(n) = if(n==4,100,if(n==3,10,if(n==2,10,if(n==1,10,if(n==0,10,local(b1 = b(n-1)); 9*b1*truncate((2*n+2)/b1)+b1))))));
(c(n) = if(n==4,12,if(n==3,10,if(n==2,8,if(n==1,6,if(n==0,4,2*n+4))))));
(A019520(n) = if(n==4,246810,if(n==3,2468,if(n==2,246,if(n==1,24,if(n==0,2, local(d1 = b(n-2)); local(d2 = c(n-2)); A019520(n-1)*(9*(9*d1*truncate(d2/d1)+d1)*truncate((2*n+2)/(9*d1*truncate(d2/d1)+d1))+9*d1*truncate(d2/d1)+d1)+2*n+2))))));
(A178500(n) = (10^n)%(10^n+n))