Addition-chain exponentiation: Difference between revisions
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addch 27182*31415
a*a =:Y*Z*Z=:Y*Y =:T*V*W*X*X*X=:W*W=:V*V=:U*U=:T*T =:N*O*P*S*S*S=:R*R=:Q*Q=:P*P=:O*O=:N*N =:A*B*C*E*I*K*M*M*M=:L*L=:K*K=:J*J=:I*I=:H*H=:G*G=:F*F=:E*E=:D*D=:C*C=:B*B=:A*A</lang>
I tried to compute the expression given by addch 31415 using matrix multiplication as my multiplier, and using
<lang j>A=: ".;._2]0 :0
4 _3 4r3 _1r4
_13r3 19r4 _7r3 11r24
3r2 _2 7r6 _1r4
_1r6 1r4 _1r6 1r24
)</lang>
However, I ran out of memory needed to represent the arbitrary precision intermediate results.
When I use floating point values instead of arbitrary precision, the result I got was:
<lang j> mul=: +/ .*
do addch 31415
_ __ _ __
__ _ __ _
_ __ _ __
__ _ __ _</lang>
Here a single underline represents floating point infinity and a double underline represents negative floating point infinity.
So I have elected to not try to compute the other requested results.
That said, note that this approach exceeds the values given in the A003313 by 1 in 22 cases, when considering the first 100 values in the sequence.
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