Ackermann's Function Letter 2 to GŁnter Dotzel

November 28, 1991

19628 Via Monte Drive
Saratoga, CA 95070

GŁnter Dotzel, ModulaWare GmbH
Wilhelmstr. 17A, W-8520
Erlangen, GERMANY

Re your letter dated 21-Nov-1991

Dear Gunter,

I agree that the Ackermann function is "A function to end all functions." You asked if I tried Ackermann(4,3). Well yes, but my program VPCalc only handles a value up to about 10^15,032,385,525 and can only handle 114,639 decimal digits in the mantissa. A(4,2) fits my niche well, but A(4,3) is way out there. It would take more than A(4,2) seconds to compute A(4,3) and the computer would need more than A(4,2) bits of memory. This cannot be done in this universe. Remember A(4,2) = 2.00352...E+19728.

I am surprised that Mathematica on a SUN Sparc Station takes over 20 minutes to compute A(4,2) = 2^(2^(2^(2^2))) - 3 when My VPCalc program on a 33 Mhz 486 DX machine does it in 29 seconds. Try the form: A(4,2) = Sqr(Sqr(Sqr(...Sqr(2)...))) - 3, where there are 16 Sqr (square) operations and see if it goes faster. They may be using exponential and log functions to do the powers. VPCalc has an efficient use of squares and multiplies to raise values to integer powers.

Please feel free to distribute the copy of VPCalc that I sent you, it is Shareware.

You may edit my letters as you see fit and include any part of them as a letter to the editor in The ModulaTor. I would like to receive your news letter (via surface mail) as you offered for 12 months at no obligation.


Harry J. Smith

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