The Postcomputer History of


Comparison of "Time Per Digit"
in certain calculations of
YearComputerTime# of digitsTime per digit
1807Wm. Shanks (by hand)~ 15 years7071 week!
1844Johann Dase (by hand)< 2 months2007 hours
1947D. F. Ferguson, desk calculator~ 1 year80811 hours
1949U.S. Army, ENIAC70 hours2,0372 minutes
1954S. C. Nicholson, J. Jeenel, NORC13 minutes30890.25 seconds
1958F. Genuys, IBM 704100 minutes10,0000.6 seconds
1961D. Shanks, J. W. Wrench, IBM 70908.72 hours100,2001/3 second
1973J. Guilloud, CDC 760023.3 hours1,000,0001/12 second
1983Y. Tamura, Y. Kanada, HITAC M-28OH< 30 hours16,000,000< 0.0065 second
1986D. H. Bailey, NASA, Cray-228 hours> 29,360,000< 0.00035 second
1986Y. Kanada, Hitachi S-810/8208 hours> 33,554,000< 0.00086 second
1988Y. Kanada, Hitachi S-8206 hours201,326,000< 0.00011 second
1997Y. Kanada and D. Takahashi, Hitachi SR220129 hours and 7 minutes51,539,600,000 about 0.000002 second

To further highlight the improvements in our abilities to compute in recent years, consider this: The 1961 computation of 100,000 decimal digits of required roughly 105,000 full-precision operations, while a modern algorithm, devised by Jonathan and Peter Borwein in 1984, takes only 112 full-precision operations to achieve the same accuracy. A mere 8 iterations of their algorithm (roughly 56 operations) will produce 694 digits of (thus reducing Wm. Shanks' 15 year calculation to a matter of seconds).

On to Archimedes' method of exhaustion.


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Neal Carothers - carother@bgnet.bgsu.edu