From To Computer Processor Program # dec. Time Speed Nr max dec.
---- -- -------- --------- ------- ------ ---- ----- -----------
1988-02-25 1988-02-27 Apple II+ 6502 @ 1MHz Calpi 9 43000C 22520 57h 54m 1.0 43,000
1991-02-09 1991-02-12 Atari Mega ST4 68000 @ 8MHz Calpi AST 10 64504 79h 28m 14s 6.0 65,000
1995-07-27 1995-07-27 Risc PC 600 ARM610 @ 30Mhz Armpi 1 200000 15h 05m 50s 300 600,000,000
1995-07-28 1995-07-28 Risc PC 600 ARM610 @ 30Mhz Armpi 2 200000 9h 12m 19s 500 600,000,000
1995-08-05 1995-08-05 Risc PC 600 ARM610 @ 30Mhz Armpi 3 200000 7h 40m 07s 600 600,000,000
1995-08-07 1995-08-07 Risc PC 600 ARM610 @ 30Mhz Armpi 4 200000 6h 54m 04s 660 600,000,000
1996-11-06 1996-11-06 Risc PC 600 SA-110 @202MHz Armpi 4sa 200000 1h 59m 11s 2300 600,000,000
In each case, the following formula is used: pi/4 = arctan 1/2 + arctan 1/3.
But the algorithms are different. Concerning the long division by n, tables
are always used. On the Apple II, all the calculations are directly performed
in decimal; on the Atari and the Risc PC, pi is calculated in binary then
converted into decimal. Armpi 1 performs a 8-bit conversion (1 decimal digit
processed at once), Armpi 2 performs a 32-bit conversion (4 digits at once).
Armpi 3 groups the divisions by n, contrary to the previous programs:
(1/2^n + 1/3^n) / n is calculated, factorizing the division, instead of
(1/2^n) / n + (1/3^n) / n. Armpi 4 has a conversion that is a little faster.
The calculation is performed in a time proportional to the square of the number
of the calculated decimals, so that one can give a speed that does not depend
on the number of decimals. The speed given above has been normalized to 1 for
the Apple II.