**tstorm@vu44.UUCP (Theo van der Storm)** (08/03/85)

In article <423@ist.UUCP> bco@ist.UUCP (Brian Collins) writes: >Following Ken Yap's posting, which soaks up 2 hours of CPU to >calculate Pi to 1000 decimal places, may I offer the >following sh/bc script that takes just over 6 mins on my >Pyramid. > >bc <<! > /* Computes Pi to $1 places */ > t = 3 * 10^${1-100} > for (i = 1; t != 0; i++) { > p = p + t > t = t * (2 * i - 1) * (2 * i - 1) / (8 * i * (2 * i + 1)) > } > p >! > > ...differential of asin( x) ; asin( 0.5) = pi / 6 ... > >Any advance on 6 minutes? > >Brian Collins ...mcvax!ist!bco (bco@ist) >Imperial Software Technology, London Using Ken Yap's formula (!) here is a bc program (written by me), which is almost twice as fast as YOUR program: [Replace =+, =/, etc. by +=, /=, etc. if necessary] bc << EOF n = $1 t = 16 * (10^n) / 5 e = 1 s = 0 while (t != 0){ s =+ t / e t =/ -25 e =+ 2 } t = 4 * (10^n) / 239 e = 1 while (t != 0){ s =- t / e t =/ -57121 e =+ 2 } s Apparently, Ken Yap's implementation was not very efficient :-) -- Theo van der Storm, 052 19'08"N / 004 51'16"E UUCP: {seismo|decvax|philabs}!mcvax!vu44!tstorm UUCP: {ark|botter|klipper|tjalk|vu45|vu60}!vu44!tstorm

**bco@ist.UUCP (Brian Collins)** (08/07/85)

```
Following Ken Yap's posting, which soaks up 2 hours of CPU to
calculate Pi to 1000 decimal places, may I offer the
following sh/bc script that takes just over 6 mins on my
Pyramid.
[ I can't be bothered to shar it just for 9 lines! ]
bc <<!
/* Computes Pi to $1 places */
t = 3 * 10^${1-100}
for (i = 1; t != 0; i++) {
p = p + t
t = t * (2 * i - 1) * (2 * i - 1) / (8 * i * (2 * i + 1))
}
p
!
The cost is guaranteed better than quadratic in the number of
decimal places, since each term is less than a quarter of the
previous one.
The recurrence relation is easily deduced from first principles
by:
integrating the
binomial expansion of the
differential of
asin( x)
one term at a time, and using this to compute
asin( 0.5)
which is (of course)
pi / 6
Any advance on 6 minutes?
--
Brian Collins ...mcvax!ist!bco (bco@ist)
Imperial Software Technology, London
```