aboutsummaryrefslogtreecommitdiffstats
path: root/doc/gawktexi.in
diff options
context:
space:
mode:
Diffstat (limited to 'doc/gawktexi.in')
-rw-r--r--doc/gawktexi.in74
1 files changed, 74 insertions, 0 deletions
diff --git a/doc/gawktexi.in b/doc/gawktexi.in
index 96c0a76c..2600011f 100644
--- a/doc/gawktexi.in
+++ b/doc/gawktexi.in
@@ -30098,6 +30098,80 @@ function div(numerator, denominator, result, i)
@c endfile
@end example
+The following example program, contributed by Katie Wasserman,
+uses @code{div()} to
+compute the digits of @value{PI} to as many places as you
+choose to set:
+
+@example
+@c file eg/prog/pi.awk
+# pi.awk --- compute the digits of pi
+@c endfile
+@c endfile
+@ignore
+@c file eg/prog/pi.awk
+#
+# Katie Wasserman, katie@@wass.net
+# August 2014
+@c endfile
+@end ignore
+@c file eg/prog/pi.awk
+
+BEGIN @{
+ digits = 100000
+ two = 2 * 10 ^ digits
+ pi = two
+ for (m = digits * 4; m > 0; --m) @{
+ d = m * 2 + 1
+ x = pi * m
+ div(x, d, result)
+ pi = result["quotient"]
+ pi = pi + two
+ @}
+ print pi
+@}
+@c endfile
+@end example
+
+@ignore
+Date: Wed, 20 Aug 2014 10:19:11 -0400
+To: arnold@skeeve.com
+From: Katherine Wasserman <katie@wass.net>
+Subject: Re: computation of digits of pi?
+
+Arnold,
+
+>The program that you sent to compute the digits of pi using div(). Is
+>that some standard algorithm that every math student knows? If so,
+>what's it called?
+
+It's not that well known but it's not that obscure either
+
+It's Euler's modification to Newton's method for calculating pi.
+
+Take a look at lines (23) - (25) here: http://mathworld.wolfram.com/PiFormulas.htm
+
+The algorithm I wrote simply expands the multiply by 2 and works from the innermost expression outwards. I used this to program HP calculators because it's quite easy to modify for tiny memory devices with smallish word sizes.
+
+http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/articles.cgi?read=899
+
+-Katie
+@end ignore
+
+When asked about the algorithm used, Katie replied:
+
+@quotation
+It's not that well known but it's not that obscure either.
+It's Euler's modification to Newton's method for calculating pi.
+Take a look at lines (23) - (25) here: @uref{http://mathworld.wolfram.com/PiFormulas.htm}.
+
+The algorithm I wrote simply expands the multiply by 2 and works from
+the innermost expression outwards. I used this to program HP calculators
+because it's quite easy to modify for tiny memory devices with smallish
+word sizes. See
+@uref{http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/articles.cgi?read=899}.
+@end quotation
+
@node POSIX Floating Point Problems
@section Standards Versus Existing Practice