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diff --git a/doc/gawk.texi b/doc/gawk.texi index ebaafbf3..5315422f 100644 --- a/doc/gawk.texi +++ b/doc/gawk.texi @@ -31004,6 +31004,80 @@ 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 |