algorithm for finding Pi in C

[aarklon]

Hi all,

see:- http://mathforum.org/library/drmath/view/54456.html

[noagbodjivictor]

On May 26, 4:38*am, Richard Heathfield <[e-mail].i nvalidwrote:

James Dow Allen said:

On May 24, 5:41 pm, Richard Heathfield <[e-mail].i nvalidwrote:

spinoza1111 said:
On May 24, 2:44 pm, Richard Heathfield <[e-mail].i nvalidwrote:
Presumably you want Pi? Easy. It's about 3.

I'm disappointed no one in the thread mentioned the
almost unbelievable expression due to Ramanujan:
\frac{1}{\pi} = \frac{2\sqrt{2} }{9801}
* * *\sum^\infty_{k =0} \frac{(4k)!(110 3+26390k)}{(k!) ^4 396^{4k}}

But someone did mention it. In case you missed the article, the message ID
is <4afeda9c-ee40-43de-a0ac-e61dd8b84...@f2 4g2000prh.googl egroups.com-
check it out!

Admittedly, this formula may have little interest for those
for whom "about 3" is an adequate approximation.

<grinWell, "about 3" *is* an adequate approximation - on occasion. That
doesn't mean it's adequate for *all* uses.

--
Richard Heathfield <http://www.cpax.org.uk >
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

Well I also learned a sentence for PI to 20 something digits, but I
forgot it. It may be wandering somewhere online...

[Richard Heathfield]

no************* @gmail.com said:

On May 26, 4:38 am, Richard Heathfield <[e-mail].i nvalidwrote:

<snip>

><grinWell, "about 3" *is* an adequate approximation - on occasion.
That doesn't mean it's adequate for *all* uses.

Well I also learned a sentence for PI to 20 something digits, but I
forgot it. It may be wandering somewhere online...

Sir, I bear a rhyme excelling
In mystic force and magic spelling;
Celestial sprites elucidate
All my own striving can't relate.

From memory - except for one word which I wasn't sure that I'd remembered
properly, so I just whizzed through the first twenty places of pi in my
head to check that, even if my choice ("striving") was wrong, at least it
had the right number of letters. That's the trouble with mnemonics -
they're so hard to remember.

--
Richard Heathfield <http://www.cpax.org.uk >
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

[Richard Tobin]

In article <fe************ *************** *******@8g2000h se.googlegroups .com>,
no************* @gmail.com <no************ *@gmail.comwrot e:

>Well I also learned a sentence for PI to 20 som
ething digits, but I
forgot it. It may be wandering somewhere online...

Now I, even I, would celebrate in rhymes unapt
The great immortal Syracusan rivaled[*] nevermore
Who in his wondrous lore passed on before
Gave men his guidance how to circles mensurate.
[*] Must be American

-- Richard
--
In the selection of the two characters immediately succeeding the numeral 9,
consideration shall be given to their replacement by the graphics 10 and 11 to
facilitate the adoption of the code in the sterling monetary area. (X3.4-1963)

[Joachim Schmitz]

Richard Heathfield wrote:

no************* @gmail.com said:

>On May 26, 4:38 am, Richard Heathfield <[e-mail].i nvalidwrote:

<snip>

>><grinWell, "about 3" *is* an adequate approximation - on occasion.
That doesn't mean it's adequate for *all* uses.

Well I also learned a sentence for PI to 20 something digits, but I
forgot it. It may be wandering somewhere online...

Sir, I bear a rhyme excelling
In mystic force and magic spelling;
Celestial sprites elucidate
All my own striving can't relate.

Or locate they who can cogitate
And so finally terminate. Finis.

Extends Pi to 31 digits...

Bye, Jojo

[Bartc]

"Richard Heathfield" <rj*@see.sig.in validwrote in message
news:DZ******** *************** *******@bt.com. ..

no************* @gmail.com said:

>On May 26, 4:38 am, Richard Heathfield <[e-mail].i nvalidwrote:

<snip>

>><grinWell, "about 3" *is* an adequate approximation - on occasion.
That doesn't mean it's adequate for *all* uses.

Well I also learned a sentence for PI to 20 something digits, but I
forgot it. It may be wandering somewhere online...

Sir, I bear a rhyme excelling
In mystic force and magic spelling;
Celestial sprites elucidate
All my own striving can't relate.

From memory - except for one word which I wasn't sure that I'd remembered
properly, so I just whizzed through the first twenty places of pi in my
head to check that, even if my choice ("striving") was wrong, at least it
had the right number of letters. That's the trouble with mnemonics -
they're so hard to remember.

Good thing there wasn't a '0' in the first 20 places.

--
bartc

[Richard Heathfield]

Bartc said:

"Richard Heathfield" <rj*@see.sig.in validwrote in message
news:DZ******** *************** *******@bt.com. ..

<snip>

>>
Sir, I bear a rhyme excelling
In mystic force and magic spelling;
Celestial sprites elucidate
All my own striving can't relate.

From memory - except for one word which I wasn't sure that I'd
remembered properly, so I just whizzed through the first twenty places
of pi in my head to check [...]. That's the trouble
with mnemonics - they're so hard to remember.

Good thing there wasn't a '0' in the first 20 places.

I am given to understand that the canonical technique for '0' is to use a
ten-letter word (e.g. "understand ").

--
Richard Heathfield <http://www.cpax.org.uk >
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999

[Dann Corbit]

"pete" <pf*****@mindsp ring.comwrote in message
news:e7******** *************** *******@earthli nk.com...

aa*****@gmail.c om wrote:

>Hi all,

see:- http://mathforum.org/library/drmath/view/54456.html

This works for me:

#include <float.h>
/*
** pi == (atan(1.0 / 3) + atan(1.0 / 2)) * 4
*/
static double fs_pi(void);

static double fs_pi(void)
{
unsigned n;
double a, b;
static double p;
static int initialized;

if (!initialized) {
initialized = 1;
n = 1;
a = 3;
do {
a /= 9;
b = a / n;
n += 2;
a /= 9;
b -= a / n;
n += 2;
p += b;
} while (b DBL_EPSILON / 4);
n = 1;
a = 2;
do {
a /= 4;
b = a / n;
n += 2;
a /= 4;
b -= a / n;
n += 2;
p += b;
} while (b DBL_EPSILON / 2);
p *= 4;
}
return p;
}

It's not really any better, but p can do double duty:

#include <float.h>
/*
** pi == (atan(1.0 / 3) + atan(1.0 / 2)) * 4
*/
static double fs_pi(void);

static double fs_pi(void)
{
unsigned n;
double a,
b;
static double p = 0;

if (!p) {
n = 1;
a = 3;
do {
a /= 9;
b = a / n;
n += 2;
a /= 9;
b -= a / n;
n += 2;
p += b;
} while (b DBL_EPSILON / 4);
n = 1;
a = 2;
do {
a /= 4;
b = a / n;
n += 2;
a /= 4;
b -= a / n;
n += 2;
p += b;
} while (b DBL_EPSILON / 2);
p *= 4;
}
return p;
}

#ifdef UNIT_TEST
#include <stdio.h>
#include <math.h>
int main(void)
{
const double d = fs_pi();
printf("Pi approximation = %30.20g\n", d);
printf("Error is approximately %30.20g\n",
fabs(d - 3.1415926535897 932384626433832 795028841971693 993751));
return 0;
}
#endif
** Posted from http://www.teranews.com **

[aarklon]

On May 26, 8:10 pm, Richard Heathfield <[e-mail].i nvalidwrote:

noagbodjivic... @gmail.com said:

On May 26, 4:38 am, Richard Heathfield <[e-mail].i nvalidwrote:

<snip>

<grinWell, "about 3" *is* an adequate approximation - on occasion.
That doesn't mean it's adequate for *all* uses.

Well I also learned a sentence for PI to 20 something digits, but I
forgot it. It may be wandering somewhere online...

Sir, I bear a rhyme excelling
In mystic force and magic spelling;
Celestial sprites elucidate
All my own striving can't relate.

From memory - except for one word which I wasn't sure that I'd remembered
properly, so I just whizzed through the first twenty places of pi in my
head to check that, even if my choice ("striving") was wrong, at least it
had the right number of letters. That's the trouble with mnemonics -
they're so hard to remember.

see:- http://en.wikiquote.org/wiki/English...s_mnemonics#Pi

[James Dow Allen]

On May 26, 3:38*pm, Richard Heathfield <[e-mail].i nvalidwrote:

James Dow Allen said:

I'm disappointed no one in the thread mentioned the
almost unbelievable expression due to Ramanujan:

But someone did mention it. In case you missed the article,
the message ID
is <4afeda9c-ee40-43de-a0ac-
e61dd8b84...@f2 4g2000prh.googl egroups.com-
check it out!

Color me gullible, but I did search for this message,
which, in Google, seems to need an "Advanced" option.

But I agree: Great article!

>
<grinWell, "about 3" *is* an adequate approximation
- on occasion. That
doesn't mean it's adequate for *all* uses.

I wanted to post a rejoinder based on the famous
Tennessee legislation, but I discover that's an
urban legend. Indiana did, once, *almost* legislate
a rational value for pi, as shown in an
article by Mark Brader, of rec.puzzles fame:
http://www-personal.umich.edu/~jlawler/aux/pi.html

While Googling for pi = 3, I also found that
this approximation is dictated by the Bible
in Chronicles II: 4:2-5.

Anyway, AFAIK, bank software doesn't use trig.
How *did* you divert all those half-farthings to
your account, Richard? :-)

James

[Richard Heathfield]

James Dow Allen said:

On May 26, 3:38 pm, Richard Heathfield <[e-mail].i nvalidwrote:

>James Dow Allen said:

I'm disappointed no one in the thread mentioned the
almost unbelievable expression due to Ramanujan:

But someone did mention it. In case you missed the article,
the message ID
is <4afeda9c-ee40-43de-a0ac-
e61dd8b84...@f 24g2000prh.goog legroups.com-
check it out!

Color me gullible,

No such word.

I wanted to post a rejoinder based on the famous
Tennessee legislation, but I discover that's an
urban legend. Indiana did, once, *almost* legislate
a rational value for pi,

Oddly, a rational value of pi is irrational, whereas an irrational value is
rational.

as shown in an
article by Mark Brader, of rec.puzzles fame:

and indeed comp.lang.c fame (erstwhilely).

While Googling for pi = 3, I also found that
this approximation is dictated by the Bible
in Chronicles II: 4:2-5.

Hardly a diktat - merely a reasonable estimate, and not at all bad for 2500
years ago. Even Archimedes (250 or so years later) could only manage to
establish that the true value was somewhere between 223/71 and 7/2.

Anyway, AFAIK, bank software doesn't use trig.
How *did* you divert all those half-farthings to
your account, Richard? :-)

I could tell you, but then I'd have to bankrupt you.

--
Richard Heathfield <http://www.cpax.org.uk >
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999