Calculate the constant e to 14+ decimal places using integer maths. Post: 303039716

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Top Forums Shell Programming and Scripting Calculate the constant e to 14+ decimal places using integer maths. Post 303039716 by wisecracker on Sunday 13th of October 2019 10:40:33 AM

10-13-2019

Registered User

Calculate the constant e to 14+ decimal places using integer maths.

Hi guys...

I am loving this integer maths thing.
64 bit systems are certainly easier than 32 bit, but hey, I don't intend to leave out my fav' platform.
Using one of the 'Brothers' methods, URL inside the code.

Code:

#!/bin/sh
#
# #!/usr/local/bin/dash
# e_constant.sh
# Brother's formula [2].
# http://www.brotherstechnology.com/math/e-formulas.html
# e=2.718281828459045 from Python 3.8.0.
# Google's value, e=2.71828182846.
#
# For *NIX 64 bit or greater systems, 32 bit systems commented out.
# (Also tested on AMIGA OS_3.1 using ADE the UNIX emulator and ksh88.)

echo ""
echo "Calculate e to 14+ decimal places, 64 bit, (7+ decimal places, 32 bit),"
echo "integer maths inside 'dash' or 'sh'."
echo ""

initial_e=0

# 32 bit version for AMIGA ADE.
# e=200000000

# Default 64 bit version.
e=2000000000000000
k=0
factorial=1
diff=$(( e - initial_e ))
while [ ${diff} -gt 1 ]
do
    initial_e=${e}
    k=$(( k + 1 ))
    factorial=$(( factorial * 2 * k * (2 * k + 1) ))

    # 32 bit version.
    # e=$(( e + (((2 * k + 2) * 100000000) / factorial) ))

    # Default 64 bit version.
    e=$(( e + (((2 * k + 2) * 1000000000000000) / factorial) ))
    diff=$(( e - initial_e ))
done

# 32 bit version.
# printf "%.8f\n" $(( e ))e-8

# Default 64 bit version.
result=$( printf "%.15f\n" $(( e ))e-15 )
# Result: 2.718281828459041
echo "${result}"

echo ""
echo "Python 3.8.0 value, e = 2.718281828459045."
echo "Number of iterations = ${k}."
echo ""

Result in 64 bit mode, my usual platform.

Code:

Last login: Sun Oct 13 15:21:17 on ttys000
AMIGA:amiga~> cd Desktop/Code/Shell
AMIGA:amiga~/Desktop/Code/Shell> ./e_constant.sh

Calculate e to 14+ decimal places, 64 bit, (7+ decimal places, 32 bit),
integer maths inside 'dash' or 'sh'.

2.718281828459041

Python 3.8.0 value, e = 2.718281828459045.
Number of iterations = 9.

AMIGA:amiga~/Desktop/Code/Shell> _

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xdiff_string_patch

XDIFF_STRING_PATCH(3)							 1						     XDIFF_STRING_PATCH(3)

xdiff_string_patch - Patch a string with an unified diff

SYNOPSIS

       string xdiff_string_patch (string  $str, string	$patch, [int  $flags], [string	&$error])

DESCRIPTION

	Patches  a  $str  string  with	an  unified  patch in $patch parameter and returns the result. $patch has to be an unified diff created by
       xdiff_file_diff(3)/xdiff_string_diff(3) function. An optional $flags parameter specifies mode of operation. Any rejected parts of the patch
       will be stored inside $error variable if it is provided.

PARAMETERS

	      o $str
		- The original string.

	      o $patch
		- The unified patch string. It has to be created using xdiff_string_diff(3), xdiff_file_diff(3) functions or compatible tools.

	      o $flags
		-$flags can be either XDIFF_PATCH_NORMAL (default mode, normal patch) or XDIFF_PATCH_REVERSE (reversed patch).	Starting from ver-
		sion 1.5.0, you can also use binary OR to enable XDIFF_PATCH_IGNORESPACE flag.

	      o $error
		- If provided then rejected parts are stored inside this variable.

RETURN VALUES

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EXAMPLES

       Example #1

	      xdiff_string_patch(3) example

	       The following code applies changes to some article.

	      <?php
	      $old_article = file_get_contents('./old_article.txt');
	      $diff = $_SERVER['patch']; /* Let's say that someone pasted a patch to html form */

	      $errors = '';

	      $new_article = xdiff_string_patch($old_article, $diff, XDIFF_PATCH_NORMAL, $errors);
	      if (is_string($new_article)) {
		  echo "New article:
";
		  echo $new_article;
	      }

	      if (strlen($errors)) {
		  echo "Rejects: 
";
		  echo $errors;
	      }

	      ?>

SEE ALSO

       xdiff_string_diff(3).

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