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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echo

echo(1B)					     SunOS/BSD Compatibility Package Commands						  echo(1B)

NAME

       echo - echo arguments to standard output

SYNOPSIS

       /usr/ucb/echo [-n] [argument]

DESCRIPTION

       echo writes its arguments, separated by BLANKs and terminated by a NEWLINE, to the standard output.

       echo  is useful for producing diagnostics in command files and for sending known data into a pipe, and for displaying the contents of envi-
       ronment variables.

       For example, you can use echo to determine how many subdirectories below the root directory (/) is your current directory, as follows:

	   o	  echo your current-working-directory's full pathname

	   o	  pipe the output through tr to translate the path's embedded slash-characters into space-characters

	   o	  pipe that output through wc -w for a count of the names in your path.

		    example% /usr/bin/echo "echo $PWD | tr '/' ' ' | wc -w"

       See tr(1) and wc(1) for their functionality.

       The shells csh(1), ksh(1), and sh(1), each have an echo built-in command, which, by default, will have precedence, and will be  invoked	if
       the  user  calls  echo without a full pathname. /usr/ucb/echo and csh's echo() have an -n option, but do not understand back-slashed escape
       characters. sh's echo(), ksh's echo(), and /usr/bin/echo, on the other hand, understand the  black-slashed  escape  characters,	and  ksh's
       echo() also understands a as the audible bell character; however, these commands do not have an -n option.

OPTIONS

       -n    Do not add the NEWLINE to the output.

ATTRIBUTES

       See attributes(5) for descriptions of the following attributes:

       +-----------------------------+-----------------------------+
       |      ATTRIBUTE TYPE	     |	    ATTRIBUTE VALUE	   |
       +-----------------------------+-----------------------------+
       |Availability		     |SUNWscpu			   |
       +-----------------------------+-----------------------------+

SEE ALSO

       csh(1), echo(1), ksh(1), sh(1), tr(1), wc(1), attributes(5)

NOTES

       The -n option is a transition aid for BSD applications, and may not be supported in future  releases.

SunOS 5.11							    3 Aug 1994								  echo(1B)