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(1) 						      General Commands Manual							   echo(1)

NAME

       echo - echo (print) arguments

SYNOPSIS

       [arg] ...

DESCRIPTION

       writes  its  arguments  separated by blanks and terminated by a new-line on the standard output.  It also understands C-like escape conven-
       tions; beware of conflicts with the shell's use of

	      write an alert character
	      backspace
	      print line without appending a new-line
	      form-feed
	      new-line
	      carriage return
	      tab
	      vertical tab
	      backslash
	      the 8-bit character whose
			ASCII code is the 1-, 2-, 3- or 4-digit octal number n, whose first character must be a zero.
	      write an 8-bit value that is the zero-, one-, two- or three-digit octal number
			num

       is useful for producing diagnostics in command files and for sending known data into a pipe.

   Notes
       Berkeley differs from this implementation.  The former does not implement the backslash escapes.  However, the semantics of the escape  can
       be obtained by using the option.  The echo command implemented as a built-in function of follows the Berkeley semantics (see csh(1)).

EXTERNAL INFLUENCES

   Environment Variables
       determines the interpretation of arg as single and/or multi-byte characters.

       If is not specified in the environment or is set to the empty string, the value of is used as a default for each unspecified or empty vari-
       able.  If is not specified or is set to the empty string, a default of "C" (see lang(5)) is used instead  of  If  any  internationalization
       variable contains an invalid setting, behaves as if all internationalization variables are set to "C".  See environ(5).

   International Code Set Support
       Single- and multi-byte character code sets are supported.

AUTHOR

       was developed by OSF and HP.

SEE ALSO

       sh(1).

BUGS

       No characters are printed after the first This is not normally a problem.

STANDARDS CONFORMANCE

																	   echo(1)