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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LEARN ABOUT DEBIAN

first

FIRST(1)						      General Commands Manual							  FIRST(1)

NAME

       first - Yagi-Uda project quick antenna builder

SYNOPSIS

       first filename  elements f_min f_design f_max f_step diameter

DESCRIPTION

       The  program  first  is	one  of  a  number of executable programs that forms part of a set of programs, collectively known as the Yagi-Uda
       project , which were designed for analysis and optimisation of Yagi-Uda antennas.  first is used to define an antenna quickly, if  you  are
       not  interested	in  analysing a specific design (in which case use input ) but need to get a design that is half-way reasonable so that it
       may be optimised. It is much faster in use (since its not interactive) than input The design methodology that first is  the  DL6WU  antenna
       designs,  which	are  valid  for  10  or more elements, although first will calculate for any number of elements. DL6WU reccomends a folded
       dipole, but the designs here are for a simple dipole, since I don't yet know how to calculate the self  and  mutual  impedances	of  folded
       dipoles.

LIMITATIONS

       Filenames, including full path, can't exceed 90 characters.

       Does not take into account the variation of impedance of a dipole with change in wavelength/diameter of elements.

FILES

       filename 	 Yagi description, created by first.
       filename.out	 Binary data file, created by yagi.
       filename.dat	 Performance of antenna, created by output.
       filename.gai	 Gain of antenna, created by output.

       The  DOS  .EXE files as distributed require a 387 maths coprocessor to be present and will not run without it. A 486, Pentium, and I assume
       later processors of this series will run it without any extra hardware.

PLATFORMS

       Both DOS and and Unix versions have been built. The DOS version as distributed requires a 386 PC with a 387 maths coprocessor. The DOS ver-
       sion is no longer being developed, so the DOS executables included with the distribution are not upto date with the current source code.

AUTHORS

       Dr.  David  Kirkby  G8WRB  (david.kirkby@onetel.net).   with  help  with  the  conversion  to  the DOS/PC enviroment from Dr. Joe Mack NA3T
       (mack@fcrfv2.ncifcrf.gov)

SEE ALSO

       input(1), output(1), yagi(1), optimise(1).

BUGS

       Bugs should be reported to: David Kirkby G8WRB (david.kirkby@onetel.net).  Bugs tend actually to be fixed if they can be isolated, so it is
       in your interest to report them in such a way that they can be easily reproduced.

       If the input file is edited manually and done incorrectly, there can be unpredictable results.

       Options are not checked for sensible numbers. A negative length can be entered!

Version 1.10							  Fri Dec  2 1994							  FIRST(1)