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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
Old 10-13-2019
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(1) 							   User Commands							   echo(1)

NAME
echo - echo arguments SYNOPSIS
/usr/bin/echo [string]... DESCRIPTION
The echo utility writes its arguments, separated by BLANKs and terminated by a NEWLINE, to the standard output. If there are no arguments, only the NEWLINE character is written. echo is useful for producing diagnostics in command files, for sending known data into a pipe, and for displaying the contents of environ- ment variables. The C shell, the Korn shell, and the Bourne shell all have echo built-in commands, which, by default, is invoked if the user calls echo without a full pathname. See shell_builtins(1). sh's echo, ksh's echo, ksh93's echo, and /usr/bin/echo understand the back-slashed escape characters, except that sh's echo does not understand a as the alert character. In addition, ksh's and ksh93's echo does not have an -n option. sh's echo and /usr/bin/echo have an -n option if the SYSV3 environment variable is set (see ENVIRONMENT VARIABLES below). csh's echo and /usr/ucb/echo, on the other hand, have an -n option, but do not understand the back-slashed escape characters. sh and ksh deter- mine whether /usr/ucb/echo is found first in the PATH and, if so, they adapt the behavior of the echo builtin to match /usr/ucb/echo. OPERANDS
The following operand is supported: string A string to be written to standard output. If any operand is "-n", it is treated as a string, not an option. The following char- acter sequences is recognized within any of the arguments: a Alert character.  Backspace. c Print line without new-line. All characters following the c in the argument are ignored. f Form-feed. New-line. Carriage return. Tab. v Vertical tab. \ Backslash. n Where n is the 8-bit character whose ASCII code is the 1-, 2- or 3-digit octal number representing that character. USAGE
Portable applications should not use -n (as the first argument) or escape sequences. The printf(1) utility can be used portably to emulate any of the traditional behaviors of the echo utility as follows: o The Solaris 2.6 operating environment or compatible version's /usr/bin/echo is equivalent to: printf "%b " "$*" o The /usr/ucb/echo is equivalent to: if [ "X$1" = "X-n" ] then shift printf "%s" "$*" else printf "%s " "$*" fi New applications are encouraged to use printf instead of echo. EXAMPLES
Example 1 Finding how far below root your current directory is located 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 $PWD | tr '/' ' ' | wc -w See tr(1) and wc(1) for their functionality. Below are the different flavors for echoing a string without a NEWLINE: Example 2 /usr/bin/echo example% /usr/bin/echo "$USER's current directory is $PWDc" Example 3 sh/ksh shells example$ echo "$USER's current directory is $PWDc" Example 4 csh shell example% echo -n "$USER's current directory is $PWD" Example 5 /usr/ucb/echo example% /usr/ucb/echo -n "$USER's current directory is $PWD" ENVIRONMENT VARIABLES
See environ(5) for descriptions of the following environment variables that affect the execution of echo: LANG, LC_ALL, LC_CTYPE, LC_MES- SAGES, and NLSPATH. SYSV3 This environment variable is used to provide compatibility with INTERACTIVE UNIX System and SCO UNIX installation scripts. It is intended for compatibility only and should not be used in new scripts. This variable is applicable only for Solaris x86 platforms, not Solaris SPARC systems. EXIT STATUS
The following error values are returned: 0 Successful completion. >0 An error occurred. ATTRIBUTES
See attributes(5) for descriptions of the following attributes: +-----------------------------+-----------------------------+ | ATTRIBUTE TYPE | ATTRIBUTE VALUE | +-----------------------------+-----------------------------+ |Availability |SUNWcsu | +-----------------------------+-----------------------------+ |CSI |Enabled | +-----------------------------+-----------------------------+ |Interface Stability |Committed | +-----------------------------+-----------------------------+ |Standard |See standards(5). | +-----------------------------+-----------------------------+ SEE ALSO
ksh93(1), printf(1), shell_builtins(1), tr(1), wc(1), echo(1B), ascii(5), attributes(5), environ(5), standards(5) NOTES
When representing an 8-bit character by using the escape convention n, the n must always be preceded by the digit zero(0). For example, typing: echo 'WARNING:7' prints the phrase WARNING: and sounds the "bell" on your terminal. The use of single (or double) quotes (or two backslashes) is required to protect the "" that precedes the "07". Following the , up to three digits are used in constructing the octal output character. If, following the n, you want to echo addi- tional digits that are not part of the octal representation, you must use the full 3-digit n. For example, if you want to echo "ESC 7" you must use the three digits "033" rather than just the two digits "33" after the . 2 digits Incorrect: echo "337" | od -xc produces: df0a (hex) 337 (ascii) 3 digits Correct: echo "0337" | od -xc produces: lb37 0a00 (hex) 033 7 (ascii) For the octal equivalents of each character, see ascii(5). SunOS 5.11 8 Apr 2008 echo(1)

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