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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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INTVAL(3)								 1								 INTVAL(3)

intval - Get the integer value of a variable

SYNOPSIS
int intval (mixed $var, [int $base = 10]) DESCRIPTION
Returns the integer value of $var, using the specified $base for the conversion (the default is base 10). intval(3) should not be used on objects, as doing so will emit an E_NOTICE level error and return 1. PARAMETERS
o $var - The scalar value being converted to an integer o $base - The base for the conversion Note If $base is 0, the base used is determined by the format of $var: o if string includes a "0x" (or "0X") prefix, the base is taken as 16 (hex); otherwise, o if string starts with "0", the base is taken as 8 (octal); otherwise, o the base is taken as 10 (decimal). RETURN VALUES
The integer value of $var on success, or 0 on failure. Empty arrays return 0, non-empty arrays return 1. The maximum value depends on the system. 32 bit systems have a maximum signed integer range of -2147483648 to 2147483647. So for example on such a system, intval('1000000000000') will return 2147483647. The maximum signed integer value for 64 bit systems is 9223372036854775807. Strings will most likely return 0 although this depends on the leftmost characters of the string. The common rules of integer casting apply. EXAMPLES
Example #1 intval(3) examples The following examples are based on a 32 bit system. <?php echo intval(42); // 42 echo intval(4.2); // 4 echo intval('42'); // 42 echo intval('+42'); // 42 echo intval('-42'); // -42 echo intval(042); // 34 echo intval('042'); // 42 echo intval(1e10); // 1410065408 echo intval('1e10'); // 1 echo intval(0x1A); // 26 echo intval(42000000); // 42000000 echo intval(420000000000000000000); // 0 echo intval('420000000000000000000'); // 2147483647 echo intval(42, 8); // 42 echo intval('42', 8); // 34 echo intval(array()); // 0 echo intval(array('foo', 'bar')); // 1 ?> NOTES
Note The $base parameter has no effect unless the $var parameter is a string. CHANGELOG
+--------+---------------------------------------------------+ |Version | | | | | | | Description | | | | +--------+---------------------------------------------------+ | 5.1.0 | | | | | | | Throws E_NOTICE and returns 1, when an object is | | | passed to $var. | | | | +--------+---------------------------------------------------+ SEE ALSO
boolval(3), floatval(3), strval(3), settype(3), is_numeric(3), Type juggling, BCMath Arbitrary Precision Mathematics Functions. PHP Documentation Group INTVAL(3)
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