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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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ROUND(3)								 1								  ROUND(3)

round - Rounds a float

SYNOPSIS
float round (float $val, [int $precision], [int $mode = PHP_ROUND_HALF_UP]) DESCRIPTION
Returns the rounded value of $val to specified $precision (number of digits after the decimal point). $precision can also be negative or zero (default). Note PHP doesn't handle strings like "12,300.2" correctly by default. See converting from strings. PARAMETERS
o $val - The value to round o $precision - The optional number of decimal digits to round to. o $mode - Use one of the following constants to specify the mode in which rounding occurs. +--------------------+---------------------------------------------------+ | Constant | | | | | | | Description | | | | +--------------------+---------------------------------------------------+ | | | | PHP_ROUND_HALF_UP | | | | | | | Round $val up to $precision decimal places away | | | from zero, when it is half way there. Making 1.5 | | | into 2 and -1.5 into -2. | | | | | | | |PHP_ROUND_HALF_DOWN | | | | | | | Round $val down to $precision decimal places | | | towards zero, when it is half way there. Making | | | 1.5 into 1 and -1.5 into -1. | | | | | | | |PHP_ROUND_HALF_EVEN | | | | | | | Round $val to $precision decimal places towards | | | the next even value. | | | | | | | |PHP_ROUND_HALF_ODD | | | | | | | Round $val to $precision decimal places towards | | | the next odd value. | | | | +--------------------+---------------------------------------------------+ RETURN VALUES
The rounded value EXAMPLES
Example #1 round(3) examples <?php echo round(3.4); // 3 echo round(3.5); // 4 echo round(3.6); // 4 echo round(3.6, 0); // 4 echo round(1.95583, 2); // 1.96 echo round(1241757, -3); // 1242000 echo round(5.045, 2); // 5.05 echo round(5.055, 2); // 5.06 ?> Example #2 $mode examples <?php echo round(9.5, 0, PHP_ROUND_HALF_UP); // 10 echo round(9.5, 0, PHP_ROUND_HALF_DOWN); // 9 echo round(9.5, 0, PHP_ROUND_HALF_EVEN); // 10 echo round(9.5, 0, PHP_ROUND_HALF_ODD); // 9 echo round(8.5, 0, PHP_ROUND_HALF_UP); // 9 echo round(8.5, 0, PHP_ROUND_HALF_DOWN); // 8 echo round(8.5, 0, PHP_ROUND_HALF_EVEN); // 8 echo round(8.5, 0, PHP_ROUND_HALF_ODD); // 9 ?> Example #3 $mode with precision examples <?php /* Using PHP_ROUND_HALF_UP with 1 decimal digit precision */ echo round( 1.55, 1, PHP_ROUND_HALF_UP); // 1.6 echo round( 1.54, 1, PHP_ROUND_HALF_UP); // 1.5 echo round(-1.55, 1, PHP_ROUND_HALF_UP); // -1.6 echo round(-1.54, 1, PHP_ROUND_HALF_UP); // -1.5 /* Using PHP_ROUND_HALF_DOWN with 1 decimal digit precision */ echo round( 1.55, 1, PHP_ROUND_HALF_DOWN); // 1.5 echo round( 1.54, 1, PHP_ROUND_HALF_DOWN); // 1.5 echo round(-1.55, 1, PHP_ROUND_HALF_DOWN); // -1.5 echo round(-1.54, 1, PHP_ROUND_HALF_DOWN); // -1.5 /* Using PHP_ROUND_HALF_EVEN with 1 decimal digit precision */ echo round( 1.55, 1, PHP_ROUND_HALF_EVEN); // 1.6 echo round( 1.54, 1, PHP_ROUND_HALF_EVEN); // 1.5 echo round(-1.55, 1, PHP_ROUND_HALF_EVEN); // -1.6 echo round(-1.54, 1, PHP_ROUND_HALF_EVEN); // -1.5 /* Using PHP_ROUND_HALF_ODD with 1 decimal digit precision */ echo round( 1.55, 1, PHP_ROUND_HALF_ODD); // 1.5 echo round( 1.54, 1, PHP_ROUND_HALF_ODD); // 1.5 echo round(-1.55, 1, PHP_ROUND_HALF_ODD); // -1.5 echo round(-1.54, 1, PHP_ROUND_HALF_ODD); // -1.5 ?> CHANGELOG
+--------+---------------------------------------------------+ |Version | | | | | | | Description | | | | +--------+---------------------------------------------------+ | 5.3.0 | | | | | | | The $mode parameter was introduced. | | | | | 5.2.7 | | | | | | | The inner workings of round(3) was changed to | | | conform to the C99 standard. | | | | +--------+---------------------------------------------------+ SEE ALSO
ceil(3), floor(3), number_format(3). PHP Documentation Group ROUND(3)
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