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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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portal(5)							File Formats Manual							 portal(5)

NAME
portal - a "window to the future" for applications SYNOPSIS
DESCRIPTION
This header file is a "window to the future" for applications. It will help you to: o Write code that is portable across 32-bit and 64-bit systems, o Avoid undocumented assumptions about sizes of integral types, o Write portable code that needs to be explicit about the sizes of integral types, o Write code that is portable to a platform which has different sizes of integral types, and o Share frequently used macros that are portable across 32-bit and 64-bit systems. In addition to the macros defined in this file, it includes the header files (see limits(5)) and (see inttypes(5)). The following macros are defined in This macro can be used to create a mask that has one bit set. bit_num is the position of the bit to set, and type is the data type of the mask. A -1 is returned in the case of overflow or underflow. This macro can be used to set a bit in a mask. mask is the current value of the mask, bit_num is the position of the bit to set, and type is the data type of the mask. This macro can be used to return the bit position of the sign bit for the specified data type. type is the data type for which to return the position of the sign bit. This macro can be used to return a mask for the sign bit for the specified data type. type is the data type for which to return the sign bit mask. This macro can be used to do a sign extension from one data type to another. value is the current value that is to be sign-extended. old_type is the current data type of value and new_type is the new data type of value. This macro can be used to check if code has been compiled big or little endian. endian is an integer in which the result will be returned. The following macros can be used for print formatting and scan formatting of values of data types that can change in size based upon the compilation flag Examples of such data types are off_t and fpos_t. EXAMPLES
The macro in the following example will turn on the high bit in a 64-bit integer. The macro in the following example will be used to turn on all bits except the sign bit in a 32-bit integer. The macro in the following example will turn on the three least significant bits of the maximum integer. The macro in the following example will return the position of the sign bit in a 32-bit integer. The macro in the following example will return a sign bit mask for a 32-bit integer. The macro in the following example will convert the 8-bit integer stored in a char data type to a 64-bit integer and correctly extend the sign. The macro in the following example will store a 1 in endian if the compilation was big endian; otherwise, it will store a 0 in endian. AUTHOR
was developed by HP. FILES
SEE ALSO
inttypes(5), limits(5), printf(3S), scanf(3S). portal(5)
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