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Full Discussion: PI day.
Operating Systems OS X (Apple) PI day. Post 303014677 by wisecracker on Sunday 18th of March 2018 06:45:02 AM
Old 03-18-2018
PI day.

Hi guys and gals...
OSX 10.13.3, default bash terminal calling ksh in the code.
I decided to have a go at creating PI using ksh only as a bit of fun.
I also decided on a Taylor series to do such a task.
This was the fun bit of code that generates PI to 6 decimal places although it could easily be set to continuous running and calculate within the limits of ksh's floating point precision.
It takes around 35 seconds to calculate to six decimal places...
Code:
#!/bin/ksh
# !/usr/local/bin/dash
# PI using the Taylor series.
# PI/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11......

clear
OP="-"
BASE=3.0
VAL=1.0
N=1
MYPI=0.0
while true
do
	if [ $(( $N % 2 )) -eq 0 ]
	then
		OP="+"
	fi
	if [ $(( $N % 2 )) -gt 0 ]
	then
		OP="-"
	fi
	VAL=$(( ($VAL * 1.0) $OP (1.0 / $BASE) ))
	BASE=$(( $BASE + 2.0 ))
	N=$(( $N + 1 ))
	MYPI=$(( $VAL * 4.0 ))
	# Hard coded known value to exit loop without interaction.
	if [ "${MYPI:0:8}" == "3.141592" ]
	then
		break
	fi
done
printf "PI to six decimal places = %.6f...\nIterations = $N...\n" "$MYPI"

Result:
Code:
PI to six decimal places = 3.141592...
Iterations = 1530012...
AMIGA:amiga~/Desktop/Code/Shell> _

Enjoy and hope to see other solutions on this thread...

Last edited by wisecracker; 03-18-2018 at 07:54 AM..
 

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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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