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Kahan summation: Difference between revisions
modified example to comply with revised task and subtask
(included subtask code and comparison of the results) |
(modified example to comply with revised task and subtask) |
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=={{header|PHP}}==
===Script===
<lang php><?php
// Main task
// 1. Do all arithmetic in decimal to a precision of six digits.
// PHP does not have a way of restricting overall precision
// 2. Write a function/method/procedure/subroutine/... to perform Kahan
// summation on an ordered collection of numbers, (such as a list of numbers). )
function kahansum($input) {
$sum = $c = 0;
foreach($input as $item) {
$y = $item + $c;
$t = $sum + $y;
$c = ($t - $sum) - $y;
$sum = $t;
}
return $sum;
}
// 3. Create the three numbers a, b, c equal to 10000.0, 3.14159, 2.71828
// respectively.
$input = array(10000.0, 3.14159, 2.71828);
list($a, $b, $c) = $input;
// 4. show that the simple left-to-right summation, equivalent to (a + b) + c
// gives an answer of 10005.8 )
$sumabc = ($a + $b) + $c;
echo "Main task - Left to right summation: ";
echo sprintf("%6.1f", $sumabc).PHP_EOL;
// 10005.9
// 5. Show that the Kahan function applied to the sequence of values a, b, c
// results in the more precise answer of 10005.9
echo "Main task - Kahan summation: ";
echo sprintf("%6.1f", kahansum($input)).PHP_EOL;
// 10005.9
// Let's use the substask
$epsilon = 1.0;
while ((1.0 + $epsilon) != 1.0) {
$epsilon /= 2.0;
}
echo "Trying the subtask".PHP_EOL."epsilon: ";
echo $epsilon.PHP_EOL;
// 1.1102230246252E-16
$a = 1.0;
$b = $epsilon;
$c = -$epsilon;
$input = array($a, $b, $c);
// left-to-right summation
$sumabc = ($a + $b) + $c;
echo "Sub task - Left to right summation: ";
echo sprintf("%.1f", $sumabc).PHP_EOL;
// kahan summation
echo "Sub task - Kahan summation: ";
echo sprintf("%.1f", kahansum($input)).PHP_EOL;
// but, are they really the same or is an artifact?
echo "Are the results the same?".PHP_EOL;
var_dump((($a + $b) + $c) === kahansum($input));
// ok, then what is the difference?
echo "Difference between the operations: ";
$diff = (($a + $b) + $c) - kahansum($input);
echo $diff.PHP_EOL;
</lang>
Script output
<lang bash>
$ php kahansum.php
Main task - Left to right summation: 10005.9
Main task - Kahan summation: 10005.9
Trying the subtask
epsilon: 1.1102230246252E-16
Sub task - Left to right summation: 1.0
Sub task - Kahan summation: 1.0
Are the results the same?
bool(false)
Difference between the operations: 1.1102230246252E-16
</lang>
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