/*
Example: 57 * 18
57 18
Halving the first column:
28 18
14
7
3
1
Doubling the second column:
28 36
14 72
7 144
3 288
1 576
Remove rows whose first cell is even:
18
28 36 x
14 72 x
7 144
3 288
1 576
Sum the remaining numbers in the right-hand column:
18
28 -
14 -
7 162
3 288
1 576
====
1026
*/
function ethiopianMultiply($a, $b) {
$sum = 0;
while ($a > 0) {
if ($a % 2 == 1) { // keep only odd rows
$sum += $b;
echo "sum = $sum\n";
}
$a = intdiv($a, 2); // halve left side
$b = $b * 2; // double right side
echo "a = $a b = $b\n";
}
return $sum;
}
$a = 57;
$b = 18;
echo ethiopianMultiply($a, $b) . "\n";
/*
run:
sum = 18
a = 28 b = 36
a = 14 b = 72
a = 7 b = 144
sum = 162
a = 3 b = 288
sum = 450
a = 1 b = 576
sum = 1026
a = 0 b = 1152
1026
*/
