PHP Loops - Runtime - Very advanced fine tuning - Calculate blending ratios - php

Question

I want to calculate blending ratios, but I have runtime problems,
It seems 7 components with a precision of 4% are the limit in PHP ...
So I try to find a way to avoid superfluous loops, to calculate faster.
I have ingredients and a limit (here 6). I want find all combinations
lower than 6. In a secound step (not shown here) I just order these
hits after price. I would like to find the cheapest combination with
ingredient_x lower than 6.
I try two ways, to do this, just simple sum the ingredients, and step by step, to abort the loops early (to safe loops).
<?php
$beginn = microtime(true);
$loops = 0;
$hits = 0;
$m = array();
// 1. TEST
$component[0]['ingredient_x'] = 6.95;
$component[1]['ingredient_x'] = 65.7;
$component[2]['ingredient_x'] = '';
$component[3]['ingredient_x'] = 2;
$component[4]['ingredient_x'] = '';
$component[5]['ingredient_x'] = '';
$component[6]['ingredient_x'] = '';
/*
Results:
With abort Loops
Loops: 285.188
Hits: 285.077
Seconds: 1,707 sec.
Without:
Loops: 736.281
Hits: 285.077
Seconds: 6,582 sec.
*/
// 2. TEST
$component[0]['ingredient_x'] = 6.95;
$component[1]['ingredient_x'] = 6.7;
$component[2]['ingredient_x'] = '';
$component[3]['ingredient_x'] = 2;
$component[4]['ingredient_x'] = '';
$component[5]['ingredient_x'] = '';
$component[6]['ingredient_x'] = '';
/*
Results:
With abort Loops
Loops: 735.244
Hits: 735.167
Seconds: 4,467 sec.
Without:
Loops: 736.281
Hits: 735.167
Seconds: 3,191 sec.
*/
$abort_loops = 1;
for ($m[0] = 0; $m[0] <= 100; $m[0] += 4) {
for ($m[1] = 0; $m[1] <= (100 - $m[0]); $m[1] += 4) {
for ($m[2] = 0; $m[2] <= (100 - $m[0] - $m[1]); $m[2] += 4) {
for ($m[3] = 0; $m[3] <= (100 - $m[0] - $m[1] - $m[2]); $m[3] += 4) {
for ($m[4] = 0; $m[4] <= (100 - $m[0] - $m[1] - $m[2] - $m[3]); $m[4] += 4) {
for ($m[5] = 0; $m[5] <= (100 - $m[0] - $m[1] - $m[2] - $m[3] - $m[4]); $m[5] += 4) {
$m[6] = (100 - $m[0] - $m[1] - $m[2] - $m[3] - $m[4] - $m[5]);
$loops++;
if ($abort_loops) {
$r = 0;
$do_break = 0;
// Checking ingredient_x sum, component by component
for ($i = 0; $i <= 6; $i++) {
$r += ($m[$i] * ($component[$i]['ingredient_x'] / 100));
// If Limit is reached, end all following loops
if ($r > 6) {
$m[$i] = 100;
// Cant break here, because of inner loop ...
$do_break = 1;
}
}
// ... so do it outside
if ($do_break) {
break;
}
$hits++;
} else {
// just sum ingredient_x
$r = ($m[0] * ($component[0]['ingredient_x'] / 100)) +
($m[1] * ($component[1]['ingredient_x'] / 100)) +
($m[2] * ($component[2]['ingredient_x'] / 100)) +
($m[3] * ($component[3]['ingredient_x'] / 100)) +
($m[4] * ($component[4]['ingredient_x'] / 100)) +
($m[5] * ($component[5]['ingredient_x'] / 100)) +
($m[6] * ($component[6]['ingredient_x'] / 100));
if ($r <= 6) {
$hits++;
}
}
}
}
}
}
}
}
print('Loops: ' . number_format($loops, 0, '', '.') . '<br>');
print('Hits: ' . number_format($hits, 0, '', '.') . '<br>');
print('Seconds: ' . number_format((microtime(true) - $beginn), 3, ',', '') . ' sec.');
?>
But this depends very on the ingredients. As you can see in Test 1
(abort loops is 5 times faster) and Test 2 (the simple sum way is faster).
Is it possible to make these loop faster? Better "abort loop" code?
Is there a faster way to find the cheapest combination?

Answer 1

One approach is to use simple math to improve your summing up:
// just sum ingredient_x
$r = (
$m[0] * $component[0]['ingredient_x'] +
$m[1] * $component[1]['ingredient_x'] +
$m[2] * $component[2]['ingredient_x'] +
$m[3] * $component[3]['ingredient_x'] +
$m[4] * $component[4]['ingredient_x'] +
$m[5] * $component[5]['ingredient_x'] +
$m[6] * $component[6]['ingredient_x']
);
;
if ($r <= 600) {
$hits++;
}
Allt thos divisons by 100 can be completely dropped if you simply raise your limit to 100 times your limit.
a0 / 100 + a1 / 100 + a2/100 + ... a6/100
is the same as
(a0 + a1 + a2 + ... + a6) /100
This will just need one division instead of 7.
Even this division can be avoided if you adjust your limit to 100 * your limit.
Speed improvement on my machine is about 10-15%.