#!/usr/bin/php
<?php

define('FIX_PAD',       12); // -1 for no padding
define('MIN_POW',        2);
define('MAX_POW',        2);
define('ONLY_IM',     true);
define('SHOW_RESULT', true);
define('SHOW_DIST',   true);
define('BEGIN_PROGR',    0); // allows continuation of calculation
define('OUT_FILE', 'complex.out');

# -------------------------------------------------

if (BEGIN_PROGR == 0) {
	echo "COMPLEX IMMORTAL NUMBER SEARCH 1.0\n";
	echo "\n";
	echo "Parameters:  Min base     = 10\n";
	echo "             Max base     = 10\n";
	echo "             Min power    = ".MIN_POW."\n";
	echo "             Max power    = ".MAX_POW."\n";
	echo "             Only Im(z)>0 = ".(ONLY_IM ? 'Yes' : 'No')."\n";
	echo "\n";
}

for ($progress=BEGIN_PROGR; true; $progress++) {
	echo "Progress: $progress\r";
	for ($i=0; $i<$progress; $i++) {
		_go($i, $progress, FIX_PAD<0 ? strlen($progress) : FIX_PAD);
		_go($progress, $i, FIX_PAD<0 ? strlen($progress) : FIX_PAD);
	}
	_go($progress, $progress, FIX_PAD<0 ? strlen($progress) : FIX_PAD);
}

# -------------------------------------------------

function bcabs($x) {
	return str_replace('-', '', $x);
}

function bcadd2($a,$b) {
	return gmp_add($a,$b);
}

function bcsub2($a,$b) {
	return gmp_sub($a,$b);
}

function bcmul2($a,$b) {
	return gmp_mul($a,$b);
}

function is_immortal($xx, $x) {
	$x = bcabs($x);
	$xx = bcabs($xx);
	return substr($xx, -strlen($x)) == $x;
}

function complex_multiply($z1, $z2) {
	$a = $z1[0];
	$b = $z1[1];
	$c = $z2[0];
	$d = $z2[1];
	# return array(($a*$c)-($b*$d), ($a*$d)+($b*$c));
	return array(bcsub2(bcmul2($a,$c),bcmul2($b,$d)), bcadd2(bcmul2($a,$d),bcmul2($b,$c)));
}

function _go($x, $y, $pad) {
	if ($y%2 == 1) return; // y must be even because "2xy === y"

	$z = array($x, $y);
	$z_orig = $z;
	for ($p=2; $p<=MAX_POW; $p++) {
		$z = complex_multiply($z, $z_orig);
		if ($p<MIN_POW) continue;
		if (is_immortal($z[0],$x) && is_immortal($z[1],$y)) {
			if (($z[1] == 0) && (ONLY_IM)) continue;
			$line = '';
			$dist = round(sqrt($x*$x + $y*$y));
			if (SHOW_DIST) $line .= "[".str_pad($dist,$pad,'0',STR_PAD_LEFT)."] ";
			$line .= "IMMORTAL: (".str_pad($x,$pad,' ',STR_PAD_LEFT)." + ".str_pad($y,$pad,' ',STR_PAD_LEFT)."i) ^ $p";
			if (SHOW_RESULT) $line .= " = (".$z[0]." + ".$z[1]."i)";
			$line .= "\n";
			file_put_contents(OUT_FILE, $line, FILE_APPEND);
			echo "\r$line";

			file_put_contents(__DIR__.'/x_vals.out', str_pad($x,$pad,'0',STR_PAD_LEFT)."\n", FILE_APPEND);
			file_put_contents(__DIR__.'/y_vals.out', str_pad($y,$pad,'0',STR_PAD_LEFT)."\n", FILE_APPEND);
		}
	}
}