\n";
  echo $README;
}

$au = sprintf("%f",floatval(1.49597871e11)); // m 
$Msol = sprintf("%f",floatval(1.9891e30)); // kg

// defaults

$f2 = 1e20; // emitted frequency, Hz
if (isset($_GET['f2']))
 $f2 = sprintf("%f",floatval($_GET['f2']));

$R1 = bcmul($au,"1"); // observer distance, meters 
if (isset($_GET['R1']))
  $R1 = sprintf("%f",floatval(trim($_GET['R1'],"+")));

$Mtest = bcmul($Msol,"1"); // black hole mass, kg
if (isset($_GET['M'])) {
  $Mtest = bcmul(sprintf("%.53f", floatval($_GET['M'])),$Msol);
//  error_log("Input M: " . floatval($_GET['M']));
}
//error_log("M = " . $Mtest);

// calculate the EH radius
$Rs = schwarzschild($Mtest); // got it, in meters.
//error_log("Rs = " . floatval($Rs));
if (floatval($Rs) >= floatval($R1) ) // sanity
  $R1 = bcmul($Rs,"2.0");

//error_log("R1 = " . $R1);
// phase 1:  redshift from different emission heights
echo "

";
echo "Mass M = " . $Mtest/$Msol . " Msol\n"
     ."Schwarzschild radius Rs = " . $Rs/$au . " a.u. (" . $Rs/1000 . "km)\n";;

echo "\nPhase 1:  emitter moves towards event horizon\n"
     ."Emission distance R2 = Rs + d (variable)\n"
     ."Observer distance R1 = " . sprintf("%e",$R1) . "m\n"
     ."Emitted frequency f2 = " . $f2 . "Hz\n\n"
    ."    d [m]          f1 [Hz]        z \n";
$p1s = sprintf("%f",max(1e12,$R1));
if (isset($_GET['p1s']))
  $p1s = sprintf("%.53f", floatval($_GET['p1s']));
$p1d = 10;
if (isset($_GET['p1d']))
  $p1d = sprintf("%.53f", floatval($_GET['p1d']));
if ( $p1d == 0 )
  $p1d = 2;
$p1e = 1e-25; 
if (isset($_GET['p1e']))
  $p1e = sprintf("%.53f", floatval($_GET['p1e']));
for ($d = $p1s; $d > $p1e; $d = bcdiv("$d","$p1d") ) { // loop over emitter distances
  $R2 = bcadd("$Rs","$d");
  $Rs2 = bcsub("$R2","$Rs");
  $Rs1 = bcsub("$R1","$Rs");
  $f1 = $f2*floatval(bcsqrt(bcdiv(bcmul($R1,$Rs2),bcmul($R2,$Rs1))));
  if ($f1 > 0) {
    $z = bcdiv(sprintf("%.53f","".$f2-$f1.""),sprintf("%.53f",$f1));
    echo sprintf("%e",$d) . "\t " . sprintf("%e",$f1) 
    . "\t" . sprintf("%e",$z) . " (" . sprintf("%.2f",$z) . ")\n";
  }
  else {
    $z = "inf";
    echo sprintf("%e",$d) . "\t " . sprintf("%e",$f1) 
    . "\t" . $z . "\n";
  }
 }

// phase 2:  redshift from different observer heights

$d = "0.001"; // how many meters above Rs to emit at phase 2
if (isset($_GET['d'])) {
//  error_log("getd=" . sprintf("%.53f",floatval($_GET['d'])));
  $d = bcadd("".sprintf("%.53f",floatval($_GET['d']))."","0.0");
//  error_log("d=".$d);
}

echo "\n\n"
    . "\nPhase 2:  observer moves away from the horizon"
    ."\nEmission distance R2 = Rs + " . sprintf("%e",$d) . "m\nObserver distance R1 = variable\nEmitted frequency f2 = " . $f2 . "Hz\n\n"
    ."R1 = Rs + [m]      f1 [Hz]        z \n";

$p2s = sprintf("%.53f", "1");
if (isset($_GET['p2s']))
  $p2s = sprintf("%.53f", floatval($_GET['p2s']));
$p2d = 10;
if (isset($_GET['p2d']))
  $p2d = sprintf("%.53f", floatval($_GET['p2d']));
if ($p2d <= 1 )
  $p2d = 2;
$p2e = 1e19;
if (isset($_GET['p2e']))
  $p2e = sprintf("%.53f", floatval($_GET['p2e']));
for ($i = $p2s; $i <= $p2e; $i = bcmul("$i","$p2d") ) { // loop over obser distances
  $R1 = bcadd("$Rs", "$i");
  $R2 = bcadd("$Rs","$d"); // change this to emit closer to/farther from event horizon
  $Rs2 = bcsub("$R2","$Rs");
  $Rs1 = bcsub("$R1","$Rs");
  $f1 = $f2*floatval(bcsqrt(bcdiv(bcmul($R1,$Rs2),bcmul($R2,$Rs1))));
  $z = bcdiv(sprintf("%.53f","".$f2-$f1.""),sprintf("%.53f",$f1));
  echo sprintf("%e",bcsub($R1,$Rs)) . "\t" . sprintf("%e",$f1)
    . "\t" . sprintf("%.2f", $z) . "\n";

 }

if (php_sapi_name() != "cli" ) {
  echo "

\n";
  echo "
";
  echo "\n  Bonus GET parameters for controlling the loops:\n"
     . "        p1s = phase 1 loop start, 'outerspace', f.e. 1e24\n"
     . "        p1d = phase 1 loop step divider, f.e. 10 or 1e1 (must be > 1)\n"
     . "        p1e = phase 1 loop end, ~event horizon, f.e. 1e-32\n"
     . "\n"
     . "        p2s = phase 2 loop start, ~event horizon, f.e. 1e-24\n"
     . "        p2d = phase 2 loop step multiplier, f.e. 10 or 1e1\n"
     . "        p2e = phase 2 loop end, 'outerspace', f.e. 1e32\n"
     . "\n"
     . "  Input is handled via PHPs sprintf, which limits \n"
     . "  numerical range for mass/distance to about 53 decades;\n"
     . "  the proton mass divided by solar mass is < 1e-57, and therefore\n"
     . "  proton horizon is intractable (until I maybe fix it).\n"
     . "\n"
     . "Example: http://rubor.org/schwarzschildarb.php?p1s=1e18&p1d=2&p1e=1e-32"
     . "\n\n"
    . "Creative Commons Attribution by jussi.kantola @ gmail.com 2017"
    . "\nVisualizations by Professor Andrew Hamilton and used with permission."
    . "\n"
    . "No guarantees on accuracy or correctness of the results. source code.";

echo "