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$sum = 0; 
...
$SoS += sqrt( ( $_ - 127.5 )**2 ) for (0)x128, (255)x128; 
print $SoS, "\t", $stdDev = $SoS / 256;;
32640    127.5

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$sum = 0; 
$sum += $_ for (0)x128, (255)x127, 254; 
...
$SoS += sqrt( ( $_ - $mean )**2 ) for(0)x128, (255)x127, 254; 
print $SoS, "\t", $stdDev = $SoS / 256;;
32639    127.49609375

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3350850684932979117652665123754814942022584063591740702576779884286208
+799035732771005626138126763314259280802118502282445926550135522251856
+727692533193070412811083330325659322041700029792166250734253390513754
+466045711240338462701034020262992581378423147276636643647155396305352
+541105541439434840109915068285430675068591638581980604162940383356586
+739198268782104924614076605793562865241982176207428620969776803149467
+431386807972438247689158656000000000000000000000000000000000000000000
+000000000000000000000