sub rshift {int($_[0]/(1<<$_[1])+($_[0]<0?-0.5:0.5))}

for (2140837940,-1934825877,-2004116368,1978483312,-293893010) {
    print "$_ >> 8 = ",rshift($_,8),"\n"
}
__END__
2140837940 >> 8 = 8362648
-1934825877 >> 8 = -7557914
-2004116368 >> 8 = -7828580
1978483312 >> 8 = 7728450
-293893010 >> 8 = -1148020