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printf "dp:%u : %35.*f\n", $_, $_, 3.1415926535897932384626433832795 f
+or 14 .. 20;;
dp:14 :                    3.14159265358979
...
dp:18 :                3.141592653589793100
dp:19 :               3.1415926535897931000
dp:20 :              3.14159265358979310000

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[0] Perl> printf "dp:%u : %.*f\n", $_, $_, 123e-308 for 300 .. 320;;
dp:300 : 0.000 {300 zeros ellided} 000000000000
...
dp:318 : 0.000 {300 zeros ellided} 000000000000000001230000000000
dp:319 : 0.000 {300 zeros ellided} 0000000000000000012300000000000
dp:320 : 0.000 {300 zeros ellided} 00000000000000000123000000000000

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use Math::BigFloat;;

...
$n -= $bfd;;
print $n;;
0.0000000000000001384626433832795

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    3.14159265358979310
  + 0.0000000000000001384626433832795
  = 3.1415926535897932384626433832795 == 3.141592653589793238462643383
+2795 (the input)