Rmpfr_dump( Math::MPFR->new($r.at(0)) );

In executing that, you are assigning 15-significant-decimal-digit strings (eg 0.816545445367819) to a 53-bit precision float (double) ... and then observing that the assignment populates all 53 bits:

D:\>perl -MMath::MPFR=":mpfr" -MPDL -le "for(1..10) {$r = PDL->random(
+); Rmpfr_dump(Math::MPFR->new($r.at(0)))}"
0.11101001100100000110110101110010100111100110010011000E-1
0.10110010100010010011101011001111010011110001011001001E-2
0.11101000000110110001010100000001011101100000111011111E-3
0.10110010010001101100111011100101000000001001100100011E0
0.11010000000101010100010000110000010010011110111101111E0
0.11101010010011100000100010101111011100001010000100111E-3
0.11001010100111101101000101101010111011100110010001111E-1
0.11111111111011111000010100111010010010001010101010110E-1
0.10111001110100001011011100010100001101011001101011010E-2
0.11011111011110110001110011111111011111010111110001100E-1
[download]

But you'll see the same thing if you use 15-significant-decimal-digit representations of values provided by rand():

D:\>perl -MMath::MPFR=":mpfr" -MPDL -le "for(1..10) {Rmpfr_dump(Math::
+MPFR->new(sprintf '%.15g', rand()))}"
0.11011001011111100110011011010010100010000000100011011E-3
0.10001011110110011101000101001110110001101111000000110E-1
0.11001011001111001101010100001100101010001000110000110E-2
0.11110111001110000011011110111000011000101111000111101E0
0.11110111100000100111010101111111100011010001010100010E0
0.10001110111001111100101011010111110111111111011111000E-1
0.10101100000000101101100111000011001011001010110111010E-1
0.11010110011101110001001101010011001011010001010111111E0
0.11111010001001001100100110011111101100110100011110010E-3
0.11010111110100100001010011100100000011000000000000100E-4
[download]

Yet, we already know (and you have just shown it) that rand() does not populate the 5 lowest bits.
This behaviour is inevitable when double-precision values are rounded to 15 decimal digit precision, and then assigned back in.
If 17 decimal digits of precision were provided, this capacity to mislead would go away:

D:\>perl -MMath::MPFR=":mpfr" -le "for(1..10) { Rmpfr_dump(Math::MPFR-
+>new(sprintf '%.17g', rand()))}"
0.10110100110110100010000010011000101000100000001000000E-1
0.10001101011001100001100001100010110001101111000000000E-1
0.11111010010100100101001100000101001010100010001100000E0
0.11000011010000000101111010100100110001011110010000000E-1
0.11111000011001100111110000100011000110100010101000000E-1
0.11101100001000111011110010101111011111111110000000000E-3
0.10001001000110010110010011000011100101100101011100000E0
0.10100000101110001010101010001101001011010001011000000E0
0.11100000100010000001100011100101111101100110100100000E0
0.10000000011000110110000011000010000001100000000000000E-3
[download]

Unfortunately, there's not much to be gleaned from looking at double-precision values rounded to 15-significant-decimal-digit strings.
We need to be looking at how those values were derived.

Update: Mind you, I could be barking up the wrong tree, anyway - which is even more likely if this issue you've identified is limited to threading.

Cheers,
Rob

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