"The value returned by any of the drand48(), erand48(), jrand48(), lrand48(), mrand48(), or nrand48() functions is computed by first generating the next 48-bit Xi in the sequence. Then the appropriate number of bits, according to the type of data item to be returned, are copied from the high-order (leftmost) bits of Xi and transformed into the returned value."
Unfortunately, the article doesn't go on to mention how this transformation takes place. Is it simple bitshifting, or are implementations allowed to apply rotations, negations, etc? Especially for a deterministic/reproducible PRNG this is a pretty important property.
I've compared various implementations (the BSDs, macOS, Linux and Solaris) and it miraculously looks like all of them use the same scheme for translating the 48-bits LCG state to the return value. The implementations differ here and there, but they effectively do this:
drand48() and erand48(): ldexp(lcgstate, -48)
jrand48() and mrand48(): (int32_t)(lcgstate >> 16)
lrand48() and nrand48(): lcgstate >> 17
"Then the appropriate number of bits, according to the type of data item to be returned, are copied from the high-order (leftmost) bits of Xi and transformed into the returned value."
with:
"Xi is then converted to the return value as follows.
- For drand48() and erand48(): 2^-48 * Xi
- For jrand48() and mrand48(): floor(2^-16 * Xi), followed by a conversion to int32_t
- For lrand48() and nrand48(): floor(2^-17 * Xi)"
At the same time I'd suggest that we add an example to this article that contains some test vectors, so that it becomes easier for people to write compliant implementations. Attached to this bug report you'll find a source file.
rand48-test-vectors.c [^] (2,409 bytes) 2016-12-08 15:09 
