Gromacs
2021.1

#include <gromacs/random/threefry.h>
General implementation class for ThreeFry counterbased random engines.
This class is used to implement several different ThreeFry2x64 random engines differing in the number of rounds executed in and the number of bits reserved for the internal counter. It is compatible with C++11 random engines, and can be used e.g. with all random distributions from the standard library.
ThreeFry is a counterbased rather than statebased random engine. This means that we seed it with a "key", after which we can get the N:th random number in a sequence (specified by a counter) directly. This means we are guaranteed the same sequence of numbers even when running in parallel if using e.g. step and atom index as counters.
However, it is also useful to be able to use it as a normal random engine, for instance if you need more than 2 64bit random values for a specific counter value, not to mention where you just need good normal random numbers. To achieve this, this implementation uses John Salmon's idea of reserving a couple of the highest bits in the userprovided counter for an internal counter. For instance, if reserving 3 bits, this means you get a stream of 8 iterations (each with 2 random values) after every restart. If you call the engine after these bits have been exhausted, it will throw an exception to make sure you don't get overlapping streams by mistake. Reserving 3 bits also means you can only use 643=61 bits of the highest word when restarting (i.e., setting) the counters.
This version also supports using internalCounterBits=0. In this case the random engine will be able to return a single counter round, i.e. 2 64bit values for ThreeFry2x64, after which an exception is thrown. In this case no high bits are reserved, which means the class implements the raw ThreeFry2x64 random function.
rounds  The number of encryption iterations used when generating. This can in principle be any value, but 20 rounds has been shown to pass all BigCrush random tests, and with 13 rounds only one fails. This is a very stringent test, and the standard Mersenne Twister engine fails two, so 13 rounds should be a perfectly fine balance in most cases. 
internalCounterBits  Number of high bits in the userprovided counter reserved for the internal counter. The number of values the engine can return after each restart will be words*2^internalCounterBits. 
Public Types  
typedef uint64_t  result_type 
Integer type for output.  
typedef std::array < result_type, 2 >  counter_type 
Use array for counter & key states so it is allocated on the stack.  
Public Member Functions  
ThreeFry2x64General (uint64_t key0=0, RandomDomain domain=RandomDomain::Other)  
Construct random engine with 2x64 key values. More...  
ThreeFry2x64General (uint64_t key0, uint64_t key1)  
Construct random engine from 2x64bit unsigned integers. More...  
void  seed (uint64_t key0=0, RandomDomain domain=RandomDomain::Other) 
Seed 2x64 random engine with two 64bit key values. More...  
void  seed (uint64_t key0, uint64_t key1) 
Seed random engine from 2x64bit unsigned integers. More...  
void  restart (uint64_t ctr0=0, uint64_t ctr1=0) 
Restart 2x64 random engine counter from 2 64bit values. More...  
result_type  operator() () 
Generate the next random number. More...  
void  discard (uint64_t n) 
Skip next n random numbers. More...  
bool  operator== (const ThreeFry2x64General< rounds, internalCounterBits > &x) const 
Return true if two ThreeFry2x64 engines are identical. More...  
bool  operator!= (const ThreeFry2x64General< rounds, internalCounterBits > &x) const 
Return true of two ThreeFry2x64 engines are not identical. More...  
Static Public Member Functions  
static constexpr result_type  min () 
Smallest value that can be returned from random engine.  
static constexpr result_type  max () 
Largest value that can be returned from random engine.  

inline 
Construct random engine with 2x64 key values.
This constructor takes two values, and should only be used with the 2x64 implementations.
key0  Random seed in the form of a 64bit unsigned value. 
domain  Random domain. This is used to guarantee that different applications of a random engine inside the code get different streams of random numbers, without requiring the user to provide lots of random seeds. Pick a value from the RandomDomain class, or RandomDomain::Other if it is not important. In the latter case you might want to use gmx::DefaultRandomEngine instead. 
InternalError  if the high bits needed to encode the number of counter bits are nonzero. 

inline 
Construct random engine from 2x64bit unsigned integers.
This constructor assigns the raw 128 bit key data from unsigned integers. It is meant for the case when you want full control over the key, for instance to compare with reference values of the ThreeFry function during testing.
key0  First word of key/random seed. 
key1  Second word of key/random seed. 
InternalError  if the high bits needed to encode the number of counter bits are nonzero. To test arbitrary values, use 0 internal counter bits. 

inline 
Skip next n random numbers.
Moves the internal random stream for the give key/counter value n positions forward. The count is based on the number of random values returned, such that skipping 5 values gives exactly the same result as drawing 5 values that are ignored.
n  Number of values to jump forward. 
InternalError  if the internal counter space is exhausted. 

inline 
Return true of two ThreeFry2x64 engines are not identical.
x  Instance to compare with. 
This routine should return true if the two engines will generate different random streams when drawing.

inline 
Generate the next random number.
This will return the next stored 64bit value if one is available, and otherwise generate a new block, update the internal counters, and return the first value while storing the others.
InternalError  if the internal counter space is exhausted. 

inline 
Return true if two ThreeFry2x64 engines are identical.
x  Instance to compare with. 
This routine should return true if the two engines will generate identical random streams when drawing.

inline 
Restart 2x64 random engine counter from 2 64bit values.
ctr0  First word of new counter, in the form of 64bit unsigned values. 
ctr1  Second word of new counter 
Restarting the engine with a new counter is extremely fast with ThreeFry64, and basically just consists of storing the counter value, so you should use this liberally in your innermost loops to restart the engine with e.g. the current step and atom index as counter values.
InternalError  if any of the highest bits that are reserved for the internal part of the counter are set. The number of reserved bits is to the last template parameter to the class. 

inline 
Seed 2x64 random engine with two 64bit key values.
key0  First word of random seed, in the form of 64bit unsigned values. 
domain  Random domain. This is used to guarantee that different applications of a random engine inside the code get different streams of random numbers, without requiring the user to provide lots of random seeds. Pick a value from the RandomDomain class, or RandomDomain::Other if it is not important. In the latter case you might want to use gmx::DefaultRandomEngine instead. 
Reinitialized the seed similar to the counter constructor. Same rules apply: The highest few bits of the last word are reserved to encode the number of internal counter bits, but to save the user the trouble of making sure these are zero when using e.g. a random device, we just ignore them.

inline 
Seed random engine from 2x64bit unsigned integers.
This assigns the raw 128 bit key data from unsigned integers. It is meant for the case when you want full control over the key, for instance to compare with reference values of the ThreeFry function during testing.
key0  First word of key/random seed. 
key1  Second word of key/random seed. 
InternalError  if the high bits needed to encode the number of counter bits are nonzero. To test arbitrary values, use 0 internal counter bits. 