Fluctuating (Randomized, Thermalized) LBM

• get random number from external field, add kernel to test suite @winterhalter
• physical test case to check random number correlation (auto correlation function?) @kuron
• final version should compute random numbers in the kernel itself. 'mulhi' / 'mullo' functions are required - philox RNG - write a pystencils function similar to bitoperations for these operations - on x86 there are intrinsics for mulhi/mullo, alternatively one could also use AES instead of philox since there is also a intrinsic for that - on GPU there should also be an intrinsic - C fallback as one-liner - two versions required for drawing float & double random numbers - fast versions produce 2 or more RN per step, how to handle this?

Fixes walberla/walberla#80 (closed)

Counter-based RNG: Philox from https://doi.org/10.1145/2063384.2063405

• Download from https://www.deshawresearch.com/downloads/download_random123.cgi/Random123-1.09.tar.gz
• std::random interface at https://github.com/DEShawResearch/Random123-Boost
• Implemented in cuRAND: https://docs.nvidia.com/cuda/curand

For CUDA, see /usr/local/cuda-9.0/include/curand_philox4x32_x.h:

#define QUALIFIERS static __forceinline__ __device__

#define PHILOX_W32_0   (0x9E3779B9)
#define PHILOX_W32_1   (0xBB67AE85)
#define PHILOX_M4x32_0 (0xD2511F53)
#define PHILOX_M4x32_1 (0xCD9E8D57)

QUALIFIERS uint32 mulhilo32(uint32 a, uint32 b, uint32* hip)
{
#ifndef __CUDA_ARCH__
    // host code
	uint64 product = ((uint64)a) * ((uint64)b);
	*hip = product >> 32;
	return (uint32)product;
#else
    // device code
    *hip = __umulhi(a,b);
    return a*b;
#endif
}

QUALIFIERS uint32* _philox4x32round(uint32* ctr, uint32* key)
{
	uint32 hi0;
	uint32 hi1;
	uint32 lo0 = mulhilo32(PHILOX_M4x32_0, ctr[0], &hi0);
	uint32 lo1 = mulhilo32(PHILOX_M4x32_1, ctr[2], &hi1);

	ctr[0] = hi1^ctr[1]^key[0];
	ctr[1] = lo1;
	ctr[2] = hi0^ctr[3]^key[1];
	ctr[3] = lo0;

	return ctr;
}

QUALIFIERS uint32* _philox4x32bumpkey( uint32* key)
{
	key[0] += PHILOX_W32_0;
	key[1] += PHILOX_W32_1;
	return key;
}

QUALIFIERS void curand_Philox4x32_10(uint32x4 ctr, uint32x2 key, uint32* out)
{
	ctr = _philox4x32round(ctr, key);                                 // 1 
	key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 2
    key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 3
	key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 4
    key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 5
	key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 6
    key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 7
	key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 8
    key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 9
	key = _philox4x32bumpkey(key); ctr = _philox4x32round(ctr, key);  // 10
	for(int i=0; i<4; i++)	out[i] = ctr[i];
	return;
}

Test for RNG quality https://arxiv.org/abs/0906.2425

assigned to @bauer and unassigned @winterhalter

Would be nice for Walberla 4.0

Random123 is fully templated, so it might be possible to just add operator overloads for the SIMD-packed datatypes to get vectorization.

mentioned in issue walberla/walberla#80 (closed)

changed the description

First WIP draft finally from my end in software/pystencils!37

marked the checklist item final version should compute random numbers in the kernel itself. 'mulhi' / 'mullo' functions are required as completed

mentioned in merge request !1 (closed)

Missing pieces:

• seeding the RNG (make the second key settable from the constructor)
• correct passthrough of AST objects everywhere. The assignment handling works with the changes in the test_martin branch, but CSE does not.

mentioned in merge request walberla/walberla!220 (merged)

marked the checklist item get random number from external field, add kernel to test suite @winterhalter as completed

marked the checklist item get random number from external field, add kernel to test suite @winterhalter as incomplete

marked the checklist item physical test case to check random number correlation (auto correlation function?) @kuron as completed

marked the checklist item physical test case to check random number correlation (auto correlation function?) @kuron as incomplete

mentioned in merge request !2 (closed)

mentioned in merge request lbmpy_walberla!1 (merged)

mentioned in merge request !3 (merged)

closed via merge request !3 (merged)

mentioned in commit 1c4dfcf8