I have a simple CUDA kernel which I thought was accessing global memory efficiently. The Nvidia profiler however reports that I am performing inefficient global memory accesses. My kernel code is:
__global__ void update_particles_kernel
(
float4 *pos,
float4 *vel,
float4 *acc,
float dt,
int numParticles
)
{
int index = threadIdx.x + blockIdx.x * blockDim.x;
int offset = 0;
while(index + offset < numParticles)
{
vel[index + offset].x += dt*acc[index + offset].x; // line 247
vel[index + offset].y += dt*acc[index + offset].y;
vel[index + offset].z += dt*acc[index + offset].z;
pos[index + offset].x += dt*vel[index + offset].x; // line 251
pos[index + offset].y += dt*vel[index + offset].y;
pos[index + offset].z += dt*vel[index + offset].z;
offset += blockDim.x * gridDim.x;
}
In particular the profiler reports the following:
From the CUDA best practices guide it says:
"For devices of compute capability 2.x, the requirements can be summarized quite easily: the concurrent accesses of the threads of a warp will coalesce into a number of transactions equal to the number of cache lines necessary to service all of the threads of the warp. By default, all accesses are cached through L1, which as 128-byte lines. For scattered access patterns, to reduce overfetch, it can sometimes be useful to cache only in L2, which caches shorter 32-byte segments (see the CUDA C Programming Guide).
For devices of compute capability 3.x, accesses to global memory are cached only in L2; L1 is reserved for local memory accesses. Some devices of compute capability 3.5, 3.7, or 5.2 allow opt-in caching of globals in L1 as well."
Now in my kernel based on this information I would expect that 16 accesses would be required to service a 32 thread warp because float4 is 16 bytes and on my card (770m compute capability 3.0) reads from the L2 cache are performed in 32 bytes chunks (16 bytes * 32 threads / 32 bytes cache lines = 16 accesses). Indeed as you can see the profiler reports that I am doing 16 access. What I don't understand is why the profiler reports that the ideal access would involve 8 L2 transactions per access for line 247 and only 4 L2 transactions per access for the remaining lines. Can someone explain what I am missing here?
I have a simple CUDA kernel which I thought was accessing global memory efficiently. The Nvidia profiler however reports that I am performing inefficient global memory accesses.
To take one example, your float4 vel array is stored in memory like this:
0.x 0.y 0.z 0.w 1.x 1.y 1.z 1.w 2.x 2.y 2.z 2.w 3.x 3.y 3.z 3.w ...
^ ^ ^ ^ ...
thread0 thread1 thread2 thread3
So when you do this:
vel[index + offset].x += ...; // line 247
you are accessing (storing) at the locations (.x) that I have marked above. The gaps in between each ^ mark indicate an inefficient access pattern, which the profiler is pointing out. (It does not matter that in the very next line of code, you are storing to the .y locations.)
There are at least 2 solutions, one of which would be a classical AoS -> SoA reorganization of your data, with appropriate code adjustments. This is well documented (e.g. here on the cuda tag and elsewhere) in terms of what it means, and how to do it, so I will let you look that up.
The other typical solution is to load a float4 quantity per thread, when you need it, and store a float4 quantity per thread, when you need to. Your code can be trivially reworked to do this, which should give improved profiling results:
//preceding code need not change
while(index + offset < numParticles)
{
float4 my_vel = vel[index + offset];
float4 my_acc = acc[index + offset];
my_vel.x += dt*my_acc.x;
my_vel.y += dt*my_acc.y;
my_vel.z += dt*my_acc.z;
vel[index + offset] = my_vel;
float4 my_pos = pos[index + offset];
my_pos.x += dt*my_vel.x;
my_pos.y += dt*my_vel.y;
my_pos.z += dt*my_vel.z;
pos[index + offset] = my_pos;
offset += blockDim.x * gridDim.x;
}
Even though you might think that this code is "less efficient" than your code, because your code "appears" to be only loading and storing .x, .y, .z, whereas mine "appears" to also load and store .w, in fact there is essentially no difference, due to the way a GPU loads and stores to/from global memory. Although your code does not appear to touch .w, in the process of accessing the adjacent elements, the GPU will load the .w elements from global memory, and also (eventually) store the .w elements back to global memory.
What I don't understand is why the profiler reports that the ideal access would involve 8 L2 transactions per access for line 247
For line 247 in your original code, you are accessing one float quantity per thread for the load operation of acc.x, and one float quantity per thread for the load operation of vel.x. A float quantity per thread by itself should require 128 bytes for a warp, which is 4 32-byte L2 cachelines. Two loads together would require 8 L2 cacheline loads. This is the ideal case, which assumes that the quantities are packed together nicely (SoA). But that is not what you have (you have AoS).
I have a very large set (billions or more, it's expected to grow exponentially to some level), and I want to generate seemingly random elements from it without repeating. I know I can pick a random number and repeat and record the elements I have generated, but that takes more and more memory as numbers are generated, and wouldn't be practical after couple millions elements out.
I mean, I could say 1, 2, 3 up to billions and each would be constant time without remembering all the previous, or I can say 1,3,5,7,9 and on then 2,4,6,8,10, but is there a more sophisticated way to do that and eventually get a seemingly random permutation of that set?
Update
1, The set does not change size in the generation process. I meant when the user's input increases linearly, the size of the set increases exponentially.
2, In short, the set is like the set of every integer from 1 to 10 billions or more.
3, In long, it goes up to 10 billion because each element carries the information of many independent choices, for example. Imagine an RPG character that have 10 attributes, each can go from 1 to 100 (for my problem different choices can have different ranges), thus there's 10^20 possible characters, number "10873456879326587345" would correspond to a character that have "11, 88, 35...", and I would like an algorithm to generate them one by one without repeating, but makes it looks random.
Thanks for the interesting question. You can create a "pseudorandom"* (cyclic) permutation with a few bytes using modular exponentiation. Say we have n elements. Search for a prime p that's bigger than n+1. Then find a primitive root g modulo p. Basically by definition of primitive root, the action x --> (g * x) % p is a cyclic permutation of {1, ..., p-1}. And so x --> ((g * (x+1))%p) - 1 is a cyclic permutation of {0, ..., p-2}. We can get a cyclic permutation of {0, ..., n-1} by repeating the previous permutation if it gives a value bigger (or equal) n.
I implemented this idea as a Go package. https://github.com/bwesterb/powercycle
package main
import (
"fmt"
"github.com/bwesterb/powercycle"
)
func main() {
var x uint64
cycle := powercycle.New(10)
for i := 0; i < 10; i++ {
fmt.Println(x)
x = cycle.Apply(x)
}
}
This outputs something like
0
6
4
1
2
9
3
5
8
7
but that might vary off course depending on the generator chosen.
It's fast, but not super-fast: on my five year old i7 it takes less than 210ns to compute one application of a cycle on 1000000000000000 elements. More details:
BenchmarkNew10-8 1000000 1328 ns/op
BenchmarkNew1000-8 500000 2566 ns/op
BenchmarkNew1000000-8 50000 25893 ns/op
BenchmarkNew1000000000-8 200000 7589 ns/op
BenchmarkNew1000000000000-8 2000 648785 ns/op
BenchmarkApply10-8 10000000 170 ns/op
BenchmarkApply1000-8 10000000 173 ns/op
BenchmarkApply1000000-8 10000000 172 ns/op
BenchmarkApply1000000000-8 10000000 169 ns/op
BenchmarkApply1000000000000-8 10000000 201 ns/op
BenchmarkApply1000000000000000-8 10000000 204 ns/op
Why did I say "pseudorandom"? Well, we are always creating a very specific kind of cycle: namely one that uses modular exponentiation. It looks pretty pseudorandom though.
I would use a random number and swap it with an element at the beginning of the set.
Here's some pseudo code
set = [1, 2, 3, 4, 5, 6]
picked = 0
Function PickNext(set, picked)
If picked > Len(set) - 1 Then
Return Nothing
End If
// random number between picked (inclusive) and length (exclusive)
r = RandomInt(picked, Len(set))
// swap the picked element to the beginning of the set
result = set[r]
set[r] = set[picked]
set[picked] = result
// update picked
picked++
// return your next random element
Return temp
End Function
Every time you pick an element there is one swap and the only extra memory being used is the picked variable. The swap can happen if the elements are in a database or in memory.
EDIT Here's a jsfiddle of a working implementation http://jsfiddle.net/sun8rw4d/
JavaScript
var set = [];
set.picked = 0;
function pickNext(set) {
if(set.picked > set.length - 1) { return null; }
var r = set.picked + Math.floor(Math.random() * (set.length - set.picked));
var result = set[r];
set[r] = set[set.picked];
set[set.picked] = result;
set.picked++;
return result;
}
// testing
for(var i=0; i<100; i++) {
set.push(i);
}
while(pickNext(set) !== null) { }
document.body.innerHTML += set.toString();
EDIT 2 Finally, a random binary walk of the set. This can be accomplished with O(Log2(N)) stack space (memory) which for 10billion is only 33. There's no shuffling or swapping involved. Using trinary instead of binary might yield even better pseudo random results.
// on the fly set generator
var count = 0;
var maxValue = 64;
function nextElement() {
// restart the generation
if(count == maxValue) {
count = 0;
}
return count++;
}
// code to pseudo randomly select elements
var current = 0;
var stack = [0, maxValue - 1];
function randomBinaryWalk() {
if(stack.length == 0) { return null; }
var high = stack.pop();
var low = stack.pop();
var mid = ((high + low) / 2) | 0;
// pseudo randomly choose the next path
if(Math.random() > 0.5) {
if(low <= mid - 1) {
stack.push(low);
stack.push(mid - 1);
}
if(mid + 1 <= high) {
stack.push(mid + 1);
stack.push(high);
}
} else {
if(mid + 1 <= high) {
stack.push(mid + 1);
stack.push(high);
}
if(low <= mid - 1) {
stack.push(low);
stack.push(mid - 1);
}
}
// how many elements to skip
var toMid = (current < mid ? mid - current : (maxValue - current) + mid);
// skip elements
for(var i = 0; i < toMid - 1; i++) {
nextElement();
}
current = mid;
// get result
return nextElement();
}
// test
var result;
var list = [];
do {
result = randomBinaryWalk();
list.push(result);
} while(result !== null);
document.body.innerHTML += '<br/>' + list.toString();
Here's the results from a couple of runs with a small set of 64 elements. JSFiddle http://jsfiddle.net/yooLjtgu/
30,46,38,34,36,35,37,32,33,31,42,40,41,39,44,45,43,54,50,52,53,51,48,47,49,58,60,59,61,62,56,57,55,14,22,18,20,19,21,16,15,17,26,28,29,27,24,25,23,6,2,4,5,3,0,1,63,10,8,7,9,12,11,13
30,14,22,18,16,15,17,20,19,21,26,28,29,27,24,23,25,6,10,8,7,9,12,13,11,2,0,63,1,4,5,3,46,38,42,44,45,43,40,41,39,34,36,35,37,32,31,33,54,58,56,55,57,60,59,61,62,50,48,49,47,52,51,53
As I mentioned in my comment, unless you have an efficient way to skip to a specific point in your "on the fly" generation of the set this will not be very efficient.
if it is enumerable then use a pseudo-random integer generator adjusted to the period 0 .. 2^n - 1 where the upper bound is just greater than the size of your set and generate pseudo-random integers discarding those more than the size of your set. Use those integers to index items from your set.
Pre- compute yourself a series of indices (e.g. in a file), which has the properties you need and then randomly choose a start index for your enumeration and use the series in a round-robin manner.
The length of your pre-computed series should be > the maximum size of the set.
If you combine this (depending on your programming language etc.) with file mappings, your final nextIndex(INOUT state) function is (nearly) as simple as return mappedIndices[state++ % PERIOD];, if you have a fixed size of each entry (e.g. 8 bytes -> uint64_t).
Of course, the returned value could be > your current set size. Simply draw indices until you get one which is <= your sets current size.
Update (In response to question-update):
There is another option to achieve your goal if it is about creating 10Billion unique characters in your RPG: Generate a GUID and write yourself a function which computes your number from the GUID. man uuid if you are are on a unix system. Else google it. Some parts of the uuid are not random but contain meta-info, some parts are either systematic (such as your network cards MAC address) or random, depending on generator algorithm. But they are very very most likely unique. So, whenever you need a new unique number, generate a uuid and transform it to your number by means of some algorithm which basically maps the uuid bytes to your number in a non-trivial way (e.g. use hash functions).
I am new to parallel programming using MPI... I need to parallelize a 300x200 Lattice Boltzman cube.. I managed chunking row wise by dividing 200 into chunks depending on size... However my code works only when there are 4 and 8 cores... I need to run the program on 16 cores..Can anyone please direct me as to how to divide 200 for 16 cores..
I am splitting currently in the following manner:
.
.
.
MPI_Init( &argc, &argv );
/* size and rank will become ubiquitous */
/* get no of process (size) & rank of each proces*/
MPI_Comm_size( MPI_COMM_WORLD, &size );
MPI_Comm_rank( MPI_COMM_WORLD, &rank );
start= (200 / size) * rank;
end = start + (200 / size);
.
.
.
for(ii=start;ii<end;ii++) {
for(jj=0;jj<300;jj++)
.
.
.
}
.
.
CLearly the above technique would work only if 200%size = 0, for 16 cores size=16, and hence the approach would fail.. Could anyone please suggest a more generalized chunking approach approach..which would make the program independent (if possible) of number of cores I would be running it on..
The easiest way to fix that would be to calculate 'start' and 'end' as
slice_size = (200 + size - 1)/size; // max. amount of rows per core
start = rank * slice_size;
end = min(start + slice_size, 200);
In this case, some cores can be underloaded.
A better scalability could be achieved if the lattice is divided not by rows only, but both by rows and columns, or even in non-rectangular areas, for example, using a linear representation of the lattice, like this:
total_cells = rows * columns;
common_piece_size = (total_cells + size - 1) / size;
start = rank * common_piece_size;
end = min(start + common_piece_size, total_size);
for (i = start; i < end; i++) {
row = i / columns;
col = i % columns;
// process cell [col, row]
}
. This would require more complex inter-process communication though.
I am currently reading "Linux Kernel Development" by Robert Love, and I got a few questions about the CFS.
My question is how calc_delta_mine calculates :
delta_exec_weighted= (delta_exec * weight)/lw->weight
I guess it is done by two steps :
calculation the (delta_exec * 1024) :
if (likely(weight > (1UL << SCHED_LOAD_RESOLUTION)))
tmp = (u64)delta_exec * scale_load_down(weight);
else
tmp = (u64)delta_exec;
calculate the /lw->weight ( or * lw->inv_weight ) :
if (!lw->inv_weight) {
unsigned long w = scale_load_down(lw->weight);
if (BITS_PER_LONG > 32 && unlikely(w >= WMULT_CONST))
lw->inv_weight = 1;
else if (unlikely(!w))
lw->inv_weight = WMULT_CONST;
else
lw->inv_weight = WMULT_CONST / w;
}
/*
* Check whether we'd overflow the 64-bit multiplication:
*/
if (unlikely(tmp > WMULT_CONST))
tmp = SRR(SRR(tmp, WMULT_SHIFT/2) * lw->inv_weight,
WMULT_SHIFT/2);
else
tmp = SRR(tmp * lw->inv_weight, WMULT_SHIFT);
return (unsigned long)min(tmp, (u64)(unsigned long)LONG_MAX);
The SRR (Shift right and round) macro is defined via :
#define SRR(x, y) (((x) + (1UL << ((y) - 1))) >> (y))
And the other MACROS are defined :
#if BITS_PER_LONG == 32
# define WMULT_CONST (~0UL)
#else
# define WMULT_CONST (1UL << 32)
#endif
#define WMULT_SHIFT 32
Can someone please explain how exactly the SRR works and how does this check the 64-bit multiplication overflow?
And please explain the definition of the MACROS in this function((~0UL) ,(1UL << 32))?
The code you posted is basically doing calculations using 32.32 fixed-point arithmetic, where a single 64-bit quantity holds the integer part of the number in the high 32 bits, and the decimal part of the number in the low 32 bits (so, for example, 1.5 is 0x0000000180000000 in this system). WMULT_CONST is thus an approximation of 1.0 (using a value that can fit in a long for platform efficiency considerations), and so dividing WMULT_CONST by w computes 1/w as a 32.32 value.
Note that multiplying two 32.32 values together as integers produces a result that is 232 times too large; thus, WMULT_SHIFT (=32) is the right shift value needed to normalize the result of multiplying two 32.32 values together back down to 32.32.
The necessity of using this improved precision for scheduling purposes is explained in a comment in sched/sched.h:
/*
* Increase resolution of nice-level calculations for 64-bit architectures.
* The extra resolution improves shares distribution and load balancing of
* low-weight task groups (eg. nice +19 on an autogroup), deeper taskgroup
* hierarchies, especially on larger systems. This is not a user-visible change
* and does not change the user-interface for setting shares/weights.
*
* We increase resolution only if we have enough bits to allow this increased
* resolution (i.e. BITS_PER_LONG > 32). The costs for increasing resolution
* when BITS_PER_LONG <= 32 are pretty high and the returns do not justify the
* increased costs.
*/
As for SRR, mathematically, it computes the rounded result of x / 2y.
To round the result of a division x/q you can calculate x + q/2 floor-divided by q; this is what SRR does by calculating x + 2y-1 floor-divided by 2y.