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Out of curiosity I ran coded up several different versions of matrix Multiplication and ran cachegrind against it. In my results below, I was wondering which parts were L1,L2,L3 misses and references and what it all really means? Below is my code for the matrix multiplications also, in case anyone needs that.
#define SLOWEST
==6933== Cachegrind, a cache and branch-prediction profiler
==6933== Copyright (C) 2002-2012, and GNU GPL'd, by Nicholas Nethercote et al.
==6933== Using Valgrind-3.8.1 and LibVEX; rerun with -h for copyright info
==6933== Command: ./a.out 500
==6933==
--6933-- warning: L3 cache found, using its data for the LL simulation.
--6933-- warning: pretending that LL cache has associativity 24 instead of actual 16
Multiplied matrix A and B in 60.7487 seconds.
==6933==
==6933== I refs: 6,039,791,314
==6933== I1 misses: 1,611
==6933== LLi misses: 1,519
==6933== I1 miss rate: 0.00%
==6933== LLi miss rate: 0.00%
==6933==
==6933== D refs: 2,892,704,678 (2,763,005,485 rd + 129,699,193 wr)
==6933== D1 misses: 136,223,560 ( 136,174,705 rd + 48,855 wr)
==6933== LLd misses: 53,675 ( 5,247 rd + 48,428 wr)
==6933== D1 miss rate: 4.7% ( 4.9% + 0.0% )
==6933== LLd miss rate: 0.0% ( 0.0% + 0.0% )
==6933==
==6933== LL refs: 136,225,171 ( 136,176,316 rd + 48,855 wr)
==6933== LL misses: 55,194 ( 6,766 rd + 48,428 wr)
==6933== LL miss rate: 0.0% ( 0.0% + 0.0% )
#define SLOWER
==8463== Cachegrind, a cache and branch-prediction profiler
==8463== Copyright (C) 2002-2012, and GNU GPL'd, by Nicholas Nethercote et al.
==8463== Using Valgrind-3.8.1 and LibVEX; rerun with -h for copyright info
==8463== Command: ./a.out 500
==8463==
--8463-- warning: L3 cache found, using its data for the LL simulation.
--8463-- warning: pretending that LL cache has associativity 24 instead of actual 16
Multiplied matrix A and B in 49.7397 seconds.
==8463==
==8463== I refs: 4,537,213,120
==8463== I1 misses: 1,571
==8463== LLi misses: 1,487
==8463== I1 miss rate: 0.00%
==8463== LLi miss rate: 0.00%
==8463==
==8463== D refs: 2,891,485,608 (2,761,862,312 rd + 129,623,296 wr)
==8463== D1 misses: 59,961,522 ( 59,913,256 rd + 48,266 wr)
==8463== LLd misses: 53,113 ( 5,246 rd + 47,867 wr)
==8463== D1 miss rate: 2.0% ( 2.1% + 0.0% )
==8463== LLd miss rate: 0.0% ( 0.0% + 0.0% )
==8463==
==8463== LL refs: 59,963,093 ( 59,914,827 rd + 48,266 wr)
==8463== LL misses: 54,600 ( 6,733 rd + 47,867 wr)
==8463== LL miss rate: 0.0% ( 0.0% + 0.0% )
#define SLOW
==9174== Cachegrind, a cache and branch-prediction profiler
==9174== Copyright (C) 2002-2012, and GNU GPL'd, by Nicholas Nethercote et al.
==9174== Using Valgrind-3.8.1 and LibVEX; rerun with -h for copyright info
==9174== Command: ./a.out 500
==9174==
--9174-- warning: L3 cache found, using its data for the LL simulation.
--9174-- warning: pretending that LL cache has associativity 24 instead of actual 16
Multiplied matrix A and B in 35.8901 seconds.
==9174==
==9174== I refs: 3,039,713,059
==9174== I1 misses: 1,570
==9174== LLi misses: 1,486
==9174== I1 miss rate: 0.00%
==9174== LLi miss rate: 0.00%
==9174==
==9174== D refs: 1,893,235,586 (1,763,112,301 rd + 130,123,285 wr)
==9174== D1 misses: 63,285,950 ( 62,987,684 rd + 298,266 wr)
==9174== LLd misses: 53,113 ( 5,246 rd + 47,867 wr)
==9174== D1 miss rate: 3.3% ( 3.5% + 0.2% )
==9174== LLd miss rate: 0.0% ( 0.0% + 0.0% )
==9174==
==9174== LL refs: 63,287,520 ( 62,989,254 rd + 298,266 wr)
==9174== LL misses: 54,599 ( 6,732 rd + 47,867 wr)
==9174== LL miss rate: 0.0% ( 0.0% + 0.0% )
#define MEDIUM
==7838== Cachegrind, a cache and branch-prediction profiler
==7838== Copyright (C) 2002-2012, and GNU GPL'd, by Nicholas Nethercote et al.
==7838== Using Valgrind-3.8.1 and LibVEX; rerun with -h for copyright info
==7838== Command: ./a.out 500
==7838==
--7838-- warning: L3 cache found, using its data for the LL simulation.
--7838-- warning: pretending that LL cache has associativity 24 instead of actual 16
Multiplied matrix A and B in 23.4097 seconds.
==7838==
==7838== I refs: 2,548,967,151
==7838== I1 misses: 1,610
==7838== LLi misses: 1,522
==7838== I1 miss rate: 0.00%
==7838== LLi miss rate: 0.00%
==7838==
==7838== D refs: 1,399,237,303 (1,267,363,440 rd + 131,873,863 wr)
==7838== D1 misses: 592,807 ( 293,091 rd + 299,716 wr)
==7838== LLd misses: 53,147 ( 5,248 rd + 47,899 wr)
==7838== D1 miss rate: 0.0% ( 0.0% + 0.2% )
==7838== LLd miss rate: 0.0% ( 0.0% + 0.0% )
==7838==
==7838== LL refs: 594,417 ( 294,701 rd + 299,716 wr)
==7838== LL misses: 54,669 ( 6,770 rd + 47,899 wr)
==7838== LL miss rate: 0.0% ( 0.0% + 0.0% )
#define MEDIUMISH
==8438== Cachegrind, a cache and branch-prediction profiler
==8438== Copyright (C) 2002-2012, and GNU GPL'd, by Nicholas Nethercote et al.
==8438== Using Valgrind-3.8.1 and LibVEX; rerun with -h for copyright info
==8438== Command: ./a.out 500
==8438==
--8438-- warning: L3 cache found, using its data for the LL simulation.
--8438-- warning: pretending that LL cache has associativity 24 instead of actual 16
Multiplied matrix A and B in 24.0327 seconds.
==8438==
==8438== I refs: 2,550,211,553
==8438== I1 misses: 1,576
==8438== LLi misses: 1,488
==8438== I1 miss rate: 0.00%
==8438== LLi miss rate: 0.00%
==8438==
==8438== D refs: 1,400,107,343 (1,267,610,303 rd + 132,497,040 wr)
==8438== D1 misses: 339,977 ( 42,583 rd + 297,394 wr)
==8438== LLd misses: 53,114 ( 5,248 rd + 47,866 wr)
==8438== D1 miss rate: 0.0% ( 0.0% + 0.2% )
==8438== LLd miss rate: 0.0% ( 0.0% + 0.0% )
==8438==
==8438== LL refs: 341,553 ( 44,159 rd + 297,394 wr)
==8438== LL misses: 54,602 ( 6,736 rd + 47,866 wr)
==8438== LL miss rate: 0.0% ( 0.0% + 0.0% )
Matrix Multiplication Code.
#if defined(SLOWEST)
void multiply (float **A, float **B, float **out, int size) {
for (int row=0;row<size;row++)
for (int col=0;col<size;col++)
for (int in=0;in<size;in++)
out[row][col] += A[row][in] * B[in][col];
}
// Takes in 1-D arrays, same as before.
#elif defined(SLOWER)
void multiply (float *A, float *B, float *out, int size) {
for (int row=0;row<size;row++)
for (int col=0;col<size;col++)
for (int in=0;in<size;in++)
out[row * size + col] += A[row * size + in] * B[in * size + col];
}
// Flips first and second loops
#elif defined(SLOW)
void multiply (float *A, float *B, float *out, int size) {
for (int col=0;col<size;col++)
for (int row=0;row<size;row++) {
float curr = 0; // prevents from calculating position each time through
for (int in=0;in<size;in++)
curr += A[row * size + in] * B[in *size + col];
out[row * size + col] = curr;
}
}
#elif defined(MEDIUM)
// Keeps it organized for future codes.
float dotProduct(float *A, float *B, int size) {
float curr = 0;
for (int i=0;i<size;i++)
curr += A[i] * B[i];
return curr;
}
void multiply (float *A, float *B, float *out, int size) {
float *temp = new float[size];
for (int col=0;col<size;col++) {
for (int i=0;i<size;i++) // stores column into sequential array
temp[i] = B[i * size + col];
for (int row=0;row<size;row++)
out[row * size + col] = dotProduct(&A[row], temp, size); // uses function above for dot product.
}
delete[] temp;
}
#elif defined(MEDIUMISH)
float dotProduct(float *A, float *B, int size) {
float curr = 0;
for (int i=0;i<size;i++)
curr += A[i] * B[i];
return curr;
}
void multiply (float *A, float *B, float *out, int size) {
for (int i=0;i<size-1;i++)
for (int j=i+1;j<size;j++)
std::swap(B[i * size + j], B[j * size + i]);
for (int col=0;col<size;col++)
for (int row=0;row<size;row++)
out[row * size + col] = dotProduct(&A[row], &B[row], size); // uses function above for dot product.
}
#elif defined(FAST)
#elif defined(FASTER)
#endif
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Cachegrind simulates how your program interacts with a machine's cache hierarchy and (optionally) branch predictor. It simulates a machine with independent first-level instruction and data caches (I1 and D1), backed by a unified second-level cache (L2). This exactly matches the configuration of many modern machines.
What Is a Cache Miss? A cache miss is an event in which a system or application makes a request to retrieve data from a cache, but that specific data is not currently in cache memory. Contrast this to a cache hit, in which the requested data is successfully retrieved from the cache.
According to the documentation cachegrind only simulate the first and the last level caches:
Cachegrind simulates how your program interacts with a machine's cache hierarchy and (optionally) branch predictor. It simulates a machine with independent first-level instruction and data caches (I1 and D1), backed by a unified second-level cache (L2). This exactly matches the configuration of many modern machines.
However, some modern machines have three or four levels of cache. For these machines (in the cases where Cachegrind can auto-detect the cache configuration) Cachegrind simulates the first-level and last-level caches. The reason for this choice is that the last-level cache has the most influence on runtime, as it masks accesses to main memory. Furthermore, the L1 caches often have low associativity, so simulating them can detect cases where the code interacts badly with this cache (eg. traversing a matrix column-wise with the row length being a power of 2).
What that means is that you can't get L2 information but only L1 and L3 in your case.
The first part of cachegrind's output reports information about L1 instructions cache. In all your example, the number of L1 instruction caches misses is insignifiant, the miss rate is always 0%. It means that all your programs fit in your L1 instruction cache.
The second part of the output reports information about L1 and LL (last level cache, L3 in your case) data caches. Using the D1 miss rate: information you should see which version of your matrix multiplication algorithm is "the most cache efficient"
The final part of cachegrind output summs up information about LL (last level cache, L3 in your case) for both instructions and data. It thus gives the number of memory accesses and the percentage of memory requests served by the cache.
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