Cache 优化（矩阵乘积为例）
2 * (blockSize)2 * wordSize = L1 cache size.
Degrees of Latency
The latency of data access becomes greater with each cache level. Latency of memory access is best measured in CPU clock cycles. One cycle occupies from 4 to 6 nanoseconds, depending on the CPU clock speed. The latencies to the different levels of the memory hierarchy are as follows:
-
CPU Register: 0 cycles.
-
L1 cache hit: 2 or 3 cycles.
-
L1 cache miss satisfied by L2 cache hit: 8 to 10 cycles.
-
L2 cache miss satisfied from main memory, no TLB miss: 75 to 250 cycles; that is, 300 to 1100 nanoseconds, depending on the node where the memory resides (see Table 1-3).
-
TLB miss requiring only reload of the TLB to refer to a virtual page already in memory: approximately 2000 cycles.
-
TLB miss requiring virtual page to load from backing store: hundreds of millions of cycles; that is, tens to hundreds of milliseconds.
A miss at each level of the memory hierarchy multiplies the latency by an order of magnitude or more. Clearly a program can sustain high performance only by achieving a very high ratio of cache hits at every level. Fortunately, hit ratios of 95% and higher are commonly achieved.
Cache Efficient Matrix Multiplication
Chapter 6. Optimizing Cache Utilization
test_std_fastertest_std_mul#include "../../profile.h"
#include
#include
#include
void test(int *arr, const int N, const int K)
{
for(int i=0; i template
void test_std_faster(T** a, T** b, T** c, int n)
{
int i,j,k;
LIGHT_PROFILE_FUNCTION_SCOPE();
for (k = 0; k < n; k++)
{
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
c[i][j] = c[i][j] + a[i][k]*b[k][j];
}
}
}
}
template
void test_std_mul(T** a, T** b, T** c, int n)
{
int i,j,k;
LIGHT_PROFILE_FUNCTION_SCOPE();
for (k = 0; k < n; k++)
{
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
c[k][i] = c[k][i] + a[k][j]*b[j][i];
}
}
}
}
int main()
{
using namespace light;
typedef float real;
typedef int large;
large m=1000, n=1000;
real** A=new_array2d(m,n);
real** B=new_array2d(m,n);
real** C=new_array2d(m,n);
test_std_mul(A,B,C,n);
test_std_faster(A,B,C,n);
delete_array2d(A);
delete_array2d(B);
delete_array2d(C);
const int dimX=64, dimY=1024, dimZ=1024;
const int len=dimX*dimY*dimZ;
int *arr=new int[dimX*dimY*dimZ];
{
int K=1;
PROFILE_SCOPE("test1");
test(arr, len, K);
}
for(int k=1; k<128; k+=2){
char str[20];
sprintf(str, "K=%d", k);
{
PROFILE_SCOPE(str);
test(arr, len, k);
}
}
delete []arr;
return 0;
}
具体结果：In [test_std_mul]:7.69271374 seconds
In [test_std_faster]:1.06887197 seconds
In [test1]:0.126983577 seconds
In [K=1]:0.071336323 seconds
In [K=3]:0.070501934 seconds
In [K=5]:0.070173198 seconds
In [K=7]:0.069914513 seconds
In [K=9]:0.070830328 seconds
In [K=11]:0.069679724 seconds
In [K=13]:0.070218294 seconds
In [K=15]:0.070343338 seconds
In [K=17]:0.06793199 seconds
In [K=19]:0.065443525 seconds
In [K=21]:0.063027865 seconds
In [K=23]:0.059502513 seconds
In [K=25]:0.055603195 seconds
In [K=27]:0.05297714 seconds
In [K=29]:0.050074194 seconds
In [K=31]:0.048622758 seconds
In [K=33]:0.042584798 seconds
In [K=35]:0.0476709 seconds
In [K=37]:0.034328566 seconds
In [K=39]:0.046996806 seconds
In [K=41]:0.039327118 seconds
In [K=43]:0.028445512 seconds
In [K=45]:0.03679236 seconds
In [K=47]:0.039664869 seconds
In [K=49]:0.040579371 seconds
In [K=51]:0.03415459 seconds
In [K=53]:0.034461676 seconds
In [K=55]:0.022190094 seconds
In [K=57]:0.031438485 seconds
In [K=59]:0.031826945 seconds
In [K=61]:0.031029584 seconds
In [K=63]:0.030291529 seconds
In [K=65]:0.029730277 seconds
In [K=67]:0.029219664 seconds
In [K=69]:0.027173476 seconds
In [K=71]:0.026998234 seconds
In [K=73]:0.019982384 seconds
In [K=75]:0.027318676 seconds
In [K=77]:0.026787412 seconds
In [K=79]:0.026784303 seconds
In [K=81]:0.024683844 seconds
In [K=83]:0.023558035 seconds
In [K=85]:0.015945637 seconds
In [K=87]:0.023418765 seconds
In [K=89]:0.018921708 seconds
In [K=91]:0.016292988 seconds
In [K=93]:0.022331199 seconds
In [K=95]:0.012433372 seconds
In [K=97]:0.021208601 seconds
In [K=99]:0.01638945 seconds
In [K=101]:0.01571856 seconds
In [K=103]:0.019857388 seconds
In [K=105]:0.010748321 seconds
In [K=107]:0.01605354 seconds
In [K=109]:0.013885589 seconds
In [K=111]:0.015515276 seconds
In [K=113]:0.014337689 seconds
In [K=115]:0.012188802 seconds
In [K=117]:0.015207584 seconds
In [K=119]:0.009342447 seconds
In [K=121]:0.018276332 seconds
In [K=123]:0.008979882 seconds
In [K=125]:0.015199975 seconds
In [K=127]:0.010937606 seconds
Reduce demands on memory bandwidth by pre-loading into local variables
while( … ) {
*res++ = filter[0]*signal[0]
+ filter[1]*signal[1]
+ filter[2]*signal[2];
signal++;
}float f0 = filter[0];
float f1 = filter[1];
float f2 = filter[2];
while( … ) {
*res++ = f0*signal[0]
+ f1*signal[1]
+ f2*signal[2];
signal++;
}Expose instruction-level parallelism
float f0 = filter[0], f1 = filter[1], f2 = filter[2];
float s0 = signal[0], s1 = signal[1], s2 = signal[2];
*res++ = f0*s0 + f1*s1 + f2*s2;
do {
signal += 3;
s0 = signal[0];
res[0] = f0*s1 + f1*s2 + f2*s0;
s1 = signal[1];
res[1] = f0*s2 + f1*s0 + f2*s1;
s2 = signal[2];
res[2] = f0*s0 + f1*s1 + f2*s2;
res += 3;
} while( … );Copy input operands or blocks
Reduce cache conflicts
Constant array offsets for fixed size blocks
Expose page-level locality