- #1
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What this is saying is that for the definition below, C stores the elements in what is called row-major order.
int arr[3][3] = {{1, 1, 1}, {2, 2, 2}, {3, 3, 3}};What same matrix? The matrix (the terminology is "array" in programming) I was talking about is the one in my example.
I don't know this for certain, but I would bet that a lot of the back-end code is implemented in Fortran. There are lots of math libraries, such as LINPACK and many others that do the heavy lifting for matrix inversion, eigenvalue/eigenvector calculation, solving differential equations, and so on.
int a[b][c];Perhaps I should have been more specific. In mathematics, matrix indices or subscripts are normally in row,column order. So the C syntax is much more natural for a mathematician.
I think you got it wrong. It is not about C syntax. C does not have any idea of what a matrix is. Yes, if we talk about [itex]A_{m,n}[/itex], I would agree with you that, undoubtedly, [itex]A[/itex] has [itex]m[/itex] rows and [itex]n[/itex] columns.
I stand by my statement. What voko complained about was my statement: "M[row][column] is the most natural way to reference elements of a matrix M.". I then admitted that I should have referred to the math convention.
I think I see your point. In C, M[i1][i2] could be referring to anything from a simple matrix of numbers to a set of complicated structure pointers. So the math matrix interpretation is not as paramount as I was assuming. I will concede the point.
for (i = 0; i < 5000; ++i) {
for (j = 0; j < 5000; ++j) {
/* Do something with arr[i][j] */
}
}do j=1,5000
do i=1,5000
! Do something with arr(i,j)
end do
end do$ time ./arrloop
real 0m0.752s
user 0m0.223s
sys 0m0.526s$ time ./arrloop2
real 0m5.853s
user 0m5.248s
sys 0m0.598s#define ASIZE 20000
int arr[ASIZE][ASIZE];
int main(void)
{
int i, j, res = 0;
for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
arr[i][j] = 2 * i + j;
}
}
for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
res += arr[i][j];
}
}
return res;
}#define ASIZE 5000
int arr[ASIZE][ASIZE];
int main(void)
{
int i, j, res = 0;
for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
arr[i][j] = 2 * i + j;
}
}
/* for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
res += arr[i][j];
}
} */
return res;
}-@hatsComp ~/Projects
$ gcc array.c
-@hatsComp ~/Projects
$ ./a
-@hatsComp ~/Projects
$ time ./a
real 0m0.165s
user 0m0.062s
sys 0m0.062s
-@hatsComp ~/Projects
$ nano array2.c
-@hatsComp ~/Projects
$ gcc array2.c
.
-@hatsComp ~/Projects
$ time ./a
real 0m0.596s
user 0m0.514s
sys 0m0.015s
-@hatsComp ~/Projects
$#include <chrono>
#include <stdio.h>
#define ASIZE 5000
int arr[ASIZE][ASIZE];
int main()
{
int i, j, res = 0;
/* first loop - touch all pages */
for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
arr[i][j] = 2 * i + j;
}
}
static auto const now = []() {return std::chrono::high_resolution_clock::now();};
static auto const us = [](decltype(now() - now()) dur) { return std::chrono::nanoseconds(dur).count() / 1000.0; };
auto const a = now();
for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
arr[i][j] = 2 * i + j;
}
}
auto const b = now();
for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
arr[j][i] = 2 * i + j;
}
}
auto const c = now();
for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
res += arr[i][j];
}
}
auto const d = now();
for (i = 0; i < ASIZE; ++i) {
for (j = 0; j < ASIZE; ++j) {
res += arr[j][i];
}
}
auto const e = now();
printf("%f, %f, %f, %f\n", us(b - a), us(c - b), us(d - c), us(e - d));
return res;
}