Binary search for students
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I'm putting together an example for students where I would like to show how we can optimize even such basic algorithm like a binary search with respect to hardware. I do not consider threads. I wrote it in C++ and the whole example can be found here. I'm trying to show some examples of the prefetching. The basic algorithm is the following:
using Type = int64_t;
int binarySearch_basic(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (l <= r) {
int m = l + ((r - l) >> 1);
if (arr[m] == search) return m;
if (arr[m] < search) l = m + 1;
else r = m - 1;
}
return -1;
}
The first optimization simply try to prefetch possible memory in advance
int binarySearch_basic(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (l <= r) {
int m1 = arr[l + ((r - l) >> 2)]; // new code
int m2 = arr[r - ((r - l) >> 2)]; // new code
int m = l + ((r - l) >> 1);
if (arr[m] == search) return m;
if (arr[m] < search) l = m + 1;
else r = m - 1;
}
return -1;
}
The second optimization is a little bit more sophisticated. It accesses more than one item per iteration which allows read more relevant data per CPU L2 cache miss wait.
int binarySearch_duo(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (r - l > 7) {
int delta = (r - l) / 3;
int m1 = l + delta;
int m2 = r - delta;
if (arr[m1] == search) return m1;
if (arr[m2] == search) return m2;
if (arr[m1] < search) {
if (arr[m2] < search) {
l = m2 + 1;
}
else {
r = m2 - 1;
l = m1 + 1;
}
}
else {
r = m1 - 1;
}
}
for (int i = l; i <= r; i++)
{
if (arr[i] == search) return i;
}
return -1;
}
Of course, this approach can be done with more accesses per iteration (I'm testing three as well in my demo). I have several questions:
- Are there any other possible significant optimizations that could help the algorithm?
- Is my explanation of the improvement of the last algorithm correct? (is it really due to the fact that the CPU read in parallel two data items; therefore, he waits for it just once not twice like in the first algorithm).
- Are there any other comments about my code?
c++ performance binary-search
edited 15 mins ago
Toby Speight
23.9k739113
asked 45 mins ago
Radim BačaRadim Bača
1062
New contributor
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
I'm putting together an example for students where I would like to show how we can optimize even such basic algorithm like a binary search with respect to hardware. I do not consider threads. I wrote it in C++ and the whole example can be found here. I'm trying to show some examples of the prefetching. The basic algorithm is the following:
using Type = int64_t;
int binarySearch_basic(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (l <= r) {
int m = l + ((r - l) >> 1);
if (arr[m] == search) return m;
if (arr[m] < search) l = m + 1;
else r = m - 1;
}
return -1;
}
The first optimization simply try to prefetch possible memory in advance
int binarySearch_basic(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (l <= r) {
int m1 = arr[l + ((r - l) >> 2)]; // new code
int m2 = arr[r - ((r - l) >> 2)]; // new code
int m = l + ((r - l) >> 1);
if (arr[m] == search) return m;
if (arr[m] < search) l = m + 1;
else r = m - 1;
}
return -1;
}
The second optimization is a little bit more sophisticated. It accesses more than one item per iteration which allows read more relevant data per CPU L2 cache miss wait.
int binarySearch_duo(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (r - l > 7) {
int delta = (r - l) / 3;
int m1 = l + delta;
int m2 = r - delta;
if (arr[m1] == search) return m1;
if (arr[m2] == search) return m2;
if (arr[m1] < search) {
if (arr[m2] < search) {
l = m2 + 1;
}
else {
r = m2 - 1;
l = m1 + 1;
}
}
else {
r = m1 - 1;
}
}
for (int i = l; i <= r; i++)
{
if (arr[i] == search) return i;
}
return -1;
}
Of course, this approach can be done with more accesses per iteration (I'm testing three as well in my demo). I have several questions:
- Are there any other possible significant optimizations that could help the algorithm?
- Is my explanation of the improvement of the last algorithm correct? (is it really due to the fact that the CPU read in parallel two data items; therefore, he waits for it just once not twice like in the first algorithm).
- Are there any other comments about my code?
c++ performance binary-search
edited 15 mins ago
Toby Speight
23.9k739113
asked 45 mins ago
Radim BačaRadim Bača
1062
New contributor
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I'm putting together an example for students where I would like to show how we can optimize even such basic algorithm like a binary search with respect to hardware. I do not consider threads. I wrote it in C++ and the whole example can be found here. I'm trying to show some examples of the prefetching. The basic algorithm is the following:
using Type = int64_t;
int binarySearch_basic(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (l <= r) {
int m = l + ((r - l) >> 1);
if (arr[m] == search) return m;
if (arr[m] < search) l = m + 1;
else r = m - 1;
}
return -1;
}
The first optimization simply try to prefetch possible memory in advance
int binarySearch_basic(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (l <= r) {
int m1 = arr[l + ((r - l) >> 2)]; // new code
int m2 = arr[r - ((r - l) >> 2)]; // new code
int m = l + ((r - l) >> 1);
if (arr[m] == search) return m;
if (arr[m] < search) l = m + 1;
else r = m - 1;
}
return -1;
}
The second optimization is a little bit more sophisticated. It accesses more than one item per iteration which allows read more relevant data per CPU L2 cache miss wait.
int binarySearch_duo(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (r - l > 7) {
int delta = (r - l) / 3;
int m1 = l + delta;
int m2 = r - delta;
if (arr[m1] == search) return m1;
if (arr[m2] == search) return m2;
if (arr[m1] < search) {
if (arr[m2] < search) {
l = m2 + 1;
}
else {
r = m2 - 1;
l = m1 + 1;
}
}
else {
r = m1 - 1;
}
}
for (int i = l; i <= r; i++)
{
if (arr[i] == search) return i;
}
return -1;
}
Of course, this approach can be done with more accesses per iteration (I'm testing three as well in my demo). I have several questions:
- Are there any other possible significant optimizations that could help the algorithm?
- Is my explanation of the improvement of the last algorithm correct? (is it really due to the fact that the CPU read in parallel two data items; therefore, he waits for it just once not twice like in the first algorithm).
- Are there any other comments about my code?
c++ performance binary-search
edited 15 mins ago
Toby Speight
23.9k739113
asked 45 mins ago
Radim BačaRadim Bača
1062
New contributor
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm putting together an example for students where I would like to show how we can optimize even such basic algorithm like a binary search with respect to hardware. I do not consider threads. I wrote it in C++ and the whole example can be found here. I'm trying to show some examples of the prefetching. The basic algorithm is the following:
using Type = int64_t;
int binarySearch_basic(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (l <= r) {
int m = l + ((r - l) >> 1);
if (arr[m] == search) return m;
if (arr[m] < search) l = m + 1;
else r = m - 1;
}
return -1;
}
The first optimization simply try to prefetch possible memory in advance
int binarySearch_basic(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (l <= r) {
int m1 = arr[l + ((r - l) >> 2)]; // new code
int m2 = arr[r - ((r - l) >> 2)]; // new code
int m = l + ((r - l) >> 1);
if (arr[m] == search) return m;
if (arr[m] < search) l = m + 1;
else r = m - 1;
}
return -1;
}
The second optimization is a little bit more sophisticated. It accesses more than one item per iteration which allows read more relevant data per CPU L2 cache miss wait.
int binarySearch_duo(size_t item_count, const Type arr, int search)
{
int l = 0;
int r = item_count - 1;
while (r - l > 7) {
int delta = (r - l) / 3;
int m1 = l + delta;
int m2 = r - delta;
if (arr[m1] == search) return m1;
if (arr[m2] == search) return m2;
if (arr[m1] < search) {
if (arr[m2] < search) {
l = m2 + 1;
}
else {
r = m2 - 1;
l = m1 + 1;
}
}
else {
r = m1 - 1;
}
}
for (int i = l; i <= r; i++)
{
if (arr[i] == search) return i;
}
return -1;
}
Of course, this approach can be done with more accesses per iteration (I'm testing three as well in my demo). I have several questions:
- Are there any other possible significant optimizations that could help the algorithm?
- Is my explanation of the improvement of the last algorithm correct? (is it really due to the fact that the CPU read in parallel two data items; therefore, he waits for it just once not twice like in the first algorithm).
- Are there any other comments about my code?
c++ performance binary-search
c++ performance binary-search
edited 15 mins ago
Toby Speight
23.9k739113
asked 45 mins ago
Radim BačaRadim Bača
1062
New contributor
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 15 mins ago
Toby Speight
23.9k739113
asked 45 mins ago
Radim BačaRadim Bača
1062
New contributor
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 15 mins ago
Toby Speight
23.9k739113
edited 15 mins ago
Toby Speight
23.9k739113
edited 15 mins ago
Toby Speight
23.9k739113
23.9k739113
asked 45 mins ago
Radim BačaRadim Bača
1062
New contributor
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 45 mins ago
Radim BačaRadim Bača
1062
asked 45 mins ago
Radim BačaRadim Bača
1062
1062
New contributor
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Radim Bača is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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