jsguy jsguy - 2 months ago 8
C++ Question

Why isn't the G++ compiler smart enough to realize that these two functions are exactly the same?

I have an array

A
with zeros and ones. I want to find the sum of all numbers in
A
. I want to test two functions:

First function

void test1(int curIndex){
if(curIndex == size) return;
test1(curIndex+1);
s+=A[curIndex];
}


Second function

void test2(int curIndex){
if(curIndex == size) return;
s+=A[curIndex];
test2(curIndex+1);
}


I used the PAPI library to count the number of instructions, here is the entire experiment:

#include <iostream>
#include <fstream>
#include "Statistics.h"

using namespace std;


int size;
int *A;
int s;

void test3(int curIndex){
if(curIndex == size) return;
test3(curIndex+1);
s+=A[curIndex];
}

int main(int argc, char* argv[]){

size = atoi(argv[1]);
if(argc!=2){
cout<<"type ./executable size{odd integer}"<<endl;
return 1;
}
if(size%2!=1){
cout<<"size must be an odd number"<<endl;
return 1;
}
A = new int[size];
int i;
for(i=0;i<size;i++){
if(i%2==0){
A[i] = false;
}
else{
A[i] = true;
}
}

Statistics stat(1);
stat.start();
test3(0);
stat.stop();
stat.printWithHelp();
cout<<s<<endl;

return 0;
}


Here is the
Statistics.h
file:

#ifndef TRIPLETPARSER_STATISTICS_H
#define TRIPLETPARSER_STATISTICS_H

#include <time.h>
#include <unistd.h>
#include <fstream>
#include <papi.h>
#include <iostream>
#include <iostream>

#define BILLION 1000000000LL

using namespace std;

class Statistics {

private:
timespec s, e;
/*
PAPI_BR_CN Conditional branch instructions
PAPI_BR_INS Branch instructions
PAPI_BR_MSP Conditional branch instructions mispredicted
PAPI_BR_NTK Conditional branch instructions not taken
PAPI_BR_PRC Conditional branch instructions correctly predicted
PAPI_BR_TKN Conditional branch instructions taken
PAPI_BR_UCN Unconditional branch instructions
PAPI_BRU_IDL Cycles branch units are idle
PAPI_BTAC_M Branch target address cache misses

PAPI_TLB_DM Data translation lookaside buffer misses
*/
int events[10]; // , PAPI_L2_TCA,PAPI_L3_TCM,PAPI_L3_TCA PAPI_BR_CN, PAPI_BR_PRC}; //type of events we are interested in
int num_hwcntrs; //total amount of events stored in 'events' array
long long values[10];
long long counters[10];

void handle_error(int err){
std::cerr << "PAPI error: " << err << std::endl;
}

public:
Statistics(int papi){
for(size_t i = 0; i< 10; i++)
counters[i]=0.0;

switch(papi){
case 0:
num_hwcntrs = 0;
break;
case 1:
num_hwcntrs = 6;
events[0] = PAPI_L2_TCA;
events[1] = PAPI_L3_TCA;
events[2] = PAPI_L3_TCM;
events[3] = PAPI_TOT_INS;
events[4] = PAPI_BR_INS;
events[5] = PAPI_BR_MSP;
break;
}

}

void start(){

for(size_t i = 0; i< 10; i++)
counters[i]=0.0;

if (num_hwcntrs != 0 && PAPI_start_counters(events, num_hwcntrs) != PAPI_OK)
handle_error(1);
}


void start(float ratio){

if (num_hwcntrs != 0 && PAPI_start_counters(events, num_hwcntrs) != PAPI_OK)
handle_error(1);
}


void stop(){
if (num_hwcntrs != 0 && PAPI_stop_counters(values, num_hwcntrs) != PAPI_OK)
handle_error(1);
update();
}

void stop(float ratio){
if (num_hwcntrs != 0 && PAPI_stop_counters(values, num_hwcntrs) != PAPI_OK)
handle_error(1);
update();
}


void update(){
for(size_t i = 0; i < num_hwcntrs; i++)
counters[i] += values[i];
}

void print(){
for(int i=0;i<num_hwcntrs;i++)
std::cout << counters[i] << "\t";
//cout<<"L2 cache miss ratio: "<<counters[1]/(double)counters[0]<<endl;
//cout<<"L3 cache miss ratio: "<<counters[3]/(double)counters[2]<<endl;
}

void printWithHelp(){
cout<<"L2 accesses: "<<counters[0]<<endl;
cout<<"L2 miss/access ratio: "<<(double)counters[1]/counters[0]<<endl;
cout<<"L3 accesses: "<<counters[1]<<endl;
cout<<"L3 misses: "<<counters[2]<<endl;
cout<<"L3 miss/access ratio: "<<(double)counters[2]/counters[1]<<endl;
cout<<"Instructions: "<<counters[3]<<endl;
cout<<"Branches: "<<counters[4]<<endl;
cout<<"Branch mispredictions: "<<counters[5]<<endl;
cout<<"Branch miss/predict ratio: "<<(double)counters[5]/counters[4]<<endl;
}

void print(float avg_ratio){
for (int i = 0; i<num_hwcntrs; i++)
std::cout << (double)(avg_ratio*counters[i]) << "\t";
}

};

#endif //TRIPLETPARSER_STATISTICS_H


This is the output that I get from the first function when the size of
A
is
111,111


L2 accesses: 24126
L2 miss/access ratio: 0.131559
L3 accesses: 3174
L3 misses: 587
L3 miss/access ratio: 0.18494
Instructions: 1022776
Branches: 178113
Branch mispredictions: 6976
Branch miss/predict ratio: 0.0391661


This is the output that I get from the second function when the size of
A
is
111,111


L2 accesses: 7090
L2 miss/access ratio: 0.163752
L3 accesses: 1161
L3 misses: 507
L3 miss/access ratio: 0.436693
Instructions: 555860
Branches: 111189
Branch mispredictions: 25
Branch miss/predict ratio: 0.000224842


Why the difference in the results? The instructions reduce by half, the branch mispredictions are almost eliminated. What is happening here?

Answer

Your second function is tail-recursive. That means the compiler can optimize it to something like:

void test2(int curIndex){
  while(true)
  {
    if(curIndex == size) return;
    s+=A[curIndex];
    curIndex = curIndex + 1;
  }
}

That reduces the numer of instructions significantly. It also reduces the number of stack frames needed to (at most) one. As a result, it uses a lot less memory, which results in the reduction of cache misses.

The compiler is not able to make this optimization for the first function.

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