64位双向量的向量比32位无符号整数的向量更快？

Question

I have two designs of code iterating over vectors of size 500. One of the designs contains arrays of 64-bit doubles and the second design uses arrays containing 32-bit integers. I was expecting the 32-bit design to be quicker because more useful data can be packed in the cache.

Compiler MSVC, CPU Ivy Bridge, compiling 64-bit mode.

This is code 1, using the 32-bit ints (runs in 2600 CPU cycles):

#include <vector>
#include <iostream>

int main(){

    std::vector<unsigned int> x1;
    std::vector<unsigned int> x2;
    std::vector<unsigned int> x3;
    x1.resize(500);
    x2.resize(500);
    x3.resize(500);

    for(int i =0; i<500; i++){
        x1[i] = i;
        x2[i] = 2*i;
        x3[i] = 4*i;
    }


    int counter = 0;
    while(counter < 1000){
        unsigned long long start = 0;
        unsigned long long end = 0;

        double m = 0;
        double n = 0;

        start = __rdtsc();

        for(int i=0; i < 500; i++){
            unsigned int a = x1[i];
            unsigned int b = x2[i];
            unsigned int g = x3[i];
            m = m + (a * g);
            n = n + (b * g);
        }

        end = __rdtscp();

        std::cout << (end-start) << "\t\t"<<m << n << std::endl;
        counter++;
    }
}

producing this asm (-Os):

start = __rdtscp(&p);
 rdtscp  
 lea         r8,[rbp+6Fh]  
 mov         dword ptr [r8],ecx  
 shl         rdx,20h  
 or          rax,rdx  
 mov         r10,rax  
        unsigned int p;
        unsigned int q;
        unsigned long long start = 0;
        unsigned long long end = 0;

        double m = 0;
 mov         r8,rbx  
 mov         r9d,1F4h  
            unsigned int a = x1[i];
            unsigned int b = x2[i];
            unsigned int g = x3[i];
 mov         edx,dword ptr [r8+r15]  
            m = m + (a * g);
 mov         ecx,edx  
 imul        ecx,dword ptr [r8+r14]  
 xorps       xmm0,xmm0  
 cvtsi2sd    xmm0,rcx  
 addsd       xmm7,xmm0  
            n = n + (b * g);
 imul        edx,dword ptr [r8]  
 mov         eax,edx  
 xorps       xmm0,xmm0  
 cvtsi2sd    xmm0,rax  
 addsd       xmm8,xmm0  

        for(int i=0; i < 500; i++){
 add         r8,4  
 dec         r9  
 jne         main+0E5h (013F681261h)  
        }

        end = __rdtscp(&q);
 rdtscp  
        }

        end = __rdtscp(&q);
 lea         r8,[rbp+6Fh]  
 mov         dword ptr [r8],ecx  
 shl         rdx,20h  
 or          rdx,rax  

This is code 2, using the 64-bit doubles (code runs in 2000 CPU cycles):

#include <vector>
#include <iostream>

int main(){

    std::vector<double> x1;
    std::vector<double> x2;
    std::vector<unsigned long long> x3;
    x1.resize(500);
    x2.resize(500);
    x3.resize(500);

    for(int i =0; i<500; i++){
        x1[i] = i;
        x2[i] = 2*i;
        x3[i] = 4*i;
    }

    int counter = 0;
    while(counter < 1000){
        unsigned int p;
        unsigned int q;
        unsigned long long start = 0;
        unsigned long long end = 0;

        double m = 0;
        double n = 0;

        start = __rdtscp(&p);

        for(int i=0; i < 500; i++){
            double a = x1[i];
            double b = x2[i];
            unsigned long long g = x3[i];
            m = m + (a * g);
            n = n + (b * g);
        }

        end = __rdtscp(&q);

        std::cout << (end-start) << "\t\t"<<m << n << std::endl;
        counter++;
    }
}

and here is the asm (-Os) produced:

start = __rdtscp(&p);
 rdtscp  
 lea         r8,[rbp+6Fh]  
 mov         dword ptr [r8],ecx  
 shl         rdx,20h  
 or          rax,rdx  
 mov         r9,rax  
        unsigned int p;
        unsigned int q;
        unsigned long long start = 0;
        unsigned long long end = 0;

        double m = 0;
 mov         rdx,rbx  
 mov         r8d,1F4h  
            double a = x1[i];
            double b = x2[i];
            unsigned long long g = x3[i];
 mov         rcx,qword ptr [rdx+r15]  
 xorps       xmm1,xmm1  
            m = m + (a * g);
 cvtsi2sd    xmm1,rcx  
 test        rcx,rcx  
 jns         main+120h (013F32129Ch)  
 addsd       xmm1,xmm9  
 movaps      xmm0,xmm1  
 mulsd       xmm0,mmword ptr [rdx+r14]  
 addsd       xmm6,xmm0  
            n = n + (b * g);
 mulsd       xmm1,mmword ptr [rdx]  
 addsd       xmm7,xmm1  

        for(int i=0; i < 500; i++){
 add         rdx,8  
 dec         r8  
 jne         main+10Ah (013F321286h)  
        }

        end = __rdtscp(&q);
 rdtscp  
        }

        end = __rdtscp(&q);
 lea         r8,[rbp+6Fh]  
 mov         dword ptr [r8],ecx  
 shl         rdx,20h  
 or          rdx,rax

Answer 1

The difference is the conversion of integers to doubles in the first code (the vectors contain unsigned int , the product is in integer arithmetic, but the accumulation uses double , in assembler this adds the cvtsi2sd instruction to your code).

In the second code, you use doubles everywhere, so you don't have a conversion and the code runs faster.

This difference would have been much more pronounced on a CPU that has a stricter distinction between the fixed and floating point processing units (the POWER platform is an example for this). The X86 platform is very forgiving in that respect.