在嵌套循环中访问数组时缓存未命中

Cache misses when accessing an array in nested loop

所以我的教授提出了这个问题,我不明白为什么 vector2vector1 更快并且缓存未命中率更低。

假设下面的代码是有效的可编译 C 代码。

向量2:

void incrementVector2(INT4* v, int n) {
     for (int k = 0; k < 100; ++k) {
          for (int i = 0; i < n; ++i) {
               v[i] = v[i] + 1;
          }
     }
}

矢量 1:

void incrementVector1(INT4* v, int n) {
     for (int i = 0; i < n; ++i) {
          for (int k = 0; k < 100; ++k) {
               v[i] = v[i] + 1;
          }
     }
}

注意: INT4 表示整数大小为 4 字节。

根据 CPU 规格:缓存大小 = 12288KB,行大小 =64B 且仅考虑与主内存交互的单个缓存。

问题

为什么 vector2 的运行时间比 vector1 快?为什么 vector1 会比 vector2 有更多的缓存未命中?

我和几个同学研究了一段时间,没弄明白。我们认为这可能是因为 vector2 具有更好的空间位置,因为内部循环不断访问数组,而在 vector1 中,一次只访问一个元素? 我们不确定这是否正确,也不确定如何将缓存行引入其中。

We thought it could be due to the fact that vector2 has better spatial locatlity, since the array is been accessed by the inner loop constantly, while in vector1, only one element is accessed at a time?

好吧,这两个代码具有相同的访问模式,以 1 的步幅遍历数组 v。缓存空间位置方面的两个代码是相同的。然而,第二个代码:

void incrementVector1(INT4* v, int n) {
     for (int i = 0; i < n; ++i) {
          for (int k = 0; k < 100; ++k) {
               v[i] = v[i] + 1;
          }
     }
}

具有更好的时间局部性,因为您访问同一个元素 100 次,而在:

void incrementVector2(INT4* v, int n) {
     for (int k = 0; k < 100; ++k) {
          for (int i = 0; i < n; ++i) {
               v[i] = v[i] + 1;
          }
     }
}

每 'n' 次迭代只能访问一次。

所以要么你做错了,要么你的老师在玩某种奇怪的游戏,要么我遗漏了一些明显的东西。

确定您是说 incrementVector2 更快吗?

正如 dreamcast 指出的那样,incrementVector1 具有更好的时间局部性,因此 应该更快。

而且,从基准测试来看,1 比 2 快

对于大小为 1000 的数组,速度提高了 50 倍。

这令人惊讶,因为数组小到足以成为[并保持]缓存热。

并且,incrementVector1 的反汇编代码大小比 incrementVector2 小得多(在 -O3)。

incrementVector1 是 105 个字节,incrementVector2 是 203 个字节。

这有点令人惊讶,因为我认为虽然存在一些差异,但我不希望出现如此大的差异[见下文]。


程序输出如下:

0.000002238 incrementVector1
0.000019535 incrementVector2
8.729x slower

0.000000280 incrementVector1
0.000022454 incrementVector2
80.193x slower

0.000000452 incrementVector1
0.000019617 incrementVector2
43.400x slower

0.000000377 incrementVector1
0.000020632 incrementVector2
54.727x slower

0.000000361 incrementVector1
0.000022612 incrementVector2
62.637x slower

这是我使用的程序:

#include <stdio.h>
#include <time.h>

typedef long long tsc_t;
typedef int INT4;

tsc_t
tscget(void)
{
    struct timespec ts;
    tsc_t tsc;

    clock_gettime(CLOCK_MONOTONIC,&ts);
    tsc = ts.tv_sec;
    tsc *= 1000000000;
    tsc += ts.tv_nsec;

    return tsc;
}

double
tscsec(tsc_t tsc)
{
    double sec;

    sec = tsc;
    sec /= 1e9;

    return sec;
}

typedef void (*incfnc_p)(INT4 *v, int n);

void
incrementVector2(INT4 *v, int n)
{
    for (int k = 0; k < 100; ++k) {
        for (int i = 0; i < n; ++i) {
            v[i] = v[i] + 1;
        }
    }
}

void
incrementVector1(INT4 *v, int n)
{
    for (int i = 0; i < n; ++i) {
        for (int k = 0; k < 100; ++k) {
            v[i] = v[i] + 1;
        }
    }
}

INT4 v[1000] = { 0 };

#define DOFNC(_fnc) \
    dofnc(_fnc,#_fnc)

tsc_t
dofnc(incfnc_p fnc,const char *sym)
{
    tsc_t tscbeg;
    tsc_t tscend;

    tscbeg = tscget();
    fnc(v,sizeof(v) / sizeof(v[0]));
    tscend = tscget();
    tscend -= tscbeg;

    printf("%.9f %s\n",tscsec(tscend),sym);

    return tscend;
}

void
dotest(void)
{
    tsc_t tsc1 = DOFNC(incrementVector1);
    tsc_t tsc2 = DOFNC(incrementVector2);
    double ratio;
    const char *tag;

    if (tsc1 > tsc2) {
        tag = "faster";
        ratio = tsc1;
        ratio /= tsc2;
    }
    else {
        tag = "slower";
        ratio = tsc2;
        ratio /= tsc1;
    }

    printf("%.3fx %s\n",ratio,tag);
}

int
main(void)
{

    for (int testno = 1;  testno <= 5;  ++testno) {
        printf("\n");
        dotest();
    }

    return 0;
}

这里是反汇编:

00000000004011c0 <incrementVector2>:
  4011c0:   85 f6                   test   %esi,%esi
  4011c2:   0f 8e be 00 00 00       jle    401286 <L06>
  4011c8:   89 f2                   mov    %esi,%edx
  4011ca:   41 89 f3                mov    %esi,%r11d
  4011cd:   66 0f 6f 0d 8b 0e 00    movdqa 0xe8b(%rip),%xmm1        # 402060 <__dso_handle+0x58>
  4011d4:   00
  4011d5:   49 89 f8                mov    %rdi,%r8
  4011d8:   c1 ea 02                shr    [=12=]x2,%edx
  4011db:   44 8d 56 ff             lea    -0x1(%rsi),%r10d
  4011df:   41 83 e3 fc             and    [=12=]xfffffffc,%r11d
  4011e3:   41 b9 01 00 00 00       mov    [=12=]x1,%r9d
  4011e9:   48 c1 e2 04             shl    [=12=]x4,%rdx
  4011ed:   48 01 fa                add    %rdi,%rdx
  4011f0:L00    41 83 fa 02             cmp    [=12=]x2,%r10d
  4011f4:   0f 86 8d 00 00 00       jbe    401287 <L07>
  4011fa:   48 89 f8                mov    %rdi,%rax
  4011fd:L01    f3 0f 6f 00             movdqu (%rax),%xmm0
  401201:   48 83 c0 10             add    [=12=]x10,%rax
  401205:   66 0f fe c1             paddd  %xmm1,%xmm0
  401209:   0f 11 40 f0             movups %xmm0,-0x10(%rax)
  40120d:   48 39 d0                cmp    %rdx,%rax
  401210:   75 eb                   jne    4011fd <L01>
  401212:   44 89 d8                mov    %r11d,%eax
  401215:   44 39 de                cmp    %r11d,%esi
  401218:   74 22                   je     40123c <L03>
  40121a:L02    48 63 c8                movslq %eax,%rcx
  40121d:   83 04 8f 02             addl   [=12=]x2,(%rdi,%rcx,4)
  401221:   8d 48 01                lea    0x1(%rax),%ecx
  401224:   39 ce                   cmp    %ecx,%esi
  401226:   7e 14                   jle    40123c <L03>
  401228:   48 63 c9                movslq %ecx,%rcx
  40122b:   83 c0 02                add    [=12=]x2,%eax
  40122e:   83 04 8f 02             addl   [=12=]x2,(%rdi,%rcx,4)
  401232:   39 c6                   cmp    %eax,%esi
  401234:   7e 06                   jle    40123c <L03>
  401236:   48 98                   cltq
  401238:   83 04 87 02             addl   [=12=]x2,(%rdi,%rax,4)
  40123c:L03    41 8d 41 01             lea    0x1(%r9),%eax
  401240:   41 83 c1 02             add    [=12=]x2,%r9d
  401244:   41 83 f9 63             cmp    [=12=]x63,%r9d
  401248:   75 a6                   jne    4011f0 <L00>
  40124a:   be 65 00 00 00          mov    [=12=]x65,%esi
  40124f:   4a 8d 7c 97 04          lea    0x4(%rdi,%r10,4),%rdi
  401254:   29 c6                   sub    %eax,%esi
  401256:   66 2e 0f 1f 84 00 00    nopw   %cs:0x0(%rax,%rax,1)
  40125d:   00 00 00
  401260:L04    41 8b 10                mov    (%r8),%edx
  401263:   8d 42 01                lea    0x1(%rdx),%eax
  401266:   01 f2                   add    %esi,%edx
  401268:   0f 1f 84 00 00 00 00    nopl   0x0(%rax,%rax,1)
  40126f:   00
  401270:L05    89 c1                   mov    %eax,%ecx
  401272:   83 c0 01                add    [=12=]x1,%eax
  401275:   39 d0                   cmp    %edx,%eax
  401277:   75 f7                   jne    401270 <L05>
  401279:   41 89 08                mov    %ecx,(%r8)
  40127c:   49 83 c0 04             add    [=12=]x4,%r8
  401280:   49 39 f8                cmp    %rdi,%r8
  401283:   75 db                   jne    401260 <L04>
  401285:   c3                      retq
  401286:L06    c3                      retq
  401287:L07    31 c0                   xor    %eax,%eax
  401289:   eb 8f                   jmp    40121a <L02>
  40128b:   0f 1f 44 00 00          nopl   0x0(%rax,%rax,1)

0000000000401290 <incrementVector1>:
  401290:   85 f6                   test   %esi,%esi
  401292:   7e 5f                   jle    4012f3 <L02>
  401294:   8d 46 ff                lea    -0x1(%rsi),%eax
  401297:   83 f8 02                cmp    [=12=]x2,%eax
  40129a:   76 59                   jbe    4012f5 <L04>
  40129c:   89 f2                   mov    %esi,%edx
  40129e:   66 0f 6f 0d ca 0d 00    movdqa 0xdca(%rip),%xmm1        # 402070 <__dso_handle+0x68>
  4012a5:   00
  4012a6:   48 89 f8                mov    %rdi,%rax
  4012a9:   c1 ea 02                shr    [=12=]x2,%edx
  4012ac:   48 c1 e2 04             shl    [=12=]x4,%rdx
  4012b0:   48 01 fa                add    %rdi,%rdx
  4012b3:L00    f3 0f 6f 00             movdqu (%rax),%xmm0
  4012b7:   48 83 c0 10             add    [=12=]x10,%rax
  4012bb:   66 0f fe c1             paddd  %xmm1,%xmm0
  4012bf:   0f 11 40 f0             movups %xmm0,-0x10(%rax)
  4012c3:   48 39 d0                cmp    %rdx,%rax
  4012c6:   75 eb                   jne    4012b3 <L00>
  4012c8:   89 f0                   mov    %esi,%eax
  4012ca:   83 e0 fc                and    [=12=]xfffffffc,%eax
  4012cd:   39 f0                   cmp    %esi,%eax
  4012cf:   74 23                   je     4012f4 <L03>
  4012d1:L01    48 63 d0                movslq %eax,%rdx
  4012d4:   83 04 97 64             addl   [=12=]x64,(%rdi,%rdx,4)
  4012d8:   8d 50 01                lea    0x1(%rax),%edx
  4012db:   39 f2                   cmp    %esi,%edx
  4012dd:   7d 14                   jge    4012f3 <L02>
  4012df:   48 63 d2                movslq %edx,%rdx
  4012e2:   83 c0 02                add    [=12=]x2,%eax
  4012e5:   83 04 97 64             addl   [=12=]x64,(%rdi,%rdx,4)
  4012e9:   39 c6                   cmp    %eax,%esi
  4012eb:   7e 06                   jle    4012f3 <L02>
  4012ed:   48 98                   cltq
  4012ef:   83 04 87 64             addl   [=12=]x64,(%rdi,%rax,4)
  4012f3:L02    c3                      retq
  4012f4:L03    c3                      retq
  4012f5:L04    31 c0                   xor    %eax,%eax
  4012f7:   eb d8                   jmp    4012d1 <L01>
  4012f9:   0f 1f 80 00 00 00 00    nopl   0x0(%rax)

这是 -S -fverbose-asm 的输出:

    .globl  incrementVector2
    .type   incrementVector2, @function
incrementVector2:
.LFB13:
    .cfi_startproc
    testl   %esi, %esi  # n
    jle .L19    #,
    movl    %esi, %edx  # n, bnd.1
    movl    %esi, %r11d # n, niters_vector_mult_vf.2
    movdqa  .LC1(%rip), %xmm1   #, tmp152
    movq    %rdi, %r8   # v, ivtmp.33
    shrl    , %edx    #,
    leal    -1(%rsi), %r10d #,
    andl    $-4, %r11d  #, niters_vector_mult_vf.2
# orig.c:38:        for (int i = 0; i < n; ++i) {
    movl    , %r9d    #, ivtmp.47
    salq    , %rdx    #, tmp150
    addq    %rdi, %rdx  # v, _144
.L10:
    cmpl    , %r10d   #, _72
    jbe .L14    #,
# orig.c:36: {
    movq    %rdi, %rax  # v, ivtmp.36
.L8:
# orig.c:39:            v[i] = v[i] + 1;
    movdqu  (%rax), %xmm0   # MEM[base: _138, offset: 0B], vect__42.13
    addq    , %rax   #, ivtmp.36
    paddd   %xmm1, %xmm0    # tmp152, vect__42.13
# orig.c:39:            v[i] = v[i] + 1;
    movups  %xmm0, -16(%rax)    # vect__42.13, MEM[base: _138, offset: 0B]
    cmpq    %rdx, %rax  # _144, ivtmp.36
    jne .L8 #,
# orig.c:38:        for (int i = 0; i < n; ++i) {
    movl    %r11d, %eax # niters_vector_mult_vf.2, i
    cmpl    %r11d, %esi # niters_vector_mult_vf.2, n
    je  .L9 #,
.L13:
# orig.c:39:            v[i] = v[i] + 1;
    movslq  %eax, %rcx  # i, i
# orig.c:39:            v[i] = v[i] + 1;
    addl    , (%rdi,%rcx,4)   #, *_40
# orig.c:38:        for (int i = 0; i < n; ++i) {
    leal    1(%rax), %ecx   #, i
# orig.c:38:        for (int i = 0; i < n; ++i) {
    cmpl    %ecx, %esi  # i, n
    jle .L9 #,
# orig.c:39:            v[i] = v[i] + 1;
    movslq  %ecx, %rcx  # i, i
# orig.c:38:        for (int i = 0; i < n; ++i) {
    addl    , %eax    #, i
# orig.c:39:            v[i] = v[i] + 1;
    addl    , (%rdi,%rcx,4)   #, *_107
# orig.c:38:        for (int i = 0; i < n; ++i) {
    cmpl    %eax, %esi  # i, n
    jle .L9 #,
# orig.c:39:            v[i] = v[i] + 1;
    cltq
# orig.c:39:            v[i] = v[i] + 1;
    addl    , (%rdi,%rax,4)   #, *_58
.L9:
    leal    1(%r9), %eax    #, _147
    addl    , %r9d    #, ivtmp.47
    cmpl    , %r9d   #, ivtmp.47
    jne .L10    #,
    movl    1, %esi  #, tmp147
    leaq    4(%rdi,%r10,4), %rdi    #, _134
    subl    %eax, %esi  # _147, tmp146
    .p2align 4,,10
    .p2align 3
.L12:
    movl    (%r8), %edx # MEM[base: _126, offset: 0B], _2
    leal    1(%rdx), %eax   #, ivtmp.21
    addl    %esi, %edx  # tmp146, _122
    .p2align 4,,10
    .p2align 3
.L11:
    movl    %eax, %ecx  # ivtmp.21, _25
    addl    , %eax    #, ivtmp.21
# orig.c:38:        for (int i = 0; i < n; ++i) {
    cmpl    %edx, %eax  # _122, ivtmp.21
    jne .L11    #,
    movl    %ecx, (%r8) # _25, MEM[base: _126, offset: 0B]
    addq    , %r8 #, ivtmp.33
# orig.c:37:    for (int k = 0; k < 100; ++k) {
    cmpq    %rdi, %r8   # _134, ivtmp.33
    jne .L12    #,
    ret
.L19:
    ret
.L14:
# orig.c:38:        for (int i = 0; i < n; ++i) {
    xorl    %eax, %eax  # i
    jmp .L13    #
    .cfi_endproc
.LFE13:
    .size   incrementVector2, .-incrementVector2
    .p2align 4,,15
    .globl  incrementVector1
    .type   incrementVector1, @function
incrementVector1:
.LFB14:
    .cfi_startproc
# orig.c:47:    for (int i = 0; i < n; ++i) {
    testl   %esi, %esi  # n
    jle .L20    #,
    leal    -1(%rsi), %eax  #, tmp118
    cmpl    , %eax    #, tmp118
    jbe .L27    #,
    movl    %esi, %edx  # n, bnd.51
    movdqa  .LC2(%rip), %xmm1   #, tmp131
    movq    %rdi, %rax  # v, ivtmp.62
    shrl    , %edx    #,
    salq    , %rdx    #, tmp121
    addq    %rdi, %rdx  # v, _58
.L23:
    movdqu  (%rax), %xmm0   # MEM[base: _53, offset: 0B], vect__8.57
    addq    , %rax   #, ivtmp.62
    paddd   %xmm1, %xmm0    # tmp131, vect__8.57
    movups  %xmm0, -16(%rax)    # vect__8.57, MEM[base: _53, offset: 0B]
    cmpq    %rdx, %rax  # _58, ivtmp.62
    jne .L23    #,
    movl    %esi, %eax  # n, tmp.53
    andl    $-4, %eax   #, tmp.53
    cmpl    %esi, %eax  # n, tmp.53
    je  .L29    #,
.L22:
# orig.c:49:            v[i] = v[i] + 1;
    movslq  %eax, %rdx  # tmp.53, tmp.53
    addl    0, (%rdi,%rdx,4) #, *_3
# orig.c:47:    for (int i = 0; i < n; ++i) {
    leal    1(%rax), %edx   #, i
# orig.c:47:    for (int i = 0; i < n; ++i) {
    cmpl    %esi, %edx  # n, i
    jge .L20    #,
# orig.c:49:            v[i] = v[i] + 1;
    movslq  %edx, %rdx  # i, i
# orig.c:47:    for (int i = 0; i < n; ++i) {
    addl    , %eax    #, i
    addl    0, (%rdi,%rdx,4) #, *_47
# orig.c:47:    for (int i = 0; i < n; ++i) {
    cmpl    %eax, %esi  # i, n
    jle .L20    #,
# orig.c:49:            v[i] = v[i] + 1;
    cltq
    addl    0, (%rdi,%rax,4) #, *_25
.L20:
# orig.c:52: }
    ret
.L29:
    ret
.L27:
# orig.c:47:    for (int i = 0; i < n; ++i) {
    xorl    %eax, %eax  # tmp.53
    jmp .L22    #
    .cfi_endproc
.LFE14:
    .size   incrementVector1, .-incrementVector1
    .section    .rodata.str1.1,"aMS",@progbits,1
.LC3: