Cache misses when accessing an array in nested loop

Question

So I have this question from my professor, and I can not figure out why vector2 is faster and has less cache misses than vector1.

Assume that the code below is a valid compilable C code.

Vector2:

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;
          }
     }
}

Vector1:

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;
          }
     }
}

NOTE: INT4 means the integer is 4 Bytes in size.

In terms of CPU specs: cache size = 12288KB, line size=64B and only considering this single cache interacting with main memory.

Question

Why does vector2 have a faster runtime than vector1? And why vector1 will have more cache misses than vector2?

Me and a few classmates worked on this for a while and couldn't figure it out. 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? we are not sure if this is correct, and also not sure how to bring cache lines in to this either.

Answer 1

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?

Well, both codes have the same accessing pattern, iterating over the array v with a stride of 1. Cache spacial-locality-wise both codes are the same. However, the second code:

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;
          }
     }
}

Has a better temporal-locality because you access the same element 100 times, whereas in:

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;
          }
     }
}

you only access it once on every 'n' iterations.

So either you did a mistake, your teacher is playing some kind of strange game or I am missing something obvious.

Answer 2

Are you sure that you mean that incrementVector2 is faster?

As dreamcast pointed out, incrementVector1 has better temporal locality, so it should be faster.

And, from benchmarks, 1 is faster than 2

50x faster for an array size of 1000.

This is surprising because the array is small enough to become [and stay] cache hot.

And, incrementVector1 has a much smaller disassembled code size than incrementVector2 (at -O3).

incrementVector1 is 105 bytes and incrementVector2 is 203 bytes.

This is somewhat surprising since I would think that although there is some variation, I would not expect such a large discrepancy [See below].

---

Here is the program output:

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

---

Here's the program I used:

#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;
}

---

Here is the disassembly:

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    $0x2,%edx
  4011db:   44 8d 56 ff             lea    -0x1(%rsi),%r10d
  4011df:   41 83 e3 fc             and    $0xfffffffc,%r11d
  4011e3:   41 b9 01 00 00 00       mov    $0x1,%r9d
  4011e9:   48 c1 e2 04             shl    $0x4,%rdx
  4011ed:   48 01 fa                add    %rdi,%rdx
  4011f0:L00    41 83 fa 02             cmp    $0x2,%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    $0x10,%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   $0x2,(%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    $0x2,%eax
  40122e:   83 04 8f 02             addl   $0x2,(%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   $0x2,(%rdi,%rax,4)
  40123c:L03    41 8d 41 01             lea    0x1(%r9),%eax
  401240:   41 83 c1 02             add    $0x2,%r9d
  401244:   41 83 f9 63             cmp    $0x63,%r9d
  401248:   75 a6                   jne    4011f0 <L00>
  40124a:   be 65 00 00 00          mov    $0x65,%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    $0x1,%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    $0x4,%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    $0x2,%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    $0x2,%edx
  4012ac:   48 c1 e2 04             shl    $0x4,%rdx
  4012b0:   48 01 fa                add    %rdi,%rdx
  4012b3:L00    f3 0f 6f 00             movdqu (%rax),%xmm0
  4012b7:   48 83 c0 10             add    $0x10,%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    $0xfffffffc,%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   $0x64,(%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    $0x2,%eax
  4012e5:   83 04 97 64             addl   $0x64,(%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   $0x64,(%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)

---

Here is the output of -S -fverbose-asm:

    .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    $2, %edx    #,
    leal    -1(%rsi), %r10d #,
    andl    $-4, %r11d  #, niters_vector_mult_vf.2
# orig.c:38:        for (int i = 0; i < n; ++i) {
    movl    $1, %r9d    #, ivtmp.47
    salq    $4, %rdx    #, tmp150
    addq    %rdi, %rdx  # v, _144
.L10:
    cmpl    $2, %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    $16, %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    $2, (%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    $2, %eax    #, i
# orig.c:39:            v[i] = v[i] + 1;
    addl    $2, (%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    $2, (%rdi,%rax,4)   #, *_58
.L9:
    leal    1(%r9), %eax    #, _147
    addl    $2, %r9d    #, ivtmp.47
    cmpl    $99, %r9d   #, ivtmp.47
    jne .L10    #,
    movl    $101, %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    $1, %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    $4, %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    $2, %eax    #, tmp118
    jbe .L27    #,
    movl    %esi, %edx  # n, bnd.51
    movdqa  .LC2(%rip), %xmm1   #, tmp131
    movq    %rdi, %rax  # v, ivtmp.62
    shrl    $2, %edx    #,
    salq    $4, %rdx    #, tmp121
    addq    %rdi, %rdx  # v, _58
.L23:
    movdqu  (%rax), %xmm0   # MEM[base: _53, offset: 0B], vect__8.57
    addq    $16, %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    $100, (%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    $2, %eax    #, i
    addl    $100, (%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    $100, (%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: