OV - attention-gcc-skl512 - Loop 11

	Loop Id: 11	Module: attention-gcc-skl512	Source: attention_v2.cpp:26-33	Coverage: 0.51%

0x2120 MOV	%EDI,%ESI

0x2122 VXORPD	%XMM4,%XMM4,%XMM4

0x2126 XOR	%EAX,%EAX

0x2128 NOPL	(%RAX,%RAX,1)

  (10) 0x2130 LEA	(%RAX,%RCX,1),%R10D

  (10) 0x2134 INC	%EAX

  (10) 0x2136 VCVTSS2SD	(%RBX,%R10,4),%XMM1,%XMM0

  (10) 0x213c MOV	%ESI,%R10D

  (10) 0x213f VMOVAPD	%XMM0,%XMM2

  (10) 0x2143 ADD	%R8D,%ESI

  (10) 0x2146 VCVTSS2SD	(%R14,%R10,4),%XMM1,%XMM0

  (10) 0x214c VFMADD231SD	%XMM0,%XMM2,%XMM4

  (10) 0x2151 CMP	%R8D,%EAX

  (10) 0x2154 JB	2130

0x2156 LEA	(%RDI,%RCX,1),%EAX

0x2159 INC	%EDI

0x215b VCVTSD2SS	%XMM4,%XMM4,%XMM4

0x215f VMOVSS	%XMM4,(%R13,%RAX,4)

0x2166 CMP	%R8D,%EDI

0x2169 JB	2120

/home/eoseret/Applications/llm-attention/attention_v2.cpp: 26 - 33

--------------------------------------------------------------------------------

26:    for (unsigned int i = 0; i < M; ++i) {

27:       for (unsigned int j = 0; j < N; ++j) {  //vectorized

28:          double sum = 0.0;

29: #pragma clang loop vectorize(enable)

30:          for (unsigned int k = 0; k < K; ++k) { //vectorized

31:             sum += (double)A[i * K + k] * (double)B[k * N + j];

32:          }

33:          C[i * N + j] = alpha * static_cast<float>(sum);

Coverage (%)	Name	Source Location	Module
►100.00+	__libc_init_first		libc.so.6
○	__libc_start_main		libc.so.6
○	_start	new_allocator.h:183	attention-gcc-skl512

min	med	avg	max

Percentile Index	10	20	30	40	50	60	70	80	90	100
Value

min	med	avg	max

Percentile Index	10	20	30	40	50	60	70	80	90	100
Value

Path /

Metric	Value
CQA speedup if no scalar integer	1.67
CQA speedup if FP arith vectorized	1.00
CQA speedup if fully vectorized	14.55
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	2.00
Bottlenecks	micro-operation queue,
Function	main
Source	attention_v2.cpp:26-30,attention_v2.cpp:33-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	2.50
CQA cycles if no scalar integer	1.50
CQA cycles if FP arith vectorized	2.50
CQA cycles if fully vectorized	0.17
Front-end cycles	2.50
P0 cycles	1.25
P1 cycles	1.25
P2 cycles	0.33
P3 cycles	0.33
P4 cycles	1.00
P5 cycles	1.25
P6 cycles	1.25
P7 cycles	0.33
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	10.00
Nb uops	10.00
Nb loads	0.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	0.00
Nb FLOP add-sub	0.00
Nb FLOP mul	0.00
Nb FLOP fma	0.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	1.60
Bytes prefetched	0.00
Bytes loaded	0.00
Bytes stored	4.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	2.00
Stride indirect	0.00
Vectorization ratio all	25.00
Vectorization ratio load	NA
Vectorization ratio store	0.00
Vectorization ratio mul	NA
Vectorization ratio add_sub	NA
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	33.33
Vector-efficiency ratio all	12.50
Vector-efficiency ratio load	NA
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	14.58

Metric	Value
CQA speedup if no scalar integer	1.67
CQA speedup if FP arith vectorized	1.00
CQA speedup if fully vectorized	14.55
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	2.00
Bottlenecks	micro-operation queue,
Function	main
Source	attention_v2.cpp:26-30,attention_v2.cpp:33-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	2.50
CQA cycles if no scalar integer	1.50
CQA cycles if FP arith vectorized	2.50
CQA cycles if fully vectorized	0.17
Front-end cycles	2.50
P0 cycles	1.25
P1 cycles	1.25
P2 cycles	0.33
P3 cycles	0.33
P4 cycles	1.00
P5 cycles	1.25
P6 cycles	1.25
P7 cycles	0.33
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	10.00
Nb uops	10.00
Nb loads	0.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	0.00
Nb FLOP add-sub	0.00
Nb FLOP mul	0.00
Nb FLOP fma	0.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	1.60
Bytes prefetched	0.00
Bytes loaded	0.00
Bytes stored	4.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	2.00
Stride indirect	0.00
Vectorization ratio all	25.00
Vectorization ratio load	NA
Vectorization ratio store	0.00
Vectorization ratio mul	NA
Vectorization ratio add_sub	NA
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	33.33
Vector-efficiency ratio all	12.50
Vector-efficiency ratio load	NA
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	14.58

Path /

Average path: Display a virtual path defined by average values of all real paths

Function	main
Source file and lines	attention_v2.cpp:26-33
Module	attention-gcc-skl512

The loop is defined in /home/eoseret/Applications/llm-attention/attention_v2.cpp:26-33.

Analyzed code is defined in /home/eoseret/Applications/llm-attention/attention_v2.cpp:26-30,33.

Warnings:
Non-innermost loop: analyzing only self part (ignoring child loops).

gain
potential
hint
expert

Code clean check

Detected a slowdown caused by scalar integer instructions (typically used for address computation). By removing them, you can lower the cost of an iteration from 2.50 to 1.50 cycles (1.67x speedup).

Workaround

Try to reorganize arrays of structures to structures of arrays
Consider to permute loops (see vectorization gain report)

Vectorization

Your loop is probably not vectorized. Only 12% of vector register length is used (average across all SSE/AVX instructions). By vectorizing your loop, you can lower the cost of an iteration from 2.50 to 0.17 cycles (14.55x speedup).

Details

Store and arithmetical SSE/AVX instructions are used in scalar version (process only one data element in vector registers). Since your execution units are vector units, only a vectorized loop can use their full power.

Workaround

Try another compiler or update/tune your current one
Remove inter-iterations dependences from your loop and make it unit-stride:
- If your arrays have 2 or more dimensions, check whether elements are accessed contiguously and, otherwise, try to permute loops accordingly: C storage order is row-major: for(i) for(j) a[j][i] = b[j][i]; (slow, non stride 1) => for(i) for(j) a[i][j] = b[i][j]; (fast, stride 1)
- If your loop streams arrays of structures (AoS), try to use structures of arrays instead (SoA): for(i) a[i].x = b[i].x; (slow, non stride 1) => for(i) a.x[i] = b.x[i]; (fast, stride 1)

Execution units bottlenecks

Found no such bottlenecks but see expert reports for more complex bottlenecks.

No data for this section

Complex instructions

Detected COMPLEX INSTRUCTIONS.

Details

These instructions generate more than one micro-operation and only one of them can be decoded during a cycle and the extra micro-operations increase pressure on execution units.

VCVTSD2SS: 1 occurrences►
- /home/eoseret/Applications/llm-attention/attention_v2.cpp:33

Slow data structures access

Detected data structures (typically arrays) that cannot be efficiently read/written

Details

Constant unknown stride: 2 occurrence(s)

Non-unit stride (uncontiguous) accesses are not efficiently using data caches

Workaround

Try to reorganize arrays of structures to structures of arrays
Consider to permute loops (see vectorization gain report)

Conversion instructions

Detected expensive conversion instructions.

Details

VCVTSD2SS (FP64 to FP32, scalar): 1 occurrences►
- /home/eoseret/Applications/llm-attention/attention_v2.cpp:33

Workaround

Avoid mixing data with different types. In particular, check if the type of constants is the same as array elements. Use double instead of single precision only when/where needed by numerical stability and avoid mixing precision. In C/C++, FP constants are double precision by default and must be suffixed by 'f' to make them single precision.

Type of elements and instruction set

No instructions are processing arithmetic or math operations on FP elements. This loop is probably writing/copying data or processing integer elements.

Matching between your loop (in the source code) and the binary loop

The binary loop does not contain any FP arithmetical operations. The binary loop is storing 4 bytes.

General properties

nb instructions	10
nb uops	10
loop length	37
used x86 registers	6
used mmx registers	0
used xmm registers	1
used ymm registers	0
used zmm registers	0
nb stack references	0

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	2.50 cycles
front end	2.50 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7
uops	1.25	1.25	0.33	0.33	1.00	1.25	1.25	0.33
cycles	1.25	1.25	0.33	0.33	1.00	1.25	1.25	0.33

Execution ports to units layout:

P0 (256 bits): VPU, BRU, ALU, DIV/SQRT
P1 (256 bits): ALU, VPU
P2 (512 bits): store address, load
P3 (512 bits): store address, load
P4 (512 bits): store data
P5 (512 bits): ALU, VPU
P6: ALU, BRU
P7: store address

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	1.00

Cycles summary

Front-end	2.50
Dispatch	1.25
Data deps.	1.00
Overall L1	2.50

Vectorization ratios

INT

all	0%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	0%

all	33%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	50%

INT+FP

all	25%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	33%

Vector efficiency ratios

INT

all	6%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	6%

all	14%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	18%

INT+FP

all	12%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	14%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 2.50 cycles. At this rate:

2% of peak store performance is reached (1.60 out of 64.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

Performance is limited by instruction throughput (loading/decoding program instructions to execution core) (front-end is a bottleneck). By removing all these bottlenecks, you can lower the cost of an iteration from 2.50 to 1.25 cycles (2.00x speedup).

ASM code

In the binary file, the address of the loop is: 2120

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	Latency	Recip. throughput	Vectorization
MOV %EDI,%ESI	1	0	0	0	0	0	0	0	0	0	0.25	scal (6.3%)
VXORPD %XMM4,%XMM4,%XMM4	1	0	0	0	0	0	0	0	0	0	0.25	vect (25.0%)
XOR %EAX,%EAX	1	0	0	0	0	0	0	0	0	0	0.25	N/A
NOPL (%RAX,%RAX,1)	1	0	0	0	0	0	0	0	0	0	0.25	N/A
LEA (%RDI,%RCX,1),%EAX	1	0	0.50	0	0	0	0.50	0	0	1	0.50	N/A
INC %EDI	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
VCVTSD2SS %XMM4,%XMM4,%XMM4	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (12.5%)
VMOVSS %XMM4,(%R13,%RAX,4)	1	0	0	0.33	0.33	1	0	0	0.33	3	1	scal (6.3%)
CMP %R8D,%EDI	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
JB 2120 <main+0xde0>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A

Function	main
Source file and lines	attention_v2.cpp:26-33
Module	attention-gcc-skl512

gain
potential
hint
expert

Code clean check

Detected a slowdown caused by scalar integer instructions (typically used for address computation). By removing them, you can lower the cost of an iteration from 2.50 to 1.50 cycles (1.67x speedup).

Workaround

Try to reorganize arrays of structures to structures of arrays
Consider to permute loops (see vectorization gain report)

Vectorization

Details

Workaround

Try another compiler or update/tune your current one
Remove inter-iterations dependences from your loop and make it unit-stride:
- If your arrays have 2 or more dimensions, check whether elements are accessed contiguously and, otherwise, try to permute loops accordingly: C storage order is row-major: for(i) for(j) a[j][i] = b[j][i]; (slow, non stride 1) => for(i) for(j) a[i][j] = b[i][j]; (fast, stride 1)
- If your loop streams arrays of structures (AoS), try to use structures of arrays instead (SoA): for(i) a[i].x = b[i].x; (slow, non stride 1) => for(i) a.x[i] = b.x[i]; (fast, stride 1)

Execution units bottlenecks

Found no such bottlenecks but see expert reports for more complex bottlenecks.

No data for this section

Complex instructions

Detected COMPLEX INSTRUCTIONS.

Details

These instructions generate more than one micro-operation and only one of them can be decoded during a cycle and the extra micro-operations increase pressure on execution units.

VCVTSD2SS: 1 occurrences►
- /home/eoseret/Applications/llm-attention/attention_v2.cpp:33

Slow data structures access

Detected data structures (typically arrays) that cannot be efficiently read/written

Details

Constant unknown stride: 2 occurrence(s)

Non-unit stride (uncontiguous) accesses are not efficiently using data caches

Workaround

Try to reorganize arrays of structures to structures of arrays
Consider to permute loops (see vectorization gain report)

Conversion instructions

Detected expensive conversion instructions.

Details

VCVTSD2SS (FP64 to FP32, scalar): 1 occurrences►
- /home/eoseret/Applications/llm-attention/attention_v2.cpp:33

Workaround

Type of elements and instruction set

No instructions are processing arithmetic or math operations on FP elements. This loop is probably writing/copying data or processing integer elements.

Matching between your loop (in the source code) and the binary loop

The binary loop does not contain any FP arithmetical operations. The binary loop is storing 4 bytes.

General properties

nb instructions	10
nb uops	10
loop length	37
used x86 registers	6
used mmx registers	0
used xmm registers	1
used ymm registers	0
used zmm registers	0
nb stack references	0

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	2.50 cycles
front end	2.50 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7
uops	1.25	1.25	0.33	0.33	1.00	1.25	1.25	0.33
cycles	1.25	1.25	0.33	0.33	1.00	1.25	1.25	0.33

Execution ports to units layout:

P0 (256 bits): VPU, BRU, ALU, DIV/SQRT
P1 (256 bits): ALU, VPU
P2 (512 bits): store address, load
P3 (512 bits): store address, load
P4 (512 bits): store data
P5 (512 bits): ALU, VPU
P6: ALU, BRU
P7: store address

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	1.00

Cycles summary

Front-end	2.50
Dispatch	1.25
Data deps.	1.00
Overall L1	2.50

Vectorization ratios

INT

all	0%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	0%

all	33%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	50%

INT+FP

all	25%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	33%

Vector efficiency ratios

INT

all	6%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	6%

all	14%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	18%

INT+FP

all	12%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	14%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 2.50 cycles. At this rate:

2% of peak store performance is reached (1.60 out of 64.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

ASM code

In the binary file, the address of the loop is: 2120

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	Latency	Recip. throughput	Vectorization
MOV %EDI,%ESI	1	0	0	0	0	0	0	0	0	0	0.25	scal (6.3%)
VXORPD %XMM4,%XMM4,%XMM4	1	0	0	0	0	0	0	0	0	0	0.25	vect (25.0%)
XOR %EAX,%EAX	1	0	0	0	0	0	0	0	0	0	0.25	N/A
NOPL (%RAX,%RAX,1)	1	0	0	0	0	0	0	0	0	0	0.25	N/A
LEA (%RDI,%RCX,1),%EAX	1	0	0.50	0	0	0	0.50	0	0	1	0.50	N/A
INC %EDI	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
VCVTSD2SS %XMM4,%XMM4,%XMM4	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (12.5%)
VMOVSS %XMM4,(%R13,%RAX,4)	1	0	0	0.33	0.33	1	0	0	0.33	3	1	scal (6.3%)
CMP %R8D,%EDI	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
JB 2120 <main+0xde0>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A

Report Configuration

Code clean check

Workaround

Vectorization

Details

Workaround

Execution units bottlenecks

Complex instructions

Details

Slow data structures access

Details

Workaround

Conversion instructions

Details

Workaround

Type of elements and instruction set

Matching between your loop (in the source code) and the binary loop

General properties

Front-end

Back-end

Cycles summary

Vectorization ratios

Vector efficiency ratios

Cycles and memory resources usage

Front-end bottlenecks

ASM code

Code clean check

Workaround

Vectorization

Details

Workaround

Execution units bottlenecks

Complex instructions

Details

Slow data structures access

Details

Workaround

Conversion instructions

Details

Workaround

Type of elements and instruction set

Matching between your loop (in the source code) and the binary loop

General properties

Front-end

Back-end

Cycles summary

Vectorization ratios

Vector efficiency ratios

Cycles and memory resources usage

Front-end bottlenecks

ASM code