OV - attention-avx512 - Loop 64

	Loop Id: 64	Module: attention-avx512	Source: attention.cpp:26-33	Coverage: 0.83%

0x4cb0 XOR	%R10D,%R10D

0x4cb3 VMOVAPD	%XMM0,%XMM1

0x4cb7 LEA	(%R8,%R10,1),%R11D

0x4cbb VMOVSS	(%R14,%R11,4),%XMM0

0x4cc1 VCVTSS2SD	%XMM0,%XMM0,%XMM2

0x4cc5 IMUL	%R13D,%R10D

0x4cc9 ADD	%R9D,%R10D

0x4ccc VMOVSS	(%R15,%R10,4),%XMM0

0x4cd2 VCVTSS2SD	%XMM0,%XMM0,%XMM0

0x4cd6 VFMADD213SD	%XMM1,%XMM2,%XMM0

0x4cdb VCVTSD2SS	%XMM0,%XMM0,%XMM0

0x4cdf LEA	(%R8,%R9,1),%R10D

0x4ce3 MOV	0x170(%RSP),%RDX

0x4ceb VMOVSS	%XMM0,(%RDX,%R10,4)

0x4cf1 INC	%R9

0x4cf4 CMP	%RBX,%R9

0x4cf7 JE	4c90

0x4cf9 VXORPS	%XMM0,%XMM0,%XMM0

0x4cfd CMP	$0x1,%EBX

0x4d00 JE	4cb0

0x4d02 MOV	%R9,%R11

0x4d05 MOV	%ESI,%EBX

0x4d07 XOR	%R10D,%R10D

0x4d0a NOPW	(%RAX,%RAX,1)

  (65) 0x4d10 LEA	-0x1(%RBX),%R15D

  (65) 0x4d14 VMOVSS	(%R14,%R15,4),%XMM1

  (65) 0x4d1a VCVTSS2SD	%XMM1,%XMM1,%XMM1

  (65) 0x4d1e MOV	%R11D,%R15D

  (65) 0x4d21 MOV	0xe8(%RSP),%RDX

  (65) 0x4d29 VMOVSS	(%RDX,%R15,4),%XMM2

  (65) 0x4d2f VCVTSS2SD	%XMM2,%XMM2,%XMM2

  (65) 0x4d33 VFMADD213SD	%XMM0,%XMM1,%XMM2

  (65) 0x4d38 MOV	%EBX,%R15D

  (65) 0x4d3b VMOVSS	(%R14,%R15,4),%XMM0

  (65) 0x4d41 VCVTSS2SD	%XMM0,%XMM0,%XMM1

  (65) 0x4d45 LEA	(%R13,%R11,1),%R15D

  (65) 0x4d4a MOV	0xe8(%RSP),%RDX

  (65) 0x4d52 VMOVSS	(%RDX,%R15,4),%XMM0

  (65) 0x4d58 MOV	0xe8(%RSP),%R15

  (65) 0x4d60 VCVTSS2SD	%XMM0,%XMM0,%XMM0

  (65) 0x4d64 VFMADD213SD	%XMM2,%XMM1,%XMM0

  (65) 0x4d69 ADD	$0x2,%R10

  (65) 0x4d6d ADD	$0x2,%EBX

  (65) 0x4d70 ADD	%RCX,%R11

  (65) 0x4d73 CMP	%R10,%RAX

  (65) 0x4d76 JNE	4d10

0x4d78 TEST	$0x1,%R13B

0x4d7c MOV	0x68(%RSP),%RBX

0x4d81 JNE	4cb3

0x4d87 JMP	4cdb

/home/eoseret/Applications/llm-attention/attention.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	Module
►100.00+	__libc_init_first	libc.so.6
○	__libc_start_main	libc.so.6
○	_start	attention-avx512

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	1.89
CQA speedup if FP arith vectorized	1.61
CQA speedup if fully vectorized	13.84
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.59
Bottlenecks
Function	main
Source	attention.cpp:26-27,attention.cpp:30-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	5.83
CQA cycles if no scalar integer	3.08
CQA cycles if FP arith vectorized	3.62
CQA cycles if fully vectorized	0.42
Front-end cycles	5.83
P0 cycles	3.67
P1 cycles	3.67
P2 cycles	1.50
P3 cycles	1.50
P4 cycles	1.00
P5 cycles	3.67
P6 cycles	3.67
P7 cycles	1.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	21.33
Nb uops	23.33
Nb loads	3.00
Nb stores	1.00
Nb stack references	1.67
FLOP/cycle	0.23
Nb FLOP add-sub	0.00
Nb FLOP mul	0.00
Nb FLOP fma	0.67
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	3.90
Bytes prefetched	0.00
Bytes loaded	18.67
Bytes stored	4.00
Stride 0	NA
Stride 1	NA
Stride n	NA
Stride unknown	NA
Stride indirect	NA
Vectorization ratio all	15.96
Vectorization ratio load	0.00
Vectorization ratio store	0.00
Vectorization ratio mul	NA
Vectorization ratio add_sub	NA
Vectorization ratio fma	0.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	25.00
Vector-efficiency ratio all	11.55
Vector-efficiency ratio load	9.03
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	12.50
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	13.19

Metric	Value
CQA speedup if no scalar integer	1.57
CQA speedup if FP arith vectorized	1.83
CQA speedup if fully vectorized	13.91
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.47
Bottlenecks	micro-operation queue,
Function	main
Source	attention.cpp:26-27,attention.cpp:30-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	5.50
CQA cycles if no scalar integer	3.50
CQA cycles if FP arith vectorized	3.00
CQA cycles if fully vectorized	0.40
Front-end cycles	5.50
P0 cycles	3.75
P1 cycles	3.75
P2 cycles	1.50
P3 cycles	1.50
P4 cycles	1.00
P5 cycles	3.75
P6 cycles	3.75
P7 cycles	1.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	20.00
Nb uops	22.00
Nb loads	3.00
Nb stores	1.00
Nb stack references	1.00
FLOP/cycle	0.36
Nb FLOP add-sub	0.00
Nb FLOP mul	0.00
Nb FLOP fma	1.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	3.64
Bytes prefetched	0.00
Bytes loaded	16.00
Bytes stored	4.00
Stride 0	NA
Stride 1	NA
Stride n	NA
Stride unknown	NA
Stride indirect	NA
Vectorization ratio all	20.00
Vectorization ratio load	0.00
Vectorization ratio store	0.00
Vectorization ratio mul	NA
Vectorization ratio add_sub	NA
Vectorization ratio fma	0.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	33.33
Vector-efficiency ratio all	11.88
Vector-efficiency ratio load	6.25
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	12.50
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	14.58

Metric	Value
CQA speedup if no scalar integer	2.38
CQA speedup if FP arith vectorized	1.00
CQA speedup if fully vectorized	13.71
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.73
Bottlenecks	micro-operation queue,
Function	main
Source	attention.cpp:26-27,attention.cpp:30-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	4.75
CQA cycles if no scalar integer	2.00
CQA cycles if FP arith vectorized	4.75
CQA cycles if fully vectorized	0.35
Front-end cycles	4.75
P0 cycles	2.75
P1 cycles	2.75
P2 cycles	1.00
P3 cycles	1.00
P4 cycles	1.00
P5 cycles	2.75
P6 cycles	2.75
P7 cycles	1.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	18.00
Nb uops	19.00
Nb loads	2.00
Nb stores	1.00
Nb stack references	2.00
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	4.21
Bytes prefetched	0.00
Bytes loaded	16.00
Bytes stored	4.00
Stride 0	1.00
Stride 1	1.00
Stride n	0.00
Stride unknown	2.00
Stride indirect	0.00
Vectorization ratio all	12.50
Vectorization ratio load	0.00
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	16.67
Vector-efficiency ratio all	11.72
Vector-efficiency ratio load	12.50
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	12.50

Metric	Value
CQA speedup if no scalar integer	1.93
CQA speedup if FP arith vectorized	2.34
CQA speedup if fully vectorized	13.87
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.61
Bottlenecks	micro-operation queue,
Function	main
Source	attention.cpp:26-27,attention.cpp:30-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	7.25
CQA cycles if no scalar integer	3.75
CQA cycles if FP arith vectorized	3.10
CQA cycles if fully vectorized	0.52
Front-end cycles	7.25
P0 cycles	4.50
P1 cycles	4.50
P2 cycles	2.00
P3 cycles	2.00
P4 cycles	1.00
P5 cycles	4.50
P6 cycles	4.50
P7 cycles	1.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	26.00
Nb uops	29.00
Nb loads	4.00
Nb stores	1.00
Nb stack references	2.00
FLOP/cycle	0.28
Nb FLOP add-sub	0.00
Nb FLOP mul	0.00
Nb FLOP fma	1.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	3.86
Bytes prefetched	0.00
Bytes loaded	24.00
Bytes stored	4.00
Stride 0	1.00
Stride 1	1.00
Stride n	0.00
Stride unknown	2.00
Stride indirect	0.00
Vectorization ratio all	15.38
Vectorization ratio load	0.00
Vectorization ratio store	0.00
Vectorization ratio mul	NA
Vectorization ratio add_sub	NA
Vectorization ratio fma	0.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	25.00
Vector-efficiency ratio all	11.06
Vector-efficiency ratio load	8.33
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	12.50
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	12.50

Path /

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

Function	main
Source file and lines	attention.cpp:26-33
Module	attention-avx512

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

Analyzed code is defined in /home/eoseret/Applications/llm-attention/attention.cpp:26-27,30-33.

Warnings:
Non-innermost loop: analyzing only self part (ignoring child loops).
This loop has 3 execution paths.

The presence of multiple execution paths is typically the main/first bottleneck.
Try to simplify control inside loop: ideally, try to remove all conditional expressions, for example by (if applicable):

hoisting them (moving them outside the loop)
turning them into conditional moves, MIN or MAX

Ex: if (x<0) x=0 => x = (x<0 ? 0 : x) (or MAX(0,x) after defining the corresponding macro)

gain
potential
hint
expert

Vectorization

Your loop is probably not vectorized. Only 11% 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 5.83 to 0.42 cycles (13.84x 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:
- recompile with ffast-math (included in Ofast) to extend loop vectorization to FP reductions.
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)

FMA

Detected 0.67 FMA (fused multiply-add) operations.

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: 0 occurrences
VCVTSS2SD: 0 occurrences

Conversion instructions

Detected expensive conversion instructions.

Details

VCVTSD2SS (FP64 to FP32, scalar): 0 occurrences
VCVTSS2SD (FP32 to FP64, scalar): 0 occurrences

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

0 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time).

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

The binary loop is composed of 1.3333333333333 FP arithmetical operations:

0.67: addition or subtraction (all inside FMA instructions)
0.67: multiply (all inside FMA instructions)

The binary loop is loading 18 bytes (2 double precision FP elements). The binary loop is storing 4 bytes (0 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.06 FP operations per loaded or stored byte.

General properties

nb instructions	21.33
nb uops	23.33
loop length	87.67
used x86 registers	10.67
used mmx registers	0
used xmm registers	2.33
used ymm registers	0
used zmm registers	0
nb stack references	1.67

Front-end

MACRO FUSION NOT POSSIBLE

micro-operation queue	5.83 cycles
front end	5.83 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7
uops	3.67	3.67	1.50	1.50	1.00	3.67	3.67	1.00
cycles	3.67	3.67	1.50	1.50	1.00	3.67	3.67	1.00

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)	0.00

Cycles summary

Front-end	5.83
Dispatch	3.67
Data deps.	0.00
Overall L1	5.83

Vectorization ratios

INT

all	0%
load	0%
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	25%
load	0%
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	43%

INT+FP

all	15%
load	0%
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

Vector efficiency ratios

INT

all	10%
load	12%
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	10%

all	12%
load	6%
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	12%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	16%

INT+FP

all	11%
load	9%
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	12%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	13%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 5.83 cycles. At this rate:

2% of peak load performance is reached (3.20 out of 128.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (0.71 out of 64.00 bytes stored per cycle (GB/s @ 1GHz))

Function	main
Source file and lines	attention.cpp:26-33
Module	attention-avx512

hoisting them (moving them outside the loop)
turning them into conditional moves, MIN or MAX

Ex: if (x<0) x=0 => x = (x<0 ? 0 : x) (or MAX(0,x) after defining the corresponding macro)

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 5.50 to 3.50 cycles (1.57x 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:
- recompile with ffast-math (included in Ofast) to extend loop vectorization to FP reductions.
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.

FMA

Detected 1 FMA (fused multiply-add) operations.

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.cpp:33
VCVTSS2SD: 2 occurrences►
- /home/eoseret/Applications/llm-attention/attention.cpp:31
- /home/eoseret/Applications/llm-attention/attention.cpp:31

Conversion instructions

Detected expensive conversion instructions.

Details

VCVTSD2SS (FP64 to FP32, scalar): 1 occurrences►
- /home/eoseret/Applications/llm-attention/attention.cpp:33
VCVTSS2SD (FP32 to FP64, scalar): 2 occurrences►
- /home/eoseret/Applications/llm-attention/attention.cpp:31
- /home/eoseret/Applications/llm-attention/attention.cpp:31

Workaround

Type of elements and instruction set

1 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time).

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

The binary loop is composed of 2 FP arithmetical operations:

1: addition or subtraction (all inside FMA instructions)
1: multiply (all inside FMA instructions)

The binary loop is loading 16 bytes (2 double precision FP elements). The binary loop is storing 4 bytes (0 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.10 FP operations per loaded or stored byte.

General properties

nb instructions	20
nb uops	22
loop length	82
used x86 registers	10
used mmx registers	0
used xmm registers	3
used ymm registers	0
used zmm registers	0
nb stack references	1

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	5.50 cycles
front end	5.50 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7
uops	3.75	3.75	1.50	1.50	1.00	3.75	3.75	1.00
cycles	3.75	3.75	1.50	1.50	1.00	3.75	3.75	1.00

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)	0.00

Cycles summary

Front-end	5.50
Dispatch	3.75
Data deps.	0.00
Overall L1	5.50

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	22%
load	0%
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	40%

INT+FP

all	20%
load	0%
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	33%

Vector efficiency ratios

INT

all	12%
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	12%

all	11%
load	6%
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	12%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	15%

INT+FP

all	11%
load	6%
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	12%
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 5.50 cycles. At this rate:

2% of peak load performance is reached (2.91 out of 128.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (0.73 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 5.50 to 3.75 cycles (1.47x speedup).

ASM code

In the binary file, the address of the loop is: 4cf9

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	Latency	Recip. throughput	Vectorization
XOR %R10D,%R10D	1	0	0	0	0	0	0	0	0	0	0.25	N/A
VMOVAPD %XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0.25	vect (25.0%)
LEA (%R8,%R10,1),%R11D	1	0	0.50	0	0	0	0.50	0	0	1	0.50	N/A
VMOVSS (%R14,%R11,4),%XMM0	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	scal (6.3%)
VCVTSS2SD %XMM0,%XMM0,%XMM2	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (6.3%)
IMUL %R13D,%R10D	1	0	1	0	0	0	0	0	0	3	1	N/A
ADD %R9D,%R10D	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
VMOVSS (%R15,%R10,4),%XMM0	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	scal (6.3%)
VCVTSS2SD %XMM0,%XMM0,%XMM0	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (6.3%)
VFMADD213SD %XMM1,%XMM2,%XMM0	1	0.50	0.50	0	0	0	0	0	0	4	0.50	scal (12.5%)
VCVTSD2SS %XMM0,%XMM0,%XMM0	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (12.5%)
LEA (%R8,%R9,1),%R10D	1	0	0.50	0	0	0	0.50	0	0	1	0.50	N/A
MOV 0x170(%RSP),%RDX	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	N/A
VMOVSS %XMM0,(%RDX,%R10,4)	1	0	0	0.33	0.33	1	0	0	0.33	3	1	scal (6.3%)
INC %R9	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
CMP %RBX,%R9	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	scal (12.5%)
JE 4c90 <main+0x14e0>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0.25	vect (25.0%)
CMP $0x1,%EBX	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
JE 4cb0 <main+0x1500>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A

Function	main
Source file and lines	attention.cpp:26-33
Module	attention-avx512

hoisting them (moving them outside the loop)
turning them into conditional moves, MIN or MAX

Ex: if (x<0) x=0 => x = (x<0 ? 0 : x) (or MAX(0,x) after defining the corresponding macro)

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 4.75 to 2.00 cycles (2.37x 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:
- recompile with ffast-math (included in Ofast) to extend loop vectorization to FP reductions.
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.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.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 loading 16 bytes. The binary loop is storing 4 bytes.

General properties

nb instructions	18
nb uops	19
loop length	73
used x86 registers	10
used mmx registers	0
used xmm registers	1
used ymm registers	0
used zmm registers	0
nb stack references	2

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	4.75 cycles
front end	4.75 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7
uops	2.75	2.75	1.00	1.00	1.00	2.75	2.75	1.00
cycles	2.75	2.75	1.00	1.00	1.00	2.75	2.75	1.00

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)	0.00

Cycles summary

Front-end	4.75
Dispatch	2.75
Data deps.	0.00
Overall L1	4.75

Vectorization ratios

INT

all	0%
load	0%
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	12%
load	0%
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	16%

Vector efficiency ratios

INT

all	10%
load	12%
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	9%

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	11%
load	12%
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	12%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 4.75 cycles. At this rate:

2% of peak load performance is reached (3.37 out of 128.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (0.84 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: 4cf9

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	Latency	Recip. throughput	Vectorization
VCVTSD2SS %XMM0,%XMM0,%XMM0	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (12.5%)
LEA (%R8,%R9,1),%R10D	1	0	0.50	0	0	0	0.50	0	0	1	0.50	N/A
MOV 0x170(%RSP),%RDX	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	N/A
VMOVSS %XMM0,(%RDX,%R10,4)	1	0	0	0.33	0.33	1	0	0	0.33	3	1	scal (6.3%)
INC %R9	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
CMP %RBX,%R9	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	scal (12.5%)
JE 4c90 <main+0x14e0>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0.25	vect (25.0%)
CMP $0x1,%EBX	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	scal (6.3%)
JE 4cb0 <main+0x1500>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A
MOV %R9,%R11	1	0	0	0	0	0	0	0	0	0	0.25	scal (12.5%)
MOV %ESI,%EBX	1	0	0	0	0	0	0	0	0	0	0.25	scal (6.3%)
XOR %R10D,%R10D	1	0	0	0	0	0	0	0	0	0	0.25	N/A
NOPW (%RAX,%RAX,1)	1	0	0	0	0	0	0	0	0	0	0.25	N/A
TEST $0x1,%R13B	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
MOV 0x68(%RSP),%RBX	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	scal (12.5%)
JNE 4cb3 <main+0x1503>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A
JMP 4cdb <main+0x152b>	1	0	0	0	0	0	0	1	0	0	1-2	N/A

Function	main
Source file and lines	attention.cpp:26-33
Module	attention-avx512

hoisting them (moving them outside the loop)
turning them into conditional moves, MIN or MAX

Ex: if (x<0) x=0 => x = (x<0 ? 0 : x) (or MAX(0,x) after defining the corresponding macro)

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 7.25 to 3.75 cycles (1.93x 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:
- recompile with ffast-math (included in Ofast) to extend loop vectorization to FP reductions.
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.

FMA

Detected 1 FMA (fused multiply-add) operations.

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.cpp:33
VCVTSS2SD: 2 occurrences►
- /home/eoseret/Applications/llm-attention/attention.cpp:31
- /home/eoseret/Applications/llm-attention/attention.cpp:31

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.cpp:33
VCVTSS2SD (FP32 to FP64, scalar): 2 occurrences►
- /home/eoseret/Applications/llm-attention/attention.cpp:31
- /home/eoseret/Applications/llm-attention/attention.cpp:31

Workaround

Type of elements and instruction set

1 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time).

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

The binary loop is composed of 2 FP arithmetical operations:

1: addition or subtraction (all inside FMA instructions)
1: multiply (all inside FMA instructions)

The binary loop is loading 24 bytes (3 double precision FP elements). The binary loop is storing 4 bytes (0 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.07 FP operations per loaded or stored byte.

General properties

nb instructions	26
nb uops	29
loop length	108
used x86 registers	12
used mmx registers	0
used xmm registers	3
used ymm registers	0
used zmm registers	0
nb stack references	2

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	7.25 cycles
front end	7.25 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7
uops	4.50	4.50	2.00	2.00	1.00	4.50	4.50	1.00
cycles	4.50	4.50	2.00	2.00	1.00	4.50	4.50	1.00

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)	0.00

Cycles summary

Front-end	7.25
Dispatch	4.50
Data deps.	0.00
Overall L1	7.25

Vectorization ratios

INT

all	0%
load	0%
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	22%
load	0%
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	40%

INT+FP

all	15%
load	0%
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

Vector efficiency ratios

INT

all	9%
load	12%
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	8%

all	11%
load	6%
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	12%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	15%

INT+FP

all	11%
load	8%
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	12%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	12%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 7.25 cycles. At this rate:

2% of peak load performance is reached (3.31 out of 128.00 bytes loaded per cycle (GB/s @ 1GHz))
0% of peak store performance is reached (0.55 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: 4cf9

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	Latency	Recip. throughput	Vectorization
VMOVAPD %XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0.25	vect (25.0%)
LEA (%R8,%R10,1),%R11D	1	0	0.50	0	0	0	0.50	0	0	1	0.50	N/A
VMOVSS (%R14,%R11,4),%XMM0	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	scal (6.3%)
VCVTSS2SD %XMM0,%XMM0,%XMM2	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (6.3%)
IMUL %R13D,%R10D	1	0	1	0	0	0	0	0	0	3	1	N/A
ADD %R9D,%R10D	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
VMOVSS (%R15,%R10,4),%XMM0	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	scal (6.3%)
VCVTSS2SD %XMM0,%XMM0,%XMM0	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (6.3%)
VFMADD213SD %XMM1,%XMM2,%XMM0	1	0.50	0.50	0	0	0	0	0	0	4	0.50	scal (12.5%)
VCVTSD2SS %XMM0,%XMM0,%XMM0	2	0.50	0.50	0	0	0	1	0	0	5	1	scal (12.5%)
LEA (%R8,%R9,1),%R10D	1	0	0.50	0	0	0	0.50	0	0	1	0.50	N/A
MOV 0x170(%RSP),%RDX	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	N/A
VMOVSS %XMM0,(%RDX,%R10,4)	1	0	0	0.33	0.33	1	0	0	0.33	3	1	scal (6.3%)
INC %R9	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
CMP %RBX,%R9	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	scal (12.5%)
JE 4c90 <main+0x14e0>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0.25	vect (25.0%)
CMP $0x1,%EBX	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	scal (6.3%)
JE 4cb0 <main+0x1500>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A
MOV %R9,%R11	1	0	0	0	0	0	0	0	0	0	0.25	N/A
MOV %ESI,%EBX	1	0	0	0	0	0	0	0	0	0	0.25	scal (6.3%)
XOR %R10D,%R10D	1	0	0	0	0	0	0	0	0	0	0.25	N/A
NOPW (%RAX,%RAX,1)	1	0	0	0	0	0	0	0	0	0	0.25	N/A
TEST $0x1,%R13B	1	0.25	0.25	0	0	0	0.25	0.25	0	1	0.25	N/A
MOV 0x68(%RSP),%RBX	1	0	0	0.50	0.50	0	0	0	0	4-5	0.50	scal (12.5%)
JNE 4cb3 <main+0x1503>	1	0.50	0	0	0	0	0	0.50	0	0	0.50-1	N/A

Report Configuration

Vectorization

Details

Workaround

FMA

Complex instructions

Details

Conversion instructions

Details

Workaround

Type of elements and instruction set

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

Arithmetic intensity

General properties

Front-end

Back-end

Cycles summary

Vectorization ratios

Vector efficiency ratios

Cycles and memory resources usage

Code clean check

Workaround

Vectorization

Details

Workaround

Execution units bottlenecks

FMA

Complex instructions

Details

Conversion instructions

Details

Workaround

Type of elements and instruction set

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

Arithmetic intensity

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

Code clean check

Workaround

Vectorization

Details

Workaround

Execution units bottlenecks

FMA

Complex instructions

Details

Slow data structures access

Details