OV - attention-avx512 - Loop 58

	Loop Id: 58	Module: attention-avx512	Source: attention.cpp:26-33	Coverage: 0.37%

0x5370 VXORPS	%XMM0,%XMM0,%XMM0

0x5374 CMP	$0x10,%R15D

0x5378 JB	5388

0x537a MOV	%R13D,%ESI

0x537d ADD	%ECX,%ESI

0x537f SETB	%SIL

0x5383 OR	%R10B,%SIL

0x5386 JE	53f0

0x5388 MOV	0x120(%RSP),%RDX

0x5390 XOR	%ESI,%ESI

0x5392 MOV	%R14,%R12

0x5395 IMUL	%RSI,%R12

0x5399 ADD	%R13,%R12

0x539c NOPL	(%RAX)

  (57) 0x53a0 LEA	(%R8,%RSI,1),%EDI

  (57) 0x53a4 INC	%RSI

  (57) 0x53a7 VMOVSS	(%RBX,%RDI,4),%XMM1

  (57) 0x53ac MOV	%R12D,%EDI

  (57) 0x53af VMOVSS	(%RDX,%RDI,4),%XMM2

  (57) 0x53b4 ADD	%R14,%R12

  (57) 0x53b7 VCVTSS2SD	%XMM1,%XMM1,%XMM1

  (57) 0x53bb VCVTSS2SD	%XMM2,%XMM2,%XMM2

  (57) 0x53bf VFMADD231SD	%XMM2,%XMM1,%XMM0

  (57) 0x53c4 CMP	%RSI,%R15

  (57) 0x53c7 JNE	53a0

0x53c9 MOV	0x150(%RSP),%RDX

0x53d1 VCVTSD2SS	%XMM0,%XMM0,%XMM0

0x53d5 LEA	(%R11,%R13,1),%ESI

0x53d9 INC	%R13

0x53dc VMOVSS	%XMM0,(%RDX,%RSI,4)

0x53e1 CMP	%R15,%R13

0x53e4 JNE	5370

0x53f0 MOV	0x120(%RSP),%RDX

0x53f8 VXORPS	%XMM0,%XMM0,%XMM0

0x53fc VXORPS	%XMM1,%XMM1,%XMM1

0x5400 VXORPS	%XMM2,%XMM2,%XMM2

0x5404 VPXOR	%XMM3,%XMM3,%XMM3

0x5408 XOR	%ESI,%ESI

0x540a NOPW	(%RAX,%RAX,1)

  (61) 0x5410 LEA	(%R8,%RSI,1),%R12D

  (61) 0x5414 VCVTPS2PD	(%RBX,%R12,4),%YMM4

  (61) 0x541a VCVTPS2PD	0x10(%RBX,%R12,4),%YMM5

  (61) 0x5421 VCVTPS2PD	0x20(%RBX,%R12,4),%YMM6

  (61) 0x5428 VCVTPS2PD	0x30(%RBX,%R12,4),%YMM7

  (61) 0x542f LEA	(%R13,%RSI,1),%R12D

  (61) 0x5434 ADD	$0x10,%RSI

  (61) 0x5438 VCVTPS2PD	(%RDX,%R12,4),%YMM8

  (61) 0x543e VCVTPS2PD	0x10(%RDX,%R12,4),%YMM9

  (61) 0x5445 VFMADD231PD	%YMM8,%YMM4,%YMM0

  (61) 0x544a VFMADD231PD	%YMM9,%YMM5,%YMM1

  (61) 0x544f VCVTPS2PD	0x20(%RDX,%R12,4),%YMM8

  (61) 0x5456 VCVTPS2PD	0x30(%RDX,%R12,4),%YMM5

  (61) 0x545d VFMADD231PD	%YMM8,%YMM6,%YMM2

  (61) 0x5462 VFMADD231PD	%YMM5,%YMM7,%YMM3

  (61) 0x5467 CMP	%RSI,%RAX

  (61) 0x546a JNE	5410

0x546c VADDPD	%YMM0,%YMM1,%YMM0

0x5470 VADDPD	%YMM2,%YMM3,%YMM1

0x5474 CMPQ	$0,0x80(%RSP)

0x547d MOV	%RAX,%RSI

0x5480 VADDPD	%YMM0,%YMM1,%YMM0

0x5484 VEXTRACTF128	$0x1,%YMM0,%XMM1

0x548a VADDPD	%XMM1,%XMM0,%XMM0

0x548e VSHUFPD	$0x1,%XMM0,%XMM0,%XMM1

0x5493 VADDSD	%XMM1,%XMM0,%XMM0

0x5497 JNE	5392

0x549d JMP	53c9

/home/eoseret/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	Source Location	Module

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	1.60
CQA speedup if FP arith vectorized	1.75
CQA speedup if fully vectorized	5.38
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.38
Bottlenecks
Function	main
Source	attention.cpp:26-27,attention.cpp:30-30,attention.cpp:33-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	3.09
CQA cycles if no scalar integer	1.94
CQA cycles if FP arith vectorized	1.77
CQA cycles if fully vectorized	0.57
Front-end cycles	3.09
P0 cycles	1.88
P1 cycles	1.88
P2 cycles	1.88
P3 cycles	1.88
P4 cycles	1.88
P5 cycles	1.88
P6 cycles	0.88
P7 cycles	0.88
P8 cycles	0.88
P9 cycles	0.88
P10 cycles	0.50
P11 cycles	0.50
P12 cycles	1.75
P13 cycles	1.75
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	26.50
Nb uops	24.75
Nb loads	2.50
Nb stores	1.00
Nb stack references	2.50
FLOP/cycle	2.42
Nb FLOP add-sub	7.50
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	8.36
Bytes prefetched	0.00
Bytes loaded	20.00
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	38.80
Vectorization ratio load	NA
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	36.67
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	45.91
Vector-efficiency ratio all	18.26
Vector-efficiency ratio load	NA
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	23.96
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	17.16

Metric	Value
CQA speedup if no scalar integer	2.33
CQA speedup if FP arith vectorized	1.00
CQA speedup if fully vectorized	13.47
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.50
Bottlenecks	micro-operation queue,
Function	main
Source	attention.cpp:26-27,attention.cpp:30-30,attention.cpp:33-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	1.75
CQA cycles if no scalar integer	0.75
CQA cycles if FP arith vectorized	1.75
CQA cycles if fully vectorized	0.13
Front-end cycles	1.75
P0 cycles	1.17
P1 cycles	1.17
P2 cycles	1.17
P3 cycles	1.17
P4 cycles	1.17
P5 cycles	1.17
P6 cycles	0.75
P7 cycles	0.75
P8 cycles	0.75
P9 cycles	0.75
P10 cycles	0.00
P11 cycles	0.00
P12 cycles	0.50
P13 cycles	0.50
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	16.00
Nb uops	14.00
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	11.43
Bytes prefetched	0.00
Bytes loaded	16.00
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	14.29
Vectorization ratio load	NA
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	25.00
Vector-efficiency ratio all	12.50
Vector-efficiency ratio load	NA
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	12.50
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	14.06

Metric	Value
CQA speedup if no scalar integer	2.38
CQA speedup if FP arith vectorized	1.00
CQA speedup if fully vectorized	14.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.30
Bottlenecks	micro-operation queue,
Function	main
Source	attention.cpp:26-27,attention.cpp:30-30,attention.cpp:33-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	2.38
CQA cycles if no scalar integer	1.00
CQA cycles if FP arith vectorized	2.38
CQA cycles if fully vectorized	0.17
Front-end cycles	2.38
P0 cycles	1.83
P1 cycles	1.83
P2 cycles	1.83
P3 cycles	1.83
P4 cycles	1.83
P5 cycles	1.83
P6 cycles	0.75
P7 cycles	0.75
P8 cycles	0.75
P9 cycles	0.75
P10 cycles	0.00
P11 cycles	0.00
P12 cycles	0.50
P13 cycles	0.50
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	21.00
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	8.42
Bytes prefetched	0.00
Bytes loaded	16.00
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	14.29
Vectorization ratio load	NA
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	25.00
Vector-efficiency ratio all	12.50
Vector-efficiency ratio load	NA
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	12.50
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	14.06

Metric	Value
CQA speedup if no scalar integer	1.33
CQA speedup if FP arith vectorized	2.78
CQA speedup if fully vectorized	4.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.33
Bottlenecks	micro-operation queue,
Function	main
Source	attention.cpp:26-27,attention.cpp:30-30,attention.cpp:33-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	4.00
CQA cycles if no scalar integer	3.00
CQA cycles if FP arith vectorized	1.44
CQA cycles if fully vectorized	1.00
Front-end cycles	4.00
P0 cycles	2.17
P1 cycles	2.17
P2 cycles	2.17
P3 cycles	2.17
P4 cycles	2.17
P5 cycles	2.17
P6 cycles	1.00
P7 cycles	1.00
P8 cycles	1.00
P9 cycles	1.00
P10 cycles	1.00
P11 cycles	1.00
P12 cycles	3.00
P13 cycles	3.00
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	33.00
Nb uops	32.00
Nb loads	3.00
Nb stores	1.00
Nb stack references	3.00
FLOP/cycle	3.75
Nb FLOP add-sub	15.00
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	7.00
Bytes prefetched	0.00
Bytes loaded	24.00
Bytes stored	4.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	1.00
Stride indirect	0.00
Vectorization ratio all	68.75
Vectorization ratio load	NA
Vectorization ratio store	0.00
Vectorization ratio mul	NA
Vectorization ratio add_sub	80.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	70.00
Vector-efficiency ratio all	25.00
Vector-efficiency ratio load	NA
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	37.50
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	20.63

Metric	Value
CQA speedup if no scalar integer	1.42
CQA speedup if FP arith vectorized	2.82
CQA speedup if fully vectorized	4.25
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.42
Bottlenecks	micro-operation queue,
Function	main
Source	attention.cpp:26-27,attention.cpp:30-30,attention.cpp:33-33
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	4.25
CQA cycles if no scalar integer	3.00
CQA cycles if FP arith vectorized	1.51
CQA cycles if fully vectorized	1.00
Front-end cycles	4.25
P0 cycles	2.33
P1 cycles	2.33
P2 cycles	2.33
P3 cycles	2.33
P4 cycles	2.33
P5 cycles	2.33
P6 cycles	1.00
P7 cycles	1.00
P8 cycles	1.00
P9 cycles	1.00
P10 cycles	1.00
P11 cycles	1.00
P12 cycles	3.00
P13 cycles	3.00
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	0
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	36.00
Nb uops	34.00
Nb loads	3.00
Nb stores	1.00
Nb stack references	3.00
FLOP/cycle	3.53
Nb FLOP add-sub	15.00
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	6.59
Bytes prefetched	0.00
Bytes loaded	24.00
Bytes stored	4.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	3.00
Stride indirect	0.00
Vectorization ratio all	57.89
Vectorization ratio load	NA
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	66.67
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	63.64
Vector-efficiency ratio all	23.03
Vector-efficiency ratio load	NA
Vector-efficiency ratio store	6.25
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	33.33
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	19.89

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/llm-attention/attention.cpp:26-33.

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

Warnings:
Non-innermost loop: analyzing only self part (ignoring child loops).
This loop has 4 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 poorly vectorized. Only 18% of vector register length is used (average across all SSE/AVX instructions).

Details

38% of SSE/AVX instructions are used in vector version (process two or more data elements in vector registers):

0% of SSE/AVX stores are used in vector version.
36% of SSE/AVX addition or subtraction instructions are used in vector version.
0% of SSE/AVX multiply instructions are used in vector version.
45% of SSE/AVX instructions that are not load, store, addition, subtraction nor multiply instructions are used in vector version.

Workaround

Read the "512-bits vectorization" report at "Potential" confidence level.

512-bits vectorization

On some x86 processors supporting 512-bits vectorization, compilers are often too conservative and limit vectorization to 256 bits. Performance can then be improved by enforcing 512-bits vectorization, especially with many vectorized and high trip count loops. 512-bits vectorization performance overhead (compared to 256-bits) is generally lower on newer processors.

Workaround

Recompile with -mprefer-vector-width=512

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): 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). 0 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in vector mode (two at a time). 1 AVX instructions are processing arithmetic or math operations on double precision FP elements in vector mode (four at a time).

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

The binary loop is composed of 7.5 FP arithmetical operations:

7.50: addition or subtraction

The binary loop is loading 20 bytes (2 double precision FP elements). The binary loop is storing 4 bytes (0 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.31 FP operations per loaded or stored byte.

General properties

nb instructions	26.50
nb uops	24.75
loop length	106.75
used x86 registers	10
used mmx registers	0
used xmm registers	2.50
used ymm registers	2
used zmm registers	0
nb stack references	2.50

Front-end

MACRO FUSION NOT POSSIBLE

micro-operation queue	3.09 cycles
front end	3.09 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	1.87	1.87	1.87	1.87	1.87	1.87	0.88	0.88	0.88	0.88	0.50	0.50	1.75	1.75	0.50	0.50
cycles	1.87	1.87	1.87	1.87	1.87	1.87	0.88	0.88	0.88	0.88	0.50	0.50	1.75	1.75	0.50	0.50

Execution ports to units layout:

P0: ALU
P1: ALU
P2: ALU
P3: ALU, BRU
P4: ALU, BRU
P5: ALU, BRU
P6 (512 bits): store address, load
P7 (512 bits): store address, load
P8 (512 bits): store address, load
P9 (512 bits): store address, load
P10 (512 bits): VPU, DIV/SQRT
P11 (512 bits): VPU, DIV/SQRT
P12 (512 bits): VPU
P13 (512 bits): VPU
P14 (512 bits): FP store data
P15 (512 bits): FP store data

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	0.00

Cycles summary

Front-end	3.09
Dispatch	2.25
Data deps.	0.00
Overall L1	3.09

Vectorization ratios

INT

all	12%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	0%
add-sub	0%
fma	NA (no fma vectorizable/vectorized instructions)
other	14%

all	55%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	80%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	67%

INT+FP

all	38%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	0%
add-sub	36%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	45%

Vector efficiency ratios

INT

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

all	20%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	37%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	20%

INT+FP

all	18%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	12%
add-sub	23%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	17%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 3.09 cycles. At this rate:

2% of peak load performance is reached (6.88 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (1.48 out of 128.00 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 1.75 to 0.75 cycles (2.33x 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 1.75 to 0.13 cycles (13.47x 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)

Execution units bottlenecks

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

No data for this section

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/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	16
nb uops	14
loop length	63
used x86 registers	9
used mmx registers	0
used xmm registers	1
used ymm registers	0
used zmm registers	0
nb stack references	2

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.75 cycles
front end	1.75 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	1.17	1.17	1.17	1.17	1.17	1.17	0.75	0.75	0.75	0.75	0.00	0.00	0.50	0.50	0.50	0.50
cycles	1.17	1.17	1.17	1.17	1.17	1.17	0.75	0.75	0.75	0.75	0.00	0.00	0.50	0.50	0.50	0.50

Execution ports to units layout:

P0: ALU
P1: ALU
P2: ALU
P3: ALU, BRU
P4: ALU, BRU
P5: ALU, BRU
P6 (512 bits): store address, load
P7 (512 bits): store address, load
P8 (512 bits): store address, load
P9 (512 bits): store address, load
P10 (512 bits): VPU, DIV/SQRT
P11 (512 bits): VPU, DIV/SQRT
P12 (512 bits): VPU
P13 (512 bits): VPU
P14 (512 bits): FP store data
P15 (512 bits): FP store data

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	0.00

Cycles summary

Front-end	1.75
Dispatch	1.17
Data deps.	0.00
Overall L1	1.75

Vectorization ratios

INT

all	0%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	0%
add-sub	0%
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	14%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	0%
add-sub	0%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

Vector efficiency ratios

INT

all	10%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	12%
add-sub	12%
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	12%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	12%
add-sub	12%
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 1.75 cycles. At this rate:

3% of peak load performance is reached (9.14 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (2.29 out of 128.00 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 1.75 to 1.17 cycles (1.50x speedup).

ASM code

In the binary file, the address of the loop is: 5370

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
CMP $0x10,%R15D	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	scal (6.3%)
JB 5388 <main+0x16e8>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV 0x120(%RSP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
XOR %ESI,%ESI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
MOV %R14,%R12	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	scal (12.5%)
IMUL %RSI,%R12	1	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	3	0.33	scal (12.5%)
ADD %R13,%R12	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	scal (12.5%)
NOPL (%RAX)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.13	N/A
MOV 0x150(%RSP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
VCVTSD2SS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
LEA (%R11,%R13,1),%ESI	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
INC %R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
VMOVSS %XMM0,(%RDX,%RSI,4)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	1	0.50	scal (6.3%)
CMP %R15,%R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
JNE 5370 <main+0x16d0>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0.33-1	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 2.38 to 1.00 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

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/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	21
nb uops	19
loop length	77
used x86 registers	11
used mmx registers	0
used xmm registers	1
used ymm registers	0
used zmm registers	0
nb stack references	2

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	2.38 cycles
front end	2.38 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	1.83	1.83	1.83	1.83	1.83	1.83	0.75	0.75	0.75	0.75	0.00	0.00	0.50	0.50	0.50	0.50
cycles	1.83	1.83	1.83	1.83	1.83	1.83	0.75	0.75	0.75	0.75	0.00	0.00	0.50	0.50	0.50	0.50

Execution ports to units layout:

P0: ALU
P1: ALU
P2: ALU
P3: ALU, BRU
P4: ALU, BRU
P5: ALU, BRU
P6 (512 bits): store address, load
P7 (512 bits): store address, load
P8 (512 bits): store address, load
P9 (512 bits): store address, load
P10 (512 bits): VPU, DIV/SQRT
P11 (512 bits): VPU, DIV/SQRT
P12 (512 bits): VPU
P13 (512 bits): VPU
P14 (512 bits): FP store data
P15 (512 bits): FP store data

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	0.00

Cycles summary

Front-end	2.38
Dispatch	1.83
Data deps.	0.00
Overall L1	2.38

Vectorization ratios

INT

all	0%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	0%
add-sub	0%
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	14%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	0%
add-sub	0%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

Vector efficiency ratios

INT

all	10%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	12%
add-sub	12%
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	12%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	12%
add-sub	12%
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 2.38 cycles. At this rate:

2% of peak load performance is reached (6.74 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (1.68 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

ASM code

In the binary file, the address of the loop is: 5370

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
CMP $0x10,%R15D	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	scal (6.3%)
JB 5388 <main+0x16e8>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV %R13D,%ESI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
ADD %ECX,%ESI	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
SETB %SIL	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
OR %R10B,%SIL	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
JE 53f0 <main+0x1750>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV 0x120(%RSP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
XOR %ESI,%ESI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
MOV %R14,%R12	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	scal (12.5%)
IMUL %RSI,%R12	1	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	3	0.33	scal (12.5%)
ADD %R13,%R12	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	scal (12.5%)
NOPL (%RAX)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.13	N/A
MOV 0x150(%RSP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
VCVTSD2SS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
LEA (%R11,%R13,1),%ESI	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
INC %R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
VMOVSS %XMM0,(%RDX,%RSI,4)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	1	0.50	scal (6.3%)
CMP %R15,%R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
JNE 5370 <main+0x16d0>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0.33-1	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 4.00 to 3.00 cycles (1.33x speedup).

Workaround

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

Vectorization

Your loop is partially vectorized. Only 25% of vector register length is used (average across all SSE/AVX instructions).

Details

68% of SSE/AVX instructions are used in vector version (process two or more data elements in vector registers):

0% of SSE/AVX stores are used in vector version.
80% of SSE/AVX addition or subtraction instructions are used in vector version.
70% of SSE/AVX instructions that are not load, store, addition, subtraction nor multiply instructions are used in vector version.

Workaround

Read the "512-bits vectorization" report at "Potential" confidence level.

Execution units bottlenecks

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

512-bits vectorization

Workaround

Recompile with -mprefer-vector-width=512

Slow data structures access

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

Details

Constant unknown stride: 1 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)

Vector unaligned load/store instructions

Detected 1 suboptimal vector unaligned load/store instructions.

Details

VEXTRACTF128: 1 occurrences►
- /home/eoseret/llm-attention/attention.cpp:30

Workaround

Pass to your compiler a micro-architecture specialization option:
- use march=native
Use vector aligned instructions:
1. align your arrays on 64 bytes boundaries: replace { void *p = malloc (size); } with { void *p; posix_memalign (&p, 64, size); }.
2. inform your compiler that your arrays are vector aligned: if array 'foo' is 64 bytes-aligned, define a pointer 'p_foo' as __builtin_assume_aligned (foo, 64) and use it instead of 'foo' in the loop.

Conversion instructions

Detected expensive conversion instructions.

Details

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

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). 1 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in vector mode (two at a time). 3 AVX instructions are processing arithmetic or math operations on double precision FP elements in vector mode (four at a time).

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

The binary loop is composed of 15 FP arithmetical operations:

15: addition or subtraction

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 0.54 FP operations per loaded or stored byte.

General properties

nb instructions	33
nb uops	32
loop length	139
used x86 registers	9
used mmx registers	0
used xmm registers	4
used ymm registers	4
used zmm registers	0
nb stack references	3

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	4.00 cycles
front end	4.00 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	2.17	2.17	2.17	2.17	2.17	2.17	1.00	1.00	1.00	1.00	1.00	1.00	3.00	3.00	0.50	0.50
cycles	2.17	2.17	2.17	2.17	2.17	2.17	1.00	1.00	1.00	1.00	1.00	1.00	3.00	3.00	0.50	0.50

Execution ports to units layout:

P0: ALU
P1: ALU
P2: ALU
P3: ALU, BRU
P4: ALU, BRU
P5: ALU, BRU
P6 (512 bits): store address, load
P7 (512 bits): store address, load
P8 (512 bits): store address, load
P9 (512 bits): store address, load
P10 (512 bits): VPU, DIV/SQRT
P11 (512 bits): VPU, DIV/SQRT
P12 (512 bits): VPU
P13 (512 bits): VPU
P14 (512 bits): FP store data
P15 (512 bits): FP store data

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	0.00

Cycles summary

Front-end	4.00
Dispatch	3.00
Data deps.	0.00
Overall L1	4.00

Vectorization ratios

INT

all	33%
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	33%

all	76%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	80%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	85%

INT+FP

all	68%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	80%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	70%

Vector efficiency ratios

INT

all	14%
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	14%

all	27%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	37%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	23%

INT+FP

all	25%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	37%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	20%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 4.00 cycles. At this rate:

2% of peak load performance is reached (6.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
0% of peak store performance is reached (1.00 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

ASM code

In the binary file, the address of the loop is: 5370

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
CMP $0x10,%R15D	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	scal (6.3%)
JB 5388 <main+0x16e8>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV %R13D,%ESI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
ADD %ECX,%ESI	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
SETB %SIL	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
OR %R10B,%SIL	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
JE 53f0 <main+0x1750>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV 0x150(%RSP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
VCVTSD2SS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
LEA (%R11,%R13,1),%ESI	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
INC %R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
VMOVSS %XMM0,(%RDX,%RSI,4)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0.50	0.50	1	0.50	scal (6.3%)
CMP %R15,%R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	scal (12.5%)
JNE 5370 <main+0x16d0>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV 0x120(%RSP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
VXORPS %XMM1,%XMM1,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
VXORPS %XMM2,%XMM2,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
VPXOR %XMM3,%XMM3,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
XOR %ESI,%ESI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
NOPW (%RAX,%RAX,1)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.13	N/A
VADDPD %YMM0,%YMM1,%YMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (50.0%)
VADDPD %YMM2,%YMM3,%YMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (50.0%)
CMPQ $0,0x80(%RSP)	1	0.17	0.17	0.17	0.17	0.17	0.17	0.25	0.25	0.25	0.25	0	0	0	0	0	0	1	0.25	N/A
MOV %RAX,%RSI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
VADDPD %YMM0,%YMM1,%YMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (50.0%)
VEXTRACTF128 $0x1,%YMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	0	3	0.50	vect (25.0%)
VADDPD %XMM1,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (25.0%)
VSHUFPD $0x1,%XMM0,%XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	1	0.25	vect (25.0%)
VADDSD %XMM1,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	scal (12.5%)
JNE 5392 <main+0x16f2>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.33-1	N/A
JMP 53c9 <main+0x1729>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.50	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 4.25 to 3.00 cycles (1.42x speedup).

Workaround

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

Vectorization

Your loop is partially vectorized. Only 23% of vector register length is used (average across all SSE/AVX instructions).

Details

57% of SSE/AVX instructions are used in vector version (process two or more data elements in vector registers):

0% of SSE/AVX stores are used in vector version.
66% of SSE/AVX addition or subtraction instructions are used in vector version.
0% of SSE/AVX multiply instructions are used in vector version.
63% of SSE/AVX instructions that are not load, store, addition, subtraction nor multiply instructions are used in vector version.

Workaround

Read the "512-bits vectorization" report at "Potential" confidence level.

Execution units bottlenecks

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

512-bits vectorization

Workaround

Recompile with -mprefer-vector-width=512

Slow data structures access

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

Details

Constant unknown stride: 3 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)

Vector unaligned load/store instructions

Detected 1 suboptimal vector unaligned load/store instructions.

Details

VEXTRACTF128: 1 occurrences►
- /home/eoseret/llm-attention/attention.cpp:30

Workaround

Pass to your compiler a micro-architecture specialization option:
- use march=native
Use vector aligned instructions:
1. align your arrays on 64 bytes boundaries: replace { void *p = malloc (size); } with { void *p; posix_memalign (&p, 64, size); }.
2. inform your compiler that your arrays are vector aligned: if array 'foo' is 64 bytes-aligned, define a pointer 'p_foo' as __builtin_assume_aligned (foo, 64) and use it instead of 'foo' in the loop.

Conversion instructions

Detected expensive conversion instructions.

Details

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

Workaround

Type of elements and instruction set

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

The binary loop is composed of 15 FP arithmetical operations:

15: addition or subtraction

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 0.54 FP operations per loaded or stored byte.

General properties

nb instructions	36
nb uops	34
loop length	148
used x86 registers	11
used mmx registers	0
used xmm registers	4
used ymm registers	4
used zmm registers	0
nb stack references	3

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	4.25 cycles
front end	4.25 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	2.33	2.33	2.33	2.33	2.33	2.33	1.00	1.00	1.00	1.00	1.00	1.00	3.00	3.00	0.50	0.50
cycles	2.33	2.33	2.33	2.33	2.33	2.33	1.00	1.00	1.00	1.00	1.00	1.00	3.00	3.00	0.50	0.50

Execution ports to units layout:

P0: ALU
P1: ALU
P2: ALU
P3: ALU, BRU
P4: ALU, BRU
P5: ALU, BRU
P6 (512 bits): store address, load
P7 (512 bits): store address, load
P8 (512 bits): store address, load
P9 (512 bits): store address, load
P10 (512 bits): VPU, DIV/SQRT
P11 (512 bits): VPU, DIV/SQRT
P12 (512 bits): VPU
P13 (512 bits): VPU
P14 (512 bits): FP store data
P15 (512 bits): FP store data

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	0.00

Cycles summary

Front-end	4.25
Dispatch	3.00
Data deps.	0.00
Overall L1	4.25

Vectorization ratios

INT

all	16%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	0%
add-sub	0%
fma	NA (no fma vectorizable/vectorized instructions)
other	25%

all	76%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	80%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	85%

INT+FP

all	57%
load	NA (no load vectorizable/vectorized instructions)
store	0%
mul	0%
add-sub	66%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	63%

Vector efficiency ratios

INT

all	13%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	12%
add-sub	12%
fma	NA (no fma vectorizable/vectorized instructions)
other	14%

all	27%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	37%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	23%

INT+FP

all	23%
load	NA (no load vectorizable/vectorized instructions)
store	6%
mul	12%
add-sub	33%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	19%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 4.25 cycles. At this rate:

2% of peak load performance is reached (5.65 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
0% of peak store performance is reached (0.94 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

ASM code

In the binary file, the address of the loop is: 5370

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
CMP $0x10,%R15D	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	scal (6.3%)
JB 5388 <main+0x16e8>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV %R13D,%ESI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
ADD %ECX,%ESI	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
SETB %SIL	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
OR %R10B,%SIL	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
JE 53f0 <main+0x1750>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV %R14,%R12	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	scal (12.5%)
IMUL %RSI,%R12	1	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0	0	3	0.33	scal (12.5%)
ADD %R13,%R12	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	scal (12.5%)
NOPL (%RAX)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.13	N/A
MOV 0x150(%RSP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
VCVTSD2SS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
LEA (%R11,%R13,1),%ESI	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
INC %R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
VMOVSS %XMM0,(%RDX,%RSI,4)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0.50	0.50	1	0.50	scal (6.3%)
CMP %R15,%R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	0	0	1	0.17	scal (12.5%)
JNE 5370 <main+0x16d0>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.33-1	N/A
MOV 0x120(%RSP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
VXORPS %XMM0,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
VXORPS %XMM1,%XMM1,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
VXORPS %XMM2,%XMM2,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
VPXOR %XMM3,%XMM3,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	vect (25.0%)
XOR %ESI,%ESI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
NOPW (%RAX,%RAX,1)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.13	N/A
VADDPD %YMM0,%YMM1,%YMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (50.0%)
VADDPD %YMM2,%YMM3,%YMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (50.0%)
CMPQ $0,0x80(%RSP)	1	0.17	0.17	0.17	0.17	0.17	0.17	0.25	0.25	0.25	0.25	0	0	0	0	0	0	1	0.25	N/A
MOV %RAX,%RSI	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
VADDPD %YMM0,%YMM1,%YMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (50.0%)
VEXTRACTF128 $0x1,%YMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	0	3	0.50	vect (25.0%)
VADDPD %XMM1,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (25.0%)
VSHUFPD $0x1,%XMM0,%XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	1	0.25	vect (25.0%)
VADDSD %XMM1,%XMM0,%XMM0	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	scal (12.5%)
JNE 5392 <main+0x16f2>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	0	0.33-1	N/A

Report Configuration

Vectorization

Details

Workaround

512-bits vectorization

Workaround

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

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

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

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

512-bits vectorization

Workaround

Slow data structures access

Details

Workaround

Vector unaligned load/store instructions