OV - attention-gcc-gnr-256 - Loop 16

0x4021c0 LEA	(%RAX,%RCX,1),%EDX

0x4021c3 VCVTSS2SD	(%R14,%RDX,4),%XMM1,%XMM0    [2]

0x4021c9 MOV	%ESI,%EDX

0x4021cb VCVTSS2SD	(%R13,%RDX,4),%XMM1,%XMM2    [1]

0x4021d2 VMULSD	%XMM2,%XMM0,%XMM0

0x4021d6 INC	%EAX

0x4021d8 ADD	%R8D,%ESI

0x4021db VADDSD	%XMM0,%XMM3,%XMM3

0x4021df CMP	%R9D,%EAX

0x4021e2 JB	4021c0

/home/eoseret/llm-attention/attention_v2.cpp: 30 - 31

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

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

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

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	1.00
CQA speedup if FP arith vectorized	2.58
CQA speedup if fully vectorized	13.33
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.64
Bottlenecks
Function	main
Source	attention_v2.cpp:30-31
Source loop unroll info	multi-versionned
Source loop unroll confidence level	max
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	3.00
CQA cycles if no scalar integer	3.00
CQA cycles if FP arith vectorized	1.16
CQA cycles if fully vectorized	0.23
Front-end cycles	1.83
P0 cycles	1.70
P1 cycles	1.50
P2 cycles	0.67
P3 cycles	0.67
P4 cycles	0.00
P5 cycles	1.60
P6 cycles	1.60
P7 cycles	0.00
P8 cycles	0.00
P9 cycles	0.00
P10 cycles	1.60
P11 cycles	0.67
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	3
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	10.00
Nb uops	9.00
Nb loads	2.00
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	0.67
Nb FLOP add-sub	1.00
Nb FLOP mul	1.00
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	2.67
Bytes prefetched	0.00
Bytes loaded	8.00
Bytes stored	0.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	2.00
Stride indirect	0.00
Vectorization ratio all	0.00
Vectorization ratio load	0.00
Vectorization ratio store	NA
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	0.00
Vector-efficiency ratio all	8.75
Vector-efficiency ratio load	6.25
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	9.38
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	6.25

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	2.58
CQA speedup if fully vectorized	13.33
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.64
Bottlenecks
Function	main
Source	attention_v2.cpp:30-31
Source loop unroll info	multi-versionned
Source loop unroll confidence level	max
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	3.00
CQA cycles if no scalar integer	3.00
CQA cycles if FP arith vectorized	1.16
CQA cycles if fully vectorized	0.23
Front-end cycles	1.83
P0 cycles	1.70
P1 cycles	1.50
P2 cycles	0.67
P3 cycles	0.67
P4 cycles	0.00
P5 cycles	1.60
P6 cycles	1.60
P7 cycles	0.00
P8 cycles	0.00
P9 cycles	0.00
P10 cycles	1.60
P11 cycles	0.67
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	3
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	10.00
Nb uops	9.00
Nb loads	2.00
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	0.67
Nb FLOP add-sub	1.00
Nb FLOP mul	1.00
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	2.67
Bytes prefetched	0.00
Bytes loaded	8.00
Bytes stored	0.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	2.00
Stride indirect	0.00
Vectorization ratio all	0.00
Vectorization ratio load	0.00
Vectorization ratio store	NA
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	0.00
Vector-efficiency ratio all	8.75
Vector-efficiency ratio load	6.25
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	9.38
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	6.25

Path /

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

Function	main
Source file and lines	attention_v2.cpp:30-31
Module	attention-gcc-gnr-256

The loop is defined in /home/eoseret/llm-attention/attention_v2.cpp:30-31.

The related source loop is multi-versionned.

gain
potential
hint
expert

Vectorization

Your loop is not vectorized. Only 8% 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 3.00 to 0.22 cycles (13.33x speedup).

Details

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

Workaround

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

Execution units bottlenecks

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

FMA

Presence of both ADD/SUB and MUL operations.

Workaround

Recompile with march=sapphirerapids. CQA target is Granite_Rapids_ad (Intel(R) Xeon(R) Granite Rapids) but specialization flags are -march=graniterapids
Try to change order in which elements are evaluated (using parentheses) in arithmetic expressions containing both ADD/SUB and MUL operations to enable your compiler to generate FMA instructions wherever possible. For instance a + b*c is a valid FMA (MUL then ADD). However (a+b)* c cannot be translated into an FMA (ADD then MUL).

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

VCVTSS2SD (FP32 to FP64, scalar): 2 occurrences►
- /home/eoseret/llm-attention/attention_v2.cpp:31
- /home/eoseret/llm-attention/attention_v2.cpp:31

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

2 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
1: multiply

The binary loop is loading 8 bytes (1 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.25 FP operations per loaded or stored byte.

General properties

nb instructions	10
nb uops	9
loop length	36
used x86 registers	8
used mmx registers	0
used xmm registers	4
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.83 cycles
front end	1.83 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	1.70	1.50	0.67	0.67	0.00	1.60	1.60	0.00	0.00	0.00	1.60	0.67
cycles	1.70	1.50	0.67	0.67	0.00	1.60	1.60	0.00	0.00	0.00	1.60	0.67

Execution ports to units layout:

P0 (256 bits): VPU, BRU, ALU, DIV/SQRT
P1 (256 bits): ALU, VPU
P2 (512 bits): load
P3 (512 bits): load
P4 (512 bits): store data
P5 (512 bits): ALU, VPU
P6: ALU, BRU
P7: store address
P8: store address
P9 (512 bits): store data
P10: ALU
P11 (512 bits): load

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	3.00

Cycles summary

Front-end	1.83
Dispatch	1.70
Data deps.	3.00
Overall L1	3.00

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	0%
fma	NA (no fma vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

FP

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

INT+FP

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

Vector efficiency ratios

INT

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

FP

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

INT+FP

all	8%
load	6%
store	NA (no store vectorizable/vectorized instructions)
mul	12%
add-sub	9%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	6%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 3.00 cycles. At this rate:

1% of peak load performance is reached (2.67 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))

Front-end bottlenecks

Found no such bottlenecks.

ASM code

In the binary file, the address of the loop is: 4021c0

Instruction	Nb FU	P0	P1	P2	P3	P5	P6	P10	P11	Latency	Recip. throughput	Vectorization
LEA (%RAX,%RCX,1),%EDX	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1-2	0.20	N/A
VCVTSS2SD (%R14,%RDX,4),%XMM1,%XMM0	1	0.50	0.50	0.33	0.33	0	0	0	0.33	4-5	0.50	scal (6.3%)
MOV %ESI,%EDX	1	0	0	0	0	0	0	0	0	1	0.17	N/A
VCVTSS2SD (%R13,%RDX,4),%XMM1,%XMM2	1	0.50	0.50	0.33	0.33	0	0	0	0.33	4-5	0.50	scal (6.3%)
VMULSD %XMM2,%XMM0,%XMM0	1	0.50	0.50	0	0	0	0	0	0	4	0.50	scal (12.5%)
INC %EAX	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1	0.20	N/A
ADD %R8D,%ESI	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1	0.20	scal (6.3%)
VADDSD %XMM0,%XMM3,%XMM3	1	0	0.50	0	0	0.50	0	0	0	3	0.50	scal (12.5%)
CMP %R9D,%EAX	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1	0.20	N/A
JB 4021c0 <main+0xec0>	1	0.50	0	0	0	0	0.50	0	0	0	0.50	N/A

Function	main
Source file and lines	attention_v2.cpp:30-31
Module	attention-gcc-gnr-256

The loop is defined in /home/eoseret/llm-attention/attention_v2.cpp:30-31.

The related source loop is multi-versionned.

gain
potential
hint
expert

Vectorization

Your loop is not vectorized. Only 8% 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 3.00 to 0.22 cycles (13.33x speedup).

Details

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

Workaround

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

Execution units bottlenecks

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

FMA

Presence of both ADD/SUB and MUL operations.

Workaround

Recompile with march=sapphirerapids. CQA target is Granite_Rapids_ad (Intel(R) Xeon(R) Granite Rapids) but specialization flags are -march=graniterapids
Try to change order in which elements are evaluated (using parentheses) in arithmetic expressions containing both ADD/SUB and MUL operations to enable your compiler to generate FMA instructions wherever possible. For instance a + b*c is a valid FMA (MUL then ADD). However (a+b)* c cannot be translated into an FMA (ADD then MUL).

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

VCVTSS2SD (FP32 to FP64, scalar): 2 occurrences►
- /home/eoseret/llm-attention/attention_v2.cpp:31
- /home/eoseret/llm-attention/attention_v2.cpp:31

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

2 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
1: multiply

The binary loop is loading 8 bytes (1 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.25 FP operations per loaded or stored byte.

General properties

nb instructions	10
nb uops	9
loop length	36
used x86 registers	8
used mmx registers	0
used xmm registers	4
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.83 cycles
front end	1.83 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	1.70	1.50	0.67	0.67	0.00	1.60	1.60	0.00	0.00	0.00	1.60	0.67
cycles	1.70	1.50	0.67	0.67	0.00	1.60	1.60	0.00	0.00	0.00	1.60	0.67

Execution ports to units layout:

P0 (256 bits): VPU, BRU, ALU, DIV/SQRT
P1 (256 bits): ALU, VPU
P2 (512 bits): load
P3 (512 bits): load
P4 (512 bits): store data
P5 (512 bits): ALU, VPU
P6: ALU, BRU
P7: store address
P8: store address
P9 (512 bits): store data
P10: ALU
P11 (512 bits): load

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	3.00

Cycles summary

Front-end	1.83
Dispatch	1.70
Data deps.	3.00
Overall L1	3.00

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	0%
fma	NA (no fma vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

FP

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

INT+FP

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

Vector efficiency ratios

INT

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

FP

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

INT+FP

all	8%
load	6%
store	NA (no store vectorizable/vectorized instructions)
mul	12%
add-sub	9%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	6%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 3.00 cycles. At this rate:

1% of peak load performance is reached (2.67 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))

Front-end bottlenecks

Found no such bottlenecks.

ASM code

In the binary file, the address of the loop is: 4021c0

Instruction	Nb FU	P0	P1	P2	P3	P5	P6	P10	P11	Latency	Recip. throughput	Vectorization
LEA (%RAX,%RCX,1),%EDX	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1-2	0.20	N/A
VCVTSS2SD (%R14,%RDX,4),%XMM1,%XMM0	1	0.50	0.50	0.33	0.33	0	0	0	0.33	4-5	0.50	scal (6.3%)
MOV %ESI,%EDX	1	0	0	0	0	0	0	0	0	1	0.17	N/A
VCVTSS2SD (%R13,%RDX,4),%XMM1,%XMM2	1	0.50	0.50	0.33	0.33	0	0	0	0.33	4-5	0.50	scal (6.3%)
VMULSD %XMM2,%XMM0,%XMM0	1	0.50	0.50	0	0	0	0	0	0	4	0.50	scal (12.5%)
INC %EAX	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1	0.20	N/A
ADD %R8D,%ESI	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1	0.20	scal (6.3%)
VADDSD %XMM0,%XMM3,%XMM3	1	0	0.50	0	0	0.50	0	0	0	3	0.50	scal (12.5%)
CMP %R9D,%EAX	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1	0.20	N/A
JB 4021c0 <main+0xec0>	1	0.50	0	0	0	0	0.50	0	0	0	0.50	N/A

Report Configuration

Vectorization

Details

Workaround

Execution units bottlenecks

FMA

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

Front-end bottlenecks

ASM code

Vectorization

Details

Workaround

Execution units bottlenecks

FMA

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

Front-end bottlenecks

ASM code