OV - attention-avx512 - Loop 39

0x6130 VMOVUPS	(%RDI,%R13,4),%ZMM0    [2]

0x6137 VSUBPS	0x200(%RSP),%ZMM0,%ZMM0    [1]

0x613f CALL	69b0 <@plt_start@+0x20>

0x6144 VMULPS	0x280(%RSP),%ZMM0,%ZMM0    [1]

0x614c MOV	0x140(%RSP),%RCX    [1]

0x6154 MOV	0x20(%RSP),%RDI    [1]

0x6159 VMOVUPS	%ZMM0,(%RCX,%R13,4)    [3]

0x6160 ADD	$0x10,%R13

0x6164 CMP	%R13,0x1c0(%RSP)    [1]

0x616c JNE	6130

/home/eoseret/llm-attention/attention.cpp: 55 - 56

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

55:       for (int idx = 0; idx <= row; ++idx)  //vectorised

56:          P[row * N + idx] = expf(S_row[idx] - max_val) / 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	1.00
CQA speedup if fully vectorized	1.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.45
Bottlenecks	P6, P7, P8, P9,
Function	main
Source	attention.cpp:55-56
Source loop unroll info	unrolled by 16
Source loop unroll confidence level	max
Unroll/vectorization loop type	main
Unroll factor	16
CQA cycles	2.00
CQA cycles if no scalar integer	1.25
CQA cycles if FP arith vectorized	2.00
CQA cycles if fully vectorized	2.00
Front-end cycles	1.38
P0 cycles	0.33
P1 cycles	0.33
P2 cycles	0.33
P3 cycles	0.67
P4 cycles	0.67
P5 cycles	0.67
P6 cycles	2.00
P7 cycles	2.00
P8 cycles	2.00
P9 cycles	2.00
P10 cycles	0.50
P11 cycles	0.50
P12 cycles	0.50
P13 cycles	0.50
P14 cycles	1.00
P15 cycles	1.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	10.00
Nb uops	11.00
Nb loads	6.00
Nb stores	1.00
Nb stack references	5.00
FLOP/cycle	16.00
Nb FLOP add-sub	16.00
Nb FLOP mul	16.00
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	140.00
Bytes prefetched	0.00
Bytes loaded	216.00
Bytes stored	64.00
Stride 0	1.00
Stride 1	2.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	100.00
Vectorization ratio load	100.00
Vectorization ratio store	100.00
Vectorization ratio mul	100.00
Vectorization ratio add_sub	100.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	100.00
Vector-efficiency ratio load	100.00
Vector-efficiency ratio store	100.00
Vector-efficiency ratio mul	100.00
Vector-efficiency ratio add_sub	100.00
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	NA

Metric	Value
CQA speedup if no scalar integer	1.60
CQA speedup if FP arith vectorized	1.00
CQA speedup if fully vectorized	1.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.45
Bottlenecks	P6, P7, P8, P9,
Function	main
Source	attention.cpp:55-56
Source loop unroll info	unrolled by 16
Source loop unroll confidence level	max
Unroll/vectorization loop type	main
Unroll factor	16
CQA cycles	2.00
CQA cycles if no scalar integer	1.25
CQA cycles if FP arith vectorized	2.00
CQA cycles if fully vectorized	2.00
Front-end cycles	1.38
P0 cycles	0.33
P1 cycles	0.33
P2 cycles	0.33
P3 cycles	0.67
P4 cycles	0.67
P5 cycles	0.67
P6 cycles	2.00
P7 cycles	2.00
P8 cycles	2.00
P9 cycles	2.00
P10 cycles	0.50
P11 cycles	0.50
P12 cycles	0.50
P13 cycles	0.50
P14 cycles	1.00
P15 cycles	1.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	10.00
Nb uops	11.00
Nb loads	6.00
Nb stores	1.00
Nb stack references	5.00
FLOP/cycle	16.00
Nb FLOP add-sub	16.00
Nb FLOP mul	16.00
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	140.00
Bytes prefetched	0.00
Bytes loaded	216.00
Bytes stored	64.00
Stride 0	1.00
Stride 1	2.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	100.00
Vectorization ratio load	100.00
Vectorization ratio store	100.00
Vectorization ratio mul	100.00
Vectorization ratio add_sub	100.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	100.00
Vector-efficiency ratio load	100.00
Vector-efficiency ratio store	100.00
Vector-efficiency ratio mul	100.00
Vector-efficiency ratio add_sub	100.00
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	NA

Path /

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

Function	main
Source file and lines	attention.cpp:55-56
Module	attention-avx512

The loop is defined in /home/eoseret/llm-attention/attention.cpp:55-56.

It is main loop of related source loop which is unrolled by 16 (including vectorization).

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 2.00 to 1.25 cycles (1.60x speedup).

Workaround

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

Vectorization

Your loop is fully vectorized, using full register length.

Details

All SSE/AVX instructions are used in vector version (process two or more data elements in vector registers).

Execution units bottlenecks

Performance is limited by:

reading data from caches/RAM (load units are a bottleneck)
writing data to caches/RAM (the store unit is a bottleneck)

By removing all these bottlenecks, you can lower the cost of an iteration from 2.00 to 1.38 cycles (1.45x speedup).

Workaround

Read less array elements
Write less array elements
Provide more information to your compiler:
- hardcode the bounds of the corresponding 'for' loop

FMA

Presence of both ADD/SUB and MUL operations.

Workaround

Pass to your compiler a micro-architecture specialization option:
- use march=native
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).

CALL instructions

Detected function call instructions.

Details

Calling (and then returning from) a function prevents many compiler optimizations (like vectorization), breaks control flow (which reduces pipeline performance) and executes extra instructions to save/restore the registers used inside it, which is very expensive (dozens of cycles). Consider to inline small functions.

unknown: 1 occurrences►
- /home/eoseret/llm-attention/attention.cpp:56

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.

VMOVUPS: 1 occurrences►
- /home/eoseret/llm-attention/attention.cpp:56

Vector unaligned load/store instructions

Detected 2 optimal vector unaligned load/store instructions.

Details

VMOVUPS: 2 occurrences►
- /home/eoseret/llm-attention/attention.cpp:56
- /home/eoseret/llm-attention/attention.cpp:56

Workaround

Use vector aligned instructions:

align your arrays on 64 bytes boundaries: replace { void *p = malloc (size); } with { void *p; posix_memalign (&p, 64, size); }.
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.

Type of elements and instruction set

2 AVX-512 instructions are processing arithmetic or math operations on single precision FP elements in vector mode (sixteen at a time).

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

The binary loop is composed of 32 FP arithmetical operations:

16: addition or subtraction
16: multiply

The binary loop is loading 216 bytes (54 single precision FP elements). The binary loop is storing 64 bytes (16 single precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.11 FP operations per loaded or stored byte.

General properties

nb instructions	10
nb uops	11
loop length	62
used x86 registers	4
used mmx registers	0
used xmm registers	0
used ymm registers	0
used zmm registers	1
nb stack references	5
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.38 cycles
front end	1.38 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	0.33	0.33	0.33	0.67	0.67	0.67	2.00	2.00	2.00	2.00	0.50	0.50	0.50	0.50	1.00	1.00
cycles	0.33	0.33	0.33	0.67	0.67	0.67	2.00	2.00	2.00	2.00	0.50	0.50	0.50	0.50	1.00	1.00

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)	1.00

Cycles summary

Front-end	1.38
Dispatch	2.00
Data deps.	1.00
Overall L1	2.00

Vectorization ratios

all	100%
load	100%
store	100%
mul	100%
add-sub	100%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

Vector efficiency ratios

all	100%
load	100%
store	100%
mul	100%
add-sub	100%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 2.00 cycles. At this rate:

42% of peak load performance is reached (108.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
25% of peak store performance is reached (32.00 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

Found no such bottlenecks.

ASM code

In the binary file, the address of the loop is: 6130

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
VMOVUPS (%RDI,%R13,4),%ZMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.50	vect (100.0%)
VSUBPS 0x200(%RSP),%ZMM0,%ZMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	0	0	2	0.50	vect (100.0%)
CALL 69b0 <@plt_start@+0x20>	2	0	0	0	0.33	0.33	0.33	0.25	0.25	0.25	0.25	0	0	0	0	0	0	0	0.50	N/A
VMULPS 0x280(%RSP),%ZMM0,%ZMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	0	0	3	0.50	vect (100.0%)
MOV 0x140(%RSP),%RCX	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
MOV 0x20(%RSP),%RDI	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
VMOVUPS %ZMM0,(%RCX,%R13,4)	2	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	1	4	1	vect (100.0%)
ADD $0x10,%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
CMP %R13,0x1c0(%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
JNE 6130 <main+0x2850>	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

Function	main
Source file and lines	attention.cpp:55-56
Module	attention-avx512

The loop is defined in /home/eoseret/llm-attention/attention.cpp:55-56.

It is main loop of related source loop which is unrolled by 16 (including vectorization).

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 2.00 to 1.25 cycles (1.60x speedup).

Workaround

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

Vectorization

Your loop is fully vectorized, using full register length.

Details

All SSE/AVX instructions are used in vector version (process two or more data elements in vector registers).

Execution units bottlenecks

Performance is limited by:

reading data from caches/RAM (load units are a bottleneck)
writing data to caches/RAM (the store unit is a bottleneck)

By removing all these bottlenecks, you can lower the cost of an iteration from 2.00 to 1.38 cycles (1.45x speedup).

Workaround

Read less array elements
Write less array elements
Provide more information to your compiler:
- hardcode the bounds of the corresponding 'for' loop

FMA

Presence of both ADD/SUB and MUL operations.

Workaround

Pass to your compiler a micro-architecture specialization option:
- use march=native
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).

CALL instructions

Detected function call instructions.

Details

Calling (and then returning from) a function prevents many compiler optimizations (like vectorization), breaks control flow (which reduces pipeline performance) and executes extra instructions to save/restore the registers used inside it, which is very expensive (dozens of cycles). Consider to inline small functions.

unknown: 1 occurrences►
- /home/eoseret/llm-attention/attention.cpp:56

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.

VMOVUPS: 1 occurrences►
- /home/eoseret/llm-attention/attention.cpp:56

Vector unaligned load/store instructions

Detected 2 optimal vector unaligned load/store instructions.

Details

VMOVUPS: 2 occurrences►
- /home/eoseret/llm-attention/attention.cpp:56
- /home/eoseret/llm-attention/attention.cpp:56

Workaround

Use vector aligned instructions:

align your arrays on 64 bytes boundaries: replace { void *p = malloc (size); } with { void *p; posix_memalign (&p, 64, size); }.
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.

Type of elements and instruction set

2 AVX-512 instructions are processing arithmetic or math operations on single precision FP elements in vector mode (sixteen at a time).

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

The binary loop is composed of 32 FP arithmetical operations:

16: addition or subtraction
16: multiply

The binary loop is loading 216 bytes (54 single precision FP elements). The binary loop is storing 64 bytes (16 single precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.11 FP operations per loaded or stored byte.

General properties

nb instructions	10
nb uops	11
loop length	62
used x86 registers	4
used mmx registers	0
used xmm registers	0
used ymm registers	0
used zmm registers	1
nb stack references	5
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.38 cycles
front end	1.38 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	0.33	0.33	0.33	0.67	0.67	0.67	2.00	2.00	2.00	2.00	0.50	0.50	0.50	0.50	1.00	1.00
cycles	0.33	0.33	0.33	0.67	0.67	0.67	2.00	2.00	2.00	2.00	0.50	0.50	0.50	0.50	1.00	1.00

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)	1.00

Cycles summary

Front-end	1.38
Dispatch	2.00
Data deps.	1.00
Overall L1	2.00

Vectorization ratios

all	100%
load	100%
store	100%
mul	100%
add-sub	100%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

Vector efficiency ratios

all	100%
load	100%
store	100%
mul	100%
add-sub	100%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 2.00 cycles. At this rate:

42% of peak load performance is reached (108.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
25% of peak store performance is reached (32.00 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

Found no such bottlenecks.

ASM code

In the binary file, the address of the loop is: 6130

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
VMOVUPS (%RDI,%R13,4),%ZMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.50	vect (100.0%)
VSUBPS 0x200(%RSP),%ZMM0,%ZMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	0	0	2	0.50	vect (100.0%)
CALL 69b0 <@plt_start@+0x20>	2	0	0	0	0.33	0.33	0.33	0.25	0.25	0.25	0.25	0	0	0	0	0	0	0	0.50	N/A
VMULPS 0x280(%RSP),%ZMM0,%ZMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	0	0	3	0.50	vect (100.0%)
MOV 0x140(%RSP),%RCX	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
MOV 0x20(%RSP),%RDI	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
VMOVUPS %ZMM0,(%RCX,%R13,4)	2	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	1	4	1	vect (100.0%)
ADD $0x10,%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
CMP %R13,0x1c0(%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
JNE 6130 <main+0x2850>	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

Code clean check

Workaround

Vectorization

Details

Execution units bottlenecks

Workaround

FMA

Workaround

CALL instructions

Details

Complex instructions

Details

Vector unaligned load/store 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

Execution units bottlenecks

Workaround

FMA

Workaround

CALL instructions

Details

Complex instructions

Details

Vector unaligned load/store 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