OV - K-Means scalability acfl-O3 100000000 - Loop 7

0x1ccc ADD	X13, X13, #1

0x1cd0 ADD	X15, X15, #16

0x1cd4 CMP	X13, W9,SXTW

0x1cd8 B.GE	1c98

0x1cdc LDP	D4, D3, [X15, #1016]    [3]

0x1ce0 FSUB	D3, D1, S3

0x1ce4 FSUB	D4, D0, S4

0x1ce8 FMUL	D3, D3, D3

0x1cec FMADD	D3, D4, D4, D3

0x1cf0 FCMP	D3, D2

0x1cf4 B.PL	1ccc

0x1cf8 FMOV	D2, D3

0x1cfc STR	W13, [X14, X8,LSL #2]    [2]

0x1d00 LDR	W9, [X20]    [1]

0x1d04 B	1ccc

/home/fmusial/KMEANS_Benchmarks/kmeans/main.cpp: 116 - 122

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

116:             for (int j = 0; j < k; ++j) {

117:                 double dist =

118:                     (points[i].x - centroids[j].x) * (points[i].x - centroids[j].x) +

119:                     (points[i].y - centroids[j].y) * (points[i].y - centroids[j].y);

120:                 if (dist < optimal_dist) {

121:                     optimal_dist = dist;

122:                     assignment[i] = j;

Coverage (%)	Name	Module
○96.04	__kmp_invoke_microtask	libomp.so
►3.96+	__kmp_invoke_microtask	libomp.so
○	Unknown function	ld-linux-aarch64.so.1

Coverage (%)	Name	Source Location	Module
○100.00	__kmp_invoke_microtask		libomp.so

Coverage (%)	Name	Source Location	Module
○100.00	__kmp_invoke_microtask		libomp.so

Coverage (%)	Name	Source Location	Module
○100.00	__kmp_invoke_microtask		libomp.so

Coverage (%)	Name	Source Location	Module
○100.00	__kmp_invoke_microtask		libomp.so

Coverage (%)	Name	Source Location	Module
○100.00	__kmp_invoke_microtask		libomp.so

Coverage (%)	Name	Source Location	Module
○100.00	__kmp_invoke_microtask		libomp.so

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	1.86
CQA speedup if fully vectorized	4.16
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	2.46
Bottlenecks
Function	k_means(int, point_t, point_t, int*, int, int) [clone .omp_outlined]
Source	main.cpp:116-122
Source loop unroll info	not unrolled or unrolled with no peel/tail loop
Source loop unroll confidence level	max
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	4.00
CQA cycles if no scalar integer	4.00
CQA cycles if FP arith vectorized	2.15
CQA cycles if fully vectorized	0.96
Front-end cycles	1.63
P0 cycles	1.25
P1 cycles	1.25
P2 cycles	0.75
P3 cycles	0.75
P4 cycles	0.75
P5 cycles	0.75
P6 cycles	1.38
P7 cycles	1.38
P8 cycles	1.38
P9 cycles	1.38
P10 cycles	0.75
P11 cycles	0.58
P12 cycles	0.67
P13 cycles	0.25
P14 cycles	0.25
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	4
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	13.00
Nb uops	13.00
Nb loads	NA
Nb stores	0.50
Nb stack references	0.00
FLOP/cycle	1.25
Nb FLOP add-sub	2.00
Nb FLOP mul	1.00
Nb FLOP fma	1.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	5.00
Bytes prefetched	0.00
Bytes loaded	18.00
Bytes stored	2.00
Stride 0	1.00
Stride 1	1.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	10.80
Vectorization ratio load	75.00
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	0.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	0.00
Vector-efficiency ratio all	26.56
Vector-efficiency ratio load	40.63
Vector-efficiency ratio store	12.50
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	25.00
Vector-efficiency ratio fma	25.00
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	25.00

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	1.82
CQA speedup if fully vectorized	4.80
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	2.13
Bottlenecks
Function	k_means(int, point_t, point_t, int*, int, int) [clone .omp_outlined]
Source	main.cpp:116-122
Source loop unroll info	not unrolled or unrolled with no peel/tail loop
Source loop unroll confidence level	max
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	4.00
CQA cycles if no scalar integer	4.00
CQA cycles if FP arith vectorized	2.20
CQA cycles if fully vectorized	0.83
Front-end cycles	1.88
P0 cycles	1.50
P1 cycles	1.50
P2 cycles	0.75
P3 cycles	0.75
P4 cycles	0.75
P5 cycles	0.75
P6 cycles	1.50
P7 cycles	1.50
P8 cycles	1.50
P9 cycles	1.50
P10 cycles	1.17
P11 cycles	0.83
P12 cycles	1.00
P13 cycles	0.50
P14 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	4
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	15.00
Nb uops	15.00
Nb loads	NA
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	1.25
Nb FLOP add-sub	2.00
Nb FLOP mul	1.00
Nb FLOP fma	1.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	6.00
Bytes prefetched	0.00
Bytes loaded	20.00
Bytes stored	4.00
Stride 0	2.00
Stride 1	1.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	9.09
Vectorization ratio load	50.00
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	0.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	0.00
Vector-efficiency ratio all	25.00
Vector-efficiency ratio load	31.25
Vector-efficiency ratio store	12.50
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	25.00
Vector-efficiency ratio fma	25.00
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	25.00

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	1.91
CQA speedup if fully vectorized	3.67
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	2.91
Bottlenecks
Function	k_means(int, point_t, point_t, int*, int, int) [clone .omp_outlined]
Source	main.cpp:116-122
Source loop unroll info	not unrolled or unrolled with no peel/tail loop
Source loop unroll confidence level	max
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	4.00
CQA cycles if no scalar integer	4.00
CQA cycles if FP arith vectorized	2.09
CQA cycles if fully vectorized	1.09
Front-end cycles	1.38
P0 cycles	1.00
P1 cycles	1.00
P2 cycles	0.75
P3 cycles	0.75
P4 cycles	0.75
P5 cycles	0.75
P6 cycles	1.25
P7 cycles	1.25
P8 cycles	1.25
P9 cycles	1.25
P10 cycles	0.33
P11 cycles	0.33
P12 cycles	0.33
P13 cycles	0.00
P14 cycles	0.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	4
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	11.00
Nb uops	11.00
Nb loads	NA
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	1.25
Nb FLOP add-sub	2.00
Nb FLOP mul	1.00
Nb FLOP fma	1.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	4.00
Bytes prefetched	0.00
Bytes loaded	16.00
Bytes stored	0.00
Stride 0	0.00
Stride 1	1.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	12.50
Vectorization ratio load	100.00
Vectorization ratio store	NA
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	0.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	0.00
Vector-efficiency ratio all	28.13
Vector-efficiency ratio load	50.00
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	25.00
Vector-efficiency ratio fma	25.00
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	25.00

Path /

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

Function	k_means(int, point_t, point_t, int*, int, int) [clone .omp_outlined]
Source file and lines	main.cpp:116-122
Module	kmeans-acfl-O3

The loop is defined in /home/fmusial/KMEANS_Benchmarks/kmeans/main.cpp:116-122.

The related source loop is not unrolled or unrolled with no peel/tail loop.
The structure of this loop is probably <if then [else] end>.

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 not vectorized. Only 26% of vector register length is used (average across all VPU instructions). By fully vectorizing your loop, you can lower the cost of an iteration from 4.00 to 0.96 cycles (4.16x speedup).

Details

10% of VPU instructions are used in vector version (process two or more data elements in vector registers):

75% of VPU loads are used in vector version.
0% of VPU stores are used in vector version.
0% of VPU addition or subtraction instructions are used in vector version.
0% of VPU multiply instructions are used in vector version.
0% of VPU fused multiply-add instructions are used in vector version.
0% of VPU instructions that are not load, store, addition, subtraction nor multiply instructions are used in vector version.

Since your execution units are vector units, only a fully vectorized loop can use their full power.

Workaround

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

FMA

Detected 1 FMA (fused multiply-add) operations. Presence of both ADD/SUB and MUL operations.

Workaround

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).

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

The binary loop is composed of 5 FP arithmetical operations:

3: addition or subtraction (1 inside FMA instructions)
2: multiply (1 inside FMA instructions)

The binary loop is loading 18 bytes. The binary loop is storing 2 bytes.

Arithmetic intensity

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

General properties

nb instructions	13
nb uops	13
loop length	52
used w registers	1.50
used x registers	3.50
used b registers	0
used h registers	0
used s registers	2
used d registers	5
used q registers	0
used v registers	0
used z registers	0
nb stack references	0
ADD-SUB / MUL ratio	2.00

Front-end

MACRO FUSION NOT POSSIBLE

micro-operation queue	1.63 cycles
front end	1.63 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14
uops	1.25	1.25	0.75	0.75	0.75	0.75	1.38	1.38	1.38	1.38	0.75	0.58	0.67	0.25	0.25
cycles	1.25	1.25	0.75	0.75	0.75	0.75	1.38	1.38	1.38	1.38	0.75	0.58	0.67	0.25	0.25

Execution ports to units layout:

P0: BRU
P1: BRU
P2: ALU
P3: ALU
P4: ALU
P5: ALU
P6 (128 bits): VPU, FP store data, ALU, DIV/SQRT
P7 (128 bits): VPU, ALU, FP store data
P8 (128 bits): VPU, ALU, DIV/SQRT
P9 (128 bits): ALU, VPU
P10 (256 bits): store address, load
P11 (256 bits): store address, load
P12 (256 bits): load
P13 (64 bits): store data
P14 (64 bits): store data

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	4.00

Cycles summary

Front-end	1.63
Dispatch	1.38
Data deps.	4.00
Overall L1	4.00

Vectorization ratios

INT

all	26%
load	75%
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	0%
fma	NA (no fma vectorizable/vectorized instructions)
other	0%

FP

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

INT+FP

all	10%
load	75%
store	0%
mul	0%
add-sub	0%
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	0%

Vector efficiency ratios

INT

all	29%
load	40%
store	12%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	25%
fma	NA (no fma vectorizable/vectorized instructions)
other	25%

FP

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

INT+FP

all	26%
load	40%
store	12%
mul	25%
add-sub	25%
fma	25%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

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:

4% of peak load performance is reached (4.50 out of 96.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (0.50 out of 48.00 bytes stored per cycle (GB/s @ 1GHz))

Function	k_means(int, point_t, point_t, int*, int, int) [clone .omp_outlined]
Source file and lines	main.cpp:116-122
Module	kmeans-acfl-O3

The loop is defined in /home/fmusial/KMEANS_Benchmarks/kmeans/main.cpp:116-122.

The related source loop is not unrolled or unrolled with no peel/tail loop.
The structure of this loop is probably <if then [else] end>.

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 not vectorized. Only 25% of vector register length is used (average across all VPU instructions). By fully vectorizing your loop, you can lower the cost of an iteration from 4.00 to 0.83 cycles (4.80x speedup).

Details

9% of VPU instructions are used in vector version (process two or more data elements in vector registers):

50% of VPU loads are used in vector version.
0% of VPU stores are used in vector version.
0% of VPU addition or subtraction instructions are used in vector version.
0% of VPU multiply instructions are used in vector version.
0% of VPU fused multiply-add instructions are used in vector version.
0% of VPU instructions that are not load, store, addition, subtraction nor multiply instructions are used in vector version.

Since your execution units are vector units, only a fully vectorized loop can use their full power.

Workaround

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

FMA

Detected 1 FMA (fused multiply-add) operations. Presence of both ADD/SUB and MUL operations.

Workaround

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).

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

The binary loop is composed of 5 FP arithmetical operations:

3: addition or subtraction (1 inside FMA instructions)
2: multiply (1 inside FMA instructions)

The binary loop is loading 20 bytes. The binary loop is storing 4 bytes.

Arithmetic intensity

Arithmetic intensity is 0.21 FP operations per loaded or stored byte.

General properties

nb instructions	15
nb uops	15
loop length	60
used w registers	2
used x registers	5
used b registers	0
used h registers	0
used s registers	2
used d registers	5
used q registers	0
used v registers	0
used z registers	0
nb stack references	0
ADD-SUB / MUL ratio	2.00

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	1.88 cycles
front end	1.88 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14
uops	1.50	1.50	0.75	0.75	0.75	0.75	1.50	1.50	1.50	1.50	1.17	0.83	1.00	0.50	0.50
cycles	1.50	1.50	0.75	0.75	0.75	0.75	1.50	1.50	1.50	1.50	1.17	0.83	1.00	0.50	0.50

Execution ports to units layout:

P0: BRU
P1: BRU
P2: ALU
P3: ALU
P4: ALU
P5: ALU
P6 (128 bits): VPU, FP store data, ALU, DIV/SQRT
P7 (128 bits): VPU, ALU, FP store data
P8 (128 bits): VPU, ALU, DIV/SQRT
P9 (128 bits): ALU, VPU
P10 (256 bits): store address, load
P11 (256 bits): store address, load
P12 (256 bits): load
P13 (64 bits): store data
P14 (64 bits): store data

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	4.00

Cycles summary

Front-end	1.88
Dispatch	1.50
Data deps.	4.00
Overall L1	4.00

Vectorization ratios

INT

all	20%
load	50%
store	0%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	0%
fma	NA (no fma vectorizable/vectorized instructions)
other	0%

FP

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

INT+FP

all	9%
load	50%
store	0%
mul	0%
add-sub	0%
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	0%

Vector efficiency ratios

INT

all	25%
load	31%
store	12%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	25%
fma	NA (no fma vectorizable/vectorized instructions)
other	25%

FP

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

INT+FP

all	25%
load	31%
store	12%
mul	25%
add-sub	25%
fma	25%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

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:

5% of peak load performance is reached (5.00 out of 96.00 bytes loaded per cycle (GB/s @ 1GHz))
2% of peak store performance is reached (1.00 out of 48.00 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: 1cdc

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	Latency	Recip. throughput	Vectorization
ADD X13, X13, #1	1	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	0	0	0	1	0.25	scal (25.0%)
ADD X15, X15, #16	1	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	0	0	0	1	0.25	N/A
CMP X13, W9,SXTW	1	0	0	0	0	0.50	0.50	0	0	0	0	0	0	0	0	0	2	0.50	scal (25.0%)
B.GE 1c98 <_Z7k_meansiP7point_tS0_Piii.omp_outlined+0xac>	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0.50	N/A
LDP D4, D3, [X15, #1016]	1	0	0	0	0	0	0	0	0	0	0	0.33	0.33	0.33	0	0	6	0.33	vect (50.0%)
FSUB D3, D1, S3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	2	0.25	scal (25.0%)
FSUB D4, D0, S4	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	2	0.25	scal (25.0%)
FMUL D3, D3, D3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	3	0.25	scal (25.0%)
FMADD D3, D4, D4, D3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	4	0.25	scal (25.0%)
FCMP D3, D2	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	2	1	scal (25.0%)
B.PL 1ccc <_Z7k_meansiP7point_tS0_Piii.omp_outlined+0xe0>	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0.50	N/A
FMOV D2, D3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	2	0.25	scal (25.0%)
STR W13, [X14, X8,LSL #2]	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0.50	0.50	1	0.50	scal (12.5%)
LDR W9, [X20]	1	0	0	0	0	0	0	0	0	0	0	0.33	0.33	0.33	0	0	4	0.33	scal (12.5%)
B 1ccc <_Z7k_meansiP7point_tS0_Piii.omp_outlined+0xe0>	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0.50	N/A

Function	k_means(int, point_t, point_t, int*, int, int) [clone .omp_outlined]
Source file and lines	main.cpp:116-122
Module	kmeans-acfl-O3

The loop is defined in /home/fmusial/KMEANS_Benchmarks/kmeans/main.cpp:116-122.

The related source loop is not unrolled or unrolled with no peel/tail loop.
The structure of this loop is probably <if then [else] end>.

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 not vectorized. Only 28% of vector register length is used (average across all VPU instructions). By fully vectorizing your loop, you can lower the cost of an iteration from 4.00 to 1.09 cycles (3.67x speedup).

Details

12% of VPU instructions are used in vector version (process two or more data elements in vector registers):

0% of VPU addition or subtraction instructions are used in vector version.
0% of VPU multiply instructions are used in vector version.
0% of VPU fused multiply-add instructions are used in vector version.
0% of VPU instructions that are not load, store, addition, subtraction nor multiply instructions are used in vector version.

Since your execution units are vector units, only a fully vectorized loop can use their full power.

Workaround

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

FMA

Detected 1 FMA (fused multiply-add) operations. Presence of both ADD/SUB and MUL operations.

Workaround

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).

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

The binary loop is composed of 5 FP arithmetical operations:

3: addition or subtraction (1 inside FMA instructions)
2: multiply (1 inside FMA instructions)

The binary loop is loading 16 bytes.

Arithmetic intensity

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

General properties

nb instructions	11
nb uops	11
loop length	44
used w registers	1
used x registers	2
used b registers	0
used h registers	0
used s registers	2
used d registers	5
used q registers	0
used v registers	0
used z registers	0
nb stack references	0
ADD-SUB / MUL ratio	2.00

Front-end

MACRO FUSION NOT POSSIBLE 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
uops	1.00	1.00	0.75	0.75	0.75	0.75	1.25	1.25	1.25	1.25	0.33	0.33	0.33	0.00	0.00
cycles	1.00	1.00	0.75	0.75	0.75	0.75	1.25	1.25	1.25	1.25	0.33	0.33	0.33	0.00	0.00

Execution ports to units layout:

P0: BRU
P1: BRU
P2: ALU
P3: ALU
P4: ALU
P5: ALU
P6 (128 bits): VPU, FP store data, ALU, DIV/SQRT
P7 (128 bits): VPU, ALU, FP store data
P8 (128 bits): VPU, ALU, DIV/SQRT
P9 (128 bits): ALU, VPU
P10 (256 bits): store address, load
P11 (256 bits): store address, load
P12 (256 bits): load
P13 (64 bits): store data
P14 (64 bits): store data

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	4.00

Cycles summary

Front-end	1.38
Dispatch	1.25
Data deps.	4.00
Overall L1	4.00

Vectorization ratios

INT

all	33%
load	100%
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	0%

FP

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

INT+FP

all	12%
load	100%
store	NA (no store vectorizable/vectorized instructions)
mul	0%
add-sub	0%
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	0%

Vector efficiency ratios

INT

all	33%
load	50%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	25%
fma	NA (no fma vectorizable/vectorized instructions)
other	25%

FP

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

INT+FP

all	28%
load	50%
store	NA (no store vectorizable/vectorized instructions)
mul	25%
add-sub	25%
fma	25%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

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:

4% of peak load performance is reached (4.00 out of 96.00 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: 1cdc

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	Latency	Recip. throughput	Vectorization
ADD X13, X13, #1	1	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	0	1	0.25	scal (25.0%)
ADD X15, X15, #16	1	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	0	1	0.25	N/A
CMP X13, W9,SXTW	1	0	0	0	0	0.50	0.50	0	0	0	0	0	0	0	2	0.50	scal (25.0%)
B.GE 1c98 <_Z7k_meansiP7point_tS0_Piii.omp_outlined+0xac>	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	0	1	0.50	N/A
LDP D4, D3, [X15, #1016]	1	0	0	0	0	0	0	0	0	0	0	0.33	0.33	0.33	6	0.33	vect (50.0%)
FSUB D3, D1, S3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	2	0.25	scal (25.0%)
FSUB D4, D0, S4	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	2	0.25	scal (25.0%)
FMUL D3, D3, D3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	3	0.25	scal (25.0%)
FMADD D3, D4, D4, D3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	4	0.25	scal (25.0%)
FCMP D3, D2	1	0	0	0	0	0	0	1	0	0	0	0	0	0	2	1	scal (25.0%)
B.PL 1ccc <_Z7k_meansiP7point_tS0_Piii.omp_outlined+0xe0>	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	0	1	0.50	N/A

▶Scalability Runs Description

Run run_1_thread	Number processes: 1Number nodes: 1Run Command: <executable> kmeans/input/100000000.in 1000 100000000 50 25MPI Command: Dataset: Run Directory: /home/fmusial/KMEANS_BenchmarksOMP_PROC_BIND: closeOMP_NUM_THREADS: 1OMP_PLACES: cores
Run run_2_threads	Number processes: 1Number nodes: 1Run Command: <executable> kmeans/input/100000000.in 1000 100000000 50 25MPI Command: Dataset: Run Directory: /home/fmusial/KMEANS_BenchmarksOMP_PLACES: coresOMP_PROC_BIND: closeOMP_NUM_THREADS: 2
Run run_4_threads	Number processes: 1Number nodes: 1Run Command: <executable> kmeans/input/100000000.in 1000 100000000 50 25MPI Command: Dataset: Run Directory: /home/fmusial/KMEANS_BenchmarksOMP_PLACES: coresOMP_PROC_BIND: closeOMP_NUM_THREADS: 4
Run run_8_threads	Number processes: 1Number nodes: 1Run Command: <executable> kmeans/input/100000000.in 1000 100000000 50 25MPI Command: Dataset: Run Directory: /home/fmusial/KMEANS_BenchmarksOMP_PLACES: coresOMP_PROC_BIND: closeOMP_NUM_THREADS: 8
Run run_16_threads	Number processes: 1Number nodes: 1Run Command: <executable> kmeans/input/100000000.in 1000 100000000 50 25MPI Command: Dataset: Run Directory: /home/fmusial/KMEANS_BenchmarksOMP_PLACES: coresOMP_PROC_BIND: closeOMP_NUM_THREADS: 16
Run run_32_threads	Number processes: 1Number nodes: 1Run Command: <executable> kmeans/input/100000000.in 1000 100000000 50 25MPI Command: Dataset: Run Directory: /home/fmusial/KMEANS_BenchmarksOMP_PROC_BIND: closeOMP_PLACES: coresOMP_NUM_THREADS: 32
Run run_64_threads	Number processes: 1Number nodes: 1Run Command: <executable> kmeans/input/100000000.in 1000 100000000 50 25MPI Command: Dataset: Run Directory: /home/fmusial/KMEANS_BenchmarksOMP_PROC_BIND: closeOMP_PLACES: coresOMP_NUM_THREADS: 64

(run_1_thread) Efficiency	(run_1_thread) Potential Speed-Up (%)	(run_2_threads) Efficiency	(run_2_threads) Potential Speed-Up (%)	(run_4_threads) Efficiency	(run_4_threads) Potential Speed-Up (%)	(run_8_threads) Efficiency	(run_8_threads) Potential Speed-Up (%)	(run_16_threads) Efficiency	(run_16_threads) Potential Speed-Up (%)	(run_32_threads) Efficiency	(run_32_threads) Potential Speed-Up (%)	(run_64_threads) Efficiency	(run_64_threads) Potential Speed-Up (%)
1	0	1	0.07	0.99	0.64	0.99	0.88	0.99	0.54	0.99	0.51	1.99	0

Speed-Up and Efficiency

▶Detailed Speed-Up and Efficiency

Run	Number of threads	Efficiency (ideal is 1)	Speedup	Ideal Speedup	Time (s)	Coverage (%)
run_1_thread	1	1	1	1	128.41998291016	98.841644287109
run_2_threads	2	1	2	2	64.764999389648	97.943969726563
run_4_threads	4	0.99	3.97	4	33.184993743896	96.337028503418
run_8_threads	8	0.99	7.93	8	16.76000213623	95.197799682617
run_16_threads	16	0.99	15.91	16	8.414999961853	93.548393249512
run_32_threads	32	0.99	31.81	32	4.4749994277954	86.814308166504
run_64_threads	64	1.99	127.48	64	1.9800000190735	35.160987854004

Report Configuration

Vectorization

Details

Workaround

FMA

Workaround

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

Vectorization

Details

Workaround

FMA

Workaround

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

FMA

Workaround

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

▶Scalability Runs Description

▼Columns Filter

Speed-Up and Efficiency

▶Detailed Speed-Up and Efficiency