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

0x1cf4 ADD	X13, X13, #1

0x1cf8 CMP	X13, W9,SXTW

0x1cfc B.GE	1ccc

0x1d00 LDR	Q2, [X11, X13,LSL #4]    [2]

0x1d04 FSUB	V2.2D, V0.2D, V2.2D

0x1d08 FMUL	V2.2D, V2.2D, V2.2D

0x1d0c FADDP	D2, V2.2D

0x1d10 FCMP	D2, D1

0x1d14 B.GE	1cf4

0x1d18 FMOV	D1, D2

0x1d1c STR	W13, [X14, X8,LSL #2]    [3]

0x1d20 LDR	W9, [X20]    [1]

0x1d24 B	1cf4

/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
○96.03	__kmp_invoke_microtask	libomp.so
►3.97+	__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	1.47
CQA speedup if fully vectorized	3.22
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	2.72
CQA cycles if fully vectorized	1.24
Front-end cycles	1.38
P0 cycles	1.25
P1 cycles	1.25
P2 cycles	0.50
P3 cycles	0.50
P4 cycles	0.50
P5 cycles	0.50
P6 cycles	1.13
P7 cycles	1.13
P8 cycles	1.13
P9 cycles	1.13
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	11.00
Nb uops	11.00
Nb loads	NA
Nb stores	0.50
Nb stack references	0.00
FLOP/cycle	1.25
Nb FLOP add-sub	3.00
Nb FLOP mul	2.00
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	5.00
Bytes prefetched	0.00
Bytes loaded	18.00
Bytes stored	2.00
Stride 0	1.00
Stride 1	0.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	41.67
Vectorization ratio load	75.00
Vectorization ratio store	0.00
Vectorization ratio mul	100.00
Vectorization ratio add_sub	50.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	0.00
Vector-efficiency ratio all	37.50
Vector-efficiency ratio load	40.63
Vector-efficiency ratio store	12.50
Vector-efficiency ratio mul	50.00
Vector-efficiency ratio add_sub	50.00
Vector-efficiency ratio fma	NA
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	1.44
CQA speedup if fully vectorized	3.85
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	2.77
CQA cycles if fully vectorized	1.04
Front-end cycles	1.63
P0 cycles	1.50
P1 cycles	1.50
P2 cycles	0.50
P3 cycles	0.50
P4 cycles	0.50
P5 cycles	0.50
P6 cycles	1.25
P7 cycles	1.25
P8 cycles	1.25
P9 cycles	1.25
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	13.00
Nb uops	13.00
Nb loads	NA
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	1.25
Nb FLOP add-sub	3.00
Nb FLOP mul	2.00
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	6.00
Bytes prefetched	0.00
Bytes loaded	20.00
Bytes stored	4.00
Stride 0	2.00
Stride 1	0.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	33.33
Vectorization ratio load	50.00
Vectorization ratio store	0.00
Vectorization ratio mul	100.00
Vectorization ratio add_sub	50.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	0.00
Vector-efficiency ratio all	33.33
Vector-efficiency ratio load	31.25
Vector-efficiency ratio store	12.50
Vector-efficiency ratio mul	50.00
Vector-efficiency ratio add_sub	50.00
Vector-efficiency ratio fma	NA
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	1.50
CQA speedup if fully vectorized	2.77
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	3.56
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	2.67
CQA cycles if fully vectorized	1.44
Front-end cycles	1.13
P0 cycles	1.00
P1 cycles	1.00
P2 cycles	0.50
P3 cycles	0.50
P4 cycles	0.50
P5 cycles	0.50
P6 cycles	1.00
P7 cycles	1.00
P8 cycles	1.00
P9 cycles	1.00
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	9.00
Nb uops	9.00
Nb loads	NA
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	1.25
Nb FLOP add-sub	3.00
Nb FLOP mul	2.00
Nb FLOP fma	0.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	4.00
Bytes prefetched	0.00
Bytes loaded	16.00
Bytes stored	0.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	50.00
Vectorization ratio load	100.00
Vectorization ratio store	NA
Vectorization ratio mul	100.00
Vectorization ratio add_sub	50.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	0.00
Vector-efficiency ratio all	41.67
Vector-efficiency ratio load	50.00
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	50.00
Vector-efficiency ratio add_sub	50.00
Vector-efficiency ratio fma	NA
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-Ofast

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 poorly vectorized. Only 37% 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 1.24 cycles (3.22x speedup).

Details

41% 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.
50% of VPU addition or subtraction 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
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

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
2: multiply

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	11
nb uops	11
loop length	44
used w registers	1.50
used x registers	3.50
used b registers	0
used h registers	0
used s registers	0
used d registers	2
used q registers	1
used v registers	2
used z registers	0
nb stack references	0
ADD-SUB / MUL ratio	2.00

Front-end

MACRO FUSION NOT POSSIBLE

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	1.25	1.25	0.50	0.50	0.50	0.50	1.13	1.13	1.13	1.13	0.75	0.58	0.67	0.25	0.25
cycles	1.25	1.25	0.50	0.50	0.50	0.50	1.13	1.13	1.13	1.13	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	1.38
Dispatch	1.25
Data deps.	4.00
Overall L1	4.00

Vectorization ratios

INT

all	37%
load	75%
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)
other	0%

FP

all	45%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	100%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	0%

INT+FP

all	41%
load	75%
store	0%
mul	100%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	0%

Vector efficiency ratios

INT

all	31%
load	40%
store	12%
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	25%

FP

all	41%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	50%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

INT+FP

all	37%
load	40%
store	12%
mul	50%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
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-Ofast

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 poorly vectorized. Only 33% 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 1.04 cycles (3.85x speedup).

Details

33% 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.
50% of VPU addition or subtraction 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
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

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
2: multiply

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	13
nb uops	13
loop length	52
used w registers	2
used x registers	5
used b registers	0
used h registers	0
used s registers	0
used d registers	2
used q registers	1
used v registers	2
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	1.63 cycles
front end	1.63 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14
uops	1.50	1.50	0.50	0.50	0.50	0.50	1.25	1.25	1.25	1.25	1.17	0.83	1.00	0.50	0.50
cycles	1.50	1.50	0.50	0.50	0.50	0.50	1.25	1.25	1.25	1.25	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	1.63
Dispatch	1.50
Data deps.	4.00
Overall L1	4.00

Vectorization ratios

INT

all	25%
load	50%
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)
other	0%

FP

all	40%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	100%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	0%

INT+FP

all	33%
load	50%
store	0%
mul	100%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
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	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	25%

FP

all	40%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	50%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

INT+FP

all	33%
load	31%
store	12%
mul	50%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
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: 1d00

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	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 1ccc <_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
LDR Q2, [X11, X13,LSL #4]	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 V2.2D, V0.2D, V2.2D	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	2	0.25	vect (50.0%)
FMUL V2.2D, V2.2D, V2.2D	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	3	0.25	vect (50.0%)
FADDP D2, V2.2D	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	2	0.25	scal (50.0%)
FCMP D2, D1	1	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	2	1	scal (25.0%)
B.GE 1cf4 <_Z7k_meansiP7point_tS0_Piii.omp_outlined+0xd4>	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0.50	N/A
FMOV D1, D2	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 1cf4 <_Z7k_meansiP7point_tS0_Piii.omp_outlined+0xd4>	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-Ofast

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 partially vectorized. Only 41% 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 1.44 cycles (2.77x speedup).

Details

50% of VPU instructions are used in vector version (process two or more data elements in vector registers):

50% of VPU addition or subtraction 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
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

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
2: multiply

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	9
nb uops	9
loop length	36
used w registers	1
used x registers	2
used b registers	0
used h registers	0
used s registers	0
used d registers	2
used q registers	1
used v registers	2
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	1.13 cycles
front end	1.13 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14
uops	1.00	1.00	0.50	0.50	0.50	0.50	1.00	1.00	1.00	1.00	0.33	0.33	0.33	0.00	0.00
cycles	1.00	1.00	0.50	0.50	0.50	0.50	1.00	1.00	1.00	1.00	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	1.13
Dispatch	1.00
Data deps.	4.00
Overall L1	4.00

Vectorization ratios

INT

all	50%
load	100%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	0%

FP

all	50%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	100%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	0%

INT+FP

all	50%
load	100%
store	NA (no store vectorizable/vectorized instructions)
mul	100%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	0%

Vector efficiency ratios

INT

all	37%
load	50%
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	25%

FP

all	43%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	50%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	25%

INT+FP

all	41%
load	50%
store	NA (no store vectorizable/vectorized instructions)
mul	50%
add-sub	50%
fma	NA (no fma vectorizable/vectorized instructions)
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: 1d00

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	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 1ccc <_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
LDR Q2, [X11, X13,LSL #4]	1	0	0	0	0	0	0	0	0	0	0	0.33	0.33	0.33	6	0.33	vect (50.0%)
FSUB V2.2D, V0.2D, V2.2D	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	2	0.25	vect (50.0%)
FMUL V2.2D, V2.2D, V2.2D	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	3	0.25	vect (50.0%)
FADDP D2, V2.2D	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	2	0.25	scal (50.0%)
FCMP D2, D1	1	0	0	0	0	0	0	1	0	0	0	0	0	0	2	1	scal (25.0%)
B.GE 1cf4 <_Z7k_meansiP7point_tS0_Piii.omp_outlined+0xd4>	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	0.1	0.99	0.64	0.99	0.52	0.99	0.56	1.02	0	2.07	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	120.48497772217	99.058624267578
run_2_threads	2	1	2	2	60.899993896484	98.002616882324
run_4_threads	4	0.99	3.97	4	31.110000610352	96.140312194824
run_8_threads	8	0.99	7.96	8	15.704999923706	94.916259765625
run_16_threads	16	0.99	15.9	16	8.0149984359741	93.468566894531
run_32_threads	32	1.02	32.77	32	3.9549996852875	87.127830505371
run_64_threads	64	2.07	132.4	64	1.3450000286102	33.76717376709

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