OV - exec - Loop 307

	Loop Id: 307	Module: exec	Source: stl_numeric.h:140-141	Coverage: 0.02%

0x424440 LDR	Z2, [X14, MUL VL]    [1]

0x424444 LDR	Z3, [X14, #1, MUL VL]    [1]

0x424448 ADD	X14, X14, X12

0x42444c SUBS	X13, X13, X10

0x424450 FADD	Z0.D, Z2.D, Z0.D

0x424454 FADD	Z1.D, Z3.D, Z1.D

0x424458 B.NE	424440

/usr/lib/gcc/aarch64-amazon-linux/14/../../../../include/c++/14/bits/stl_numeric.h: 140 - 141

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

140:       for (; __first != __last; ++__first)

141: 	__init = _GLIBCXX_MOVE_IF_20(__init) + *__first;

Coverage (%)	Name	Source Location	Module
►98.39+	qmcplusplus::WaveFunction::rat[...]	WaveFunction.cpp:201	exec
○	main.omp_outlined.62	miniqmc.cpp:442	exec
○	__kmp_invoke_microtask		libomp.so
○	__kmp_invoke_task_func		libomp.so
○	__kmp_launch_thread		libomp.so
○	__kmp_launch_worker(void*)		libomp.so
○	start_thread		libc.so.6
○	thread_start		libc.so.6
►1.61+	qmcplusplus::WaveFunction::rat[...]	WaveFunction.cpp:201	exec
○	main.omp_outlined.62	miniqmc.cpp:442	exec
○	__kmp_invoke_microtask		libomp.so
○	__kmp_invoke_task_func		libomp.so
○	__kmp_fork_call		libomp.so
○	__kmpc_fork_call		libomp.so
○	main	miniqmc.cpp:409	exec
○	__libc_start_call_main		libc.so.6
○	__libc_start_main		libc.so.6
○	_start	new_allocator.h:172	exec

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	1.00
CQA speedup if fully vectorized	1.12
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	2.00
Bottlenecks
Function	miniqmcreference::TwoBodyJastrowRef >::ratioGrad(qmcplusplus::ParticleSet&, int, qmcplusplus::TinyVector&)
Source	stl_numeric.h:140-141
Source loop unroll info	unrolled by 8
Source loop unroll confidence level	max
Unroll/vectorization loop type	NA
Unroll factor	8
CQA cycles	2.00
CQA cycles if no scalar integer	2.00
CQA cycles if FP arith vectorized	2.00
CQA cycles if fully vectorized	1.79
Front-end cycles	0.88
P0 cycles	0.50
P1 cycles	0.50
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	1.00
P11 cycles	1.00
P12 cycles	0.00
P13 cycles	0.00
P14 cycles	0.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	2
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	7.00
Nb uops	7.00
Nb loads	NA
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	4.00
Nb FLOP add-sub	8.00
Nb FLOP mul	0.00
Nb FLOP fma	0.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	32.00
Bytes prefetched	0.00
Bytes loaded	64.00
Bytes stored	0.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	1.00
Stride indirect	0.00
Vectorization ratio all	80.00
Vectorization ratio load	100.00
Vectorization ratio store	NA
Vectorization ratio mul	NA
Vectorization ratio add_sub	66.67
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	85.00
Vector-efficiency ratio load	100.00
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	75.00
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	NA

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	1.00
CQA speedup if fully vectorized	1.12
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	2.00
Bottlenecks
Function	miniqmcreference::TwoBodyJastrowRef >::ratioGrad(qmcplusplus::ParticleSet&, int, qmcplusplus::TinyVector&)
Source	stl_numeric.h:140-141
Source loop unroll info	unrolled by 8
Source loop unroll confidence level	max
Unroll/vectorization loop type	NA
Unroll factor	8
CQA cycles	2.00
CQA cycles if no scalar integer	2.00
CQA cycles if FP arith vectorized	2.00
CQA cycles if fully vectorized	1.79
Front-end cycles	0.88
P0 cycles	0.50
P1 cycles	0.50
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	1.00
P11 cycles	1.00
P12 cycles	0.00
P13 cycles	0.00
P14 cycles	0.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	2
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	7.00
Nb uops	7.00
Nb loads	NA
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	4.00
Nb FLOP add-sub	8.00
Nb FLOP mul	0.00
Nb FLOP fma	0.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	32.00
Bytes prefetched	0.00
Bytes loaded	64.00
Bytes stored	0.00
Stride 0	0.00
Stride 1	0.00
Stride n	0.00
Stride unknown	1.00
Stride indirect	0.00
Vectorization ratio all	80.00
Vectorization ratio load	100.00
Vectorization ratio store	NA
Vectorization ratio mul	NA
Vectorization ratio add_sub	66.67
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	85.00
Vector-efficiency ratio load	100.00
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	75.00
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	miniqmcreference::TwoBodyJastrowRef >::ratioGrad(qmcplusplus::ParticleSet&, int, qmcplusplus::TinyVector&)
Source file and lines	stl_numeric.h:140-141
Module	exec

The loop is defined in /usr/lib/gcc/aarch64-amazon-linux/14/../../../../include/c++/14/bits/stl_numeric.h:140-141.

The related source loop is unrolled by 8 (including vectorization).

gain
potential
hint
expert

Vectorization

Your loop is partially vectorized. 85% 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 2.00 to 1.79 cycles (1.12x speedup).

Details

80% of VPU instructions are used in vector version (process two or more data elements in vector registers):

66% of VPU addition or subtraction instructions are used in vector version.

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

No data for this section

Slow data structures access

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

Details

Constant unknown stride: 1 occurrence(s)

Non-unit stride (uncontiguous) accesses are not efficiently using data caches

Workaround

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

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

The binary loop is composed of 8 FP arithmetical operations:

8: addition or subtraction

The binary loop is loading 64 bytes.

Arithmetic intensity

Arithmetic intensity is 0.12 FP operations per loaded or stored byte.

General properties

nb instructions	7
nb uops	7
loop length	28
used w registers	0
used x registers	4
used b registers	0
used h registers	0
used s registers	0
used d registers	0
used q registers	0
used v registers	0
used z registers	4
nb stack references	0

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	0.88 cycles
front end	0.88 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14
uops	0.50	0.50	0.50	0.50	0.50	0.50	1.00	1.00	0.00	0.00	1.00	1.00	0.00	0.00	0.00
cycles	0.50	0.50	0.50	0.50	0.50	0.50	1.00	1.00	1.00	1.00	1.00	1.00	0.00	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)	2.00

Cycles summary

Front-end	0.88
Dispatch	1.00
Data deps.	2.00
Overall L1	2.00

Vectorization ratios

INT

all	66%
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	NA (no other vectorizable/vectorized instructions)

all	100%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
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)

INT+FP

all	80%
load	100%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	66%
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

INT

all	75%
load	100%
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	NA (no other vectorizable/vectorized instructions)

all	100%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
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)

INT+FP

all	85%
load	100%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	75%
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:

33% of peak load performance is reached (32.00 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: 424440

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P10	P11	Latency	Recip. throughput	Vectorization
LDR Z2, [X14, MUL VL]	1	0	0	0	0	0	0	0	0	0.50	0.50	6	0.50	vect (100.0%)
LDR Z3, [X14, #1, MUL VL]	1	0	0	0	0	0	0	0	0	0.50	0.50	6	0.50	vect (100.0%)
ADD X14, X14, X12	1	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.25	N/A
SUBS X13, X13, X10	1	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.33	scal (25.0%)
FADD Z0.D, Z2.D, Z0.D	1	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (100.0%)
FADD Z1.D, Z3.D, Z1.D	1	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (100.0%)
B.NE 424440 <_ZN16miniqmcreference17TwoBodyJastrowRefIN11qmcplusplus14BsplineFunctorIdEEE9ratioGradERNS1_11ParticleSetEiRNS1_10TinyVectorIdLj3EEE+0x180>	1	0.50	0.50	0	0	0	0	0	0	0	0	1	0.50	N/A

Function	miniqmcreference::TwoBodyJastrowRef >::ratioGrad(qmcplusplus::ParticleSet&, int, qmcplusplus::TinyVector&)
Source file and lines	stl_numeric.h:140-141
Module	exec

The loop is defined in /usr/lib/gcc/aarch64-amazon-linux/14/../../../../include/c++/14/bits/stl_numeric.h:140-141.

The related source loop is unrolled by 8 (including vectorization).

gain
potential
hint
expert

Vectorization

Details

80% of VPU instructions are used in vector version (process two or more data elements in vector registers):

66% of VPU addition or subtraction instructions are used in vector version.

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

No data for this section

Slow data structures access

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

Details

Constant unknown stride: 1 occurrence(s)

Non-unit stride (uncontiguous) accesses are not efficiently using data caches

Workaround

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

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

The binary loop is composed of 8 FP arithmetical operations:

8: addition or subtraction

The binary loop is loading 64 bytes.

Arithmetic intensity

Arithmetic intensity is 0.12 FP operations per loaded or stored byte.

General properties

nb instructions	7
nb uops	7
loop length	28
used w registers	0
used x registers	4
used b registers	0
used h registers	0
used s registers	0
used d registers	0
used q registers	0
used v registers	0
used z registers	4
nb stack references	0

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	0.88 cycles
front end	0.88 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14
uops	0.50	0.50	0.50	0.50	0.50	0.50	1.00	1.00	0.00	0.00	1.00	1.00	0.00	0.00	0.00
cycles	0.50	0.50	0.50	0.50	0.50	0.50	1.00	1.00	1.00	1.00	1.00	1.00	0.00	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)	2.00

Cycles summary

Front-end	0.88
Dispatch	1.00
Data deps.	2.00
Overall L1	2.00

Vectorization ratios

INT

all	66%
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	NA (no other vectorizable/vectorized instructions)

all	100%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
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)

INT+FP

all	80%
load	100%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	66%
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

INT

all	75%
load	100%
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	NA (no other vectorizable/vectorized instructions)

all	100%
load	NA (no load vectorizable/vectorized instructions)
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
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)

INT+FP

all	85%
load	100%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	75%
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:

33% of peak load performance is reached (32.00 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: 424440

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P10	P11	Latency	Recip. throughput	Vectorization
LDR Z2, [X14, MUL VL]	1	0	0	0	0	0	0	0	0	0.50	0.50	6	0.50	vect (100.0%)
LDR Z3, [X14, #1, MUL VL]	1	0	0	0	0	0	0	0	0	0.50	0.50	6	0.50	vect (100.0%)
ADD X14, X14, X12	1	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.25	N/A
SUBS X13, X13, X10	1	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.33	scal (25.0%)
FADD Z0.D, Z2.D, Z0.D	1	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (100.0%)
FADD Z1.D, Z3.D, Z1.D	1	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (100.0%)
B.NE 424440 <_ZN16miniqmcreference17TwoBodyJastrowRefIN11qmcplusplus14BsplineFunctorIdEEE9ratioGradERNS1_11ParticleSetEiRNS1_10TinyVectorIdLj3EEE+0x180>	1	0.50	0.50	0	0	0	0	0	0	0	0	1	0.50	N/A

Report Configuration

Vectorization

Details

Slow data structures access

Details

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

Slow data structures access

Details

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