OV - exec - Loop 972

0x44da80 MOVUPD	(%RDX,%RDI,8),%XMM2    [2]

0x44da85 MULPD	%XMM1,%XMM2

0x44da89 MOVUPD	(%RSI,%RDI,8),%XMM3    [1]

0x44da8e ADDPD	%XMM2,%XMM3

0x44da92 MOVUPD	%XMM3,(%RSI,%RDI,8)    [1]

0x44da97 ADD	$0x2,%RDI

0x44da9b CMP	%RCX,%RDI

0x44da9e JB	44da80

  ***  This Panel is Intentionally Left Blank.  ***

It is due to a lack of debug symbols in the given object
(loop or function).

Coverage (%)	Name	Module
►87.45+	__kmp_invoke_microtask	libiomp5.so
○	__kmp_invoke_task_func	libiomp5.so
○	__kmp_launch_thread	libiomp5.so
○	_INTERNALea951ae6::__kmp_launc[...]	libiomp5.so
○	start_thread	libc.so.6
○	__GI___clone3	libc.so.6
►7.79+	__kmp_invoke_microtask	libiomp5.so
○	__kmp_invoke_task_func	libiomp5.so
○	__kmp_launch_thread	libiomp5.so
○	_INTERNALea951ae6::__kmp_launc[...]	libiomp5.so
►2.80+	__kmp_invoke_microtask	libiomp5.so
○	__kmp_invoke_task_func	libiomp5.so
○	__kmp_fork_call	libiomp5.so
○	__kmpc_fork_call	libiomp5.so
○	Kripke::Kernel::LPlusTimes(Kri[...]	exec
○	Kripke::SteadyStateSolver(Krip[...]	exec
○	main	exec
○	__libc_start_call_main	libc.so.6
○	__libc_start_main	libc.so.6
○	_start	exec
►1.07+	__kmp_invoke_microtask	libiomp5.so
○	__kmp_invoke_task_func	libiomp5.so
○	__kmp_launch_thread	libiomp5.so
○	_INTERNALea951ae6::__kmp_launc[...]	libiomp5.so
○	start_thread	libc.so.6

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	1.33
CQA speedup if fully vectorized	4.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.14
Bottlenecks
Function	void LPlusTimesSdom::operator() >(Kripke::ArchLayoutT, Kripke::SdomId, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Field&, Kripke::Core::Field&, Kripke::Core::Field&) const [clone .extracted]
Source
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	1.00
CQA cycles if no scalar integer	1.00
CQA cycles if FP arith vectorized	0.75
CQA cycles if fully vectorized	0.25
Front-end cycles	0.88
P0 cycles	0.33
P1 cycles	0.33
P2 cycles	0.33
P3 cycles	0.33
P4 cycles	0.33
P5 cycles	0.33
P6 cycles	0.75
P7 cycles	0.75
P8 cycles	0.75
P9 cycles	0.75
P10 cycles	0.50
P11 cycles	0.50
P12 cycles	0.50
P13 cycles	0.50
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	8.00
Nb uops	7.00
Nb loads	2.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	4.00
Nb FLOP add-sub	2.00
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	48.00
Bytes prefetched	0.00
Bytes loaded	32.00
Bytes stored	16.00
Stride 0	0.00
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	25.00
Vector-efficiency ratio load	25.00
Vector-efficiency ratio store	25.00
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	25.00
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	1.33
CQA speedup if fully vectorized	4.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.14
Bottlenecks
Function	void LPlusTimesSdom::operator() >(Kripke::ArchLayoutT, Kripke::SdomId, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Field&, Kripke::Core::Field&, Kripke::Core::Field&) const [clone .extracted]
Source
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	1.00
CQA cycles if no scalar integer	1.00
CQA cycles if FP arith vectorized	0.75
CQA cycles if fully vectorized	0.25
Front-end cycles	0.88
P0 cycles	0.33
P1 cycles	0.33
P2 cycles	0.33
P3 cycles	0.33
P4 cycles	0.33
P5 cycles	0.33
P6 cycles	0.75
P7 cycles	0.75
P8 cycles	0.75
P9 cycles	0.75
P10 cycles	0.50
P11 cycles	0.50
P12 cycles	0.50
P13 cycles	0.50
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	8.00
Nb uops	7.00
Nb loads	2.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	4.00
Nb FLOP add-sub	2.00
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	48.00
Bytes prefetched	0.00
Bytes loaded	32.00
Bytes stored	16.00
Stride 0	0.00
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	25.00
Vector-efficiency ratio load	25.00
Vector-efficiency ratio store	25.00
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	25.00
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	void LPlusTimesSdom::operator() >(Kripke::ArchLayoutT, Kripke::SdomId, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Field&, Kripke::Core::Field&, Kripke::Core::Field&) const [clone .extracted]
Source file and lines
Module	exec

gain
potential
hint
expert

Vectorization

Your loop is vectorized, but using only 128 out of 512 bits (SSE/AVX-128 instructions on AVX-512 processors).

By fully vectorizing your loop, you can lower the cost of an iteration from 1.00 to 0.25 cycles (4.00x speedup).

Details

All SSE/AVX instructions are used in vector version (process two or more data elements in vector registers). Since your execution units are vector units, only a fully vectorized loop can use their full power.

Workaround

Pass to your compiler a micro-architecture specialization option:
- Please look into your compiler manual for march=native or equivalent
Use vector aligned instructions:
1. align your arrays on 64 bytes boundaries
2. inform your compiler that your arrays are vector aligned: read your compiler manual.

Execution units bottlenecks

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

FMA

Presence of both ADD/SUB and MUL operations.

Workaround

Pass to your compiler a micro-architecture specialization option:
- Please look into your compiler manual for march=native or equivalent
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).

Vector unaligned load/store instructions

Detected 3 suboptimal vector unaligned load/store instructions.

Details

MOVUPD: 3 occurrences►

Workaround

Pass to your compiler a micro-architecture specialization option:
- Please look into your compiler manual for march=native or equivalent
Use vector aligned instructions:
1. align your arrays on 64 bytes boundaries
2. inform your compiler that your arrays are vector aligned: read your compiler manual.

Type of elements and instruction set

2 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in vector mode (two at a time).

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

The binary loop is composed of 4 FP arithmetical operations:

2: addition or subtraction
2: multiply

The binary loop is loading 32 bytes (4 double precision FP elements). The binary loop is storing 16 bytes (2 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.08 FP operations per loaded or stored byte.

General properties

nb instructions	8
nb uops	7
loop length	32
used x86 registers	4
used mmx registers	0
used xmm registers	3
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	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	P15
uops	0.33	0.33	0.33	0.33	0.33	0.33	0.75	0.75	0.75	0.75	0.50	0.50	0.50	0.50	0.50	0.50
cycles	0.33	0.33	0.33	0.33	0.33	0.33	0.75	0.75	0.75	0.75	0.50	0.50	0.50	0.50	0.50	0.50

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	0.88
Dispatch	0.75
Data deps.	1.00
Overall L1	1.00

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	25%
load	25%
store	25%
mul	25%
add-sub	25%
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 1.00 cycles. At this rate:

12% of peak load performance is reached (32.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
12% of peak store performance is reached (16.00 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: 44da80

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
MOVUPD (%RDX,%RDI,8),%XMM2	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 (25.0%)
MULPD %XMM1,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	0	0	3	0.50	vect (25.0%)
MOVUPD (%RSI,%RDI,8),%XMM3	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 (25.0%)
ADDPD %XMM2,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (25.0%)
MOVUPD %XMM3,(%RSI,%RDI,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0.50	0.50	4	0.50	vect (25.0%)
ADD $0x2,%RDI	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 %RCX,%RDI	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
JB 44da80 <_ZNK14LPlusTimesSdomclIN6Kripke11ArchLayoutTINS1_12ArchT_OpenMPENS1_11LayoutT_DGZEEEEEvT_NS1_6SdomIdERKNS1_4Core3SetESB_SB_SB_RNS8_5FieldIdJNS1_6MomentENS1_5GroupENS1_4ZoneEEEERNSC_IdJNS1_9DirectionESE_SF_EEERNSC_IdJSI_SD_EEE.extracted+0x3a0>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	1	0.50-1	N/A

Function	void LPlusTimesSdom::operator() >(Kripke::ArchLayoutT, Kripke::SdomId, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Field&, Kripke::Core::Field&, Kripke::Core::Field&) const [clone .extracted]
Source file and lines
Module	exec

gain
potential
hint
expert

Vectorization

Your loop is vectorized, but using only 128 out of 512 bits (SSE/AVX-128 instructions on AVX-512 processors).

By fully vectorizing your loop, you can lower the cost of an iteration from 1.00 to 0.25 cycles (4.00x speedup).

Details

All SSE/AVX instructions are used in vector version (process two or more data elements in vector registers). Since your execution units are vector units, only a fully vectorized loop can use their full power.

Workaround

Pass to your compiler a micro-architecture specialization option:
- Please look into your compiler manual for march=native or equivalent
Use vector aligned instructions:
1. align your arrays on 64 bytes boundaries
2. inform your compiler that your arrays are vector aligned: read your compiler manual.

Execution units bottlenecks

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

FMA

Presence of both ADD/SUB and MUL operations.

Workaround

Pass to your compiler a micro-architecture specialization option:
- Please look into your compiler manual for march=native or equivalent
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).

Vector unaligned load/store instructions

Detected 3 suboptimal vector unaligned load/store instructions.

Details

MOVUPD: 3 occurrences►

Workaround

Pass to your compiler a micro-architecture specialization option:
- Please look into your compiler manual for march=native or equivalent
Use vector aligned instructions:
1. align your arrays on 64 bytes boundaries
2. inform your compiler that your arrays are vector aligned: read your compiler manual.

Type of elements and instruction set

2 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in vector mode (two at a time).

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

The binary loop is composed of 4 FP arithmetical operations:

2: addition or subtraction
2: multiply

The binary loop is loading 32 bytes (4 double precision FP elements). The binary loop is storing 16 bytes (2 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.08 FP operations per loaded or stored byte.

General properties

nb instructions	8
nb uops	7
loop length	32
used x86 registers	4
used mmx registers	0
used xmm registers	3
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	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	P15
uops	0.33	0.33	0.33	0.33	0.33	0.33	0.75	0.75	0.75	0.75	0.50	0.50	0.50	0.50	0.50	0.50
cycles	0.33	0.33	0.33	0.33	0.33	0.33	0.75	0.75	0.75	0.75	0.50	0.50	0.50	0.50	0.50	0.50

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	0.88
Dispatch	0.75
Data deps.	1.00
Overall L1	1.00

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	25%
load	25%
store	25%
mul	25%
add-sub	25%
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 1.00 cycles. At this rate:

12% of peak load performance is reached (32.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
12% of peak store performance is reached (16.00 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: 44da80

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
MOVUPD (%RDX,%RDI,8),%XMM2	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 (25.0%)
MULPD %XMM1,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	0	0	3	0.50	vect (25.0%)
MOVUPD (%RSI,%RDI,8),%XMM3	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 (25.0%)
ADDPD %XMM2,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	2	0.50	vect (25.0%)
MOVUPD %XMM3,(%RSI,%RDI,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0.50	0.50	4	0.50	vect (25.0%)
ADD $0x2,%RDI	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 %RCX,%RDI	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
JB 44da80 <_ZNK14LPlusTimesSdomclIN6Kripke11ArchLayoutTINS1_12ArchT_OpenMPENS1_11LayoutT_DGZEEEEEvT_NS1_6SdomIdERKNS1_4Core3SetESB_SB_SB_RNS8_5FieldIdJNS1_6MomentENS1_5GroupENS1_4ZoneEEEERNSC_IdJNS1_9DirectionESE_SF_EEERNSC_IdJSI_SD_EEE.extracted+0x3a0>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	0	0	1	0.50-1	N/A

Report Configuration

Vectorization

Details

Workaround

Execution units bottlenecks

FMA

Workaround

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

Vectorization

Details

Workaround

Execution units bottlenecks

FMA

Workaround

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