OV - exec - Loop 811

0x447680 VMOVUPD	(%RDX,%R11,8),%YMM2    [2]

0x447686 VFMADD213PD	(%RCX,%R11,8),%YMM1,%YMM2    [1]

0x44768c VMOVUPD	%YMM2,(%RCX,%R11,8)    [1]

0x447692 ADD	$0x4,%R11

0x447696 CMP	%RSI,%R11

0x447699 JLE	447680

/home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/policy/loop/forall.hpp: 59 - 59

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

59:   for (decltype(distance_it) i = 0; i < distance_it; ++i) {

/home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/src/Kripke/Kernel/LPlusTimes.cpp: 57 - 57

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

57:             rhs(d,g,z) += ell_plus(d, nm) * phi_out(nm, g, z);

Coverage (%)	Name	Source Location	Module
►100.00+	__kmp_invoke_microtask		libiomp5.so
○	__kmp_invoke_task_func		libiomp5.so

Path /

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	1.41
CQA speedup if fully vectorized	2.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.50
Bottlenecks	micro-operation queue, P0,
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	forall.hpp:59-59,LPlusTimes.cpp:57-57
Source loop unroll info	unrolled by 4
Source loop unroll confidence level	max
Unroll/vectorization loop type	main
Unroll factor	4
CQA cycles	1.00
CQA cycles if no scalar integer	1.00
CQA cycles if FP arith vectorized	0.71
CQA cycles if fully vectorized	0.50
Front-end cycles	1.00
P0 cycles	1.00
P1 cycles	0.50
P2 cycles	0.67
P3 cycles	0.67
P4 cycles	0.50
P5 cycles	0.00
P6 cycles	0.50
P7 cycles	0.50
P8 cycles	0.50
P9 cycles	0.50
P10 cycles	0.00
P11 cycles	0.67
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	6.00
Nb uops	5.00
Nb loads	2.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	8.00
Nb FLOP add-sub	0.00
Nb FLOP mul	0.00
Nb FLOP fma	4.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	96.00
Bytes prefetched	0.00
Bytes loaded	64.00
Bytes stored	32.00
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	NA
Vectorization ratio add_sub	NA
Vectorization ratio fma	100.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	50.00
Vector-efficiency ratio load	50.00
Vector-efficiency ratio store	50.00
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	50.00
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	1.41
CQA speedup if fully vectorized	2.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.50
Bottlenecks	micro-operation queue, P0,
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	forall.hpp:59-59,LPlusTimes.cpp:57-57
Source loop unroll info	unrolled by 4
Source loop unroll confidence level	max
Unroll/vectorization loop type	main
Unroll factor	4
CQA cycles	1.00
CQA cycles if no scalar integer	1.00
CQA cycles if FP arith vectorized	0.71
CQA cycles if fully vectorized	0.50
Front-end cycles	1.00
P0 cycles	1.00
P1 cycles	0.50
P2 cycles	0.67
P3 cycles	0.67
P4 cycles	0.50
P5 cycles	0.00
P6 cycles	0.50
P7 cycles	0.50
P8 cycles	0.50
P9 cycles	0.50
P10 cycles	0.00
P11 cycles	0.67
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	6.00
Nb uops	5.00
Nb loads	2.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	8.00
Nb FLOP add-sub	0.00
Nb FLOP mul	0.00
Nb FLOP fma	4.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	96.00
Bytes prefetched	0.00
Bytes loaded	64.00
Bytes stored	32.00
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	NA
Vectorization ratio add_sub	NA
Vectorization ratio fma	100.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	50.00
Vector-efficiency ratio load	50.00
Vector-efficiency ratio store	50.00
Vector-efficiency ratio mul	NA
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	50.00
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	forall.hpp:59-59
Module	exec

The loop is defined in:

/home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/policy/loop/forall.hpp:59
/home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/src/Kripke/Kernel/LPlusTimes.cpp:57

It is main loop of related source loop which is unrolled by 4 (including vectorization).

gain
potential
hint
expert

Vectorization

Your loop is vectorized, but using only 256 out of 512 bits (AVX/AVX2 instructions on AVX-512 processors).

Details

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

Workaround

Read the "512-bits vectorization" report at "Potential" confidence level.

Execution units bottlenecks

Performance is limited by execution of FP multiply or FMA (fused multiply-add) operations (the FP multiply/FMA unit is a bottleneck). By removing all these bottlenecks, you can lower the cost of an iteration from 1.00 to 0.67 cycles (1.50x speedup).

Workaround

Reduce the number of FP multiply/FMA instructions

512-bits vectorization

On some x86 processors supporting 512-bits vectorization, compilers are often too conservative and limit vectorization to 256 bits. Performance can then be improved by enforcing 512-bits vectorization, especially with many vectorized and high trip count loops. 512-bits vectorization performance overhead (compared to 256-bits) is generally lower on newer processors.

Workaround

Recompile with -mprefer-vector-width=512

FMA

Detected 4 FMA (fused multiply-add) operations.

Vector unaligned load/store instructions

Detected 2 optimal vector unaligned load/store instructions.

Details

VMOVUPD: 2 occurrences►
- /home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/src/Kripke/Kernel/LPlusTimes.cpp:57
- /home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/src/Kripke/Kernel/LPlusTimes.cpp:57

Workaround

Use vector aligned instructions:

align your arrays on 64 bytes boundaries: replace { void *p = malloc (size); } with { void *p; posix_memalign (&p, 64, size); }.
inform your compiler that your arrays are vector aligned: if array 'foo' is 64 bytes-aligned, define a pointer 'p_foo' as __builtin_assume_aligned (foo, 64) and use it instead of 'foo' in the loop.

Type of elements and instruction set

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

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

The binary loop is composed of 8 FP arithmetical operations:

4: addition or subtraction (all inside FMA instructions)
4: multiply (all inside FMA instructions)

The binary loop is loading 64 bytes (8 double precision FP elements). The binary loop is storing 32 bytes (4 double precision FP elements).

Arithmetic intensity

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

General properties

nb instructions	6
nb uops	5
loop length	27
used x86 registers	4
used mmx registers	0
used xmm registers	0
used ymm registers	2
used zmm registers	0
nb stack references	0

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.00 cycles
front end	1.00 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	1.00	0.50	0.67	0.67	0.50	0.00	0.50	0.50	0.50	0.50	0.00	0.67
cycles	1.00	0.50	0.67	0.67	0.50	0.00	0.50	0.50	0.50	0.50	0.00	0.67

Execution ports to units layout:

P0 (256 bits): VPU, BRU, ALU, DIV/SQRT
P1 (256 bits): ALU, VPU
P2 (512 bits): load
P3 (512 bits): load
P4 (512 bits): store data
P5 (512 bits): ALU, VPU
P6: ALU, BRU
P7: store address
P8: store address
P9 (512 bits): store data
P10: ALU
P11 (512 bits): load

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	1.00

Cycles summary

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

Vectorization ratios

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

Vector efficiency ratios

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

33% of peak load performance is reached (64.00 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))
25% of peak store performance is reached (32.00 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

Performance is limited by instruction throughput (loading/decoding program instructions to execution core) (front-end is a bottleneck). By removing all these bottlenecks, you can lower the cost of an iteration from 1.00 to 0.67 cycles (1.50x speedup).

ASM code

In the binary file, the address of the loop is: 447680

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	Latency	Recip. throughput	Vectorization
VMOVUPD (%RDX,%R11,8),%YMM2	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	0-1	0.33	vect (50.0%)
VFMADD213PD (%RCX,%R11,8),%YMM1,%YMM2	1	0.50	0.50	0.33	0.33	0	0	0	0	0	0	0	0.33	4	0.50	vect (50.0%)
VMOVUPD %YMM2,(%RCX,%R11,8)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	0-1	0.50	vect (50.0%)
ADD $0x4,%R11	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
CMP %RSI,%R11	1	0.20	0.20	0	0	0	0.20	0.20	0	0	0	0.20	0	1	0.20	N/A
JLE 447680 <_ZNK14LPlusTimesSdomclIN6Kripke11ArchLayoutTINS1_12ArchT_OpenMPENS1_11LayoutT_DGZEEEEEvT_NS1_6SdomIdERKNS1_4Core3SetESB_SB_SB_RNS8_5FieldIdJNS1_6MomentENS1_5GroupENS1_4ZoneEEEERNSC_IdJNS1_9DirectionESE_SF_EEERNSC_IdJSI_SD_EEE.extracted+0x3b0>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	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	forall.hpp:59-59
Module	exec

The loop is defined in:

/home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/policy/loop/forall.hpp:59
/home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/src/Kripke/Kernel/LPlusTimes.cpp:57

It is main loop of related source loop which is unrolled by 4 (including vectorization).

gain
potential
hint
expert

Vectorization

Your loop is vectorized, but using only 256 out of 512 bits (AVX/AVX2 instructions on AVX-512 processors).

Details

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

Workaround

Read the "512-bits vectorization" report at "Potential" confidence level.

Execution units bottlenecks

Performance is limited by execution of FP multiply or FMA (fused multiply-add) operations (the FP multiply/FMA unit is a bottleneck). By removing all these bottlenecks, you can lower the cost of an iteration from 1.00 to 0.67 cycles (1.50x speedup).

Workaround

Reduce the number of FP multiply/FMA instructions

512-bits vectorization

On some x86 processors supporting 512-bits vectorization, compilers are often too conservative and limit vectorization to 256 bits. Performance can then be improved by enforcing 512-bits vectorization, especially with many vectorized and high trip count loops. 512-bits vectorization performance overhead (compared to 256-bits) is generally lower on newer processors.

Workaround

Recompile with -mprefer-vector-width=512

FMA

Detected 4 FMA (fused multiply-add) operations.

Vector unaligned load/store instructions

Detected 2 optimal vector unaligned load/store instructions.

Details

VMOVUPD: 2 occurrences►
- /home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/src/Kripke/Kernel/LPlusTimes.cpp:57
- /home/eoseret/qaas_runs_GNR/173-926-6874/intel/Kripke/build/Kripke/src/Kripke/Kernel/LPlusTimes.cpp:57

Workaround

Use vector aligned instructions:

align your arrays on 64 bytes boundaries: replace { void *p = malloc (size); } with { void *p; posix_memalign (&p, 64, size); }.
inform your compiler that your arrays are vector aligned: if array 'foo' is 64 bytes-aligned, define a pointer 'p_foo' as __builtin_assume_aligned (foo, 64) and use it instead of 'foo' in the loop.

Type of elements and instruction set

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

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

The binary loop is composed of 8 FP arithmetical operations:

4: addition or subtraction (all inside FMA instructions)
4: multiply (all inside FMA instructions)

The binary loop is loading 64 bytes (8 double precision FP elements). The binary loop is storing 32 bytes (4 double precision FP elements).

Arithmetic intensity

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

General properties

nb instructions	6
nb uops	5
loop length	27
used x86 registers	4
used mmx registers	0
used xmm registers	0
used ymm registers	2
used zmm registers	0
nb stack references	0

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.00 cycles
front end	1.00 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	1.00	0.50	0.67	0.67	0.50	0.00	0.50	0.50	0.50	0.50	0.00	0.67
cycles	1.00	0.50	0.67	0.67	0.50	0.00	0.50	0.50	0.50	0.50	0.00	0.67

Execution ports to units layout:

P0 (256 bits): VPU, BRU, ALU, DIV/SQRT
P1 (256 bits): ALU, VPU
P2 (512 bits): load
P3 (512 bits): load
P4 (512 bits): store data
P5 (512 bits): ALU, VPU
P6: ALU, BRU
P7: store address
P8: store address
P9 (512 bits): store data
P10: ALU
P11 (512 bits): load

Cycles executing div or sqrt instructions	NA
Longest recurrence chain latency (RecMII)	1.00

Cycles summary

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

Vectorization ratios

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

Vector efficiency ratios

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

33% of peak load performance is reached (64.00 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))
25% of peak store performance is reached (32.00 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

Performance is limited by instruction throughput (loading/decoding program instructions to execution core) (front-end is a bottleneck). By removing all these bottlenecks, you can lower the cost of an iteration from 1.00 to 0.67 cycles (1.50x speedup).

ASM code

In the binary file, the address of the loop is: 447680

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	Latency	Recip. throughput	Vectorization
VMOVUPD (%RDX,%R11,8),%YMM2	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	0-1	0.33	vect (50.0%)
VFMADD213PD (%RCX,%R11,8),%YMM1,%YMM2	1	0.50	0.50	0.33	0.33	0	0	0	0	0	0	0	0.33	4	0.50	vect (50.0%)
VMOVUPD %YMM2,(%RCX,%R11,8)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	0-1	0.50	vect (50.0%)
ADD $0x4,%R11	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
CMP %RSI,%R11	1	0.20	0.20	0	0	0	0.20	0.20	0	0	0	0.20	0	1	0.20	N/A
JLE 447680 <_ZNK14LPlusTimesSdomclIN6Kripke11ArchLayoutTINS1_12ArchT_OpenMPENS1_11LayoutT_DGZEEEEEvT_NS1_6SdomIdERKNS1_4Core3SetESB_SB_SB_RNS8_5FieldIdJNS1_6MomentENS1_5GroupENS1_4ZoneEEEERNSC_IdJNS1_9DirectionESE_SF_EEERNSC_IdJSI_SD_EEE.extracted+0x3b0>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	N/A

Report Configuration

Vectorization

Details

Workaround

Execution units bottlenecks

Workaround

512-bits vectorization

Workaround

FMA

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

Workaround

512-bits vectorization

Workaround

FMA

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