OV - exec - Loop 1856

	Loop Id: 1856	Module: exec	Source: For.hpp:137-137 [...]	Coverage: 0.22%

0x48fda0 MOVSD	-0x38(%R10,%R13,1),%XMM1    [1]

0x48fda7 MULSD	%XMM0,%XMM1

0x48fdab MULSD	-0x38(%R14,%R13,1),%XMM1    [2]

0x48fdb2 ADDSD	%XMM3,%XMM1

0x48fdb6 MOVSD	-0x30(%R10,%R13,1),%XMM2    [1]

0x48fdbd MULSD	%XMM0,%XMM2

0x48fdc1 MULSD	-0x30(%R14,%R13,1),%XMM2    [2]

0x48fdc8 MOVSD	-0x28(%R10,%R13,1),%XMM3    [1]

0x48fdcf MULSD	%XMM0,%XMM3

0x48fdd3 MULSD	-0x28(%R14,%R13,1),%XMM3    [2]

0x48fdda ADDSD	%XMM2,%XMM3

0x48fdde MOVSD	-0x20(%R10,%R13,1),%XMM2    [1]

0x48fde5 MULSD	%XMM0,%XMM2

0x48fde9 MULSD	-0x20(%R14,%R13,1),%XMM2    [2]

0x48fdf0 MOVSD	-0x18(%R10,%R13,1),%XMM4    [1]

0x48fdf7 MULSD	%XMM0,%XMM4

0x48fdfb MULSD	-0x18(%R14,%R13,1),%XMM4    [2]

0x48fe02 ADDSD	%XMM1,%XMM3

0x48fe06 ADDSD	%XMM2,%XMM4

0x48fe0a MOVSD	-0x10(%R10,%R13,1),%XMM1    [1]

0x48fe11 MULSD	%XMM0,%XMM1

0x48fe15 MULSD	-0x10(%R14,%R13,1),%XMM1    [2]

0x48fe1c ADDSD	%XMM4,%XMM1

0x48fe20 ADDSD	%XMM3,%XMM1

0x48fe24 MOVSD	-0x8(%R10,%R13,1),%XMM2    [1]

0x48fe2b MULSD	%XMM0,%XMM2

0x48fe2f MULSD	-0x8(%R14,%R13,1),%XMM2    [2]

0x48fe36 MOVSD	(%R10,%R13,1),%XMM3    [1]

0x48fe3c MULSD	%XMM0,%XMM3

0x48fe40 MULSD	(%R14,%R13,1),%XMM3    [2]

0x48fe46 ADDSD	%XMM2,%XMM3

0x48fe4a ADDSD	%XMM1,%XMM3

0x48fe4e ADD	$0x40,%R13

0x48fe52 DEC	%RCX

0x48fe55 JNE	48fda0

/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/pattern/kernel/For.hpp: 137 - 137

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

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

/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/util/Operators.hpp: 334 - 334

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

334:     return Ret{lhs} + rhs;

/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/src/Kripke/Kernel/Population.cpp: 58 - 58

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

58:           part_red += w(d) * psi(d,g,z) * volume(z);

Coverage (%)	Name	Source Location	Module
►96.14+	__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
►2.46+	__kmp_invoke_microtask		libiomp5.so
○	__kmp_invoke_task_func		libiomp5.so
○	__kmp_fork_call		libiomp5.so
○	__kmpc_fork_call		libiomp5.so
○	void PopulationSdom::operator([...]	reduce.hpp:58	exec
○	population	ArchLayout.h:193	exec
○	SteadyStateSolver	SteadyStateSolver.cpp:107	exec
○	main	kripke.cpp:504	exec
○	__libc_start_call_main		libc.so.6
○	__libc_start_main		libc.so.6
○	_start	kripke.cpp:0	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	2.00
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.88
Bottlenecks	P10, P11,
Function	void PopulationSdom::operator() >(Kripke::ArchLayoutT, Kripke::SdomId, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Field&, Kripke::Core::Field&, Kripke::Core::Field&, double*) const [clone .extracted]
Source	For.hpp:137-137,Operators.hpp:334-334,Population.cpp:58-58
Source loop unroll info	multi-versionned
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	8.00
CQA cycles if no scalar integer	8.00
CQA cycles if FP arith vectorized	4.00
CQA cycles if fully vectorized	1.00
Front-end cycles	4.25
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	4.00
P7 cycles	4.00
P8 cycles	4.00
P9 cycles	4.00
P10 cycles	8.00
P11 cycles	8.00
P12 cycles	4.00
P13 cycles	4.00
P14 cycles	0.00
P15 cycles	0.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	8
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	35.00
Nb uops	34.00
Nb loads	16.00
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	3.00
Nb FLOP add-sub	8.00
Nb FLOP mul	16.00
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	16.00
Bytes prefetched	0.00
Bytes loaded	128.00
Bytes stored	0.00
Stride 0	0.00
Stride 1	2.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	0.00
Vectorization ratio load	0.00
Vectorization ratio store	NA
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	12.50
Vector-efficiency ratio load	12.50
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	12.50
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	2.00
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.88
Bottlenecks	P10, P11,
Function	void PopulationSdom::operator() >(Kripke::ArchLayoutT, Kripke::SdomId, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Field&, Kripke::Core::Field&, Kripke::Core::Field&, double*) const [clone .extracted]
Source	For.hpp:137-137,Operators.hpp:334-334,Population.cpp:58-58
Source loop unroll info	multi-versionned
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	8.00
CQA cycles if no scalar integer	8.00
CQA cycles if FP arith vectorized	4.00
CQA cycles if fully vectorized	1.00
Front-end cycles	4.25
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	4.00
P7 cycles	4.00
P8 cycles	4.00
P9 cycles	4.00
P10 cycles	8.00
P11 cycles	8.00
P12 cycles	4.00
P13 cycles	4.00
P14 cycles	0.00
P15 cycles	0.00
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	8
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	35.00
Nb uops	34.00
Nb loads	16.00
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	3.00
Nb FLOP add-sub	8.00
Nb FLOP mul	16.00
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	16.00
Bytes prefetched	0.00
Bytes loaded	128.00
Bytes stored	0.00
Stride 0	0.00
Stride 1	2.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	0.00
Vectorization ratio load	0.00
Vectorization ratio store	NA
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	12.50
Vector-efficiency ratio load	12.50
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	12.50
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 PopulationSdom::operator() >(Kripke::ArchLayoutT, Kripke::SdomId, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Field&, Kripke::Core::Field&, Kripke::Core::Field&, double*) const [clone .extracted]
Source file and lines	For.hpp:137-137
Module	exec

The loop is defined in:

/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/pattern/kernel/For.hpp:137
/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/util/Operators.hpp:334
/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/src/Kripke/Kernel/Population.cpp:58

The related source loop is multi-versionned.

gain
potential
hint
expert

Vectorization

Your loop is not vectorized. 8 data elements could be processed at once in vector registers.

By vectorizing your loop, you can lower the cost of an iteration from 8.00 to 1.00 cycles (8.00x speedup).

Details

All SSE/AVX instructions are used in scalar version (process only one data element in vector registers). Since your execution units are vector units, only a 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)

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 8.00 to 4.25 cycles (1.88x speedup).

Workaround

Reduce the number of FP multiply/FMA instructions

FMA

Presence of both ADD/SUB and MUL operations.

Workaround

Pass to your compiler a micro-architecture specialization option:
- use march=native
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).

Type of elements and instruction set

24 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time).

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

The binary loop is composed of 24 FP arithmetical operations:

8: addition or subtraction
16: multiply

The binary loop is loading 128 bytes (16 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.19 FP operations per loaded or stored byte.

Unroll opportunity

Loop is potentially data access bound.

Workaround

Unroll your loop if trip count is significantly higher than target unroll factor and if some data references are common to consecutive iterations. This can be done manually. Or with the unroll (resp. unroll_and_jam) directive on top of the inner (resp. surrounding) loop. You can enforce an unroll factor: #pragma unroll_and_jam N, unroll_and_jam(N), unroll N or unroll(N)

General properties

nb instructions	35
nb uops	34
loop length	187
used x86 registers	4
used mmx registers	0
used xmm registers	5
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	0.50

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	4.25 cycles
front end	4.25 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	4.00	4.00	4.00	4.00	8.00	8.00	4.00	4.00	0.00	0.00
cycles	0.33	0.33	0.33	0.33	0.33	0.33	4.00	4.00	4.00	4.00	8.00	8.00	4.00	4.00	0.00	0.00

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)	8.00

Cycles summary

Front-end	4.25
Dispatch	8.00
Data deps.	8.00
Overall L1	8.00

Vectorization ratios

all	0%
load	0%
store	NA (no store vectorizable/vectorized instructions)
mul	0%
add-sub	0%
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	12%
load	12%
store	NA (no store vectorizable/vectorized instructions)
mul	12%
add-sub	12%
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 8.00 cycles. At this rate:

6% of peak load performance is reached (16.00 out of 256.00 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: 48fda0

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	Latency	Recip. throughput	Vectorization
MOVSD -0x38(%R10,%R13,1),%XMM1	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x38(%R14,%R13,1),%XMM1	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM3,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
MOVSD -0x30(%R10,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x30(%R14,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
MOVSD -0x28(%R10,%R13,1),%XMM3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x28(%R14,%R13,1),%XMM3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM2,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
MOVSD -0x20(%R10,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x20(%R14,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
MOVSD -0x18(%R10,%R13,1),%XMM4	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM4	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x18(%R14,%R13,1),%XMM4	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM1,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
ADDSD %XMM2,%XMM4	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
MOVSD -0x10(%R10,%R13,1),%XMM1	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x10(%R14,%R13,1),%XMM1	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM4,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
ADDSD %XMM3,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
MOVSD -0x8(%R10,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x8(%R14,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
MOVSD (%R10,%R13,1),%XMM3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD (%R14,%R13,1),%XMM3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM2,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
ADDSD %XMM1,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
ADD $0x40,%R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
DEC %RCX	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
JNE 48fda0 <_ZNK14PopulationSdomclIN6Kripke11ArchLayoutTINS1_12ArchT_OpenMPENS1_11LayoutT_DGZEEEEEvT_NS1_6SdomIdERKNS1_4Core3SetESB_SB_RNS8_5FieldIdJNS1_9DirectionENS1_5GroupENS1_4ZoneEEEERNSC_IdJSD_EEERNSC_IdJSF_EEEPd.extracted+0x330>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	1	0.50-1	N/A

Function	void PopulationSdom::operator() >(Kripke::ArchLayoutT, Kripke::SdomId, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Set const&, Kripke::Core::Field&, Kripke::Core::Field&, Kripke::Core::Field&, double*) const [clone .extracted]
Source file and lines	For.hpp:137-137
Module	exec

The loop is defined in:

/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/pattern/kernel/For.hpp:137
/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/tpl/raja/include/RAJA/util/Operators.hpp:334
/home/eoseret/qaas_runs_ZEN5/173-940-2141/intel/Kripke/build/Kripke/src/Kripke/Kernel/Population.cpp:58

The related source loop is multi-versionned.

gain
potential
hint
expert

Vectorization

Your loop is not vectorized. 8 data elements could be processed at once in vector registers.

By vectorizing your loop, you can lower the cost of an iteration from 8.00 to 1.00 cycles (8.00x speedup).

Details

All SSE/AVX instructions are used in scalar version (process only one data element in vector registers). Since your execution units are vector units, only a 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)

Execution units bottlenecks

Workaround

Reduce the number of FP multiply/FMA instructions

FMA

Presence of both ADD/SUB and MUL operations.

Workaround

Pass to your compiler a micro-architecture specialization option:
- use march=native
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).

Type of elements and instruction set

24 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time).

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

The binary loop is composed of 24 FP arithmetical operations:

8: addition or subtraction
16: multiply

The binary loop is loading 128 bytes (16 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.19 FP operations per loaded or stored byte.

Unroll opportunity

Loop is potentially data access bound.

Workaround

General properties

nb instructions	35
nb uops	34
loop length	187
used x86 registers	4
used mmx registers	0
used xmm registers	5
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	0.50

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	4.25 cycles
front end	4.25 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	4.00	4.00	4.00	4.00	8.00	8.00	4.00	4.00	0.00	0.00
cycles	0.33	0.33	0.33	0.33	0.33	0.33	4.00	4.00	4.00	4.00	8.00	8.00	4.00	4.00	0.00	0.00

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)	8.00

Cycles summary

Front-end	4.25
Dispatch	8.00
Data deps.	8.00
Overall L1	8.00

Vectorization ratios

all	0%
load	0%
store	NA (no store vectorizable/vectorized instructions)
mul	0%
add-sub	0%
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	12%
load	12%
store	NA (no store vectorizable/vectorized instructions)
mul	12%
add-sub	12%
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 8.00 cycles. At this rate:

6% of peak load performance is reached (16.00 out of 256.00 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: 48fda0

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	Latency	Recip. throughput	Vectorization
MOVSD -0x38(%R10,%R13,1),%XMM1	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x38(%R14,%R13,1),%XMM1	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM3,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
MOVSD -0x30(%R10,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x30(%R14,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
MOVSD -0x28(%R10,%R13,1),%XMM3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x28(%R14,%R13,1),%XMM3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM2,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
MOVSD -0x20(%R10,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x20(%R14,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
MOVSD -0x18(%R10,%R13,1),%XMM4	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM4	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x18(%R14,%R13,1),%XMM4	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM1,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
ADDSD %XMM2,%XMM4	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
MOVSD -0x10(%R10,%R13,1),%XMM1	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x10(%R14,%R13,1),%XMM1	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM4,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
ADDSD %XMM3,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
MOVSD -0x8(%R10,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM2	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD -0x8(%R14,%R13,1),%XMM2	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
MOVSD (%R10,%R13,1),%XMM3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	1	0.50	scal (12.5%)
MULSD %XMM0,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	3	0.50	scal (12.5%)
MULSD (%R14,%R13,1),%XMM3	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	scal (12.5%)
ADDSD %XMM2,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
ADDSD %XMM1,%XMM3	1	0	0	0	0	0	0	0	0	0	0	0	0	0.50	0.50	2	0.50	scal (12.5%)
ADD $0x40,%R13	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
DEC %RCX	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
JNE 48fda0 <_ZNK14PopulationSdomclIN6Kripke11ArchLayoutTINS1_12ArchT_OpenMPENS1_11LayoutT_DGZEEEEEvT_NS1_6SdomIdERKNS1_4Core3SetESB_SB_RNS8_5FieldIdJNS1_9DirectionENS1_5GroupENS1_4ZoneEEEERNSC_IdJSD_EEERNSC_IdJSF_EEEPd.extracted+0x330>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	1	0.50-1	N/A

Report Configuration

Vectorization

Details

Workaround

Execution units bottlenecks

Workaround

FMA

Workaround

Type of elements and instruction set

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

Arithmetic intensity

Unroll opportunity

Workaround

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

FMA

Workaround

Type of elements and instruction set

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

Arithmetic intensity

Unroll opportunity

Workaround

General properties

Front-end

Back-end

Cycles summary

Vectorization ratios

Vector efficiency ratios

Cycles and memory resources usage

Front-end bottlenecks

ASM code