OV - exec - Loop 88

	Loop Id: 88	Module: exec	Source: ljForce.c:191-216 [...]	Coverage: 44.65%

0x40cb00 ADD	$0x18,%R15

0x40cb04 CMP	%R15,%R12

0x40cb07 JE	40cac0

0x40cb09 VMOVUPD	(%RAX),%XMM11    [1]

0x40cb0d VSUBPD	-0x10(%R13,%R15,1),%XMM11,%XMM11    [3]

0x40cb14 VMULPD	%XMM11,%XMM11,%XMM12

0x40cb19 VSHUFPD	$0x1,%XMM12,%XMM12,%XMM13

0x40cb1f VADDSD	%XMM12,%XMM13,%XMM13

0x40cb24 VMOVSD	0x10(%RAX),%XMM12    [1]

0x40cb29 VSUBSD	(%R13,%R15,1),%XMM12,%XMM12    [3]

0x40cb30 VFMADD231SD	%XMM12,%XMM12,%XMM13

0x40cb35 VUCOMISD	%XMM13,%XMM2

0x40cb3a JB	40cb00

0x40cb3c VUCOMISD	%XMM4,%XMM13

0x40cb40 JBE	40cb00

0x40cb42 VDIVSD	%XMM13,%XMM6,%XMM13

0x40cb47 VMULSD	%XMM13,%XMM13,%XMM14

0x40cb4c VMULSD	%XMM1,%XMM13,%XMM15

0x40cb50 VMULSD	%XMM15,%XMM14,%XMM14

0x40cb55 VADDSD	%XMM7,%XMM14,%XMM15

0x40cb59 VFNMADD213SD	%XMM0,%XMM14,%XMM15

0x40cb5e VMULSD	%XMM8,%XMM15,%XMM15

0x40cb63 MOV	0x30(%R11),%RDX    [2]

0x40cb67 VADDSD	(%RDX,%RSI,8),%XMM15,%XMM16    [5]

0x40cb6e VMOVSD	%XMM16,(%RDX,%RSI,8)    [5]

0x40cb75 VMOVAPD	%XMM9,%XMM16

0x40cb7b VFMADD213SD	%XMM10,%XMM14,%XMM16

0x40cb81 VMULSD	%XMM3,%XMM13,%XMM13

0x40cb85 VMULSD	%XMM14,%XMM13,%XMM13

0x40cb8a VMULSD	%XMM16,%XMM13,%XMM13

0x40cb90 MOV	0x28(%R11),%RDX    [2]

0x40cb94 VMOVDDUP	%XMM13,%XMM14

0x40cb99 VFMADD213PD	(%RDX,%RCX,8),%XMM14,%XMM11    [4]

0x40cb9f VMOVUPD	%XMM11,(%RDX,%RCX,8)    [4]

0x40cba4 VFMADD213SD	0x10(%RDX,%RCX,8),%XMM13,%XMM12    [4]

0x40cbab VMOVSD	%XMM12,0x10(%RDX,%RCX,8)    [4]

0x40cbb1 VADDSD	%XMM5,%XMM15,%XMM5

0x40cbb5 JMP	40cb00

/home/eoseret/qaas_runs_GNR/173-814-1858/intel/CoMD/build/CoMD/CoMD/src-openmp/ljForce.c: 191 - 216

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

191:             for (int jOff=jBox*MAXATOMS; jOff<(jBox*MAXATOMS+nJBox); jOff++)

[...]

197:                   dr[m] = s->atoms->r[iOff][m]-s->atoms->r[jOff][m];

198:                   r2+=dr[m]*dr[m];

199:                }

200:

201:                if ( r2 <= rCut2 && r2 > 0.0)

202:                {

203:

204:                   // Important note:

205:                   // from this point on r actually refers to 1.0/r

206:                   r2 = 1.0/r2;

207:                   real_t r6 = s6 * (r2*r2*r2);

208:                   real_t eLocal = r6 * (r6 - 1.0) - eShift;

209:                   s->atoms->U[iOff] += 0.5*eLocal;

210:                   ePot += 0.5*eLocal;

211:

212:                   // different formulation to avoid sqrt computation

213:                   real_t fr = - 4.0*epsilon*r6*r2*(12.0*r6 - 6.0);

214:                   for (int m=0; m<3; m++)

215:                   {

216:                      s->atoms->f[iOff][m] -= dr[m]*fr;

Coverage (%)	Name	Source Location	Module
►99.98+	__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	2.54
CQA speedup if fully vectorized	5.18
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.08
Bottlenecks
Function	ljForce.extracted
Source	ljForce.c:191-191,ljForce.c:197-216
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	5.17
CQA cycles if no scalar integer	5.17
CQA cycles if FP arith vectorized	2.03
CQA cycles if fully vectorized	1.00
Front-end cycles	4.17
P0 cycles	4.83
P1 cycles	4.83
P2 cycles	1.89
P3 cycles	1.89
P4 cycles	0.50
P5 cycles	3.50
P6 cycles	2.67
P7 cycles	0.50
P8 cycles	0.50
P9 cycles	0.50
P10 cycles	1.00
P11 cycles	1.89
DIV/SQRT cycles	1.33
Inter-iter dependencies cycles	3
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	22.00
Nb uops	22.00
Nb loads	5.67
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	2.90
Nb FLOP add-sub	5.00
Nb FLOP mul	4.33
Nb FLOP fma	2.67
Nb FLOP div	0.33
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	15.16
Bytes prefetched	0.00
Bytes loaded	64.00
Bytes stored	10.67
Stride 0	1.33
Stride 1	1.00
Stride n	0.00
Stride unknown	0.67
Stride indirect	0.00
Vectorization ratio all	35.93
Vectorization ratio load	47.62
Vectorization ratio store	33.33
Vectorization ratio mul	70.83
Vectorization ratio add_sub	27.78
Vectorization ratio fma	6.67
Vectorization ratio div_sqrt	0.00
Vectorization ratio other	41.11
Vector-efficiency ratio all	16.99
Vector-efficiency ratio load	18.45
Vector-efficiency ratio store	16.67
Vector-efficiency ratio mul	21.35
Vector-efficiency ratio add_sub	15.97
Vector-efficiency ratio fma	13.33
Vector-efficiency ratio div_sqrt	12.50
Vector-efficiency ratio other	17.64

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	2.10
CQA speedup if fully vectorized	6.12
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.20
Bottlenecks
Function	ljForce.extracted
Source	ljForce.c:191-191,ljForce.c:197-216
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	3.00
CQA cycles if no scalar integer	3.00
CQA cycles if FP arith vectorized	1.43
CQA cycles if fully vectorized	0.49
Front-end cycles	2.50
P0 cycles	2.50
P1 cycles	2.50
P2 cycles	1.33
P3 cycles	1.33
P4 cycles	0.00
P5 cycles	2.00
P6 cycles	2.00
P7 cycles	0.00
P8 cycles	0.00
P9 cycles	0.00
P10 cycles	1.00
P11 cycles	1.33
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	3
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	13.00
Nb uops	13.00
Nb loads	4.00
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	2.67
Nb FLOP add-sub	4.00
Nb FLOP mul	2.00
Nb FLOP fma	1.00
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	48.00
Bytes stored	0.00
Stride 0	1.00
Stride 1	1.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	44.44
Vectorization ratio load	50.00
Vectorization ratio store	NA
Vectorization ratio mul	100.00
Vectorization ratio add_sub	33.33
Vectorization ratio fma	0.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	50.00
Vector-efficiency ratio all	18.06
Vector-efficiency ratio load	18.75
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	16.67
Vector-efficiency ratio fma	12.50
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	18.75

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	3.55
CQA speedup if fully vectorized	4.75
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.06
Bottlenecks	P1,
Function	ljForce.extracted
Source	ljForce.c:191-191,ljForce.c:197-216
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	9.50
CQA cycles if no scalar integer	9.50
CQA cycles if FP arith vectorized	2.68
CQA cycles if fully vectorized	2.00
Front-end cycles	7.17
P0 cycles	9.00
P1 cycles	9.50
P2 cycles	3.00
P3 cycles	3.00
P4 cycles	1.50
P5 cycles	6.00
P6 cycles	3.00
P7 cycles	1.50
P8 cycles	1.50
P9 cycles	1.50
P10 cycles	1.00
P11 cycles	3.00
DIV/SQRT cycles	4.00
Inter-iter dependencies cycles	3
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	38.00
Nb uops	38.00
Nb loads	9.00
Nb stores	3.00
Nb stack references	0.00
FLOP/cycle	3.05
Nb FLOP add-sub	7.00
Nb FLOP mul	9.00
Nb FLOP fma	6.00
Nb FLOP div	1.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	13.47
Bytes prefetched	0.00
Bytes loaded	96.00
Bytes stored	32.00
Stride 0	2.00
Stride 1	1.00
Stride n	0.00
Stride unknown	2.00
Stride indirect	0.00
Vectorization ratio all	23.33
Vectorization ratio load	42.86
Vectorization ratio store	33.33
Vectorization ratio mul	12.50
Vectorization ratio add_sub	16.67
Vectorization ratio fma	20.00
Vectorization ratio div_sqrt	0.00
Vectorization ratio other	40.00
Vector-efficiency ratio all	15.42
Vector-efficiency ratio load	17.86
Vector-efficiency ratio store	16.67
Vector-efficiency ratio mul	14.06
Vector-efficiency ratio add_sub	14.58
Vector-efficiency ratio fma	15.00
Vector-efficiency ratio div_sqrt	12.50
Vector-efficiency ratio other	17.50

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	1.50
CQA speedup if fully vectorized	6.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.06
Bottlenecks	P0, P6,
Function	ljForce.extracted
Source	ljForce.c:191-191,ljForce.c:197-216
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	3.00
CQA cycles if no scalar integer	3.00
CQA cycles if FP arith vectorized	2.00
CQA cycles if fully vectorized	0.50
Front-end cycles	2.83
P0 cycles	3.00
P1 cycles	2.50
P2 cycles	1.33
P3 cycles	1.33
P4 cycles	0.00
P5 cycles	2.50
P6 cycles	3.00
P7 cycles	0.00
P8 cycles	0.00
P9 cycles	0.00
P10 cycles	1.00
P11 cycles	1.33
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	3
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	15.00
Nb uops	15.00
Nb loads	4.00
Nb stores	0.00
Nb stack references	0.00
FLOP/cycle	2.67
Nb FLOP add-sub	4.00
Nb FLOP mul	2.00
Nb FLOP fma	1.00
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	48.00
Bytes stored	0.00
Stride 0	1.00
Stride 1	1.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	40.00
Vectorization ratio load	50.00
Vectorization ratio store	NA
Vectorization ratio mul	100.00
Vectorization ratio add_sub	33.33
Vectorization ratio fma	0.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	33.33
Vector-efficiency ratio all	17.50
Vector-efficiency ratio load	18.75
Vector-efficiency ratio store	NA
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	16.67
Vector-efficiency ratio fma	12.50
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	16.67

Path /

Average path: Display a virtual path defined by average values of all real paths

Function	ljForce.extracted
Source file and lines	ljForce.c:191-216
Module	exec

The loop is defined in /home/eoseret/qaas_runs_GNR/173-814-1858/intel/CoMD/build/CoMD/CoMD/src-openmp/ljForce.c:191,197-216.

The related source loop is not unrolled or unrolled with no peel/tail loop.
This loop has 3 execution paths.

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 16% of vector register length is used (average across all SSE/AVX instructions). By fully vectorizing your loop, you can lower the cost of an iteration from 5.17 to 1.00 cycles (5.18x speedup).

Details

35% of SSE/AVX instructions are used in vector version (process two or more data elements in vector registers):

47% of SSE/AVX loads are used in vector version.
33% of SSE/AVX stores are used in vector version.
27% of SSE/AVX addition or subtraction instructions are used in vector version.
70% of SSE/AVX multiply instructions are used in vector version.
6% of SSE/AVX fused multiply-add instructions are used in vector version.
0% of SSE/AVX divide and square root instructions are used in vector version.
41% of SSE/AVX 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:
- 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)

FMA

Detected 2.67 FMA (fused multiply-add) operations. 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).

Slow data structures access

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

Details

Constant unknown stride: 0 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)

Type of elements and instruction set

9 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time). 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 15 FP arithmetical operations:

7.67: addition or subtraction (2 inside FMA instructions)
7: multiply (2 inside FMA instructions)
0.33: divide

The binary loop is loading 64 bytes (8 double precision FP elements). The binary loop is storing 10 bytes (1 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.20 FP operations per loaded or stored byte.

General properties

nb instructions	22
nb uops	22
loop length	104
used x86 registers	5.33
used mmx registers	0
used xmm registers	8.67
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	2.25

Front-end

MACRO FUSION NOT POSSIBLE

micro-operation queue	4.17 cycles
front end	4.17 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	4.83	4.67	1.89	1.89	0.50	3.50	2.67	0.50	0.50	0.50	1.00	1.89
cycles	4.83	4.83	1.89	1.89	0.50	3.50	2.67	0.50	0.50	0.50	1.00	1.89

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	1.33
Longest recurrence chain latency (RecMII)	3.00

Cycles summary

Front-end	4.17
Dispatch	5.00
DIV/SQRT	1.33
Data deps.	3.00
Overall L1	5.17

Vectorization ratios

all	35%
load	47%
store	33%
mul	70%
add-sub	27%
fma	6%
div/sqrt	0%
other	41%

Vector efficiency ratios

all	16%
load	18%
store	16%
mul	21%
add-sub	15%
fma	13%
div/sqrt	12%
other	17%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 5.17 cycles. At this rate:

7% of peak load performance is reached (14.04 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))
0% of peak store performance is reached (1.12 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Function	ljForce.extracted
Source file and lines	ljForce.c:191-216
Module	exec

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 18% of vector register length is used (average across all SSE/AVX instructions). By fully vectorizing your loop, you can lower the cost of an iteration from 3.00 to 0.49 cycles (6.12x speedup).

Details

44% of SSE/AVX instructions are used in vector version (process two or more data elements in vector registers):

50% of SSE/AVX loads are used in vector version.
33% of SSE/AVX addition or subtraction instructions are used in vector version.
0% of SSE/AVX fused multiply-add instructions are used in vector version.
50% of SSE/AVX 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:
- 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

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

FMA

Detected 1 FMA (fused multiply-add) operations. Presence of both ADD/SUB and MUL operations.

Workaround

Type of elements and instruction set

4 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time). 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 8 FP arithmetical operations:

5: addition or subtraction (1 inside FMA instructions)
3: multiply (1 inside FMA instructions)

The binary loop is loading 48 bytes (6 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.17 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	13
nb uops	13
loop length	60
used x86 registers	4
used mmx registers	0
used xmm registers	4
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	3.00

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	2.50 cycles
front end	2.50 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	2.50	2.50	1.33	1.33	0.00	2.00	2.00	0.00	0.00	0.00	1.00	1.33
cycles	2.50	2.50	1.33	1.33	0.00	2.00	2.00	0.00	0.00	0.00	1.00	1.33

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)	3.00

Cycles summary

Front-end	2.50
Dispatch	2.50
Data deps.	3.00
Overall L1	3.00

Vectorization ratios

all	44%
load	50%
store	NA (no store vectorizable/vectorized instructions)
mul	100%
add-sub	33%
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	50%

Vector efficiency ratios

all	18%
load	18%
store	NA (no store vectorizable/vectorized instructions)
mul	25%
add-sub	16%
fma	12%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	18%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 3.00 cycles. At this rate:

8% of peak load performance is reached (16.00 out of 192.00 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: 40cb09

Instruction	Nb FU	P0	P1	P2	P3	P5	P6	P10	P11	Latency	Recip. throughput	Vectorization
ADD $0x18,%R15	1	0	0	0	0	0	0	0	0	1	0.17	N/A
CMP %R15,%R12	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1	0.20	N/A
JE 40cac0 <ljForce.extracted+0x2a0>	1	0.50	0	0	0	0	0.50	0	0	0	0.50	N/A
VMOVUPD (%RAX),%XMM11	1	0	0	0.33	0.33	0	0	0	0.33	0-1	0.33	vect (25.0%)
VSUBPD -0x10(%R13,%R15,1),%XMM11,%XMM11	1	0	0.50	0.33	0.33	0.50	0	0	0.33	3	0.50	vect (25.0%)
VMULPD %XMM11,%XMM11,%XMM12	1	0.50	0.50	0	0	0	0	0	0	4	0.50	vect (25.0%)
VSHUFPD $0x1,%XMM12,%XMM12,%XMM13	1	0	0.50	0	0	0.50	0	0	0	1	0.50	vect (25.0%)
VADDSD %XMM12,%XMM13,%XMM13	1	0	0.50	0	0	0.50	0	0	0	3	0.50	scal (12.5%)
VMOVSD 0x10(%RAX),%XMM12	1	0	0	0.33	0.33	0	0	0	0.33	1	0.33	scal (12.5%)
VSUBSD (%R13,%R15,1),%XMM12,%XMM12	1	0	0.50	0.33	0.33	0.50	0	0	0.33	3	0.50	scal (12.5%)
VFMADD231SD %XMM12,%XMM12,%XMM13	1	0.50	0.50	0	0	0	0	0	0	4	0.50	scal (12.5%)
VUCOMISD %XMM13,%XMM2	1	1	0	0	0	0	0	0	0	3	1	scal (12.5%)
JB 40cb00 <ljForce.extracted+0x2e0>	1	0.50	0	0	0	0	0.50	0	0	0	0.50	N/A

Function	ljForce.extracted
Source file and lines	ljForce.c:191-216
Module	exec

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 15% of vector register length is used (average across all SSE/AVX instructions). By fully vectorizing your loop, you can lower the cost of an iteration from 9.50 to 2.00 cycles (4.75x speedup).

Details

23% of SSE/AVX instructions are used in vector version (process two or more data elements in vector registers):

42% of SSE/AVX loads are used in vector version.
33% of SSE/AVX stores are used in vector version.
16% of SSE/AVX addition or subtraction instructions are used in vector version.
12% of SSE/AVX multiply instructions are used in vector version.
20% of SSE/AVX fused multiply-add instructions are used in vector version.
0% of SSE/AVX divide and square root instructions are used in vector version.
40% of SSE/AVX 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:
- 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 9.50 to 9.00 cycles (1.06x speedup).

Workaround

Reduce the number of FP multiply/FMA instructions

FMA

Detected 6 FMA (fused multiply-add) operations. Presence of both ADD/SUB and MUL operations.

Workaround

Slow data structures access

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

Details

Constant unknown stride: 2 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)

Type of elements and instruction set

19 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time). 3 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 29 FP arithmetical operations:

13: addition or subtraction (6 inside FMA instructions)
15: multiply (6 inside FMA instructions)
1: divide

The binary loop is loading 96 bytes (12 double precision FP elements). The binary loop is storing 32 bytes (4 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.23 FP operations per loaded or stored byte.

General properties

nb instructions	38
nb uops	38
loop length	186
used x86 registers	8
used mmx registers	0
used xmm registers	17
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	0.75

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	7.17 cycles
front end	7.17 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	9.00	9.00	3.00	3.00	1.50	6.00	3.00	1.50	1.50	1.50	1.00	3.00
cycles	9.00	9.50	3.00	3.00	1.50	6.00	3.00	1.50	1.50	1.50	1.00	3.00

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	4.00
Longest recurrence chain latency (RecMII)	3.00

Cycles summary

Front-end	7.17
Dispatch	9.50
DIV/SQRT	4.00
Data deps.	3.00
Overall L1	9.50

Vectorization ratios

all	23%
load	42%
store	33%
mul	12%
add-sub	16%
fma	20%
div/sqrt	0%
other	40%

Vector efficiency ratios

all	15%
load	17%
store	16%
mul	14%
add-sub	14%
fma	15%
div/sqrt	12%
other	17%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 9.50 cycles. At this rate:

5% of peak load performance is reached (10.11 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))
2% of peak store performance is reached (3.37 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: 40cb09

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	Latency	Recip. throughput	Vectorization
ADD $0x18,%R15	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
CMP %R15,%R12	1	0.20	0.20	0	0	0	0.20	0.20	0	0	0	0.20	0	1	0.20	N/A
JE 40cac0 <ljForce.extracted+0x2a0>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	N/A
VMOVUPD (%RAX),%XMM11	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	0-1	0.33	vect (25.0%)
VSUBPD -0x10(%R13,%R15,1),%XMM11,%XMM11	1	0	0.50	0.33	0.33	0	0.50	0	0	0	0	0	0.33	3	0.50	vect (25.0%)
VMULPD %XMM11,%XMM11,%XMM12	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	vect (25.0%)
VSHUFPD $0x1,%XMM12,%XMM12,%XMM13	1	0	0.50	0	0	0	0.50	0	0	0	0	0	0	1	0.50	vect (25.0%)
VADDSD %XMM12,%XMM13,%XMM13	1	0	0.50	0	0	0	0.50	0	0	0	0	0	0	3	0.50	scal (12.5%)
VMOVSD 0x10(%RAX),%XMM12	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	scal (12.5%)
VSUBSD (%R13,%R15,1),%XMM12,%XMM12	1	0	0.50	0.33	0.33	0	0.50	0	0	0	0	0	0.33	3	0.50	scal (12.5%)
VFMADD231SD %XMM12,%XMM12,%XMM13	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
VUCOMISD %XMM13,%XMM2	1	1	0	0	0	0	0	0	0	0	0	0	0	3	1	scal (12.5%)
JB 40cb00 <ljForce.extracted+0x2e0>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	N/A
VUCOMISD %XMM4,%XMM13	1	1	0	0	0	0	0	0	0	0	0	0	0	3	1	scal (12.5%)
JBE 40cb00 <ljForce.extracted+0x2e0>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	N/A
VDIVSD %XMM13,%XMM6,%XMM13	1	1	0	0	0	0	0	0	0	0	0	0	0	13-15	4	scal (12.5%)
VMULSD %XMM13,%XMM13,%XMM14	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
VMULSD %XMM1,%XMM13,%XMM15	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
VMULSD %XMM15,%XMM14,%XMM14	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
VADDSD %XMM7,%XMM14,%XMM15	1	0	0.50	0	0	0	0.50	0	0	0	0	0	0	3	0.50	scal (12.5%)
VFNMADD213SD %XMM0,%XMM14,%XMM15	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
VMULSD %XMM8,%XMM15,%XMM15	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
MOV 0x30(%R11),%RDX	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
VADDSD (%RDX,%RSI,8),%XMM15,%XMM16	1	0	0.50	0.33	0.33	0	0.50	0	0	0	0	0	0.33	3	0.50	scal (12.5%)
VMOVSD %XMM16,(%RDX,%RSI,8)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	1	0.50	scal (12.5%)
VMOVAPD %XMM9,%XMM16	1	0	0	0	0	0	0	0	0	0	0	0	0	0-1	0.17	vect (25.0%)
VFMADD213SD %XMM10,%XMM14,%XMM16	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
VMULSD %XMM3,%XMM13,%XMM13	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
VMULSD %XMM14,%XMM13,%XMM13	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
VMULSD %XMM16,%XMM13,%XMM13	1	0.50	0.50	0	0	0	0	0	0	0	0	0	0	4	0.50	scal (12.5%)
MOV 0x28(%R11),%RDX	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
VMOVDDUP %XMM13,%XMM14	1	0	0	0	0	0	1	0	0	0	0	0	0	1	1	scal (12.5%)
VFMADD213PD (%RDX,%RCX,8),%XMM14,%XMM11	1	0.50	0.50	0.33	0.33	0	0	0	0	0	0	0	0.33	4	0.50	vect (25.0%)
VMOVUPD %XMM11,(%RDX,%RCX,8)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	0-1	0.50	vect (25.0%)
VFMADD213SD 0x10(%RDX,%RCX,8),%XMM13,%XMM12	1	0.50	0.50	0.33	0.33	0	0	0	0	0	0	0	0.33	4	0.50	scal (12.5%)
VMOVSD %XMM12,0x10(%RDX,%RCX,8)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	1	0.50	scal (12.5%)
VADDSD %XMM5,%XMM15,%XMM5	1	0	0.50	0	0	0	0.50	0	0	0	0	0	0	3	0.50	scal (12.5%)
JMP 40cb00 <ljForce.extracted+0x2e0>	1	0	0	0	0	0	0	0	0	0	0	0	0	0	2.08	N/A

Function	ljForce.extracted
Source file and lines	ljForce.c:191-216
Module	exec

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 17% of vector register length is used (average across all SSE/AVX instructions). By fully vectorizing your loop, you can lower the cost of an iteration from 3.00 to 0.50 cycles (6.00x speedup).

Details

40% of SSE/AVX instructions are used in vector version (process two or more data elements in vector registers):

50% of SSE/AVX loads are used in vector version.
33% of SSE/AVX addition or subtraction instructions are used in vector version.
0% of SSE/AVX fused multiply-add instructions are used in vector version.
33% of SSE/AVX 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:
- 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

Detected 1 FMA (fused multiply-add) operations. Presence of both ADD/SUB and MUL operations.

Workaround

Type of elements and instruction set

5 SSE or AVX instructions are processing arithmetic or math operations on double precision FP elements in scalar mode (one at a time). 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 8 FP arithmetical operations:

5: addition or subtraction (1 inside FMA instructions)
3: multiply (1 inside FMA instructions)

The binary loop is loading 48 bytes (6 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.17 FP operations per loaded or stored byte.

General properties

nb instructions	15
nb uops	15
loop length	66
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	3.00

Front-end

MACRO FUSION NOT POSSIBLE FIT IN UOP CACHE

micro-operation queue	2.83 cycles
front end	2.83 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	3.00	2.50	1.33	1.33	0.00	2.50	3.00	0.00	0.00	0.00	1.00	1.33
cycles	3.00	2.50	1.33	1.33	0.00	2.50	3.00	0.00	0.00	0.00	1.00	1.33

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)	3.00

Cycles summary

Front-end	2.83
Dispatch	3.00
Data deps.	3.00
Overall L1	3.00

Vectorization ratios

all	40%
load	50%
store	NA (no store vectorizable/vectorized instructions)
mul	100%
add-sub	33%
fma	0%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	33%

Vector efficiency ratios

all	17%
load	18%
store	NA (no store vectorizable/vectorized instructions)
mul	25%
add-sub	16%
fma	12%
div/sqrt	NA (no div/sqrt vectorizable/vectorized instructions)
other	16%

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 3.00 cycles. At this rate:

8% of peak load performance is reached (16.00 out of 192.00 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: 40cb09

Instruction	Nb FU	P0	P1	P2	P3	P5	P6	P10	P11	Latency	Recip. throughput	Vectorization
ADD $0x18,%R15	1	0	0	0	0	0	0	0	0	1	0.17	N/A
CMP %R15,%R12	1	0.20	0.20	0	0	0.20	0.20	0.20	0	1	0.20	N/A
JE 40cac0 <ljForce.extracted+0x2a0>	1	0.50	0	0	0	0	0.50	0	0	0	0.50	N/A
VMOVUPD (%RAX),%XMM11	1	0	0	0.33	0.33	0	0	0	0.33	0-1	0.33	vect (25.0%)
VSUBPD -0x10(%R13,%R15,1),%XMM11,%XMM11	1	0	0.50	0.33	0.33	0.50	0	0	0.33	3	0.50	vect (25.0%)
VMULPD %XMM11,%XMM11,%XMM12	1	0.50	0.50	0	0	0	0	0	0	4	0.50	vect (25.0%)
VSHUFPD $0x1,%XMM12,%XMM12,%XMM13	1	0	0.50	0	0	0.50	0	0	0	1	0.50	vect (25.0%)
VADDSD %XMM12,%XMM13,%XMM13	1	0	0.50	0	0	0.50	0	0	0	3	0.50	scal (12.5%)
VMOVSD 0x10(%RAX),%XMM12	1	0	0	0.33	0.33	0	0	0	0.33	1	0.33	scal (12.5%)
VSUBSD (%R13,%R15,1),%XMM12,%XMM12	1	0	0.50	0.33	0.33	0.50	0	0	0.33	3	0.50	scal (12.5%)
VFMADD231SD %XMM12,%XMM12,%XMM13	1	0.50	0.50	0	0	0	0	0	0	4	0.50	scal (12.5%)
VUCOMISD %XMM13,%XMM2	1	1	0	0	0	0	0	0	0	3	1	scal (12.5%)
JB 40cb00 <ljForce.extracted+0x2e0>	1	0.50	0	0	0	0	0.50	0	0	0	0.50	N/A
VUCOMISD %XMM4,%XMM13	1	1	0	0	0	0	0	0	0	3	1	scal (12.5%)
JBE 40cb00 <ljForce.extracted+0x2e0>	1	0.50	0	0	0	0	0.50	0	0	0	0.50	N/A

Report Configuration

Vectorization

Details

Workaround

FMA

Workaround

Slow data structures access

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

Vectorization

Details

Workaround

Execution units bottlenecks

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

Slow data structures access

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

FMA

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