OV - exec - Loop 371

	Loop Id: 371	Module: exec	Source: ams.c:3664-3682	Coverage: 15.05%

0x24d7e0 INC	%RAX

0x24d7e3 CMP	%R13,%RAX

0x24d7e6 JG	24d88f

0x24d7ec MOV	(%RSI,%RAX,8),%RDI

0x24d7f0 MOV	-0x58(%RBP),%RBX

0x24d7f4 VMOVSD	(%RDX,%RDI,8),%XMM0

0x24d7f9 VUCOMISD	(%RBX),%XMM0

0x24d7fd JNE	24d801

0x24d7ff JNP	24d7e0

0x24d801 MOV	-0x50(%RBP),%RBX

0x24d805 MOV	0x8(%RSI,%RAX,8),%R14

0x24d80a VMOVSD	(%RBX,%RAX,8),%XMM0

0x24d80f CMP	%R14,%RDI

0x24d812 JGE	24d837

0x24d814 NOPW	%CS:(%RAX,%RAX,1)

  (373) 0x24d820 MOV	(%R8,%RDI,8),%RBX

  (373) 0x24d824 VMOVSD	(%RDX,%RDI,8),%XMM1

  (373) 0x24d829 INC	%RDI

  (373) 0x24d82c VFNMADD231SD	(%R9,%RBX,8),%XMM1,%XMM0

  (373) 0x24d832 CMP	%RDI,%R14

  (373) 0x24d835 JNE	24d820

0x24d837 MOV	(%R10,%RAX,8),%RDI

0x24d83b MOV	0x8(%R10,%RAX,8),%R14

0x24d840 CMP	%R14,%RDI

0x24d843 JGE	24d868

0x24d845 NOPW	%CS:(%RAX,%RAX,1)

  (372) 0x24d850 MOV	(%R11,%RDI,8),%RBX

  (372) 0x24d854 VMOVSD	(%R15,%RDI,8),%XMM1

  (372) 0x24d85a INC	%RDI

  (372) 0x24d85d VFNMADD231SD	(%R12,%RBX,8),%XMM1,%XMM0

  (372) 0x24d863 CMP	%RDI,%R14

  (372) 0x24d866 JNE	24d850

0x24d868 MOV	0x50(%RBP),%RDI

0x24d86c MOV	-0x48(%RBP),%RBX

0x24d870 VMULSD	(%RDI),%XMM0,%XMM0

0x24d874 VDIVSD	(%RBX,%RAX,8),%XMM0,%XMM0

0x24d879 VADDSD	(%RCX,%RAX,8),%XMM0,%XMM0

0x24d87e VMOVSD	%XMM0,(%RCX,%RAX,8)

0x24d883 INC	%RAX

0x24d886 CMP	%R13,%RAX

0x24d889 JLE	24d7ec

/home/eoseret/qaas_runs_ZEN5/173-989-6379/intel/AMG/build/AMG/AMG/parcsr_ls/ams.c: 3664 - 3682

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

3664:       for (i = 0; i < n; i++)

3665:       {

3666:          /*-----------------------------------------------------------

3667:           * If diagonal is nonzero, relax point i; otherwise, skip it.

3668:           *-----------------------------------------------------------*/

3669:          if (A_diag_data[A_diag_i[i]] != zero)

3670:          {

3671:             res = f_data[i];

3672:             for (jj = A_diag_i[i]; jj < A_diag_i[i+1]; jj++)

3673:             {

3674:                ii = A_diag_j[jj];

3675:                res -= A_diag_data[jj] * Vtemp_data[ii];

3676:             }

3677:             for (jj = A_offd_i[i]; jj < A_offd_i[i+1]; jj++)

3678:             {

3679:                ii = A_offd_j[jj];

3680:                res -= A_offd_data[jj] * Vext_data[ii];

3681:             }

3682:             u_data[i] += (relax_weight*res)/l1_norms[i];

Coverage (%)	Name	Source Location	Module
►96.47+	__kmp_invoke_microtask		libomp.so
○	__kmp_invoke_task_func		libomp.so
○	__kmp_launch_thread		libomp.so
○	__kmp_launch_worker(void*)		libomp.so
○	start_thread		libc.so.6
○	__GI___clone3		libc.so.6
►2.81+	__kmp_invoke_microtask		libomp.so
○	__kmp_invoke_task_func		libomp.so
○	__kmp_fork_call		libomp.so
○	__kmpc_fork_call		libomp.so
○	hypre_ParCSRRelaxThreads	ams.c:3662	exec
○	hypre_BoomerAMGCycle	par_cycle.c:334	exec
○	hypre_BoomerAMGSolve	par_amg_solve.c:243	exec
○	hypre_PCGSolve	pcg.c:545	exec
○	main	amg.c:419	exec
○	__libc_start_call_main		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	1.64
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.07
Bottlenecks	P10, P11,
Function	hypre_ParCSRRelaxThreads.omp_outlined.28
Source	ams.c:3664-3664,ams.c:3669-3672,ams.c:3677-3677,ams.c:3682-3682
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	4.00
CQA cycles if no scalar integer	4.00
CQA cycles if FP arith vectorized	2.44
CQA cycles if fully vectorized	0.50
Front-end cycles	3.38
P0 cycles	1.67
P1 cycles	1.67
P2 cycles	1.67
P3 cycles	2.00
P4 cycles	2.00
P5 cycles	2.00
P6 cycles	3.75
P7 cycles	3.75
P8 cycles	3.75
P9 cycles	3.75
P10 cycles	1.00
P11 cycles	1.00
P12 cycles	1.00
P13 cycles	1.00
P14 cycles	1.00
P15 cycles	1.00
DIV/SQRT cycles	4.00
Inter-iter dependencies cycles	NA
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	29.00
Nb uops	27.00
Nb loads	14.00
Nb stores	1.00
Nb stack references	4.00
FLOP/cycle	0.75
Nb FLOP add-sub	1.00
Nb FLOP mul	1.00
Nb FLOP fma	0.00
Nb FLOP div	1.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	30.00
Bytes prefetched	0.00
Bytes loaded	112.00
Bytes stored	8.00
Stride 0	NA
Stride 1	NA
Stride n	NA
Stride unknown	NA
Stride indirect	NA
Vectorization ratio all	0.00
Vectorization ratio load	0.00
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	0.00
Vectorization ratio other	0.00
Vector-efficiency ratio all	12.50
Vector-efficiency ratio load	12.50
Vector-efficiency ratio store	12.50
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	12.50
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	12.50
Vector-efficiency ratio other	12.50

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	1.64
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.07
Bottlenecks	P10, P11,
Function	hypre_ParCSRRelaxThreads.omp_outlined.28
Source	ams.c:3664-3664,ams.c:3669-3672,ams.c:3677-3677,ams.c:3682-3682
Source loop unroll info	NA
Source loop unroll confidence level	NA
Unroll/vectorization loop type	NA
Unroll factor	NA
CQA cycles	4.00
CQA cycles if no scalar integer	4.00
CQA cycles if FP arith vectorized	2.44
CQA cycles if fully vectorized	0.50
Front-end cycles	3.38
P0 cycles	1.67
P1 cycles	1.67
P2 cycles	1.67
P3 cycles	2.00
P4 cycles	2.00
P5 cycles	2.00
P6 cycles	3.75
P7 cycles	3.75
P8 cycles	3.75
P9 cycles	3.75
P10 cycles	1.00
P11 cycles	1.00
P12 cycles	1.00
P13 cycles	1.00
P14 cycles	1.00
P15 cycles	1.00
DIV/SQRT cycles	4.00
Inter-iter dependencies cycles	NA
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	29.00
Nb uops	27.00
Nb loads	14.00
Nb stores	1.00
Nb stack references	4.00
FLOP/cycle	0.75
Nb FLOP add-sub	1.00
Nb FLOP mul	1.00
Nb FLOP fma	0.00
Nb FLOP div	1.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	30.00
Bytes prefetched	0.00
Bytes loaded	112.00
Bytes stored	8.00
Stride 0	NA
Stride 1	NA
Stride n	NA
Stride unknown	NA
Stride indirect	NA
Vectorization ratio all	0.00
Vectorization ratio load	0.00
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	0.00
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	0.00
Vectorization ratio other	0.00
Vector-efficiency ratio all	12.50
Vector-efficiency ratio load	12.50
Vector-efficiency ratio store	12.50
Vector-efficiency ratio mul	12.50
Vector-efficiency ratio add_sub	12.50
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	12.50
Vector-efficiency ratio other	12.50

Path /

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

Function	hypre_ParCSRRelaxThreads.omp_outlined.28
Source file and lines	ams.c:3664-3682
Module	exec

The loop is defined in /home/eoseret/qaas_runs_ZEN5/173-989-6379/intel/AMG/build/AMG/AMG/parcsr_ls/ams.c:3664-3682.

Analyzed code is defined in /home/eoseret/qaas_runs_ZEN5/173-989-6379/intel/AMG/build/AMG/AMG/parcsr_ls/ams.c:3664,3669-3672,3677,3682.

Warnings:

Non-innermost loop: analyzing only self part (ignoring child loops).
Ignoring paths for analysis
Too many paths. Rerun with max-paths=9
RecMII not computed since number of paths is unknown or > max_paths
Streams not analyzed since number of paths is unknown or > max_paths

Try to simplify control and/or increase the maximum number of paths per function/loop through the 'max-paths-nb' option.

This loop has 9 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 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 4.00 to 0.50 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 divide and square root operations (the divide/square root unit is a bottleneck). By removing all these bottlenecks, you can lower the cost of an iteration from 4.00 to 3.75 cycles (1.07x speedup).

Workaround

Reduce the number of division or square root instructions:
- If denominator is constant over iterations, use reciprocal (replace x/y with x*(1/y)). Check precision impact. This will be done by your compiler with ffast-math or Ofast
Check whether you really need double precision. If not, switch to single precision to speedup execution

Expensive FP math instructions/calls

Detected performance impact from expensive FP math instructions/calls. By removing/reexpressing them, you can lower the cost of an iteration from 4.00 to 3.50 cycles (1.14x speedup).

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).

Complex instructions

Detected COMPLEX INSTRUCTIONS.

Details

These instructions generate more than one micro-operation and only one of them can be decoded during a cycle and the extra micro-operations increase pressure on execution units.

VUCOMISD: 1 occurrences►
- /home/eoseret/qaas_runs_ZEN5/173-989-6379/intel/AMG/build/AMG/AMG/parcsr_ls/ams.c:3669

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).

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

The binary loop is composed of 3 FP arithmetical operations:

1: addition or subtraction
1: multiply
1: divide

The binary loop is loading 112 bytes (14 double precision FP elements). The binary loop is storing 8 bytes (1 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.02 FP operations per loaded or stored byte.

General properties

nb instructions	29
nb uops	27
loop length	128
used x86 registers	10
used mmx registers	0
used xmm registers	1
used ymm registers	0
used zmm registers	0
nb stack references	4
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	3.38 cycles
front end	3.38 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	1.67	1.67	1.67	2.00	2.00	2.00	3.75	3.75	3.75	3.75	1.00	1.00	1.00	1.00	1.00	1.00
cycles	1.67	1.67	1.67	2.00	2.00	2.00	3.75	3.75	3.75	3.75	1.00	1.00	1.00	1.00	1.00	1.00

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

4.00

Cycles summary

Front-end	3.38
Dispatch	3.75
DIV/SQRT	4.00
Overall L1	4.00

Vectorization ratios

INT

all	0%
load	0%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	0%

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

INT+FP

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

Vector efficiency ratios

INT

all	12%
load	12%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	12%

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

INT+FP

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

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 4.00 cycles. At this rate:

10% of peak load performance is reached (28.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (2.00 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: 24d7ec

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
INC %RAX	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 %R13,%RAX	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	scal (12.5%)
JG 24d88f <hypre_ParCSRRelaxThreads.omp_outlined.28+0x19f>	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
MOV (%RSI,%RAX,8),%RDI	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
MOV -0x58(%RBP),%RBX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
VMOVSD (%RDX,%RDI,8),%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	1	0.50	scal (12.5%)
VUCOMISD (%RBX),%XMM0	2	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	0.50	0.50	6	0.50	scal (12.5%)
JNE 24d801 <hypre_ParCSRRelaxThreads.omp_outlined.28+0x111>	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
JNP 24d7e0 <hypre_ParCSRRelaxThreads.omp_outlined.28+0xf0>	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
MOV -0x50(%RBP),%RBX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
MOV 0x8(%RSI,%RAX,8),%R14	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	scal (12.5%)
VMOVSD (%RBX,%RAX,8),%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	1	0.50	scal (12.5%)
CMP %R14,%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	scal (12.5%)
JGE 24d837 <hypre_ParCSRRelaxThreads.omp_outlined.28+0x147>	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
NOPW %CS:(%RAX,%RAX,1)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.09	N/A
MOV (%R10,%RAX,8),%RDI	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
MOV 0x8(%R10,%RAX,8),%R14	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	scal (12.5%)
CMP %R14,%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	scal (12.5%)
JGE 24d868 <hypre_ParCSRRelaxThreads.omp_outlined.28+0x178>	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
NOPW %CS:(%RAX,%RAX,1)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.09	N/A
MOV 0x50(%RBP),%RDI	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
MOV -0x48(%RBP),%RBX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
VMULSD (%RDI),%XMM0,%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	0	0	3	0.50	scal (12.5%)
VDIVSD (%RBX,%RAX,8),%XMM0,%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	0	0	13	4	scal (12.5%)
VADDSD (%RCX,%RAX,8),%XMM0,%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	0	0	2	0.50	scal (12.5%)
VMOVSD %XMM0,(%RCX,%RAX,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0.50	0.50	1	0.50	scal (12.5%)
INC %RAX	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 %R13,%RAX	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
JLE 24d7ec <hypre_ParCSRRelaxThreads.omp_outlined.28+0xfc>	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	hypre_ParCSRRelaxThreads.omp_outlined.28
Source file and lines	ams.c:3664-3682
Module	exec

Non-innermost loop: analyzing only self part (ignoring child loops).
Ignoring paths for analysis
Too many paths. Rerun with max-paths=9
RecMII not computed since number of paths is unknown or > max_paths
Streams not analyzed since number of paths is unknown or > max_paths

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
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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 4.00 to 0.50 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 division or square root instructions:
- If denominator is constant over iterations, use reciprocal (replace x/y with x*(1/y)). Check precision impact. This will be done by your compiler with ffast-math or Ofast
Check whether you really need double precision. If not, switch to single precision to speedup execution

Expensive FP math instructions/calls

Detected performance impact from expensive FP math instructions/calls. By removing/reexpressing them, you can lower the cost of an iteration from 4.00 to 3.50 cycles (1.14x speedup).

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).

Complex instructions

Detected COMPLEX INSTRUCTIONS.

Details

These instructions generate more than one micro-operation and only one of them can be decoded during a cycle and the extra micro-operations increase pressure on execution units.

VUCOMISD: 1 occurrences►
- /home/eoseret/qaas_runs_ZEN5/173-989-6379/intel/AMG/build/AMG/AMG/parcsr_ls/ams.c:3669

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).

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

The binary loop is composed of 3 FP arithmetical operations:

1: addition or subtraction
1: multiply
1: divide

The binary loop is loading 112 bytes (14 double precision FP elements). The binary loop is storing 8 bytes (1 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.02 FP operations per loaded or stored byte.

General properties

nb instructions	29
nb uops	27
loop length	128
used x86 registers	10
used mmx registers	0
used xmm registers	1
used ymm registers	0
used zmm registers	0
nb stack references	4
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	3.38 cycles
front end	3.38 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	1.67	1.67	1.67	2.00	2.00	2.00	3.75	3.75	3.75	3.75	1.00	1.00	1.00	1.00	1.00	1.00
cycles	1.67	1.67	1.67	2.00	2.00	2.00	3.75	3.75	3.75	3.75	1.00	1.00	1.00	1.00	1.00	1.00

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

4.00

Cycles summary

Front-end	3.38
Dispatch	3.75
DIV/SQRT	4.00
Overall L1	4.00

Vectorization ratios

INT

all	0%
load	0%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	0%

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

INT+FP

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

Vector efficiency ratios

INT

all	12%
load	12%
store	NA (no store vectorizable/vectorized instructions)
mul	NA (no mul vectorizable/vectorized instructions)
add-sub	NA (no add-sub vectorizable/vectorized instructions)
fma	NA (no fma vectorizable/vectorized instructions)
other	12%

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

INT+FP

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

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 4.00 cycles. At this rate:

10% of peak load performance is reached (28.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
1% of peak store performance is reached (2.00 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: 24d7ec

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
INC %RAX	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 %R13,%RAX	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	scal (12.5%)
JG 24d88f <hypre_ParCSRRelaxThreads.omp_outlined.28+0x19f>	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
MOV (%RSI,%RAX,8),%RDI	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
MOV -0x58(%RBP),%RBX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
VMOVSD (%RDX,%RDI,8),%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	1	0.50	scal (12.5%)
VUCOMISD (%RBX),%XMM0	2	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	0.50	0.50	6	0.50	scal (12.5%)
JNE 24d801 <hypre_ParCSRRelaxThreads.omp_outlined.28+0x111>	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
JNP 24d7e0 <hypre_ParCSRRelaxThreads.omp_outlined.28+0xf0>	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
MOV -0x50(%RBP),%RBX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
MOV 0x8(%RSI,%RAX,8),%R14	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	scal (12.5%)
VMOVSD (%RBX,%RAX,8),%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	1	0.50	scal (12.5%)
CMP %R14,%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	scal (12.5%)
JGE 24d837 <hypre_ParCSRRelaxThreads.omp_outlined.28+0x147>	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
NOPW %CS:(%RAX,%RAX,1)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.09	N/A
MOV (%R10,%RAX,8),%RDI	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
MOV 0x8(%R10,%RAX,8),%R14	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	scal (12.5%)
CMP %R14,%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	scal (12.5%)
JGE 24d868 <hypre_ParCSRRelaxThreads.omp_outlined.28+0x178>	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
NOPW %CS:(%RAX,%RAX,1)	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.09	N/A
MOV 0x50(%RBP),%RDI	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
MOV -0x48(%RBP),%RBX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0	0	3	0.25	N/A
VMULSD (%RDI),%XMM0,%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	0	0	3	0.50	scal (12.5%)
VDIVSD (%RBX,%RAX,8),%XMM0,%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	0	0	13	4	scal (12.5%)
VADDSD (%RCX,%RAX,8),%XMM0,%XMM0	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	0	0	2	0.50	scal (12.5%)
VMOVSD %XMM0,(%RCX,%RAX,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	0.50	0.50	1	0.50	scal (12.5%)
INC %RAX	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 %R13,%RAX	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
JLE 24d7ec <hypre_ParCSRRelaxThreads.omp_outlined.28+0xfc>	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

Workaround

Expensive FP math instructions/calls

FMA

Workaround

Complex instructions

Details

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

Expensive FP math instructions/calls

FMA

Workaround

Complex instructions

Details

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