OV - exec - Loop 4672

	Loop Id: 4672	Module: exec	Source: par_csr_matop.c:946-965 [...]	Coverage: 0.99%

0x55ad00 MOV	%RAX,(%RDI,%R10,8)    [1]

0x55ad04 MOVSD	%XMM1,(%R12,%RAX,8)    [3]

0x55ad0a MOV	-0x50(%RBP),%R9    [2]

0x55ad0e MOV	%R10,(%R9,%RAX,8)    [4]

0x55ad12 INC	%RAX

0x55ad15 MOV	-0x80(%RBP),%RDX    [2]

0x55ad19 MOV	0x8(%RDX,%RSI,8),%R9    [5]

0x55ad1e INC	%R8

0x55ad21 CMP	%R9,%R8

0x55ad24 JGE	55ad5f

0x55ad26 MOV	-0x110(%RBP),%RDX    [2]

0x55ad2d MOV	(%RDX,%R8,8),%R10    [7]

0x55ad31 MOV	(%RDI,%R10,8),%R11    [1]

0x55ad35 MOV	-0x108(%RBP),%RDX    [2]

0x55ad3c MOVSD	(%RDX,%R8,8),%XMM1    [6]

0x55ad42 MULSD	%XMM0,%XMM1

0x55ad46 CMP	%RBX,%R11

0x55ad49 JL	55ad00

0x55ad4b ADDSD	(%R12,%R11,8),%XMM1    [3]

0x55ad51 MOVSD	%XMM1,(%R12,%R11,8)    [3]

0x55ad57 INC	%R8

0x55ad5a CMP	%R9,%R8

0x55ad5d JL	55ad26

/home/eoseret/qaas_runs_ZEN5/173-989-6379/intel/AMG/build/AMG/AMG/parcsr_mv/par_csr_matop.c: 946 - 965

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

946:          for (jj3 = B_diag_i[i2]; jj3 < B_diag_i[i2+1]; jj3++)

947:          {

948:             i3 = B_diag_j[jj3];

[...]

956:             if (B_marker[i3] < jj_row_begin_diag)

957:             {

958:                B_marker[i3] = jj_count_diag;

959:                C_diag_data[jj_count_diag] = a_entry*B_diag_data[jj3];

960:                C_diag_j[jj_count_diag] = i3;

961:                jj_count_diag++;

962:             }

963:             else

964:             {

965:                C_diag_data[B_marker[i3]] += a_entry*B_diag_data[jj3];

Coverage (%)	Name	Source Location	Module
►96.76+	__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
►2.92+	__kmp_invoke_microtask		libiomp5.so
○	__kmp_invoke_task_func		libiomp5.so
○	__kmp_fork_call		libiomp5.so
○	__kmpc_fork_call		libiomp5.so
○	hypre_ParMatmul	par_csr_matop.c:829	exec
○	hypre_BoomerAMGSetup	par_amg_setup.c:1226	exec
○	hypre_PCGSetup	pcg.c:234	exec
○	main	amg.c:398	exec
○	__libc_start_call_main		libc.so.6
○	__libc_start_main		libc.so.6
○	_start		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	2.25
CQA speedup if FP arith vectorized	2.15
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.24
Bottlenecks
Function	hypre_ParMatmul.extracted.12
Source	par_csr_matop.c:946-948,par_csr_matop.c:956-965
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	2.25
CQA cycles if no scalar integer	1.00
CQA cycles if FP arith vectorized	1.05
CQA cycles if fully vectorized	0.28
Front-end cycles	1.81
P0 cycles	0.75
P1 cycles	0.75
P2 cycles	0.75
P3 cycles	0.75
P4 cycles	0.75
P5 cycles	0.75
P6 cycles	2.25
P7 cycles	2.25
P8 cycles	2.25
P9 cycles	2.25
P10 cycles	0.50
P11 cycles	0.50
P12 cycles	0.25
P13 cycles	0.25
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	15.50
Nb uops	14.50
Nb loads	7.00
Nb stores	2.00
Nb stack references	3.00
FLOP/cycle	0.67
Nb FLOP add-sub	0.50
Nb FLOP mul	1.00
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	32.00
Bytes prefetched	0.00
Bytes loaded	56.00
Bytes stored	16.00
Stride 0	1.00
Stride 1	3.00
Stride n	0.00
Stride unknown	0.50
Stride indirect	1.50
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	NA
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	NA
Vector-efficiency ratio other	12.50

Metric	Value
CQA speedup if no scalar integer	1.75
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	1.17
Bottlenecks	P6, P7, P8, P9,
Function	hypre_ParMatmul.extracted.12
Source	par_csr_matop.c:946-948,par_csr_matop.c:956-965
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	1.75
CQA cycles if no scalar integer	1.00
CQA cycles if FP arith vectorized	0.88
CQA cycles if fully vectorized	0.22
Front-end cycles	1.50
P0 cycles	0.67
P1 cycles	0.67
P2 cycles	0.67
P3 cycles	0.67
P4 cycles	0.67
P5 cycles	0.67
P6 cycles	1.75
P7 cycles	1.75
P8 cycles	1.75
P9 cycles	1.75
P10 cycles	0.50
P11 cycles	0.50
P12 cycles	0.50
P13 cycles	0.50
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	13.00
Nb uops	12.00
Nb loads	6.00
Nb stores	1.00
Nb stack references	2.00
FLOP/cycle	1.14
Nb FLOP add-sub	1.00
Nb FLOP mul	1.00
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	32.00
Bytes prefetched	0.00
Bytes loaded	48.00
Bytes stored	8.00
Stride 0	1.00
Stride 1	2.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	2.00
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	NA
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	NA
Vector-efficiency ratio other	12.50

Metric	Value
CQA speedup if no scalar integer	2.75
CQA speedup if FP arith vectorized	2.26
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.29
Bottlenecks	P6, P7, P8, P9,
Function	hypre_ParMatmul.extracted.12
Source	par_csr_matop.c:946-948,par_csr_matop.c:956-965
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	2.75
CQA cycles if no scalar integer	1.00
CQA cycles if FP arith vectorized	1.22
CQA cycles if fully vectorized	0.34
Front-end cycles	2.13
P0 cycles	0.83
P1 cycles	0.83
P2 cycles	0.83
P3 cycles	0.83
P4 cycles	0.83
P5 cycles	0.83
P6 cycles	2.75
P7 cycles	2.75
P8 cycles	2.75
P9 cycles	2.75
P10 cycles	0.50
P11 cycles	0.50
P12 cycles	0.00
P13 cycles	0.00
P14 cycles	0.50
P15 cycles	0.50
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	18.00
Nb uops	17.00
Nb loads	8.00
Nb stores	3.00
Nb stack references	4.00
FLOP/cycle	0.36
Nb FLOP add-sub	0.00
Nb FLOP mul	1.00
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	32.00
Bytes prefetched	0.00
Bytes loaded	64.00
Bytes stored	24.00
Stride 0	1.00
Stride 1	4.00
Stride n	0.00
Stride unknown	1.00
Stride indirect	1.00
Vectorization ratio all	0.00
Vectorization ratio load	0.00
Vectorization ratio store	0.00
Vectorization ratio mul	0.00
Vectorization ratio add_sub	NA
Vectorization ratio fma	NA
Vectorization ratio div_sqrt	NA
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	NA
Vector-efficiency ratio fma	NA
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	12.50

Path /

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

Function	hypre_ParMatmul.extracted.12
Source file and lines	par_csr_matop.c:946-965
Module	exec

The loop is defined in /home/eoseret/qaas_runs_ZEN5/173-989-6379/intel/AMG/build/AMG/AMG/parcsr_mv/par_csr_matop.c:946-948,956-965.

The related source loop is not unrolled or unrolled with no peel/tail loop.
The structure of this loop is probably <if then [else] end>.

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 2.25 to 0.28 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)

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).

Slow data structures access

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

Details

Constant unknown stride: 0 occurrence(s)
Irregular (variable stride) or indirect: 1 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)
Try to remove indirect accesses. If applicable, precompute elements out of the innermost loop.

Type of elements and instruction set

1 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 1.5 FP arithmetical operations:

0.50: addition or subtraction
1: multiply

The binary loop is loading 56 bytes (7 double precision FP elements). The binary loop is storing 16 bytes (2 double precision FP elements).

Arithmetic intensity

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

Unroll opportunity

Loop is 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	15.50
nb uops	14.50
loop length	66
used x86 registers	10
used mmx registers	0
used xmm registers	2
used ymm registers	0
used zmm registers	0
nb stack references	3
ADD-SUB / MUL ratio	1.00

Front-end

MACRO FUSION NOT POSSIBLE

micro-operation queue	1.81 cycles
front end	1.81 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	0.75	0.75	0.75	0.75	0.75	0.75	2.25	2.25	2.25	2.25	0.50	0.50	0.25	0.25	0.50	0.50
cycles	0.75	0.75	0.75	0.75	0.75	0.75	2.25	2.25	2.25	2.25	0.50	0.50	0.25	0.25	0.50	0.50

Execution ports to units layout:

P0: ALU
P1: ALU
P2: ALU
P3: ALU, BRU
P4: ALU, BRU
P5: ALU, BRU
P6 (512 bits): store address, load
P7 (512 bits): store address, load
P8 (512 bits): store address, load
P9 (512 bits): store address, load
P10 (512 bits): VPU, DIV/SQRT
P11 (512 bits): VPU, DIV/SQRT
P12 (512 bits): VPU
P13 (512 bits): VPU
P14 (512 bits): FP store data
P15 (512 bits): FP store data

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

Cycles summary

Front-end	1.81
Dispatch	2.25
Data deps.	1.00
Overall L1	2.25

Vectorization ratios

INT

all	0%
load	NA (no load vectorizable/vectorized instructions)
store	0%
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	NA (no div/sqrt vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

INT+FP

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

Vector efficiency ratios

INT

all	12%
load	NA (no load vectorizable/vectorized instructions)
store	12%
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	NA (no div/sqrt vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

INT+FP

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

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 2.25 cycles. At this rate:

9% of peak load performance is reached (25.35 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
5% of peak store performance is reached (6.65 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Function	hypre_ParMatmul.extracted.12
Source file and lines	par_csr_matop.c:946-965
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

Code clean check

Detected a slowdown caused by scalar integer instructions (typically used for address computation). By removing them, you can lower the cost of an iteration from 1.75 to 1.00 cycles (1.75x speedup).

Workaround

Try to reorganize arrays of structures to structures of arrays
Consider to permute loops (see vectorization gain report)

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 1.75 to 0.22 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:

reading data from caches/RAM (load units are a bottleneck)
writing data to caches/RAM (the store unit is a bottleneck)

By removing all these bottlenecks, you can lower the cost of an iteration from 1.75 to 1.50 cycles (1.17x speedup).

Workaround

Read less array elements
Write less array elements
Provide more information to your compiler:
- hardcode the bounds of the corresponding 'for' loop
- use the 'restrict' C99 keyword

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).

Slow data structures access

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

Details

Irregular (variable stride) or indirect: 2 occurrence(s)

Non-unit stride (uncontiguous) accesses are not efficiently using data caches

Workaround

Try to remove indirect accesses. If applicable, precompute elements out of the innermost loop.

Type of elements and instruction set

2 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 2 FP arithmetical operations:

1: addition or subtraction
1: multiply

The binary loop is loading 48 bytes (6 double precision FP elements). The binary loop is storing 8 bytes (1 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.04 FP operations per loaded or stored byte.

Unroll opportunity

Loop is data access bound.

Workaround

General properties

nb instructions	13
nb uops	12
loop length	57
used x86 registers	9
used mmx registers	0
used xmm registers	2
used ymm registers	0
used zmm registers	0
nb stack references	2
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.50 cycles
front end	1.50 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	0.67	0.67	0.67	0.67	0.67	0.67	1.75	1.75	1.75	1.75	0.50	0.50	0.50	0.50	0.50	0.50
cycles	0.67	0.67	0.67	0.67	0.67	0.67	1.75	1.75	1.75	1.75	0.50	0.50	0.50	0.50	0.50	0.50

Execution ports to units layout:

P0: ALU
P1: ALU
P2: ALU
P3: ALU, BRU
P4: ALU, BRU
P5: ALU, BRU
P6 (512 bits): store address, load
P7 (512 bits): store address, load
P8 (512 bits): store address, load
P9 (512 bits): store address, load
P10 (512 bits): VPU, DIV/SQRT
P11 (512 bits): VPU, DIV/SQRT
P12 (512 bits): VPU
P13 (512 bits): VPU
P14 (512 bits): FP store data
P15 (512 bits): FP store data

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

Cycles summary

Front-end	1.50
Dispatch	1.75
Data deps.	1.00
Overall L1	1.75

Vectorization ratios

INT

all	0%
load	NA (no load vectorizable/vectorized instructions)
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	NA (no div/sqrt vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

INT+FP

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

Vector efficiency ratios

INT

all	12%
load	NA (no load vectorizable/vectorized instructions)
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	NA (no div/sqrt vectorizable/vectorized instructions)
other	NA (no other vectorizable/vectorized instructions)

INT+FP

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

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 1.75 cycles. At this rate:

10% of peak load performance is reached (27.43 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
3% of peak store performance is reached (4.57 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: 55ad26

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	Latency	Recip. throughput	Vectorization
MOV -0x110(%RBP),%RDX	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 (%RDX,%R8,8),%R10	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 (%RDI,%R10,8),%R11	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 -0x108(%RBP),%RDX	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
MOVSD (%RDX,%R8,8),%XMM1	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%)
MULSD %XMM0,%XMM1	1	0	0	0	0	0	0	0	0	0	0	0.50	0.50	0	0	0	0	3	0.50	scal (12.5%)
CMP %RBX,%R11	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%)
JL 55ad00 <hypre_ParMatmul.extracted.12+0x490>	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
ADDSD (%R12,%R11,8),%XMM1	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%)
MOVSD %XMM1,(%R12,%R11,8)	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 %R8	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 %R9,%R8	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
JL 55ad26 <hypre_ParMatmul.extracted.12+0x4b6>	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_ParMatmul.extracted.12
Source file and lines	par_csr_matop.c:946-965
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

Code clean check

Detected a slowdown caused by scalar integer instructions (typically used for address computation). By removing them, you can lower the cost of an iteration from 2.75 to 1.00 cycles (2.75x speedup).

Workaround

Try to reorganize arrays of structures to structures of arrays
Consider to permute loops (see vectorization gain report)

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 2.75 to 0.34 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:

reading data from caches/RAM (load units are a bottleneck)
writing data to caches/RAM (the store unit is a bottleneck)

By removing all these bottlenecks, you can lower the cost of an iteration from 2.75 to 2.13 cycles (1.29x speedup).

Workaround

Read less array elements
Write less array elements
Provide more information to your compiler:
- hardcode the bounds of the corresponding 'for' loop
- use the 'restrict' C99 keyword

No data for this section

Slow data structures access

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

Details

Constant unknown stride: 1 occurrence(s)
Irregular (variable stride) or indirect: 1 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)
Try to remove indirect accesses. If applicable, precompute elements out of the innermost loop.

Type of elements and instruction set

1 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 1 FP arithmetical operations:

1: multiply

The binary loop is loading 64 bytes (8 double precision FP elements). The binary loop is storing 24 bytes (3 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.01 FP operations per loaded or stored byte.

Unroll opportunity

Loop is data access bound.

Workaround

General properties

nb instructions	18
nb uops	17
loop length	75
used x86 registers	11
used mmx registers	0
used xmm registers	2
used ymm registers	0
used zmm registers	0
nb stack references	4

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	2.13 cycles
front end	2.13 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	0.83	0.83	0.83	0.83	0.83	0.83	2.75	2.75	2.75	2.75	0.50	0.50	0.00	0.00	0.50	0.50
cycles	0.83	0.83	0.83	0.83	0.83	0.83	2.75	2.75	2.75	2.75	0.50	0.50	0.00	0.00	0.50	0.50

Execution ports to units layout:

P0: ALU
P1: ALU
P2: ALU
P3: ALU, BRU
P4: ALU, BRU
P5: ALU, BRU
P6 (512 bits): store address, load
P7 (512 bits): store address, load
P8 (512 bits): store address, load
P9 (512 bits): store address, load
P10 (512 bits): VPU, DIV/SQRT
P11 (512 bits): VPU, DIV/SQRT
P12 (512 bits): VPU
P13 (512 bits): VPU
P14 (512 bits): FP store data
P15 (512 bits): FP store data

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

Cycles summary

Front-end	2.13
Dispatch	2.75
Data deps.	1.00
Overall L1	2.75

Vectorization ratios

INT

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

INT+FP

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

Vector efficiency ratios

INT

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

INT+FP

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

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 2.75 cycles. At this rate:

9% of peak load performance is reached (23.27 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
6% of peak store performance is reached (8.73 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: 55ad26

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P14	P15	Latency	Recip. throughput	Vectorization
MOV %RAX,(%RDI,%R10,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	4	0.50	scal (12.5%)
MOVSD %XMM1,(%R12,%RAX,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	1	0.50	scal (12.5%)
MOV -0x50(%RBP),%R9	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
MOV %R10,(%R9,%RAX,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	4	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	1	0.17	N/A
MOV -0x80(%RBP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
MOV 0x8(%RDX,%RSI,8),%R9	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
INC %R8	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
CMP %R9,%R8	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	scal (12.5%)
JGE 55ad5f <hypre_ParMatmul.extracted.12+0x4ef>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	1	0.50-1	N/A
MOV -0x110(%RBP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
MOV (%RDX,%R8,8),%R10	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
MOV (%RDI,%R10,8),%R11	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
MOV -0x108(%RBP),%RDX	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0	0	3	0.25	N/A
MOVSD (%RDX,%R8,8),%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%)
CMP %RBX,%R11	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
JL 55ad00 <hypre_ParMatmul.extracted.12+0x490>	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

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

Unroll opportunity

Workaround

General properties

Front-end

Back-end

Cycles summary

Vectorization ratios

Vector efficiency ratios

Cycles and memory resources usage

Code clean check

Workaround

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

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

Code clean check

Workaround

Vectorization

Details

Workaround

Execution units bottlenecks

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

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