OV - exec - Loop 4166

	Loop Id: 4166	Module: exec	Source: csr_matop.c:286-298	Coverage: 0.39%

0x4da3b0 VADDSD	(%R8,%R11,8),%XMM1,%XMM1    [1]

0x4da3b6 VMOVSD	%XMM1,(%R8,%R11,8)    [1]

0x4da3bc INC	%RDI

0x4da3bf CMP	%R9,%RDI

0x4da3c2 JGE	4da370

0x4da3c4 MOV	(%R15,%RDI,8),%R10    [8]

0x4da3c8 MOV	(%R12,%R10,8),%R11    [6]

0x4da3cc VMULSD	(%RBX,%RDI,8),%XMM0,%XMM1    [9]

0x4da3d1 CMP	%RCX,%R11

0x4da3d4 JGE	4da3b0

0x4da3d6 LEA	(%R12,%R10,8),%R9

0x4da3da MOV	%RAX,(%R9)    [2]

0x4da3dd MOV	-0x88(%RBP),%R11    [5]

0x4da3e4 MOV	(%R11),%R11    [4]

0x4da3e7 MOV	%R10,(%R11,%RAX,8)    [3]

0x4da3eb MOV	(%R9),%R9    [2]

0x4da3ee VMOVSD	%XMM1,(%R8,%R9,8)    [1]

0x4da3f4 INC	%RAX

0x4da3f7 MOV	0x8(%R14,%RSI,8),%R9    [7]

0x4da3fc INC	%RDI

0x4da3ff CMP	%R9,%RDI

0x4da402 JL	4da3c4

/home/eoseret/qaas_runs_GNR/173-927-0874/intel/AMG/build/AMG/AMG/seq_mv/csr_matop.c: 286 - 298

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

286: 	 for (ib = B_i[ja]; ib < B_i[ja+1]; ib++)

287: 	 {

288: 	    jb = B_j[ib];

289: 	    b_entry = B_data[ib];

290: 	    if (B_marker[jb] < row_start)

291: 	    {

292: 		B_marker[jb] = counter;

293: 		C_j[B_marker[jb]] = jb;

294: 		C_data[B_marker[jb]] = a_entry*b_entry;

295: 		counter++;

296: 	    }

297: 	    else

298: 		C_data[B_marker[jb]] += a_entry*b_entry;

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

Path /

Metric	Value
CQA speedup if no scalar integer	1.56
CQA speedup if FP arith vectorized	2.07
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.22
Bottlenecks
Function	hypre_CSRMatrixMultiply.extracted
Source	csr_matop.c:286-298
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	2.33
CQA cycles if no scalar integer	1.50
CQA cycles if FP arith vectorized	1.13
CQA cycles if fully vectorized	0.29
Front-end cycles	2.33
P0 cycles	1.50
P1 cycles	0.75
P2 cycles	1.83
P3 cycles	1.83
P4 cycles	1.00
P5 cycles	0.65
P6 cycles	1.00
P7 cycles	1.00
P8 cycles	1.00
P9 cycles	1.00
P10 cycles	0.60
P11 cycles	1.83
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	13.50
Nb uops	12.50
Nb loads	5.50
Nb stores	2.00
Nb stack references	0.50
FLOP/cycle	0.64
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	25.03
Bytes prefetched	0.00
Bytes loaded	44.00
Bytes stored	16.00
Stride 0	1.00
Stride 1	2.50
Stride n	0.00
Stride unknown	1.00
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	1.89
CQA speedup if FP arith vectorized	1.89
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.21
Bottlenecks	micro-operation queue,
Function	hypre_CSRMatrixMultiply.extracted
Source	csr_matop.c:286-298
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	2.83
CQA cycles if no scalar integer	1.50
CQA cycles if FP arith vectorized	1.50
CQA cycles if fully vectorized	0.35
Front-end cycles	2.83
P0 cycles	1.50
P1 cycles	0.50
P2 cycles	2.33
P3 cycles	2.33
P4 cycles	1.50
P5 cycles	0.60
P6 cycles	1.00
P7 cycles	1.50
P8 cycles	1.50
P9 cycles	1.50
P10 cycles	0.40
P11 cycles	2.33
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	17.00
Nb uops	16.00
Nb loads	7.00
Nb stores	3.00
Nb stack references	1.00
FLOP/cycle	0.35
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	28.24
Bytes prefetched	0.00
Bytes loaded	56.00
Bytes stored	24.00
Stride 0	2.00
Stride 1	3.00
Stride n	0.00
Stride unknown	2.00
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	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

Metric	Value
CQA speedup if no scalar integer	1.22
CQA speedup if FP arith vectorized	2.44
CQA speedup if fully vectorized	8.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.22
Bottlenecks	micro-operation queue,
Function	hypre_CSRMatrixMultiply.extracted
Source	csr_matop.c:286-298
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	1.83
CQA cycles if no scalar integer	1.50
CQA cycles if FP arith vectorized	0.75
CQA cycles if fully vectorized	0.23
Front-end cycles	1.83
P0 cycles	1.50
P1 cycles	1.00
P2 cycles	1.33
P3 cycles	1.33
P4 cycles	0.50
P5 cycles	0.70
P6 cycles	1.00
P7 cycles	0.50
P8 cycles	0.50
P9 cycles	0.50
P10 cycles	0.80
P11 cycles	1.33
DIV/SQRT cycles	0.00
Inter-iter dependencies cycles	1
FE+BE cycles (UFS)	NA
Stall cycles (UFS)	NA
Nb insns	10.00
Nb uops	9.00
Nb loads	4.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	1.09
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	21.82
Bytes prefetched	0.00
Bytes loaded	32.00
Bytes stored	8.00
Stride 0	0.00
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

Path /

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

Function	hypre_CSRMatrixMultiply.extracted
Source file and lines	csr_matop.c:286-298
Module	exec

The loop is defined in /home/eoseret/qaas_runs_GNR/173-927-0874/intel/AMG/build/AMG/AMG/seq_mv/csr_matop.c:286-298.

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 2.33 to 0.29 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: 1 occurrence(s)
Irregular (variable stride) or indirect: 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)
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 44 bytes (5 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	13.50
nb uops	12.50
loop length	51
used x86 registers	11
used mmx registers	0
used xmm registers	2
used ymm registers	0
used zmm registers	0
nb stack references	0.50

Front-end

MACRO FUSION NOT POSSIBLE

micro-operation queue	2.33 cycles
front end	2.33 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	1.50	0.75	1.83	1.83	1.00	0.65	1.00	1.00	1.00	1.00	0.60	1.83
cycles	1.50	0.75	1.83	1.83	1.00	0.65	1.00	1.00	1.00	1.00	0.60	1.83

Execution ports to units layout:

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

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

Cycles summary

Front-end	2.33
Dispatch	1.92
Data deps.	1.00
Overall L1	2.33

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 2.33 cycles. At this rate:

9% of peak load performance is reached (18.61 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))
5% of peak store performance is reached (6.42 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Function	hypre_CSRMatrixMultiply.extracted
Source file and lines	csr_matop.c:286-298
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 2.83 to 1.50 cycles (1.89x 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 2.83 to 0.35 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

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

No data for this section

Slow data structures access

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

Details

Constant unknown stride: 2 occurrence(s)
Irregular (variable stride) or indirect: 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)
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 56 bytes (7 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	17
nb uops	16
loop length	64
used x86 registers	13
used mmx registers	0
used xmm registers	2
used ymm registers	0
used zmm registers	0
nb stack references	1

Front-end

ASSUMED MACRO FUSION 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	1.50	0.50	2.33	2.33	1.50	0.60	1.00	1.50	1.50	1.50	0.40	2.33
cycles	1.50	0.50	2.33	2.33	1.50	0.60	1.00	1.50	1.50	1.50	0.40	2.33

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)	1.00

Cycles summary

Front-end	2.83
Dispatch	2.33
Data deps.	1.00
Overall L1	2.83

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 2.83 cycles. At this rate:

10% of peak load performance is reached (19.76 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))
6% of peak store performance is reached (8.47 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

Performance is limited by instruction throughput (loading/decoding program instructions to execution core) (front-end is a bottleneck). By removing all these bottlenecks, you can lower the cost of an iteration from 2.83 to 2.33 cycles (1.21x speedup).

ASM code

In the binary file, the address of the loop is: 4da3c4

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	Latency	Recip. throughput	Vectorization
MOV (%R15,%RDI,8),%R10	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
MOV (%R12,%R10,8),%R11	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
VMULSD (%RBX,%RDI,8),%XMM0,%XMM1	1	0.50	0.50	0.33	0.33	0	0	0	0	0	0	0	0.33	4	0.50	scal (12.5%)
CMP %RCX,%R11	1	0.20	0.20	0	0	0	0.20	0.20	0	0	0	0.20	0	1	0.20	scal (12.5%)
JGE 4da3b0 <hypre_CSRMatrixMultiply.extracted+0x540>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	N/A
LEA (%R12,%R10,8),%R9	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0.17	N/A
MOV %RAX,(%R9)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	1	0.50	scal (12.5%)
MOV -0x88(%RBP),%R11	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
MOV (%R11),%R11	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
MOV %R10,(%R11,%RAX,8)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	1	0.50	scal (12.5%)
MOV (%R9),%R9	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
VMOVSD %XMM1,(%R8,%R9,8)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	1	0.50	scal (12.5%)
INC %RAX	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
MOV 0x8(%R14,%RSI,8),%R9	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
INC %RDI	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
CMP %R9,%RDI	1	0.20	0.20	0	0	0	0.20	0.20	0	0	0	0.20	0	1	0.20	N/A
JL 4da3c4 <hypre_CSRMatrixMultiply.extracted+0x554>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	N/A

Function	hypre_CSRMatrixMultiply.extracted
Source file and lines	csr_matop.c:286-298
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 1.83 to 1.50 cycles (1.22x 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 1.83 to 0.23 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

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

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 32 bytes (4 double precision FP elements). The binary loop is storing 8 bytes (1 double precision FP elements).

Arithmetic intensity

Arithmetic intensity is 0.05 FP operations per loaded or stored byte.

Unroll opportunity

Loop is potentially data access bound.

Workaround

General properties

nb instructions	10
nb uops	9
loop length	38
used x86 registers	9
used mmx registers	0
used xmm registers	2
used ymm registers	0
used zmm registers	0
nb stack references	0
ADD-SUB / MUL ratio	1.00

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.83 cycles
front end	1.83 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11
uops	1.50	1.00	1.33	1.33	0.50	0.70	1.00	0.50	0.50	0.50	0.80	1.33
cycles	1.50	1.00	1.33	1.33	0.50	0.70	1.00	0.50	0.50	0.50	0.80	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)	1.00

Cycles summary

Front-end	1.83
Dispatch	1.50
Data deps.	1.00
Overall L1	1.83

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 1.83 cycles. At this rate:

9% of peak load performance is reached (17.45 out of 192.00 bytes loaded per cycle (GB/s @ 1GHz))
3% of peak store performance is reached (4.36 out of 128.00 bytes stored per cycle (GB/s @ 1GHz))

Front-end bottlenecks

ASM code

In the binary file, the address of the loop is: 4da3c4

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	Latency	Recip. throughput	Vectorization
VADDSD (%R8,%R11,8),%XMM1,%XMM1	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 %XMM1,(%R8,%R11,8)	1	0	0	0	0	0.50	0	0	0.50	0.50	0.50	0	0	1	0.50	scal (12.5%)
INC %RDI	1	0	0	0	0	0	0	0	0	0	0	0	0	1	0.17	N/A
CMP %R9,%RDI	1	0.20	0.20	0	0	0	0.20	0.20	0	0	0	0.20	0	1	0.20	scal (12.5%)
JGE 4da370 <hypre_CSRMatrixMultiply.extracted+0x500>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	N/A
MOV (%R15,%RDI,8),%R10	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
MOV (%R12,%R10,8),%R11	1	0	0	0.33	0.33	0	0	0	0	0	0	0	0.33	1	0.33	N/A
VMULSD (%RBX,%RDI,8),%XMM0,%XMM1	1	0.50	0.50	0.33	0.33	0	0	0	0	0	0	0	0.33	4	0.50	scal (12.5%)
CMP %RCX,%R11	1	0.20	0.20	0	0	0	0.20	0.20	0	0	0	0.20	0	1	0.20	N/A
JGE 4da3b0 <hypre_CSRMatrixMultiply.extracted+0x540>	1	0.50	0	0	0	0	0	0.50	0	0	0	0	0	0	0.50	N/A

Report Configuration

Vectorization

Details

Workaround

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

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

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