OV - exec - Loop 703

0x253aa0 VMULPD	(%RSI,%RAX,8),%XMM0,%XMM6    [2]

0x253aa5 VFMADD231PD	(%RDX,%RAX,8),%XMM1,%XMM6    [5]

0x253aab VFMADD231PD	(%R13,%RAX,8),%XMM2,%XMM6    [1]

0x253ab2 VFMADD231PD	(%R15,%RAX,8),%XMM3,%XMM6    [4]

0x253ab8 VFMADD213PD	(%R14,%RAX,8),%XMM5,%XMM6    [3]

0x253abe VMOVUPD	%XMM6,(%R14,%RAX,8)    [3]

0x253ac4 ADD	$0x2,%RAX

0x253ac8 CMP	%RAX,%RCX

0x253acb JNE	253aa0

/home/eoseret/qaas_runs_ZEN5/173-938-0042/intel/miniqmc/build/miniqmc/src/Numerics/Spline2/MultiBsplineRef.hpp: 68 - 70

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

68:       for (size_t n = 0; n < num_splines; n++)

69:         vals[n] += pre00 *

70:             (c[0] * coefs[n] + c[1] * coefs[n + zs] + c[2] * coefs[n + 2 * zs] +

Coverage (%)	Name	Source Location	Module
►96.16+	miniqmcreference::einspline_sp[...]	einspline_spo_ref.hpp:175	exec
○	miniqmcreference::einspline_sp[...]	einspline_spo_ref.hpp:183	exec
○	qmcplusplus::SPOSet::evaluateD[...]	OhmmsVector.h:178	exec
○	miniqmcreference::DiracDetermi[...]	DiracDeterminantRef.cpp:217	exec
○	qmcplusplus::WaveFunction::eva[...]	stl_vector.h:919	exec
○	qmcplusplus::NonLocalPP<double[...]	NonLocalPP.hpp:135	exec
○	main.omp_outlined.64	NewTimer.h:249	exec
○	__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
►3.06+	miniqmcreference::einspline_sp[...]	einspline_spo_ref.hpp:175	exec
○	miniqmcreference::einspline_sp[...]	einspline_spo_ref.hpp:183	exec
○	qmcplusplus::SPOSet::evaluateD[...]	OhmmsVector.h:178	exec
○	miniqmcreference::DiracDetermi[...]	DiracDeterminantRef.cpp:217	exec
○	qmcplusplus::WaveFunction::eva[...]	stl_vector.h:919	exec
○	qmcplusplus::NonLocalPP<double[...]	NonLocalPP.hpp:135	exec
○	main.omp_outlined.64	NewTimer.h:249	exec
○	__kmp_invoke_microtask		libomp.so
○	__kmp_invoke_task_func		libomp.so
○	__kmp_fork_call		libomp.so
○	__kmpc_fork_call		libomp.so
○	main	miniqmc.cpp:411	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	1.67
CQA speedup if fully vectorized	4.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.67
Bottlenecks	P10, P11,
Function	void miniqmcreference::MultiBsplineEvalRef::evaluate_v(qmcplusplus::bspline_traits::SplineType const, double, double, double, double, unsigned long)
Source	MultiBsplineRef.hpp:68-70
Source loop unroll info	unrolled by 2
Source loop unroll confidence level	high
Unroll/vectorization loop type	main
Unroll factor	2
CQA cycles	2.50
CQA cycles if no scalar integer	2.50
CQA cycles if FP arith vectorized	1.50
CQA cycles if fully vectorized	0.63
Front-end cycles	1.00
P0 cycles	0.33
P1 cycles	0.33
P2 cycles	0.33
P3 cycles	0.33
P4 cycles	0.33
P5 cycles	0.33
P6 cycles	1.50
P7 cycles	1.50
P8 cycles	1.50
P9 cycles	1.50
P10 cycles	2.50
P11 cycles	2.50
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	9.00
Nb uops	8.00
Nb loads	5.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	7.20
Nb FLOP add-sub	0.00
Nb FLOP mul	2.00
Nb FLOP fma	8.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	38.40
Bytes prefetched	0.00
Bytes loaded	80.00
Bytes stored	16.00
Stride 0	0.00
Stride 1	5.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	100.00
Vectorization ratio load	100.00
Vectorization ratio store	100.00
Vectorization ratio mul	100.00
Vectorization ratio add_sub	NA
Vectorization ratio fma	100.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	25.00
Vector-efficiency ratio load	25.00
Vector-efficiency ratio store	25.00
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	25.00
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	NA

Metric	Value
CQA speedup if no scalar integer	1.00
CQA speedup if FP arith vectorized	1.67
CQA speedup if fully vectorized	4.00
CQA speedup if no inter-iteration dependency	NA
CQA speedup if next bottleneck killed	1.67
Bottlenecks	P10, P11,
Function	void miniqmcreference::MultiBsplineEvalRef::evaluate_v(qmcplusplus::bspline_traits::SplineType const, double, double, double, double, unsigned long)
Source	MultiBsplineRef.hpp:68-70
Source loop unroll info	unrolled by 2
Source loop unroll confidence level	high
Unroll/vectorization loop type	main
Unroll factor	2
CQA cycles	2.50
CQA cycles if no scalar integer	2.50
CQA cycles if FP arith vectorized	1.50
CQA cycles if fully vectorized	0.63
Front-end cycles	1.00
P0 cycles	0.33
P1 cycles	0.33
P2 cycles	0.33
P3 cycles	0.33
P4 cycles	0.33
P5 cycles	0.33
P6 cycles	1.50
P7 cycles	1.50
P8 cycles	1.50
P9 cycles	1.50
P10 cycles	2.50
P11 cycles	2.50
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	9.00
Nb uops	8.00
Nb loads	5.00
Nb stores	1.00
Nb stack references	0.00
FLOP/cycle	7.20
Nb FLOP add-sub	0.00
Nb FLOP mul	2.00
Nb FLOP fma	8.00
Nb FLOP div	0.00
Nb FLOP rcp	0.00
Nb FLOP sqrt	0.00
Nb FLOP rsqrt	0.00
Bytes/cycle	38.40
Bytes prefetched	0.00
Bytes loaded	80.00
Bytes stored	16.00
Stride 0	0.00
Stride 1	5.00
Stride n	0.00
Stride unknown	0.00
Stride indirect	0.00
Vectorization ratio all	100.00
Vectorization ratio load	100.00
Vectorization ratio store	100.00
Vectorization ratio mul	100.00
Vectorization ratio add_sub	NA
Vectorization ratio fma	100.00
Vectorization ratio div_sqrt	NA
Vectorization ratio other	NA
Vector-efficiency ratio all	25.00
Vector-efficiency ratio load	25.00
Vector-efficiency ratio store	25.00
Vector-efficiency ratio mul	25.00
Vector-efficiency ratio add_sub	NA
Vector-efficiency ratio fma	25.00
Vector-efficiency ratio div_sqrt	NA
Vector-efficiency ratio other	NA

Path /

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

Function	void miniqmcreference::MultiBsplineEvalRef::evaluate_v(qmcplusplus::bspline_traits::SplineType const, double, double, double, double, unsigned long)
Source file and lines	MultiBsplineRef.hpp:68-70
Module	exec

The loop is defined in /home/eoseret/qaas_runs_ZEN5/173-938-0042/intel/miniqmc/build/miniqmc/src/Numerics/Spline2/MultiBsplineRef.hpp:68-70.

It is main loop of related source loop which is unrolled by 2 (including vectorization).

gain
potential
hint
expert

Vectorization

Your loop is vectorized, but using only 128 out of 512 bits (SSE/AVX-128 instructions on AVX-512 processors).

By fully vectorizing your loop, you can lower the cost of an iteration from 2.50 to 0.62 cycles (4.00x speedup).

Details

All SSE/AVX instructions are used in vector version (process two or more data elements in vector registers). Since your execution units are vector units, only a fully vectorized loop can use their full power.

Workaround

Pass to your compiler a micro-architecture specialization option:
- use march=native
Use vector aligned instructions:
1. align your arrays on 64 bytes boundaries: replace { void *p = malloc (size); } with { void *p; posix_memalign (&p, 64, size); }.
2. inform your compiler that your arrays are vector aligned: if array 'foo' is 64 bytes-aligned, define a pointer 'p_foo' as __builtin_assume_aligned (foo, 64) and use it instead of 'foo' in the loop.

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 2.50 to 1.50 cycles (1.67x speedup).

Workaround

Reduce the number of FP multiply/FMA instructions

FMA

Detected 8 FMA (fused multiply-add) operations.

Type of elements and instruction set

5 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 18 FP arithmetical operations:

8: addition or subtraction (all inside FMA instructions)
10: multiply (8 inside FMA instructions)

The binary loop is loading 80 bytes (10 double precision FP elements). The binary loop is storing 16 bytes (2 double precision FP elements).

Arithmetic intensity

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

General properties

nb instructions	9
nb uops	8
loop length	45
used x86 registers	7
used mmx registers	0
used xmm registers	6
used ymm registers	0
used zmm registers	0
nb stack references	0

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.00 cycles
front end	1.00 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	0.33	0.33	0.33	0.33	0.33	0.33	1.50	1.50	1.50	1.50	2.50	2.50	0.00	0.00	0.50	0.50
cycles	0.33	0.33	0.33	0.33	0.33	0.33	1.50	1.50	1.50	1.50	2.50	2.50	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	1.00
Dispatch	2.50
Data deps.	1.00
Overall L1	2.50

Vectorization ratios

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

Vector efficiency ratios

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

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 2.50 cycles. At this rate:

12% of peak load performance is reached (32.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
5% of peak store performance is reached (6.40 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: 253aa0

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P14	P15	Latency	Recip. throughput	Vectorization
VMULPD (%RSI,%RAX,8),%XMM0,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	vect (25.0%)
VFMADD231PD (%RDX,%RAX,8),%XMM1,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	4	0.50	vect (25.0%)
VFMADD231PD (%R13,%RAX,8),%XMM2,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	4	0.50	vect (25.0%)
VFMADD231PD (%R15,%RAX,8),%XMM3,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	4	0.50	vect (25.0%)
VFMADD213PD (%R14,%RAX,8),%XMM5,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	4	0.50	vect (25.0%)
VMOVUPD %XMM6,(%R14,%RAX,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	4	0.50	vect (25.0%)
ADD $0x2,%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
CMP %RAX,%RCX	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
JNE 253aa0 <_ZN16miniqmcreference19MultiBsplineEvalRef10evaluate_vIdEEvPKN11qmcplusplus14bspline_traitsIT_Lj3EE10SplineTypeES4_S4_S4_PS4_m+0x770>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	1	0.50-1	N/A

Function	void miniqmcreference::MultiBsplineEvalRef::evaluate_v(qmcplusplus::bspline_traits::SplineType const, double, double, double, double, unsigned long)
Source file and lines	MultiBsplineRef.hpp:68-70
Module	exec

The loop is defined in /home/eoseret/qaas_runs_ZEN5/173-938-0042/intel/miniqmc/build/miniqmc/src/Numerics/Spline2/MultiBsplineRef.hpp:68-70.

It is main loop of related source loop which is unrolled by 2 (including vectorization).

gain
potential
hint
expert

Vectorization

Your loop is vectorized, but using only 128 out of 512 bits (SSE/AVX-128 instructions on AVX-512 processors).

By fully vectorizing your loop, you can lower the cost of an iteration from 2.50 to 0.62 cycles (4.00x speedup).

Details

All SSE/AVX instructions are used in vector version (process two or more data elements in vector registers). Since your execution units are vector units, only a fully vectorized loop can use their full power.

Workaround

Pass to your compiler a micro-architecture specialization option:
- use march=native
Use vector aligned instructions:
1. align your arrays on 64 bytes boundaries: replace { void *p = malloc (size); } with { void *p; posix_memalign (&p, 64, size); }.
2. inform your compiler that your arrays are vector aligned: if array 'foo' is 64 bytes-aligned, define a pointer 'p_foo' as __builtin_assume_aligned (foo, 64) and use it instead of 'foo' in the loop.

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 2.50 to 1.50 cycles (1.67x speedup).

Workaround

Reduce the number of FP multiply/FMA instructions

FMA

Detected 8 FMA (fused multiply-add) operations.

Type of elements and instruction set

5 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 18 FP arithmetical operations:

8: addition or subtraction (all inside FMA instructions)
10: multiply (8 inside FMA instructions)

The binary loop is loading 80 bytes (10 double precision FP elements). The binary loop is storing 16 bytes (2 double precision FP elements).

Arithmetic intensity

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

General properties

nb instructions	9
nb uops	8
loop length	45
used x86 registers	7
used mmx registers	0
used xmm registers	6
used ymm registers	0
used zmm registers	0
nb stack references	0

Front-end

ASSUMED MACRO FUSION FIT IN UOP CACHE

micro-operation queue	1.00 cycles
front end	1.00 cycles

Back-end

	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
uops	0.33	0.33	0.33	0.33	0.33	0.33	1.50	1.50	1.50	1.50	2.50	2.50	0.00	0.00	0.50	0.50
cycles	0.33	0.33	0.33	0.33	0.33	0.33	1.50	1.50	1.50	1.50	2.50	2.50	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	1.00
Dispatch	2.50
Data deps.	1.00
Overall L1	2.50

Vectorization ratios

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

Vector efficiency ratios

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

Cycles and memory resources usage

Assuming all data fit into the L1 cache, each iteration of the binary loop takes 2.50 cycles. At this rate:

12% of peak load performance is reached (32.00 out of 256.00 bytes loaded per cycle (GB/s @ 1GHz))
5% of peak store performance is reached (6.40 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: 253aa0

Instruction	Nb FU	P0	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P14	P15	Latency	Recip. throughput	Vectorization
VMULPD (%RSI,%RAX,8),%XMM0,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	3	0.50	vect (25.0%)
VFMADD231PD (%RDX,%RAX,8),%XMM1,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	4	0.50	vect (25.0%)
VFMADD231PD (%R13,%RAX,8),%XMM2,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	4	0.50	vect (25.0%)
VFMADD231PD (%R15,%RAX,8),%XMM3,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	4	0.50	vect (25.0%)
VFMADD213PD (%R14,%RAX,8),%XMM5,%XMM6	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0.50	0.50	0	0	4	0.50	vect (25.0%)
VMOVUPD %XMM6,(%R14,%RAX,8)	1	0	0	0	0	0	0	0.25	0.25	0.25	0.25	0	0	0.50	0.50	4	0.50	vect (25.0%)
ADD $0x2,%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
CMP %RAX,%RCX	1	0.17	0.17	0.17	0.17	0.17	0.17	0	0	0	0	0	0	0	0	1	0.17	N/A
JNE 253aa0 <_ZN16miniqmcreference19MultiBsplineEvalRef10evaluate_vIdEEvPKN11qmcplusplus14bspline_traitsIT_Lj3EE10SplineTypeES4_S4_S4_PS4_m+0x770>	1	0	0	0	0.33	0.33	0.33	0	0	0	0	0	0	0	0	1	0.50-1	N/A

Report Configuration

Vectorization

Details

Workaround

Execution units bottlenecks

Workaround

FMA

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

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