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Demonstrate maximal "double" Gsqrt/s performance for AVX512 CPUs
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| /* | |
| f=AVX512.vsqrtpd | |
| g++ -O3 -fopenmp -Wall -Wextra -pedantic $f.cpp -o $f | |
| cpplint --filter=-legal/copyright $f.cpp | |
| cppcheck --enable=all --suppress=missingIncludeSystem $f.cpp --check-config | |
| echo off | sudo tee /sys/devices/system/cpu/smt/control | |
| echo 0 | sudo tee /proc/sys/kernel/perf_event_paranoid | |
| perf stat -a -e fp_ops_retired_by_width.pack_512_uops_retired,cycles,instructions,task-clock ./$f | |
| Output: | |
| hermann@7950x:~$ ./$f 10 | |
| Starting hardware-bound benchmark using 16 threads... | |
| ... [AVX512F] vsqrtpd(mm512d,mm512d) completed | |
| https://www.officedaytime.com/simd512e/simdimg/unop_qword_3.png | |
| ------------------------------------------- | |
| Execution Time: 47.0373 seconds | |
| Counter: 256,000,000,000 | |
| Total Compute: 2,048 double Gsqrt/s (counter * 8) | |
| Performance: 43.5399 Gsqrt/s | |
| ------------------------------------------- | |
| hermann@7950x:~$ | |
| */ | |
| #include <omp.h> | |
| #include <inttypes.h> | |
| #include <iostream> | |
| #include <chrono> // NOLINT [build/c++11] | |
| int main(int argc, char**argv) { | |
| const int iterations = 200000000; // 2*10^8 | |
| int oloops = (argc == 1) ? 1 :atoi(argv[1]); | |
| std::cout << "Starting hardware-bound benchmark using " | |
| << omp_get_max_threads() << " threads...\n"; | |
| auto start_time = std::chrono::high_resolution_clock::now(); | |
| #pragma omp parallel | |
| { | |
| static const double four = 4.0; | |
| asm volatile( | |
| "vbroadcastsd %0, %%zmm0\n\t" | |
| "vbroadcastsd %0, %%zmm1\n\t" | |
| "vbroadcastsd %0, %%zmm2\n\t" | |
| "vbroadcastsd %0, %%zmm3\n\t" | |
| "vbroadcastsd %0, %%zmm4\n\t" | |
| "vbroadcastsd %0, %%zmm5\n\t" | |
| "vbroadcastsd %0, %%zmm6\n\t" | |
| "vbroadcastsd %0, %%zmm7" | |
| : | |
| : "m"(four) | |
| : "zmm0","zmm1","zmm2","zmm3", | |
| "zmm4","zmm5","zmm6","zmm7" | |
| ); | |
| for (int j = 0; j < oloops; ++j) { | |
| for (int i = 0; i < iterations; ++i) { | |
| asm __volatile__ ( | |
| "vsqrtpd %%zmm0, %%zmm0 \n\t" | |
| "vsqrtpd %%zmm1, %%zmm1 \n\t" | |
| "vsqrtpd %%zmm2, %%zmm2 \n\t" | |
| "vsqrtpd %%zmm3, %%zmm3 \n\t" | |
| "vsqrtpd %%zmm4, %%zmm4 \n\t" | |
| "vsqrtpd %%zmm5, %%zmm5 \n\t" | |
| "vsqrtpd %%zmm6, %%zmm6 \n\t" | |
| "vsqrtpd %%zmm7, %%zmm7 \n\t" | |
| : // No outputs | |
| : // No inputs | |
| : "zmm0", "zmm1", "zmm2", "zmm3", "zmm4", "zmm5", "zmm6", "zmm7" | |
| ); | |
| } | |
| } | |
| } | |
| std::cout << "... [AVX512F] vsqrtpd(mm512d,mm512d) completed\n"; | |
| std::cout << | |
| "https://www.officedaytime.com/simd512e/simdimg/unop_qword_3.png\n"; | |
| std::chrono::duration<double> duration = | |
| std::chrono::high_resolution_clock::now() - start_time; | |
| int64_t ops_per_loop = 8 * 8 * omp_get_max_threads(); | |
| int64_t total_ops = ops_per_loop * iterations; | |
| int64_t giga_cnt = total_ops / 8 * oloops; | |
| double giga_ops = total_ops / 1e9 * oloops; | |
| double performance = giga_ops / duration.count(); | |
| std::cout << "-------------------------------------------\n"; | |
| std::cout << "Execution Time: " << duration.count() << " seconds\n"; | |
| std::cout.imbue(std::locale("")); | |
| std::cout << "Counter: " << giga_cnt << "\n"; | |
| std::cout << "Total Compute: " << giga_ops | |
| << " double Gsqrt/s (counter * 8)\n"; | |
| std::cout << "Performance: " << performance << " Gsqrt/s\n"; | |
| std::cout << "-------------------------------------------\n"; | |
| return 0; | |
| } |
Author
Author
Main loop in C++ with inline assembly (allowing control over the 512bit register names):
hermann@7950x:~$ sed -n "/< iterations/,/^ }/p" $f.cpp
for (int i = 0; i < iterations; ++i) {
asm __volatile__ (
"vsqrtpd %%zmm0, %%zmm0 \n\t"
"vsqrtpd %%zmm1, %%zmm1 \n\t"
"vsqrtpd %%zmm2, %%zmm2 \n\t"
"vsqrtpd %%zmm3, %%zmm3 \n\t"
"vsqrtpd %%zmm4, %%zmm4 \n\t"
"vsqrtpd %%zmm5, %%zmm5 \n\t"
"vsqrtpd %%zmm6, %%zmm6 \n\t"
"vsqrtpd %%zmm7, %%zmm7 \n\t"
: // No outputs
: // No inputs
: "zmm0", "zmm1", "zmm2", "zmm3", "zmm4", "zmm5", "zmm6", "zmm7"
);
}
hermann@7950x:~$
Same loop with objdump (compiler added another unroll):
hermann@7950x:~$ objdump -d AVX512.vsqrtpd | sed -n "/vsqrtpd /,/jne/p"
1628: 62 f1 fd 48 51 c0 vsqrtpd %zmm0,%zmm0
162e: 62 f1 fd 48 51 c9 vsqrtpd %zmm1,%zmm1
1634: 62 f1 fd 48 51 d2 vsqrtpd %zmm2,%zmm2
163a: 62 f1 fd 48 51 db vsqrtpd %zmm3,%zmm3
1640: 62 f1 fd 48 51 e4 vsqrtpd %zmm4,%zmm4
1646: 62 f1 fd 48 51 ed vsqrtpd %zmm5,%zmm5
164c: 62 f1 fd 48 51 f6 vsqrtpd %zmm6,%zmm6
1652: 62 f1 fd 48 51 ff vsqrtpd %zmm7,%zmm7
1658: 62 f1 fd 48 51 c0 vsqrtpd %zmm0,%zmm0
165e: 62 f1 fd 48 51 c9 vsqrtpd %zmm1,%zmm1
1664: 62 f1 fd 48 51 d2 vsqrtpd %zmm2,%zmm2
166a: 62 f1 fd 48 51 db vsqrtpd %zmm3,%zmm3
1670: 62 f1 fd 48 51 e4 vsqrtpd %zmm4,%zmm4
1676: 62 f1 fd 48 51 ed vsqrtpd %zmm5,%zmm5
167c: 62 f1 fd 48 51 f6 vsqrtpd %zmm6,%zmm6
1682: 62 f1 fd 48 51 ff vsqrtpd %zmm7,%zmm7
1688: 83 e8 02 sub $0x2,%eax
168b: 75 9b jne 1628 <main._omp_fn.0+0x68>
hermann@7950x:~$
Author
Real world OpenMP program ml100K.cpp computing TSP tour length of 100,000 cities mona-lisa100K.tsp 500,000× (on each core) does 16*50*10^9 double sqrt and more, and reaches 16*50*10^9/20.1636s = 39.675 Gsqrt/s, very close to peak 43 double Gsqrt/s (>92%)!
C++ nested loops:
for (int i = 0; i < repeats; ++i) {
__m512i acc = _mm512_setzero_si512();
for (int i = 0; i < 2*N; i+=32) {
__m512i a = _mm512_load_si512((const __m512i*)(xy_even+i));
__m512i b = _mm512_load_si512((const __m512i*)(xy_odd+i));
__m512i dxy = _mm512_sub_epi16(a, b);
__m512i aux = DOT_PRODUCT_ACC(_mm512_setzero_si512(), dxy, dxy);
__m512d low_doubles = _mm512_cvtepi32_pd(_mm512_castsi512_si256(aux));
__m256i high_lanes = _mm512_extracti64x4_epi64(aux, 1);
__m512d high_doubles = _mm512_cvtepi32_pd(high_lanes);
__m512d sqrt_low = _mm512_sqrt_pd(low_doubles);
__m512d sqrt_high = _mm512_sqrt_pd(high_doubles);
__m512d res_low = _mm512_add_pd(sqrt_low, half_pd);
__m512d res_high = _mm512_add_pd(sqrt_high, half_pd);
__m256i int_low = _mm512_mask_cvtt_roundpd_epi32
(_mm256_undefined_si256(), 0xFF, res_low,
(_MM_FROUND_NO_EXC));
__m256i int_high = _mm512_mask_cvtt_roundpd_epi32
(_mm256_undefined_si256(), 0xFF, res_high,
(_MM_FROUND_NO_EXC));
__m512i euc_2d = _mm512_inserti64x4(_mm512_castsi256_si512(int_low),
int_high, 1);
acc = _mm512_add_epi32(acc, euc_2d);
}
sum += _mm512_reduce_add_epi32(acc);
}
same nested loop in "objdump -d":
1410: 31 c0 xor %eax,%eax <-------------------------------------+
1412: c5 e9 ef d2 vpxor %xmm2,%xmm2,%xmm2 |
1416: 66 2e 0f 1f 84 00 00 cs nopw 0x0(%rax,%rax,1) |
141d: 00 00 00 |
1420: 62 f1 7d 48 6f cc vmovdqa32 %zmm4,%zmm1 <----------------------------------+ |
1426: 62 f1 fd 48 6f 2c 01 vmovdqa64 (%rcx,%rax,1),%zmm5 | |
142d: 62 f1 55 48 f9 04 02 vpsubw (%rdx,%rax,1),%zmm5,%zmm0 | |
1434: 48 83 c0 40 add $0x40,%rax | |
1438: 62 f2 7d 48 52 c8 vpdpwssd %zmm0,%zmm0,%zmm1 16× 32bit "dx^2+dy^2" | |
143e: 62 f1 7e 48 e6 c1 vcvtdq2pd %ymm1,%zmm0 | |
1444: 62 f3 fd 48 3b c9 01 vextracti64x4 $0x1,%zmm1,%ymm1 | |
144b: 62 f1 7e 48 e6 c9 vcvtdq2pd %ymm1,%zmm1 | |
1451: 62 f1 fd 48 51 c0 vsqrtpd %zmm0,%zmm0 <==== 8× 64bit sqrt | |
1457: 62 f1 fd 48 58 c3 vaddpd %zmm3,%zmm0,%zmm0 | |
145d: 62 f1 fd 48 51 c9 vsqrtpd %zmm1,%zmm1 <==== 8× 64bit sqrt | |
1463: 62 f1 f5 48 58 cb vaddpd %zmm3,%zmm1,%zmm1 | |
1469: 62 f1 fd 18 e6 c0 vcvttpd2dq {sae},%zmm0,%ymm0 | |
146f: 62 f1 fd 18 e6 c9 vcvttpd2dq {sae},%zmm1,%ymm1 | |
1475: 62 f3 fd 48 3a c1 01 vinserti64x4 $0x1,%ymm1,%zmm0,%zmm0 | |
147c: 62 f1 6d 48 fe c0 vpaddd %zmm0,%zmm2,%zmm0 | |
1482: 62 f1 fd 48 6f d0 vmovdqa64 %zmm0,%zmm2 | |
1488: 48 3d 80 1a 06 00 cmp $0x61a80,%rax | |
148e: 75 90 jne 1420 <_Z6bench2v+0x60> -----------------------------------+ |
1490: 62 f3 fd 48 3b c1 01 vextracti64x4 $0x1,%zmm0,%ymm1 |
1497: c5 f5 fe c0 vpaddd %ymm0,%ymm1,%ymm0 |
149b: 62 f3 fd 28 39 c1 01 vextracti64x2 $0x1,%ymm0,%xmm1 |
14a2: c5 f1 fe c0 vpaddd %xmm0,%xmm1,%xmm0 |
14a6: c5 f9 70 c8 4e vpshufd $0x4e,%xmm0,%xmm1 |
14ab: c5 f1 fe c8 vpaddd %xmm0,%xmm1,%xmm1 |
14af: c5 f9 6f c1 vmovdqa %xmm1,%xmm0 |
14b3: c5 f9 70 c9 55 vpshufd $0x55,%xmm1,%xmm1 |
14b8: c5 f9 fe c1 vpaddd %xmm1,%xmm0,%xmm0 |
14bc: c5 f9 7e c0 vmovd %xmm0,%eax |
14c0: 48 98 cltq |
14c2: 49 01 c4 add %rax,%r12 |
14c5: ff ce dec %esi |
14c7: 0f 85 43 ff ff ff jne 1410 <_Z6bench2v+0x50> --------------------------------------+
Author
AMD 9950X CPU more than doubles(!) synthetic peak 43.5399 double Gsqrt/s of AMD 7950X CPU:
hermann@9950X:~$ ./$f 100
Starting hardware-bound benchmark using 16 threads...
... [AVX512F] vsqrtpd(mm512d,mm512d) completed
https://www.officedaytime.com/simd512e/simdimg/unop_qword_3.png
-------------------------------------------
Execution Time: 225.828 seconds
Counter: 2,560,000,000,000
Total Compute: 20,480 double Gsqrt/s (counter * 8)
Performance: 90.6885 Gsqrt/s
-------------------------------------------
hermann@9950X:~$
AMD 9950X CPU also more than doubles real world application ml100K.cpp 39.675 double Gsqrt/s from previous comment:
hermann@9950X:~/RR/tsp/openmp$ ./ml100K
... completed
#threads : 16
Execution Time: 9.56 seconds
double sqrt : 83.682 Gsqrt/S
euc_2d sum : 5757191
hermann@9950X:~/RR/tsp/openmp$
Reason is that AMD 9950X CPU has real AVX512 units, whereas AMD 7950X implemented AVX512 double pumped via 256bit registers.
Author
Similar synthetic double sqrt GPU benchmark shows:
| GPU | [double Gsqrt/s] |
|---|---|
| NVIDIA Tesla P100 PCIE | 193.7 |
| AMD Radeon VII | 363.5 |
| AMD Instinct MI50s | 426.9-436.7 |
Author
TIL that perf counters changed between Zen4 (7950X) and Zen5 (9950X). Not specifying "-e ..." for 9950X allows to see 5.3 GHz reported for 9950X as well:
hermann@9950X:~$ perf stat -a ./$f 100
Starting hardware-bound benchmark using 16 threads...
... [AVX512F] vsqrtpd(mm512d,mm512d) completed
https://www.officedaytime.com/simd512e/simdimg/unop_qword_3.png
-------------------------------------------
Execution Time: 225.425 seconds
Counter: 2,560,000,000,000
Total Compute: 20,480 double Gsqrt/s (counter * 8)
Performance: 90.8508 Gsqrt/s
-------------------------------------------
Performance counter stats for 'system wide':
13,877 context-switches # 3.8 cs/sec cs_per_second
3,606,839.43 msec cpu-clock # 16.0 CPUs CPUs_utilized
708 cpu-migrations # 0.2 migrations/sec migrations_per_second
1,598 page-faults # 0.4 faults/sec page_faults_per_second
37,752,961 branch-misses # 0.0 % branch_miss_rate (50.00%)
164,336,505,008 branches # 45.6 M/sec branch_frequency (50.00%)
19,228,942,031,350 cpu-cycles # 5.3 GHz cycles_frequency (66.67%)
2,906,199,640,573 instructions # 0.2 instructions insn_per_cycle (50.00%)
16,313,704,313 stalled-cycles-frontend # 0.00 frontend_cycles_idle (50.00%)
225.425950013 seconds time elapsed
hermann@9950X:~$
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One vsqrtpd does 8 double sqrt computations:
https://www.officedaytime.com/simd512e/simdimg/unop_qword_3.png