Skip to content

Commit 50c0d4e

Browse files
DTolmDTolm
committed
Multi-upload R2C and R2R algorithms
-This update removes the limit of ~2^12 for R2C and R2R systems - they can all now be done in up to three uploads with coverage ~2^32 for all dimensions, same as C2C. -Added versions of all R2C and R2R algorithms, implementad as load/store callbacks. This functionality will be enchanced in the future to support arbitrary user callbacks (I just need to find out how this can be done for a multiple-API user-interaction). -Restructured internal kernel typing enumeration.
1 parent eaf1c00 commit 50c0d4e

32 files changed

+2861
-1186
lines changed

‎README.md

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -6,10 +6,10 @@ VkFFT is an efficient GPU-accelerated multidimensional Fast Fourier Transform li
66
## Currently supported features:
77
- 1D/2D/3D/ND systems - specify VKFFT_MAX_FFT_DIMENSIONS for arbitrary number of dimensions.
88
- Forward and inverse directions of FFT.
9-
- Support for big FFT dimension sizes. Current limits: C2C or even C2R/R2C - (2^32, 2^32, 2^32). Odd C2R/R2C - (2^12, 2^32, 2^32). R2R - (2^12, 2^12, 2^12). Depends on the amount of shared memory on the device. (will be increased later).
9+
- Support for big FFT dimension sizes. Current limits: approximately 2^32 in all dimensions for all types of transforms. Depends on the amount of shared memory available on the device.
1010
- Radix-2/3/4/5/7/8/11/13 FFT. Sequences using radix 3, 5, 7, 11 and 13 have comparable performance to that of powers of 2.
1111
- Rader's FFT algorithm for primes from 17 up to max shared memory length (~10000). Inlined and done without additional memory transfers.
12-
- Bluestein's FFT algorithm for all other sequences. Full coverage of C2C range, single upload (2^12, 2^12, 2^12) for R2C/C2R/R2R. Optimized to have as few memory transfers as possible by using zero padding and merged convolution support of VkFFT.
12+
- Bluestein's FFT algorithm for all other sequences. Optimized to have as few memory transfers as possible by using zero padding and merged convolution support of VkFFT.
1313
- Single, double, half and quad (double-double) precision support. Double and quad precision uses CPU-generated LUT tables. Half precision still does all computations in single and only uses half precision to store data.
1414
- All transformations are performed in-place with no performance loss. Out-of-place transforms are supported by selecting different input/output buffers.
1515
- No additional transposition uploads. Note: Data can be reshuffled after the Four Step FFT algorithm with an additional buffer (for big sequences). Doesn't matter for convolutions - they return to the input ordering (saves memory).

‎benchmark_scripts/cuFFT_scripts/src/precision_cuFFT_half.cu

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -51,7 +51,7 @@ void launch_precision_cuFFT_half(void* inputC, void* output_cuFFT, int device_id
5151
break;
5252
}
5353
res = cufftXtMakePlanMany(
54-
planHalf, dims[3], local_dims, NULL, 1, 1, CUDA_C_16F,
54+
planHalf, dims[4], local_dims, NULL, 1, 1, CUDA_C_16F,
5555
NULL, 1, 1, CUDA_C_16F, 1, &ws, CUDA_C_16F);
5656

5757
for (int i = 0; i < 1; i++) {

‎benchmark_scripts/cuFFT_scripts/src/precision_cuFFT_r2c.cu

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -45,7 +45,7 @@ void launch_precision_cuFFT_r2c(void* inputC, void* output_cuFFT, int device_id,
4545
}
4646
cudaDeviceSynchronize();
4747
cufftDestroy(planR2C);
48-
switch (dims[3]) {
48+
switch (dims[4]) {
4949
case 1:
5050
cufftPlan1d(&planR2C, dims[0], CUFFT_C2R, 1);
5151
break;

‎benchmark_scripts/rocFFT_scripts/src/precision_rocFFT_r2c.cpp

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -44,7 +44,7 @@ void launch_precision_rocFFT_r2c(void* inputC, void* output_rocFFT, int device_i
4444
}
4545
hipDeviceSynchronize();
4646
hipfftDestroy(planR2C);
47-
switch (dims[3]) {
47+
switch (dims[4]) {
4848
case 1:
4949
hipfftPlan1d(&planR2C, dims[0], HIPFFT_C2R, 1);
5050
break;

‎benchmark_scripts/vkFFT_scripts/src/sample_15_precision_VkFFT_single_r2c.cpp

Lines changed: 12 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -75,7 +75,10 @@ VkFFTResult sample_15_precision_VkFFT_single_r2c(VkGPU* vkGPU, uint64_t file_out
7575
const int num_benchmark_samples = 277;
7676
const int num_runs = 1;
7777

78-
uint64_t benchmark_dimensions[num_benchmark_samples][5] = { {1, 1, 1, 1, 3}, {(uint64_t)pow(2,5), 1, 1, 1, 1}, {(uint64_t)pow(2,6), 1, 1, 1, 1},{(uint64_t)pow(2,7), 1, 1, 1, 1},{(uint64_t)pow(2,8), 1, 1, 1, 1},{(uint64_t)pow(2,9), 1, 1, 1, 1},{(uint64_t)pow(2,10), 1, 1, 1, 1},
78+
const int num_benchmark_samples = 318;
79+
const int num_runs = 1;
80+
81+
uint64_t benchmark_dimensions[num_benchmark_samples][5] = { {1, 1, 1, 1, 1}, {(uint64_t)pow(2,5), 1, 1, 1, 1}, {(uint64_t)pow(2,6), 1, 1, 1, 1},{(uint64_t)pow(2,7), 1, 1, 1, 1},{(uint64_t)pow(2,8), 1, 1, 1, 1},{(uint64_t)pow(2,9), 1, 1, 1, 1},{(uint64_t)pow(2,10), 1, 1, 1, 1},
7982
{(uint64_t)pow(2,11), 1, 1, 1, 1},{(uint64_t)pow(2,12), 1, 1, 1, 1},{(uint64_t)pow(2,13), 1, 1, 1, 1},{(uint64_t)pow(2,14), 1, 1, 1, 1},{(uint64_t)pow(2,15), 1, 1, 1, 1},{(uint64_t)pow(2,16), 1, 1, 1, 1},{(uint64_t)pow(2,17), 1, 1, 1, 1},{(uint64_t)pow(2,18), 1, 1, 1, 1},
8083
{(uint64_t)pow(2,19), 1, 1, 1, 1},{(uint64_t)pow(2,20), 1, 1, 1, 1},{(uint64_t)pow(2,21), 1, 1, 1, 1},{(uint64_t)pow(2,22), 1, 1, 1, 1},{(uint64_t)pow(2,23), 1, 1, 1, 1},{(uint64_t)pow(2,24), 1, 1, 1, 1},{(uint64_t)pow(2,25), 1, 1, 1, 1},{(uint64_t)pow(2,26), 1, 1, 1, 1},
8184

@@ -96,7 +99,14 @@ VkFFTResult sample_15_precision_VkFFT_single_r2c(VkGPU* vkGPU, uint64_t file_out
9699
{3, 8, 1, 1, 2},{5, 8, 1, 1, 2},{6, 8, 1, 1, 2},{7, 8, 1, 1, 2},{9, 8, 1, 1, 2},{10, 8, 1, 1, 2},{18, 8, 1, 1, 2},{12, 8, 1, 1, 2},{13, 8, 1, 1, 2},{14, 8, 1, 1, 2},
97100
{15, 8, 1, 1, 2},{17, 8, 1, 1, 2},{19, 8, 1, 1, 2},{21, 8, 1, 1, 2},{22, 8, 1, 1, 2},{23, 8, 1, 1, 2},{24, 8, 1, 1, 2},{25, 8, 1, 1, 2},{26, 8, 1, 1, 2},{27, 8, 1, 1, 2},{28, 8, 1, 1, 2},{29, 8, 1, 1, 2},{30, 8, 1, 1, 2},{31, 8, 1, 1, 2},{33, 8, 1, 1, 2},{34, 8, 1, 1, 2},{35, 8, 1, 1, 2},{37, 8, 1, 1, 2},{39, 8, 1, 1, 2},{41, 8, 1, 1, 2},{42, 8, 1, 1, 2},{44, 8, 1, 1, 2},{45, 8, 1, 1, 2},{46, 8, 1, 1, 2},{49, 8, 1, 1, 2},{52, 8, 1, 1, 2},{55, 8, 1, 1, 2},{56, 8, 1, 1, 2},{60, 8, 1, 1, 2},{65, 8, 1, 1, 2},{66, 8, 1, 1, 2},{88, 8, 1, 1, 2},
98101
{128, 8, 1, 1, 2},{125, 8, 1, 1, 2},{143, 8, 1, 1, 2},{149, 8, 1, 1, 2},{169, 8, 1, 1, 2},{229, 8, 1, 1, 2},{243, 8, 1, 1, 2},{286, 8, 1, 1, 2},{343, 8, 1, 1, 2},{429, 8, 1, 1, 2},{482, 1, 1, 1, 1},{572, 8, 1, 1, 2},{625, 8, 1, 1, 2},{720, 8, 1, 1, 2},{1080, 8, 1, 1, 2},{1008, 8, 1, 1, 2},{1181, 8, 1, 1, 2},{1287, 8, 1, 1, 2},{1400, 8, 1, 1, 2},{1440, 8, 1, 1, 2},{1920, 8, 1, 1, 2},{1951, 8, 1, 1, 2},{2160, 8, 1, 1, 2},{3024,1,1, 1, 1},{3500,1,1, 1, 1},
99-
{3840, 8, 1, 1, 2},{4000 , 8, 1, 1, 2},{4050, 8, 1, 1, 2},{4320 , 8, 1, 1, 2},{4864 , 8, 1, 1, 2},{7000,1,1, 1, 1},{7680, 8, 1, 1, 2},{9000, 8, 1, 1, 2},{4864 * 5, 8, 1, 1, 2},{7680 * 5, 8, 1, 1, 2},{39829*2, 8, 1, 1, 2},
102+
{3840, 8, 1, 1, 2},{4000 , 8, 1, 1, 2},{4050, 8, 1, 1, 2},{4320 , 8, 1, 1, 2},{4864 , 8, 1, 1, 2},{7000,1,1, 1, 1}, {9000, 1, 1, 1, 1},{11587, 1, 1, 1, 1},{7680 * 5, 1, 1, 1, 1},
103+
{15319, 1, 1, 1, 1},{21269, 1, 1, 1, 1},{27283, 1, 1, 1, 1},{39829, 1, 1, 1, 1},{52733, 1, 1, 1, 1},{2000083, 1, 1, 1, 1},{4000067, 1, 1, 1, 1},{8003869, 1, 1, 1, 1},
104+
{(uint64_t)pow(3,10), 1, 1, 1, 1},{(uint64_t)pow(3,11), 1, 1, 1, 1},{(uint64_t)pow(3,12), 1, 1, 1, 1},{(uint64_t)pow(3,13), 1, 1, 1, 1},{(uint64_t)pow(3,14), 1, 1, 1, 1},{(uint64_t)pow(3,15), 1, 1, 1, 1},
105+
{(uint64_t)pow(5,5), 1, 1, 1, 1},{(uint64_t)pow(5,6), 1, 1, 1, 1},{(uint64_t)pow(5,7), 1, 1, 1, 1},{(uint64_t)pow(5,8), 1, 1, 1, 1},{(uint64_t)pow(5,9), 1, 1, 1, 1},
106+
{(uint64_t)pow(7,4), 1, 1, 1, 1},{(uint64_t)pow(7,5), 1, 1, 1, 1},{(uint64_t)pow(7,6), 1, 1, 1, 1},{(uint64_t)pow(7,7), 1, 1, 1, 1},{(uint64_t)pow(7,8), 1, 1, 1, 1},
107+
{(uint64_t)pow(11,3), 1, 1, 1, 1},{(uint64_t)pow(11,4), 1, 1, 1, 1},{(uint64_t)pow(11,5), 1, 1, 1, 1},{(uint64_t)pow(11,6), 1, 1, 1, 1},
108+
{(uint64_t)pow(13,3), 1, 1, 1, 1},{(uint64_t)pow(13,4), 1, 1, 1, 1},{(uint64_t)pow(13,5), 1, 1, 1, 1},{(uint64_t)pow(13,6), 1, 1, 1, 1},
109+
{7680, 8, 1, 1, 2},{9000, 8, 1, 1, 2},{4864 * 5, 8, 1, 1, 2},{7680 * 5, 8, 1, 1, 2},{39829*2, 8, 1, 1, 2}, {15319, 8, 1, 1, 2},{21269, 8, 1, 1, 2},{27283, 8, 1, 1, 2},{39829, 8, 1, 1, 2},{52733, 8, 1, 1, 2},{2000083, 4, 1, 1, 2},
100110
{3, 3, 3, 3, 4},{5, 5, 5, 5, 4},{6, 6, 6, 6, 4},{7, 7, 7, 7, 4},{9, 9, 9, 9, 4},{10, 10, 10, 10, 4},{11, 11, 11, 11, 4},{12, 12, 12, 12, 4},{13, 13, 13, 13, 4},{14, 14, 14, 14, 4},
101111
{15, 15, 15, 15, 4},{17, 17, 17, 17, 4},{21, 21, 21, 21, 4},{22, 22, 22, 22, 4},{23, 23, 23, 23, 4},{24, 24, 24, 24, 4},{25, 25, 25, 25, 4},{26, 26, 26, 26, 4},{27, 27, 27, 27, 4},{28, 28, 28, 28, 4},{29, 29, 29, 29, 4},{30, 30, 30, 30, 4},{31, 31, 31, 31, 4},{33, 33, 33, 33, 4},{35, 35, 35, 35, 4},{37, 37, 37, 37, 4},{39, 39, 39, 39, 4},{41, 41, 41, 41, 4},{42, 42, 42, 42, 4},{43, 43, 43, 43, 4},{44, 44, 44, 44, 4},{45, 45, 45, 45, 4},{47, 47, 47, 47, 4},{49, 49, 49, 49, 4},{52, 52, 52, 52, 4},{53, 53, 53, 53, 4},{56, 56, 56, 56, 4},{59, 59, 59, 59, 4},{60, 60, 60, 60, 4},{61, 61, 61, 61, 4},{81, 81, 81, 81, 4},
102112
{3, 5, 7, 9, 4},{5, 3, 7, 9, 4},{9, 7, 5, 3, 4},{23, 25, 27, 29, 4},{25, 23, 27, 29, 4},{29, 27, 25, 23, 4},{123, 25, 127, 129, 4},{125, 123, 27, 129, 4},{129, 127, 125, 23, 4},

‎benchmark_scripts/vkFFT_scripts/src/sample_16_precision_VkFFT_single_dct.cpp

Lines changed: 15 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -72,16 +72,28 @@ VkFFTResult sample_16_precision_VkFFT_single_dct(VkGPU* vkGPU, uint64_t file_out
7272
fprintf(output, "16 - VkFFT/FFTW R2R DCT-I, II, III and IV precision test in single precision\n");
7373
printf("16 - VkFFT/FFTW R2R DCT-I, II, III and IV precision test in single precision\n");
7474

75-
const int num_benchmark_samples = 235;
75+
const int num_benchmark_samples = 318;
7676
const int num_runs = 1;
7777

7878
uint64_t benchmark_dimensions[num_benchmark_samples][5] = { {2, 1, 1, 1, 1},{3, 1, 1, 1, 1},{5, 1, 1, 1, 1},{6, 1, 1, 1, 1},{7, 1, 1, 1, 1},{8, 1, 1, 1, 1},{9, 1, 1, 1, 1},{10, 1, 1, 1, 1},{11, 1, 1, 1, 1},{12, 1, 1, 1, 1},{13, 1, 1, 1, 1},{14, 1, 1, 1, 1},
7979
{15, 1, 1, 1, 1},{16, 1, 1, 1, 1},{17, 1, 1, 1, 1},{21, 1, 1, 1, 1},{22, 1, 1, 1, 1},{23, 1, 1, 1, 1},{24, 1, 1, 1, 1},{25, 1, 1, 1, 1},{26, 1, 1, 1, 1},{27, 1, 1, 1, 1},{28, 1, 1, 1, 1},{29, 1, 1, 1, 1},{30, 1, 1, 1, 1},{31, 1, 1, 1, 1},{32, 1, 1, 1, 1},{33, 1, 1, 1, 1},{34, 1, 1, 1, 1},{35, 1, 1, 1, 1},{37, 1, 1, 1, 1},{38, 1, 1, 1, 1},{39, 1, 1, 1, 1},{41, 1, 1, 1, 1},{42, 1, 1, 1, 1},{44, 1, 1, 1, 1},{45, 1, 1, 1, 1},{46, 1, 1, 1, 1},{49, 1, 1, 1, 1},{52, 1, 1, 1, 1},{55, 1, 1, 1, 1},{56, 1, 1, 1, 1},{58, 1, 1, 1, 1},{60, 1, 1, 1, 1},{64, 1, 1, 1, 1},{65, 1, 1, 1, 1},{66, 1, 1, 1, 1},{81, 1, 1, 1, 1},
8080
{121, 1, 1, 1, 1},{125, 1, 1, 1, 1},{128, 1, 1, 1, 1},{143, 1, 1, 1, 1},{146, 1, 1, 1, 1}, {169, 1, 1, 1, 1},{243, 1, 1, 1, 1},{256, 1, 1, 1, 1},{283, 1, 1, 1, 1},{286, 1, 1, 1, 1},{343, 1, 1, 1, 1},{429, 1, 1, 1, 1},{512, 1, 1, 1, 1},{572, 1, 1, 1, 1},{625, 1, 1, 1, 1},{720, 1, 1, 1, 1},{1024, 1, 1, 1, 1},{1080, 1, 1, 1, 1},{1001, 1, 1, 1, 1},{1229, 1, 1, 1, 1},{1287, 1, 1, 1, 1},{1400, 1, 1, 1, 1},{1440, 1, 1, 1, 1},{1676, 1, 1, 1, 1},{1920, 1, 1, 1, 1},{2048, 1, 1, 1, 1},{2160, 1, 1, 1, 1},{3024,1,1, 1, 1},{3500,1,1, 1, 1},
81-
{3840, 1, 1, 1, 1},{4000 , 1, 1, 1, 1},{4050, 1, 1, 1, 1},{4096 , 1, 1, 1, 1},
81+
{3840, 1, 1, 1, 1},{4000 , 1, 1, 1, 1},{4050, 1, 1, 1, 1},{4096 , 1, 1, 1, 1} ,{4391, 1, 1, 1, 1},{7000,1,1, 1, 1},{7680, 1, 1, 1, 1},{7879, 1, 1, 1, 1},{9000, 1, 1, 1, 1},{11587, 1, 1, 1, 1},{7680 * 5, 1, 1, 1, 1},
82+
{15319, 1, 1, 1, 1},{21269, 1, 1, 1, 1},{27283, 1, 1, 1, 1},{39829, 1, 1, 1, 1},{52733, 1, 1, 1, 1},{2000083, 1, 1, 1, 1},{4000067, 1, 1, 1, 1},{8003869, 1, 1, 1, 1},
83+
{(uint64_t)pow(3,10), 1, 1, 1, 1},{(uint64_t)pow(3,11), 1, 1, 1, 1},{(uint64_t)pow(3,12), 1, 1, 1, 1},{(uint64_t)pow(3,13), 1, 1, 1, 1},{(uint64_t)pow(3,14), 1, 1, 1, 1},{(uint64_t)pow(3,15), 1, 1, 1, 1},
84+
{(uint64_t)pow(5,5), 1, 1, 1, 1},{(uint64_t)pow(5,6), 1, 1, 1, 1},{(uint64_t)pow(5,7), 1, 1, 1, 1},{(uint64_t)pow(5,8), 1, 1, 1, 1},{(uint64_t)pow(5,9), 1, 1, 1, 1},
85+
{(uint64_t)pow(7,4), 1, 1, 1, 1},{(uint64_t)pow(7,5), 1, 1, 1, 1},{(uint64_t)pow(7,6), 1, 1, 1, 1},{(uint64_t)pow(7,7), 1, 1, 1, 1},{(uint64_t)pow(7,8), 1, 1, 1, 1},
86+
{(uint64_t)pow(11,3), 1, 1, 1, 1},{(uint64_t)pow(11,4), 1, 1, 1, 1},{(uint64_t)pow(11,5), 1, 1, 1, 1},{(uint64_t)pow(11,6), 1, 1, 1, 1},
87+
{(uint64_t)pow(13,3), 1, 1, 1, 1},{(uint64_t)pow(13,4), 1, 1, 1, 1},{(uint64_t)pow(13,5), 1, 1, 1, 1},{(uint64_t)pow(13,6), 1, 1, 1, 1},
8288
{8, 3, 1, 1, 2},{8, 5, 1, 1, 2},{8, 6, 1, 1, 2},{8, 7, 1, 1, 2},{8, 8, 1, 1, 2},{8, 9, 1, 1, 2},{8, 10, 1, 1, 2},{8, 11, 1, 1, 2},{8, 12, 1, 1, 2},{8, 13, 1, 1, 2},{8, 14, 1, 1, 2},{8, 15, 1, 1, 2},{8, 16, 1, 1, 2},{8, 17, 1, 1, 2},{8, 21, 1, 1, 2},{8, 22, 1, 1, 2},{8, 23, 1, 1, 2},{8, 24, 1, 1, 2},
8389
{8, 25, 1, 1, 2},{8, 26, 1, 1, 2},{8, 27, 1, 1, 2},{8, 28, 1, 1, 2},{8, 29, 1, 1, 2},{8, 30, 1, 1, 2},{8, 31, 1, 1, 2},{8, 32, 1, 1, 2},{8, 33, 1, 1, 2},{8, 34, 1, 1, 2},{8, 35, 1, 1, 2},{8, 37, 1, 1, 2},{8, 38, 1, 1, 2},{8, 39, 1, 1, 2},{8, 41, 1, 1, 2},{8, 44, 1, 1, 2},{8, 45, 1, 1, 2},{8, 46, 1, 1, 2},{8, 49, 1, 1, 2},{8, 52, 1, 1, 2},{8, 56, 1, 1, 2},{8, 58, 1, 1, 2},{8, 60, 1, 1, 2},{8, 64, 1, 1, 2},{8, 66, 1, 1, 2},{8, 81, 1, 1, 2},{8, 125, 1, 1, 2},{8, 128, 1, 1, 2},{8, 243, 1, 1, 2},{8, 256, 1, 1, 2},{8, 343, 1, 1, 2},{8, 358, 1, 1, 2},{8, 429, 1, 1, 2},{8, 512, 1, 1, 2},{8, 1024, 1, 1, 2},
84-
{720, 480, 1, 1, 2},{1280, 720, 1, 1, 2},
90+
{720, 480, 1, 1, 2},{1280, 720, 1, 1, 2}, {8, 4320, 1, 1, 2},{8, 4391, 1, 1, 2},{8, 7000, 1, 1, 2},{8, 7680, 1, 1, 2},{8, 4050 * 3, 1, 1, 2},{8, 7680 * 5, 1, 1, 2}, {720, 480, 1, 1, 2},{1280, 720, 1, 1, 2},{1920, 1080, 1, 1, 2}, {2560, 1440, 1, 1, 2},{3840, 2160, 1, 1, 2},{7680, 4320, 1, 1, 2},
91+
{8,15319, 1, 1, 2},{8,21269, 1, 1, 2},{8,27283, 1, 1, 2},{8,39829, 1, 1, 2},{8,52733, 1, 1, 2},{8,2000083, 1, 1, 2},{8,4000067, 1, 1, 2},{8,8003869, 1, 1, 2},
92+
{8, (uint64_t)pow(3,10), 1, 1, 2}, {8, (uint64_t)pow(3,11), 1, 1, 2}, {8, (uint64_t)pow(3,12), 1, 1, 2}, {8, (uint64_t)pow(3,13), 1, 1, 2}, {8, (uint64_t)pow(3,14), 1, 1, 2}, {8, (uint64_t)pow(3,15), 1, 1, 2},
93+
{8, (uint64_t)pow(5,5), 1, 1, 2}, {8, (uint64_t)pow(5,6), 1, 1, 2}, {8, (uint64_t)pow(5,7), 1, 1, 2}, {8, (uint64_t)pow(5,8), 1, 1, 2}, {8, (uint64_t)pow(5,9), 1, 1, 2},
94+
{8, (uint64_t)pow(7,4), 1, 1, 2},{8, (uint64_t)pow(7,5), 1, 1, 2},{8, (uint64_t)pow(7,6), 1, 1, 2},{8, (uint64_t)pow(7,7), 1, 1, 2},{8, (uint64_t)pow(7,8), 1, 1, 2},
95+
{8, (uint64_t)pow(11,3), 1, 1, 2},{8, (uint64_t)pow(11,4), 1, 1, 2},{8, (uint64_t)pow(11,5), 1, 1, 2},{8, (uint64_t)pow(11,6), 1, 1, 2},
96+
{8, (uint64_t)pow(13,3), 1, 1, 2},{8, (uint64_t)pow(13,4), 1, 1, 2},{8, (uint64_t)pow(13,5), 1, 1, 2},{8, (uint64_t)pow(13,6), 1, 1, 2},
8597
{2, 2, 2, 1, 3},{3, 3, 3, 1, 3},{5, 5, 5, 1, 3},{6, 6, 6, 1, 3},{7, 7, 7, 1, 3},{8, 8, 8, 1, 3},{9, 9, 9, 1, 3},{10, 10, 10, 1, 3},{11, 11, 11, 1, 3},{12, 12, 12, 1, 3},{13, 13, 13, 1, 3},{14, 14, 14, 1, 3},
8698
{15, 15, 15, 1, 3},{16, 16, 16, 1, 3},{17, 17, 17, 1, 3},{21, 21, 21, 1, 3},{22, 22, 22, 1, 3},{23, 23, 23, 1, 3},{24, 24, 24, 1, 3},{25, 25, 25, 1, 3},{26, 26, 26, 1, 3},{27, 27, 27, 1, 3},{28, 28, 28, 1, 3},{29, 29, 29, 1, 3},{30, 30, 30, 1, 3},{31, 31, 31, 1, 3},{32, 32, 32, 1, 3},{33, 33, 33, 1, 3},{34, 34, 34, 1, 3},{35, 35, 35, 1, 3},{39, 39, 39, 1, 3},{42, 42, 42, 1, 3},{44, 44, 44, 1, 3},{45, 45, 45, 1, 3},{46, 46, 46, 1, 3},{49, 49, 49, 1, 3},{52, 52, 52, 1, 3},{56, 56, 56, 1, 3},{60, 60, 60, 1, 3},{64, 64, 64, 1, 3},{81, 81, 81, 1, 3},
8799
{121, 121, 121, 1, 3},{128, 128, 128, 1, 3},{125, 125, 125, 1, 3},{143, 143, 143, 1, 3},{169, 169, 169, 1, 3},{243, 243, 243, 1, 3},{256, 256, 256, 1, 3},

0 commit comments

Comments
 (0)