CMSIS DSP for PULPino

This is a port of ARM CMSIS DSP library to PULPino microcontroller(RISC-V RV32IMFD ISA with custom extensions). This project is part of Google Summer of Code (GSoC) 2017

The names of files and functions are renamed from arm to riscv. For example arm_add_q15 is changed to riscv_add_q15. Check examples or tests for more clarification.

To use optimized functions with DSP extension, add #define USE_DSP_RISCV in riscv_math.h

The library is already configured and integrated in the CMake files of PULPino in this fork.

For example, after configuring PULPino itself and installing required tools, you can simulate Benchmark_BasicMathFunctions1 by typing.

make Benchmark_BasicMathFunctions1.vsim

Note that some Transform Fucntions benchmarks needs more memory than the default (512kb instead of 32kb).

To increase memory size, three files should be changed:

• rtl/core_region.sv, where parameter DATA_RAM_SIZE changes the size of the RAM.

• sw/ref/link.common.ld, the dataram size and stack start address need to be changed in the linker script.

• sw/utils/s19toslm.py, which translates the compiler output to the format the testbench reads, tcdm_bank_size needs to be changed.

Directory Structure:

• inc/ : Include files for CMSIS DSP.

• src/ : Ported Source code.

• tests/ : some tests, used for benchmarking.

• examples/ : Ported examples.

• more_tests/ : More tests based on subset of the CMSISv5 test suite, it doesn't compare results with pre-known values but with reference implementation.

• utils/ : Python scripts to convert supported fixed-point formats to floating-point numbers, used to interpret fixed-point results.

Flow of development:

For each module:

1. Port to PULPino.
2. Test it.
3. Benchmark basic implementation.
4. Optimize the implementation with PULPino DSP extension.
5. Test it.
6. Benchmark DSP implementation.
7. Benchmark ARM m4 and compare results.

Ported Modules

1. Basic Math Functions

2. Fast Math Functions

3. Complex Math Functions

4. Statistics Functions

5. Matrix Functions

6. Support Functions

7. Filtering Functions

8. Transform Functions (without radix-2 suppressed Functions)

9. Controller Functions

10. Interpolation Functions

Benchmarks

ARM M4 Benchmarks were done with Keil simulator(CM4_FP) and CMSISv5.

ARM M4 uses its DSP Instructions by default.

The floating point arithmetic operations are slow as these results are obtained without FPU.

Improvements of DSP extension:

BasicMath Functions

These Benchmarks are performed on vectors of size 32.

Results from PULPino were compared with results from ARM m4 and also were checked by hand.

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_abs_f32	133	N/A	221
arm_abs_q7	274	185(32.5%)	297
arm_abs_q15	224	187(16.5%)	293
arm_abs_q31	254	237(6.7%)	282
arm_add_f32	5310	N/A	295
arm_add_q7	373	340(8.8%)	109
arm_add_q15	403	192(52.4%)	168
arm_add_q31	543	N/A	290
arm_dot_prod_q15	336	187(44.3%)	144
arm_dot_prod_q31	572	N/A	504
arm_dot_prod_f32	10009	N/A	311
arm_dot_prod_q7	142	57(60%)	144
arm_mult_f32	5149	N/A	295
arm_mult_q31	751	N/A	354
arm_mult_q15	302	203(32.8%)	238
arm_mult_q7	302	235(22.2%)	322
arm_negate_f32	143	N/A	221
arm_negate_q7	124	N/A	92
arm_negate_q15	192	187(2.6%)	132
arm_negate_q31	237	N/A	216
arm_offset_f32	5258	N/A	223
arm_offset_q7	339	233(31.3%)	100
arm_offset_q15	369	153(58.5%)	133
arm_offset_q31	546	N/A	216
arm_scale_f32	5239	N/A	191
arm_scale_q7	377	207(45.1%)	295
arm_scale_q15	406	207(49%)	246
arm_scale_q31	626	N/A	379
arm_shift_q7 (left)	341	190(44.3%)	300
arm_shift_q15 (left)	373	185(50.4%)	236
arm_shift_q31 (left)	642	N/A	369
arm_shift_q7 (right)	143	62(56.6%)	246
arm_shift_q15 (right)	141	91(35.5%)	203
arm_shift_q31 (right)	145	N/A	236
arm_sub_f32	5350	N/A	295
arm_sub_q7	398	340(14.6%)	109
arm_sub_q15	428	192(55.1%)	168
arm_sub_q31	622	N/A	290

FastMath Functions

Fast Math Functions doesn't operate on vectors.

Test cases are the same in the two benchmarks.

All Sin and Cosine functions uses tables but with interpolation.

sqrt for float use the built in sqrt function while sqrt for fixed point use Newton-Raphson algorithm.

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_sqrt_f32	1199	N/A	26
arm_sqrt_q15	628	N/A	83
arm_sqrt_q31	581	N/A	131
arm_cos_f32	1853	N/A	53
arm_cos_q15	37	N/A	36
arm_cos_q31	44	N/A	46
arm_sin_f32	1779	N/A	55
arm_sin_q15	28	N/A	30
arm_sin_q31	37	N/A	43

Complex Math Functions

These Benchmarks are performed on vectors of size 32 (16 complex numbers).

Most of the optimizations are in q15 data type, as float is not supported, and also q31 can't use many from the extended instructions as SIMD instructions and clip.

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_cmplx_conj_f32	129	N/A	181
arm_cmplx_conj_q31	175	N/A	173
arm_cmplx_conj_q15	185	142(23.2%)	142
arm_cmplx_dot_prod_f32	20203	N/A	379
arm_cmplx_dot_prod_q31	1013	N/A	796
arm_cmplx_dot_prod_q15	499	N/A	294
arm_cmplx_mag_f32	27036	N/A	512
arm_cmplx_mag_q31	9997	N/A	2367
arm_cmplx_mag_q15	10396	10217(1.7%)	1430
arm_cmplx_mag_squared_f32	7509	N/A	181
arm_cmplx_mag_squared_q31	267	N/A	324
arm_cmplx_mag_squared_q15	235	90(61.7%)	134
arm_cmplx_mult_cmplx_f32	15257	N/A	364
arm_cmplx_mult_cmplx_q31	565	N/A	366
arm_cmplx_mult_cmplx_q15	270	206 (23.7%)	366
arm_cmplx_mult_real_f32	5116	N/A	236
arm_cmplx_mult_real_q31	720	N/A	302
arm_cmplx_mult_real_q15	305	206(32.5%)	211

Statistics Functions

These Benchmarks are performed on vectors of size 32.

Functions that need square root operations, use the functions from FastMath as rms and var.

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_max_f32	6748	N/A	322
arm_max_q7	299	N/A	283
arm_max_q15	298	N/A	283
arm_max_q31	267	N/A	283
arm_mean_f32	5432	N/A	172
arm_mean_q7	139	77(44.6%)	146
arm_mean_q15	138	104(24.6%)	148
arm_mean_q31	416	N/A	397
arm_min_f32	6691	N/A	322
arm_min_q7	295	N/A	283
arm_min_q15	293	N/A	283
arm_min_q31	262	N/A	283
arm_power_f32	9698	N/A	232
arm_power_q7	108	45(58.3%)	109
arm_power_q15	303	168(44.6%)	107
arm_power_q31	558	N/A	434
arm_rms_f32	11254	N/A	268
arm_rms_q15	1074	935(12.9%)	386
arm_rms_q31	1282	N/A	765
arm_std_f32	17120	N/A	345
arm_std_q15	1263	1108(12.3%)	628
arm_std_q31	1749	N/A	1121
arm_var_f32	15770	N/A	455
arm_var_q15	640	488(23.8%)	551
arm_var_q31	1155	N/A	993

Matrix Functions

These Benchmarks are performed on matrices of size 4x4.

Functions with Fast version, use results or accumulators of size 32 bits instead of 64 bits. For more information refer to CMSIS DSP Software Library

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_mat_add_f32	2492	N/A	190
arm_mat_add_q15	216	114(47.2%)	124
arm_mat_add_q31	319	N/A	172
arm_mat_cmplx_mult_f32	68431	N/A	1992
arm_mat_cmplx_mult_q15	2984	2055(31.1%)	1606
arm_mat_cmplx_mult_q31	3544	N/A	3516
arm_mat_inverse_f32	29482	N/A	2994
arm_mat_inverse_f64	53268	N/A	20765
arm_mat_mult_f32	14510	N/A	1067
arm_mat_mult_q15	1110	862(22.3%)	946
arm_mat_mult_q31	1279	N/A	1531
arm_mat_mult_fast_q15	847	637(24.8%)	743
arm_mat_mult_fast_q31	1093	N/A	643
arm_mat_scale_f32	1875	N/A	144
arm_mat_scale_q15	215	116(46%)	156
arm_mat_scale_q31	315	N/A	227
arm_mat_sub_f32	2099	N/A	190
arm_mat_sub_q15	217	113(47.9%)	122
arm_mat_sub_q31	334	N/A	172
arm_mat_trans_f32	114	N/A	268
arm_mat_trans_q15	114	N/A	202
arm_mat_trans_q31	114	N/A	262

Support Functions

These Benchmarks are performed on vectors of size 32.

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_copy_f32	110	N/A	189
arm_copy_q7	70	45(35.7%)	94
arm_copy_q15	92	71(22.8%)	126
arm_copy_q31	108	N/A	182
arm_fill_f32	75	N/A	135
arm_fill_q7	63	40(36.5%)	89
arm_fill_q15	62	35(43.5%)	98
arm_fill_q31	75	N/A	118
arm_float_to_q7	7178	7036(2%)	559
arm_float_to_q15	7242	7036(2.8%)	534
arm_float_to_q31	45287	N/A	1566
arm_q7_to_float	7295	N/A	328
arm_q7_to_q15	140	N/A	156
arm_q7_to_q31	140	N/A	182
arm_q15_to_float	7327	N/A	182
arm_q15_to_q7	140	133(5%)	270
arm_q15_to_q31	138	N/A	206
arm_q31_to_float	7305	N/A	182
arm_q31_to_q7	140	115(17.6%)	156
arm_q31_to_q15	138	119(13.8%)	182

Filtering Functions

Operations are performed on vectors of size 32.

There is some functions with opt and/or fast keywords , for example there is 4 funcions for convolution for q15 data type, which are:

• Riscv_conv_q15

• Riscv_conv_fast_q15

• Riscv_conv_opt_q15

• Riscv_conv_fast_opt_q15

Normal Functions without opt or fast keywords have slower implementation, use 64-bit accumulation to avoid wrap around.

Fast functions uses a 32-bit accumulator (may overflow).

From arm documentation:

Fast versions are supported for Q31 and Q15. Cycles for Fast versions are less compared to Q31 and Q15 of conv and the design requires the input signals should be scaled down to avoid intermediate overflows.

Opt functions have faster implementation using scratch buffers for optimization(but uses more memory), but with 64 bit accumulator.

From arm documentation:

Opt versions are supported for Q15 and Q7. Design uses internal scratch buffer for getting good optimization. These versions are optimized in cycles and consumes more memory(Scratch memory) compared to Q15 and Q7 versions

Opt fast functions use scratch buffers and 32 bit accumulator.

Most of Fast and opt functions are available only for DSP extension(as in ARM).

For more refer to CMSIS DSP Software Library

Init functions are not considered in benchmarking as they are just copying a few pointers and will only be called once in real applications or can be bypassed by initializing the structure directly.

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_biquad_cas_df1_32x64_q31	3859	N/A	4200
arm_biquad_cascade_df1_f32	44970	N/A	661
arm_biquad_cascade_df1_q15	1781	1169(34.4%)	574
arm_biquad_cascade_df1_q31	2195	N/A	1493
arm_biquad_cascade_df1_fast_q15	N/A	616	472
arm_biquad_cascade_df1_fast_q31	1819	N/A	506
arm_biquad_cascade_df2T_f32	45881	N/A	537
arm_biquad_cascade_df2T_f64	70296	N/A	36912
arm_biquad_cascade_stereo_df2T_f32	102567	N/A	1007
arm_conv_f32	334063	N/A	10844
arm_conv_q7	18601	4417(76.3%)	9555
arm_conv_q15	25048	10771(57%)	7749
arm_conv_q31	27925	N/A	15322
arm_conv_opt_q7	N/A	4483	4803
arm_conv_fast_q15	N/A	4736	7087
arm_conv_opt_q15	N/A	11255	5942
arm_conv_fast_opt_q15	N/A	4704	4648
arm_conv_fast_q31	4744	N/A	10083
arm_conv_partial_f32	333142	N/A	11038
arm_conv_partial_q7	18120	4258(76.5%)	9594
arm_conv_partial_q15	24558	10861(55.8%)	7999
arm_conv_partial_q31	27433	N/A	15301
arm_conv_partial_opt_q7	N/A	4330	4410
arm_conv_partial_fast_q15	N/A	4780	7263
arm_conv_partial_opt_q15	N/A	10999	5591
arm_conv_partial_fast_opt_q15	N/A	4721	4295
arm_conv_partial_fast_q31	9897	N/A	9000
arm_correlate_f32	333911	N/A	11155
arm_correlate_q7	18791	2914(84.5%)	9153
arm_correlate_q15	25239	10502(58.4%)	6476
arm_correlate_q31	27944	N/A	15479
arm_correlate_opt_q7	N/A	4579	4969
arm_correlate_fast_q15	N/A	4911	5770
arm_correlate_opt_q15	N/A	11273	5988
arm_correlate_fast_opt_q15	N/A	4642	4707
arm_correlate_fast_q31	10032	N/A	8719
arm_fir_decimate_f32	14339	N/A	753
arm_fir_decimate_q15	1021	820(19.7%)	762
arm_fir_decimate_q31	1017	N/A	1487
arm_fir_decimate_fast_q15	N/A	571	675
arm_fir_decimate_fast_q31	887	N/A	791
arm_fir_f32	57512	N/A	1267
arm_fir_q7	1383	932(32.6%)	1327
arm_fir_q15	2551	1675(34.3%)	1185
arm_fir_q31	2961	N/A	2722
arm_fir_fast_q15	N/A	853	920
arm_fir_fast_q31	3056	N/A	1323
arm_fir_lattice_f32	120999	N/A	2195
arm_fir_lattice_q15	5483	2234(59.3%)	2280
arm_fir_lattice_q31	5106	N/A	2185
arm_fir_interpolate_f32	58641	N/A	2560
arm_fir_interpolate_q15	3967	N/A	3924
arm_fir_interpolate_q31	4288	N/A	4667
arm_iir_lattice_f32	189904	N/A	5241
arm_iir_lattice_q15	7668	5082(33.7%)	4854
arm_iir_lattice_q31	13796	N/A	7756
arm_lms_norm_f32	159993	N/A	7057
arm_lms_norm_q15	11185	9558(14.5%)	8835
arm_lms_norm_q31	14634	N/A	13127
arm_lms_f32	127573	N/A	6167
arm_lms_q15	4325	N/A	7347
arm_lms_q31	8707	N/A	9017
arm_fir_sparse_f32	55605	N/A	5447
arm_fir_sparse_q7	4113	N/A	5351
arm_fir_sparse_q15	4284	N/A	5326
arm_fir_sparse_q31	4773	N/A	6007

Transform Functions

For CFFT, Transform size was 64.

RFFT uses Transform of size 16.

DCT uses Transform of size 128.

To use most of theses tests, the RAM size has to be changed to 512kb.

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_cfft_f32(without bit reversal)	174295	N/A	3110
arm_cfft_f32(with bit reversal)	174783	N/A	3823
arm_cfft_q15(without bit reversal)	6117	4484(26.6%)	2827
arm_cfft_q15(with bit reversal)	6541	4908(25%)	3318
arm_cfft_q31(without bit reversal)	4948	N/A	5322
arm_cfft_q31(with bit reversal)	5428	N/A	6038
arm_rfft_fast_f32	48371	N/A	1930
arm_rfft_q15	1466	N/A	1228
arm_rfft_q31	2466	N/A	2727
arm_dct4_f32	584790	N/A	16037
arm_dct4_q15	17773	N/A	-
arm_dct4_q31	29773	N/A	-

Controller Functions

For PID functions, it operates on single sample at a time, this results are obtained by iterating over a vector of size 32.

Init functions are not considered in benchmarking.

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_pid_f32	29913	N/A	2158
arm_pid_q15	1428	1347(5.7%)	2318
arm_pid_q31	1327	N/A	2536
arm_clarke_f32	485	N/A	25
arm_clarke_q31	104	N/A	36
arm_inv_clarke_f32	956	N/A	24
arm_inv_clarke_q31	92	N/A	34
arm_sin_cos_f32	6690	N/A	129
arm_sin_cos_q31	284	N/A	309
arm_park_f32	922	N/A	34
arm_park_q31	185	N/A	54
arm_inv_park_f32	932	N/A	33
arm_inv_park_q31	185	N/A	54

Interpolation Functions

Function	Puplino Cycles	Puplino DSP Cycles (Imp%)	ARM M4 Cycles
arm_linear_interp_f32	525	N/A	55
arm_linear_interp_q7	22	N/A	80
arm_linear_interp_q15	36	N/A	92
arm_linear_interp_q31	29	N/A	84
arm_bilinear_interp_f32	1505	N/A	189
arm_bilinear_interp_q7	81	N/A	219
arm_bilinear_interp_q15	132	N/A	240
arm_bilinear_interp_q31	104	N/A	226

Future Work

• Port rest of test suite .
• Benchmark with FPU (when double precision instructions are implemented).

Credits

The initial port was performerd by Mostafa Saleh, for the lowRISC project in Google Summer of Code (GSoC) 2017.

License

This project in under The 3-Clause BSD License.