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Library: MATH-NEON By: Lachlan Tychsen-Smith Licence: MIT (expat) ======================================================================================= This project implements the cmath functions and some optimised matrix functions with the aim of increasing the floating point performance of ARM Cortex A-8 based platforms. As well as implementing the functions in ARM NEON assembly, they sacrifice error checking and some accuracy to achieve better performance. Function Errors: ======================================================================================= The measurement and characterisations of the inaccuracies present within these functions is really a field within itself. For the benchmark i provide the maximum absolute, maximum relative and root mean squared error compared to the cmath implementations over the specified range. However these values can be misleading, especially for functions which quickly go to infinity. So its always a good idea to test it within your actual program. In general, this library will not be as accurate as cmath, however for many functions it is close enough to be negilible. Notes: ======================================================================================= - The *_c functions are c implementations of the *_neon code. - Like cmath, The errors present in the functions are very dependent on the range which your operating in. So you should test them first. - Look in the "math_neon.h" file for discriptions of the functions. In some function files there are also notes on the specific implementation. - The *_neon functions make certain assumptions about the location of arguments that is incompatible with inlining. Contact: ======================================================================================= Name: Lachlan Tychsen-Smith Email: lachlan.ts@gmail.com PSVITA performances test results: RUNFAST: Disabled ------------------------------------------------------------------------------------------------------ MATRIX FUNCTION TESTS ------------------------------------------------------------------------------------------------------ matmul2_c = |-14.56, 5.96| |-15.35, 10.50| matmul2_neon = |-14.56, 5.96| |-15.35, 10.50| matmul2: c=174924 neon=64490 rate=2.71 matvec2_c = |-14.56, -15.35| matvec2_neon = |-14.56, -15.35| matvec2: c=88957 neon=58337 rate=1.52 matmul3_c = |-21.39, -4.68, -1.74| |-8.66, -8.97, 1.83| |15.88, 0.30, -2.23| matmul3_neon = |-21.39, -4.68, -1.74| |-8.66, -8.97, 1.83| |15.88, 0.30, -2.23| matmul3: c=552486 neon=297268 rate=1.86 matvec3_c = |-21.39, -8.66, 15.88| matvec3_neon = |-21.39, -8.66, 15.88| matvec3: c=184104 neon=128780 rate=1.43 matmul4_c = |-13.65, -1.80, -12.92, 6.56| |-10.21, 9.47, 2.73, 14.79| |0.97, 11.69, -0.64, -12.87| |20.06, 6.77, 35.61, -0.02| matmul4_neon = |-13.65, -1.80, -12.92, 6.56| |-10.21, 9.47, 2.73, 14.79| |0.97, 11.69, -0.64, -12.87| |20.06, 6.77, 35.61, -0.02| matmul4: c=1315568 neon=254227 rate=5.17 matvec4_c = |-13.65, -10.21, 0.97, 20.058556| matvec4_neon = |-13.65, -10.21, 0.97, 20.058556| matvec4: c=331712 neon=147196 rate=2.25 dot2_c = -10.903330 dot2_neon = -10.903330 dot2: c=230295 neon=168799 rate=1.36 normalize2_c = [-0.74, 0.67] normalize2_neon = [-0.74, 0.67] normalize2: c=950716 neon=965780 rate=0.98 dot3_c = -4.226746 dot3_neon = -4.226746 dot3: c=306957 neon=337316 rate=0.91 normalize3_c = [-0.69, 0.62, -0.38] normalize3_neon = [-0.69, 0.62, -0.38] normalize3: c=1180950 neon=1134557 rate=1.04 cross3_c = [-9.67, -19.39, -14.24] cross3_neon = [-9.67, -19.39, -14.24] cross3: c=659558 neon=766896 rate=0.86 dot4_c = 2.782796 dot4_neon = 2.782796 dot4: c=414233 neon=276068 rate=1.50 normalize4_c = [-0.59, 0.53, -0.32, -0.52] normalize4_neon = [-0.59, 0.53, -0.32, -0.52] normalize4: c=1364294 neon=1103327 rate=1.24 ------------------------------------------------------------------------------------------------------ CMATH FUNCTION TESTS ------------------------------------------------------------------------------------------------------ Function Range Number ABS Max Error REL Max Error RMS Error Time Rate ------------------------------------------------------------------------------------------------------ sinf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 1394459996 x1.00 sinf_c [-3.14, 3.14] 500000 7.75e-07 1.00e+02% 4.09e-07 1395128226 x1.00 sinf_neon [-3.14, 3.14] 500000 8.34e-07 1.00e+02% 4.09e-07 1395853554 x1.00 cosf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 1396644271 x1.00 cosf_c [-3.14, 3.14] 500000 7.75e-07 6.74e-01% 4.15e-07 1397360321 x1.00 cosf_neon [-3.14, 3.14] 500000 8.34e-07 6.74e-01% 4.16e-07 1398126872 x1.00 tanf [-0.79, 0.79] 500000 0.00e+00 0.00e+00% 0.00e+00 1398889596 x1.00 tanf_c [-0.79, 0.79] 500000 2.98e-06 7.94e-04% 1.31e-06 1399704712 x1.00 tanf_neon [-0.79, 0.79] 500000 1.91e-06 3.62e-04% 6.66e-07 1400612899 x1.00 asinf [-1.00, 1.00] 500000 0.00e+00 0.00e+00% 0.00e+00 1401838993 x1.00 asinf_c [-1.00, 1.00] 500000 5.54e-05 1.06e-02% nan 1402745512 x1.00 asinf_neon [-1.00, 1.00] 500000 4.66e-05 8.90e-03% nan 1403967661 x1.00 acosf [-1.00, 1.00] 500000 0.00e+00 0.00e+00% 0.00e+00 1405317842 x1.00 acosf_c [-1.00, 1.00] 500000 5.56e-05 6.46e-03% nan 1406294753 x1.00 acosf_neon [-1.00, 1.00] 500000 4.67e-05 6.35e-03% nan 1407598039 x1.00 atanf [-1.00, 1.00] 500000 0.00e+00 0.00e+00% 0.00e+00 1408314869 x1.00 atanf_c [-1.00, 1.00] 500000 1.67e-04 2.12e-02% 7.40e-05 1408872421 x1.00 atanf_neon [-1.00, 1.00] 500000 1.67e-04 2.12e-02% 7.40e-05 1409736652 x1.00 sinhf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 1411101066 x1.00 sinhf_c [-3.14, 3.14] 500000 1.91e-06 1.52e-01% 1.85e-07 1412173492 x1.00 sinhf_neon [-3.14, 3.14] 500000 1.91e-06 1.52e-01% 1.90e-07 1413205410 x1.00 coshf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 1414417802 x1.00 coshf_c [-3.14, 3.14] 500000 9.54e-07 2.38e-05% 1.64e-07 1415426083 x1.00 coshf_neon [-3.14, 3.14] 500000 1.91e-06 2.22e-05% 1.68e-07 1416412636 x1.00 tanhf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 1417684273 x1.00 tanhf_c [-3.14, 3.14] 500000 1.20e-05 2.48e-01% 5.48e-06 1418659628 x1.00 tanhf_neon [-3.14, 3.14] 500000 2.38e-07 2.47e-01% 5.40e-08 1419650721 x1.00 expf [0.00, 10.00] 500000 0.00e+00 0.00e+00% 0.00e+00 1420706074 x1.00 expf_c [0.00, 10.00] 500000 9.77e-03 6.15e-05% 1.64e-03 1421444150 x1.00 expf_neon [0.00, 10.00] 500000 9.77e-03 6.58e-05% 1.64e-03 1422203499 x1.00 logf [1.00, 1000.00] 500000 0.00e+00 0.00e+00% 0.00e+00 1423106698 x1.00 logf_c [1.00, 1000.00] 500000 6.20e-06 1.62e-02% 9.83e-07 1423735174 x1.00 logf_neon [1.00, 1000.00] 500000 7.63e-06 1.03e-02% 1.07e-06 1424434406 x1.00 log10f [1.00, 1000.00] 500000 0.00e+00 0.00e+00% 0.00e+00 1425516892 x1.00 log10f_c [1.00, 1000.00] 500000 2.86e-06 6.68e-03% 4.79e-07 1426200368 x1.00 log10f_neon [1.00, 1000.00] 500000 3.34e-06 6.68e-03% 4.84e-07 1426966844 x1.00 floorf [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1429081993 x1.00 floorf_c [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1430839273 x1.00 floorf_neon [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1433474766 x1.00 ceilf [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1435602956 x1.00 ceilf_c [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1437403711 x1.00 ceilf_neon [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1440044970 x1.00 fabsf [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1441265630 x1.00 fabsf_c [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1442491716 x1.00 fabsf_neon [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 1443680744 x1.00 sqrtf [1.00, 1000.00] 500000 0.00e+00 0.00e+00% 0.00e+00 1444844144 x1.00 sqrtf_c [1.00, 1000.00] 500000 2.33e-04 1.06e-03% 8.69e-05 1445710342 x1.00 sqrtf_neon [1.00, 1000.00] 500000 7.63e-06 2.91e-05% 1.60e-06 1446544637 x1.00 invsqrtf [1.00, 1000.00] 500000 0.00e+00 0.00e+00% 0.00e+00 1446995307 x1.00 invsqrtf_c [1.00, 1000.00] 500000 4.35e-06 4.78e-04% 2.00e-07 1447471977 x1.00 invsqrtf_neon [1.00, 1000.00] 500000 1.19e-07 2.12e-05% 4.81e-09 1447987675 x1.00 atan2f [0.10, 10.00] 10000 0.00e+00 0.00e+00% 0.00e+00 1449713108 x1.00 atan2f_c [0.10, 10.00] 10000 1.73e-04 2.23e-02% 0.00e+00 1451276575 x1.00 atan2f_neon [0.10, 10.00] 10000 1.67e-04 2.12e-02% 0.00e+00 1453093260 x1.00 powf [1.00, 10.00] 10000 0.00e+00 0.00e+00% 0.00e+00 1458606663 x1.00 powf_c [1.00, 10.00] 10000 1.08e+05 4.37e-03% 0.00e+00 1461584933 x1.00 powf_neon [1.00, 10.00] 10000 1.36e+05 5.88e-03% 0.00e+00 1464702743 x1.00 fmodf [1.00, 10.00] 10000 0.00e+00 0.00e+00% 0.00e+00 1466022029 x1.00 fmodf_c [1.00, 10.00] 10000 9.90e+00 8.06e-02% 0.00e+00 1467403015 x1.00 fmodf_neon [1.00, 10.00] 10000 9.97e+00 8.06e-02% 0.00e+00 1468767755 x1.00