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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: Enabled ------------------------------------------------------------------------------------------------------ MATRIX FUNCTION TESTS ------------------------------------------------------------------------------------------------------ matmul2_c = |-7.16, 9.42| |17.86, -10.70| matmul2_neon = |-7.16, 9.42| |17.86, -10.70| matmul2: c=183985 neon=87480 rate=2.10 matvec2_c = |-7.16, 17.86| matvec2_neon = |-7.16, 17.86| matvec2: c=98178 neon=66040 rate=1.49 matmul3_c = |11.14, -0.78, -3.98| |16.56, 17.96, 23.58| |8.73, -0.18, 1.57| matmul3_neon = |11.14, -0.78, -3.98| |16.56, 17.96, 23.58| |8.73, -0.18, 1.57| matmul3: c=551838 neon=340292 rate=1.62 matvec3_c = |11.14, 16.56, 8.73| matvec3_neon = |11.14, 16.56, 8.73| matvec3: c=98178 neon=66040 rate=1.49 matmul4_c = |17.91, -23.96, 1.86, 16.53| |4.10, -18.16, 4.17, 29.06| |6.92, -1.60, 3.12, 27.81| |-15.13, -7.46, -17.91, 22.49| matmul4_neon = |17.91, -23.96, 1.86, 16.53| |4.10, -18.16, 4.17, 29.06| |6.92, -1.60, 3.12, 27.81| |-15.13, -7.46, -17.91, 22.49| matmul4: c=1316131 neon=315444 rate=4.17 matvec4_c = |17.91, 4.10, 6.92, -15.126419| matvec4_neon = |17.91, 4.10, 6.92, -15.126419| matvec4: c=98178 neon=66040 rate=1.49 dot2_c = 5.804099 dot2_neon = 5.804099 dot2: c=291526 neon=307025 rate=0.95 normalize2_c = [0.97, 0.24] normalize2_neon = [0.97, 0.24] normalize2: c=1058588 neon=965696 rate=1.10 dot3_c = -0.817487 dot3_neon = -0.817487 dot3: c=322094 neon=444834 rate=0.72 normalize3_c = [0.50, 0.12, -0.86] normalize3_neon = [0.50, 0.12, -0.86] normalize3: c=1257201 neon=1134375 rate=1.11 cross3_c = [-13.16, -17.29, -10.19] cross3_neon = [-13.16, -17.29, -10.19] cross3: c=705298 neon=766477 rate=0.92 dot4_c = -7.880241 dot4_neon = -7.880241 dot4: c=414431 neon=506460 rate=0.82 normalize4_c = [0.45, 0.11, -0.77, -0.44] normalize4_neon = [0.45, 0.11, -0.77, -0.44] normalize4: c=1410727 neon=1102802 rate=1.28 ------------------------------------------------------------------------------------------------------ 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 647042739 x1.00 sinf_c [-3.14, 3.14] 500000 7.75e-07 1.00e+02% 4.09e-07 646276691 x1.00 sinf_neon [-3.14, 3.14] 500000 1.00e+00 1.00e+02% 7.07e-01 645546381 x1.00 cosf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 644742077 x1.00 cosf_c [-3.14, 3.14] 500000 7.75e-07 6.74e-01% 4.15e-07 643957358 x1.00 cosf_neon [-3.14, 3.14] 500000 1.00e+00 1.00e+02% 7.06e-01 643211256 x1.00 tanf [-0.79, 0.79] 500000 0.00e+00 0.00e+00% 0.00e+00 642444112 x1.00 tanf_c [-0.79, 0.79] 500000 2.98e-06 7.94e-04% 1.31e-06 641628507 x1.00 tanf_neon [-0.79, 0.79] 500000 1.00e+00 1.00e+02% nan 640740514 x1.00 asinf [-1.00, 1.00] 500000 0.00e+00 0.00e+00% 0.00e+00 639560380 x1.00 asinf_c [-1.00, 1.00] 500000 5.54e-05 1.06e-02% nan 638453383 x1.00 asinf_neon [-1.00, 1.00] 500000 1.57e+00 1.00e+02% 6.84e-01 637349653 x1.00 acosf [-1.00, 1.00] 500000 0.00e+00 0.00e+00% 0.00e+00 636078992 x1.00 acosf_c [-1.00, 1.00] 500000 5.56e-05 6.46e-03% nan 634934201 x1.00 acosf_neon [-1.00, 1.00] 500000 1.57e+00 1.02e+05% 6.84e-01 633793585 x1.00 atanf [-1.00, 1.00] 500000 0.00e+00 0.00e+00% 0.00e+00 632835241 x1.00 atanf_c [-1.00, 1.00] 500000 1.67e-04 2.12e-02% 7.40e-05 632142823 x1.00 atanf_neon [-1.00, 1.00] 500000 7.85e-01 0.00e+00% nan 631387330 x1.00 sinhf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 630142014 x1.00 sinhf_c [-3.14, 3.14] 500000 1.91e-06 1.52e-01% 1.85e-07 628992714 x1.00 sinhf_neon [-3.14, 3.14] 500000 1.15e+01 1.00e+02% 4.55e+00 627998454 x1.00 coshf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 626869866 x1.00 coshf_c [-3.14, 3.14] 500000 9.54e-07 2.38e-05% 1.64e-07 625829657 x1.00 coshf_neon [-3.14, 3.14] 500000 1.06e+01 9.14e+01% 3.92e+00 624873969 x1.00 tanhf [-3.14, 3.14] 500000 0.00e+00 0.00e+00% 0.00e+00 623689093 x1.00 tanhf_c [-3.14, 3.14] 500000 1.20e-05 2.48e-01% 5.48e-06 622547097 x1.00 tanhf_neon [-3.14, 3.14] 500000 9.96e-01 1.00e+02% 8.26e-01 621506812 x1.00 expf [0.00, 10.00] 500000 0.00e+00 0.00e+00% 0.00e+00 620497304 x1.00 expf_c [0.00, 10.00] 500000 9.77e-03 6.15e-05% 1.64e-03 619569554 x1.00 expf_neon [0.00, 10.00] 500000 2.20e+04 1.00e+02% 4.92e+03 618761400 x1.00 logf [1.00, 1000.00] 500000 0.00e+00 0.00e+00% 0.00e+00 617882765 x1.00 logf_c [1.00, 1000.00] 500000 6.20e-06 1.62e-02% 9.83e-07 617087810 x1.00 logf_neon [1.00, 1000.00] 500000 9.49e+01 inf% 9.39e+01 616388420 x1.00 log10f [1.00, 1000.00] 500000 0.00e+00 0.00e+00% 0.00e+00 615405364 x1.00 log10f_c [1.00, 1000.00] 500000 2.86e-06 6.68e-03% 4.79e-07 614442585 x1.00 log10f_neon [1.00, 1000.00] 500000 4.12e+01 inf% 4.07e+01 613671782 x1.00 floorf [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 611113689 x1.00 floorf_c [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 608159325 x1.00 floorf_neon [1.00, 1000.00] 5000000 2.00e+00 2.00e+02% 1.42e-02 604769008 x1.01 ceilf [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 601342443 x1.00 ceilf_c [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 598387998 x1.00 ceilf_neon [1.00, 1000.00] 5000000 2.00e+00 1.00e+02% 1.02e+00 594959710 x1.01 fabsf [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 592068236 x1.00 fabsf_c [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 589808748 x1.00 fabsf_neon [1.00, 1000.00] 5000000 0.00e+00 0.00e+00% 0.00e+00 587712180 x1.01 sqrtf [1.00, 1000.00] 500000 0.00e+00 0.00e+00% 0.00e+00 586496654 x1.00 sqrtf_c [1.00, 1000.00] 500000 2.33e-04 1.06e-03% 8.69e-05 585470866 x1.00 sqrtf_neon [1.00, 1000.00] 500000 0.00e+00 0.00e+00% nan 584594551 x1.00 invsqrtf [1.00, 1000.00] 500000 0.00e+00 0.00e+00% 0.00e+00 583492213 x1.00 invsqrtf_c [1.00, 1000.00] 500000 4.35e-06 4.78e-04% 2.00e-07 582448164 x1.00 invsqrtf_neon [1.00, 1000.00] 500000 0.00e+00 0.00e+00% nan 581642365 x1.00 atan2f [0.10, 10.00] 10000 0.00e+00 0.00e+00% 0.00e+00 83594269 x1.00 atan2f_c [0.10, 10.00] 10000 1.73e-04 2.23e-02% 0.00e+00 85383651 x0.98 atan2f_neon [0.10, 10.00] 10000 0.00e+00 0.00e+00% 0.00e+00 87387055 x0.96 powf [1.00, 10.00] 10000 0.00e+00 0.00e+00% 0.00e+00 93430489 x1.00 powf_c [1.00, 10.00] 10000 1.08e+05 4.37e-03% 0.00e+00 96726976 x0.97 powf_neon [1.00, 10.00] 10000 9.97e+09 1.00e+02% 0.00e+00 100185753 x0.93 fmodf [1.00, 10.00] 10000 0.00e+00 0.00e+00% 0.00e+00 101653673 x1.00 fmodf_c [1.00, 10.00] 10000 9.90e+00 8.06e-02% 0.00e+00 103177551 x0.99 fmodf_neon [1.00, 10.00] 10000 9.99e+00 1.00e+02% 0.00e+00 104771240 x0.97