This library has an example SIMD exp, exp2, and exp10 implementation for AVX512.
This library requires supports AVX512.
It currently only implements support for float.
Note that exp2 is considerably more efficient at the moment, so all else equal, prefer that.
2^(x*log2(e))
Perhaps you can fold in a multiplication by
Or, perhaps you can come up with a way to compensate for the loss of precision in x*log2(e).
These are sample benchmark results, obtained on an Intel i9 10980XE (Cascadelake, essentially Skylake-AVX512; note that this CPU still experiences downclocking when running AVX and AVX512 instructions, which later Intel and AMD CPUs do not):
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Benchmark Time CPU Iterations CACHE-MISSES CYCLES INSTRUCTIONS
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BM_simd_exp_run<4, 1>/128 101 ns 101 ns 6842615 6.138u 471.25 571
BM_simd_exp_run<4, 1>/256 170 ns 169 ns 4131515 25.4144u 764.647 1.131k
BM_simd_exp_run<4, 1>/512 295 ns 290 ns 2361965 11.0078u 1.35419k 2.251k
BM_simd_exp_run<4, 1>/1024 610 ns 599 ns 1168752 29.9465u 2.78697k 4.491k
BM_simd_exp_run<4, 1>/2048 1157 ns 1137 ns 611027 3.27318u 5.35288k 8.971k
BM_simd_exp_run<4, 1>/4096 2282 ns 2243 ns 308400 12.9702u 10.5324k 17.931k
BM_simd_exp_run<4, 1>/8192 4537 ns 4459 ns 154710 187.447u 20.9138k 35.851k
BM_simd_exp_run<4, 1>/16384 9046 ns 8892 ns 78462 433.331u 41.668k 71.691k
BM_simd_exp_run<4, 1>/32768 18111 ns 17801 ns 38988 1.59023m 83.1701k 143.371k
BM_simd_exp_run<4, 1>/65536 36405 ns 35775 ns 19297 2.12468m 168.424k 286.731k
BM_simd_exp_run<4, 1>/131072 73696 ns 72321 ns 9465 0.0293714 337.509k 573.451k
BM_simd_exp_run<4, 1>/262144 150991 ns 147968 ns 4731 1.58782 686.825k 1.14689M
BM_simd_exp_run<4, 1>/524288 305367 ns 299332 ns 2286 0.814961 1.39665M 2.29377M
BM_simd_exp_run<4, 1>/1048576 608722 ns 596229 ns 1166 15.5935 2.77903M 4.58753M
BM_simd_exp_run<4, 2>/128 94.7 ns 93.0 ns 7599033 4.60585u 434.24 570
BM_simd_exp_run<4, 2>/256 153 ns 150 ns 4667901 3.21344u 703.477 1.13k
BM_simd_exp_run<4, 2>/512 272 ns 268 ns 2617736 2.67407u 1.25361k 2.25k
BM_simd_exp_run<4, 2>/1024 563 ns 555 ns 1267139 17.3619u 2.5979k 4.49k
BM_simd_exp_run<4, 2>/2048 1076 ns 1073 ns 632306 83.8202u 5.0242k 8.97k
BM_simd_exp_run<4, 2>/4096 2127 ns 2121 ns 331384 63.3706u 9.86796k 17.93k
BM_simd_exp_run<4, 2>/8192 4168 ns 4157 ns 167369 35.8489u 19.5458k 35.85k
BM_simd_exp_run<4, 2>/16384 8322 ns 8300 ns 84826 259.354u 38.8187k 71.69k
BM_simd_exp_run<4, 2>/32768 16693 ns 16650 ns 41671 0.0357323 77.5501k 143.37k
BM_simd_exp_run<4, 2>/65536 33670 ns 33579 ns 20983 8.769m 156.457k 286.73k
BM_simd_exp_run<4, 2>/131072 68632 ns 68386 ns 10288 0.0146773 319.543k 573.45k
BM_simd_exp_run<4, 2>/262144 138004 ns 137394 ns 5145 0.0571429 638.699k 1.14689M
BM_simd_exp_run<4, 2>/524288 268805 ns 267591 ns 2611 0.20337 1.25077M 2.29377M
BM_simd_exp_run<4, 2>/1048576 550657 ns 547986 ns 1291 15.8947 2.55162M 4.58753M
BM_simd_exp_run<4, 4>/128 84.6 ns 84.3 ns 8154243 3.67907u 384.613 546
BM_simd_exp_run<4, 4>/256 132 ns 132 ns 4532082 1.10325u 617.129 1.082k
BM_simd_exp_run<4, 4>/512 271 ns 271 ns 3019497 2.64945u 1.08388k 2.154k
BM_simd_exp_run<4, 4>/1024 525 ns 524 ns 1000000 31u 2.0969k 4.298k
BM_simd_exp_run<4, 4>/2048 865 ns 863 ns 815373 11.0379u 4.05338k 8.586k
BM_simd_exp_run<4, 4>/4096 1715 ns 1710 ns 409926 80.5023u 7.94825k 17.162k
BM_simd_exp_run<4, 4>/8192 3341 ns 3333 ns 203966 29.4167u 15.7051k 34.314k
BM_simd_exp_run<4, 4>/16384 6785 ns 6767 ns 103471 0.0164007 31.2947k 68.618k
BM_simd_exp_run<4, 4>/32768 13309 ns 13277 ns 52950 1.35977m 62.4231k 137.226k
BM_simd_exp_run<4, 4>/65536 28760 ns 28256 ns 24857 9.37362m 131.023k 274.442k
BM_simd_exp_run<4, 4>/131072 56082 ns 54986 ns 12182 0.147841 255.548k 548.874k
BM_simd_exp_run<4, 4>/262144 116387 ns 115471 ns 6066 1.88328 522.225k 1.09774M
BM_simd_exp_run<4, 4>/524288 230410 ns 229408 ns 3044 1.99409 1.04952M 2.19547M
BM_simd_exp_run<4, 4>/1048576 463845 ns 461764 ns 1526 36.1606 2.13018M 4.39092M
BM_simd_exp_run<8, 1>/128 82.7 ns 82.1 ns 8386194 23.2525u 322.225 291
BM_simd_exp_run<8, 1>/256 126 ns 126 ns 5643281 2.65803u 488.924 571
BM_simd_exp_run<8, 1>/512 206 ns 205 ns 3290703 14.8904u 798.741 1.131k
BM_simd_exp_run<8, 1>/1024 402 ns 401 ns 1728617 53.8002u 1.57046k 2.251k
BM_simd_exp_run<8, 1>/2048 755 ns 753 ns 904214 36.4958u 2.94912k 4.491k
BM_simd_exp_run<8, 1>/4096 1475 ns 1471 ns 479318 227.406u 5.73544k 8.971k
BM_simd_exp_run<8, 1>/8192 2925 ns 2917 ns 237706 445.929u 11.5207k 17.931k
BM_simd_exp_run<8, 1>/16384 5842 ns 5826 ns 119177 360.808u 22.8293k 35.851k
BM_simd_exp_run<8, 1>/32768 11721 ns 11687 ns 60904 295.547u 45.5232k 71.691k
BM_simd_exp_run<8, 1>/65536 23695 ns 23631 ns 29847 837.605u 92.5272k 143.371k
BM_simd_exp_run<8, 1>/131072 51882 ns 51701 ns 13422 0.295485 201.273k 286.731k
BM_simd_exp_run<8, 1>/262144 103389 ns 102991 ns 6675 0.228464 398.021k 573.451k
BM_simd_exp_run<8, 1>/524288 210292 ns 209345 ns 3413 1.57867 825.843k 1.14689M
BM_simd_exp_run<8, 1>/1048576 451150 ns 448936 ns 1582 50.426 1.75483M 2.29377M
BM_simd_exp_run<8, 2>/128 78.1 ns 77.9 ns 8720182 8.60074u 309.117 290
BM_simd_exp_run<8, 2>/256 121 ns 119 ns 5809544 2.58196u 470.656 570
BM_simd_exp_run<8, 2>/512 191 ns 191 ns 3664864 24.8304u 759.643 1.13k
BM_simd_exp_run<8, 2>/1024 372 ns 371 ns 1881972 2.65679u 1.48123k 2.25k
BM_simd_exp_run<8, 2>/2048 702 ns 700 ns 1008921 146.691u 2.77443k 4.49k
BM_simd_exp_run<8, 2>/4096 1362 ns 1358 ns 522282 292.945u 5.37633k 8.97k
BM_simd_exp_run<8, 2>/8192 2711 ns 2703 ns 259460 281.354u 10.5614k 17.93k
BM_simd_exp_run<8, 2>/16384 5344 ns 5330 ns 130472 137.961u 20.9294k 35.85k
BM_simd_exp_run<8, 2>/32768 10608 ns 10580 ns 63997 234.386u 41.677k 71.69k
BM_simd_exp_run<8, 2>/65536 21068 ns 21010 ns 33282 2.13329m 83.4299k 143.37k
BM_simd_exp_run<8, 2>/131072 42632 ns 42468 ns 16332 5.8168m 170.6k 286.73k
BM_simd_exp_run<8, 2>/262144 99100 ns 98687 ns 7071 0.0504879 391.235k 573.45k
BM_simd_exp_run<8, 2>/524288 193061 ns 192277 ns 3584 0.341239 767.5k 1.14689M
BM_simd_exp_run<8, 2>/1048576 405535 ns 397029 ns 1786 36.5521 1.55886M 2.29377M
BM_simd_exp_run<8, 4>/128 71.1 ns 69.9 ns 10084253 3.47076u 277.693 278
BM_simd_exp_run<8, 4>/256 105 ns 104 ns 6795412 16.6289u 406.405 546
BM_simd_exp_run<8, 4>/512 169 ns 166 ns 4186879 11.9421u 654.726 1.082k
BM_simd_exp_run<8, 4>/1024 308 ns 303 ns 2358921 23.3157u 1.16844k 2.154k
BM_simd_exp_run<8, 4>/2048 564 ns 554 ns 1255645 70.8799u 2.16818k 4.298k
BM_simd_exp_run<8, 4>/4096 1076 ns 1057 ns 649894 72.3195u 4.2051k 8.586k
BM_simd_exp_run<8, 4>/8192 2106 ns 2080 ns 333605 194.841u 8.28173k 17.162k
BM_simd_exp_run<8, 4>/16384 4133 ns 4121 ns 170120 405.596u 16.3841k 34.314k
BM_simd_exp_run<8, 4>/32768 8165 ns 8142 ns 83936 250.191u 32.5139k 68.618k
BM_simd_exp_run<8, 4>/65536 16536 ns 16490 ns 42801 3.38777m 65.7706k 137.226k
BM_simd_exp_run<8, 4>/131072 34973 ns 34842 ns 19942 0.0866011 138.122k 274.442k
BM_simd_exp_run<8, 4>/262144 84259 ns 83904 ns 8331 0.175129 323.253k 548.874k
BM_simd_exp_run<8, 4>/524288 170070 ns 169364 ns 4177 0.609528 656.954k 1.09774M
BM_simd_exp_run<8, 4>/1048576 352872 ns 350997 ns 1991 118.426 1.38386M 2.19547M
BM_simd_exp_run<16, 1>/128 63.6 ns 63.1 ns 11202497 2.14238u 250.209 160
BM_simd_exp_run<16, 1>/256 85.2 ns 83.7 ns 8333738 1.91991u 332.174 312
BM_simd_exp_run<16, 1>/512 130 ns 129 ns 5475616 6.39197u 512.92 616
BM_simd_exp_run<16, 1>/1024 234 ns 233 ns 2986746 2.00888u 927.38 1.224k
BM_simd_exp_run<16, 1>/2048 420 ns 419 ns 1675759 10.7414u 1.66267k 2.44k
BM_simd_exp_run<16, 1>/4096 783 ns 781 ns 885101 109.592u 3.04656k 4.872k
BM_simd_exp_run<16, 1>/8192 1800 ns 1795 ns 369378 221.995u 7.12268k 9.736k
BM_simd_exp_run<16, 1>/16384 3661 ns 3650 ns 189671 453.417u 14.1684k 19.464k
BM_simd_exp_run<16, 1>/32768 7201 ns 7181 ns 95812 313.113u 28.1683k 38.92k
BM_simd_exp_run<16, 1>/65536 14712 ns 14672 ns 47237 2.60389m 57.2477k 77.832k
BM_simd_exp_run<16, 1>/131072 31692 ns 31582 ns 21973 0.0226187 123.573k 155.656k
BM_simd_exp_run<16, 1>/262144 80904 ns 80579 ns 8790 0.228783 312.28k 311.304k
BM_simd_exp_run<16, 1>/524288 162723 ns 162098 ns 4306 0.998607 628.659k 622.6k
BM_simd_exp_run<16, 1>/1048576 331166 ns 329628 ns 2136 67.0197 1.2704M 1.24519M
BM_simd_exp_run<16, 2>/128 62.9 ns 62.7 ns 11122896 3.8659u 243.357 153
BM_simd_exp_run<16, 2>/256 81.4 ns 81.1 ns 8581207 21.9083u 315.208 293
BM_simd_exp_run<16, 2>/512 123 ns 122 ns 5636531 887.07n 473.947 573
BM_simd_exp_run<16, 2>/1024 211 ns 211 ns 3353178 3.57869u 818.799 1.133k
BM_simd_exp_run<16, 2>/2048 374 ns 373 ns 1888826 25.4126u 1.44929k 2.253k
BM_simd_exp_run<16, 2>/4096 702 ns 700 ns 984040 0 2.725k 4.493k
BM_simd_exp_run<16, 2>/8192 1473 ns 1468 ns 476837 10.4858u 5.73827k 8.973k
BM_simd_exp_run<16, 2>/16384 2908 ns 2900 ns 237544 4.20975u 11.291k 17.933k
BM_simd_exp_run<16, 2>/32768 5740 ns 5725 ns 120373 8.30751u 22.469k 35.853k
BM_simd_exp_run<16, 2>/65536 11994 ns 11960 ns 57370 296.322u 46.7923k 71.693k
BM_simd_exp_run<16, 2>/131072 27323 ns 27230 ns 25460 4.90966m 106.755k 143.373k
BM_simd_exp_run<16, 2>/262144 78416 ns 78117 ns 8967 0.359429 301.964k 286.733k
BM_simd_exp_run<16, 2>/524288 158412 ns 157795 ns 4455 0.731089 606.875k 573.453k
BM_simd_exp_run<16, 2>/1048576 319621 ns 318216 ns 2205 52.6553 1.23362M 1.14689M
BM_simd_exp_run<16, 4>/128 58.4 ns 58.3 ns 11895571 1.26097u 226.972 147
BM_simd_exp_run<16, 4>/256 75.1 ns 74.9 ns 9355737 748.204n 294.388 281
BM_simd_exp_run<16, 4>/512 108 ns 108 ns 6434818 310.809n 424.221 549
BM_simd_exp_run<16, 4>/1024 180 ns 180 ns 3837621 1.56347u 703.301 1.085k
BM_simd_exp_run<16, 4>/2048 319 ns 318 ns 2166203 11.5409u 1.24221k 2.157k
BM_simd_exp_run<16, 4>/4096 597 ns 596 ns 1191770 11.7472u 2.33025k 4.301k
BM_simd_exp_run<16, 4>/8192 1220 ns 1216 ns 582008 6.87276u 4.75915k 8.589k
BM_simd_exp_run<16, 4>/16384 2364 ns 2358 ns 295611 47.3595u 9.33597k 17.165k
BM_simd_exp_run<16, 4>/32768 4784 ns 4770 ns 147537 142.337u 18.5228k 34.317k
BM_simd_exp_run<16, 4>/65536 9930 ns 9901 ns 71263 954.212u 38.663k 68.621k
BM_simd_exp_run<16, 4>/131072 22578 ns 22504 ns 31223 0.0443904 88.049k 137.229k
BM_simd_exp_run<16, 4>/262144 77503 ns 77196 ns 9110 0.0917673 299.796k 274.445k
BM_simd_exp_run<16, 4>/524288 155874 ns 155252 ns 4511 1.04478 599.646k 548.877k
BM_simd_exp_run<16, 4>/1048576 313546 ns 312176 ns 2248 7.6855 1.20591M 1.09774M
BM_simd_exp_run<4, 1, 2>/128 45.7 ns 45.6 ns 15372594 390.305n 211.65 475
BM_simd_exp_run<4, 1, 2>/256 96.2 ns 95.9 ns 7279447 16.3474u 440.017 939
BM_simd_exp_run<4, 1, 2>/512 190 ns 189 ns 3747724 2.66829u 868.823 1.867k
BM_simd_exp_run<4, 1, 2>/1024 432 ns 431 ns 1639872 1.21961u 1.97998k 3.723k
BM_simd_exp_run<4, 1, 2>/2048 855 ns 853 ns 833398 1.19991u 3.92348k 7.435k
BM_simd_exp_run<4, 1, 2>/4096 1708 ns 1704 ns 410284 29.248u 7.87678k 14.859k
BM_simd_exp_run<4, 1, 2>/8192 3464 ns 3455 ns 203349 536.024u 15.8041k 29.707k
BM_simd_exp_run<4, 1, 2>/16384 6920 ns 6903 ns 100087 479.583u 31.5238k 59.403k
BM_simd_exp_run<4, 1, 2>/32768 13675 ns 13642 ns 50998 372.564u 63.1191k 118.795k
BM_simd_exp_run<4, 1, 2>/65536 27908 ns 27832 ns 25300 4.38735m 127.304k 237.579k
BM_simd_exp_run<4, 1, 2>/131072 59208 ns 59017 ns 11908 0.111354 268.078k 475.147k
BM_simd_exp_run<4, 1, 2>/262144 113443 ns 113016 ns 6218 0.373271 514.947k 950.283k
BM_simd_exp_run<4, 1, 2>/524288 230293 ns 229433 ns 3072 1.389 1.04155M 1.90056M
BM_simd_exp_run<4, 1, 2>/1048576 481763 ns 479708 ns 1467 46.9127 2.16409M 3.8011M
BM_simd_exp_run<4, 2, 2>/128 43.7 ns 43.5 ns 16135203 929.644n 196.941 474
BM_simd_exp_run<4, 2, 2>/256 87.7 ns 87.4 ns 8131256 17.3405u 393.674 938
BM_simd_exp_run<4, 2, 2>/512 174 ns 173 ns 4106753 16.0711u 790.473 1.866k
BM_simd_exp_run<4, 2, 2>/1024 396 ns 395 ns 1817244 86.9448u 1.77767k 3.722k
BM_simd_exp_run<4, 2, 2>/2048 778 ns 776 ns 911274 131.684u 3.53264k 7.434k
BM_simd_exp_run<4, 2, 2>/4096 1534 ns 1520 ns 462754 1.00485m 6.98961k 14.858k
BM_simd_exp_run<4, 2, 2>/8192 3072 ns 3064 ns 226478 1.77942m 14.2051k 29.706k
BM_simd_exp_run<4, 2, 2>/16384 6310 ns 6253 ns 114623 1.68378m 28.3927k 59.402k
BM_simd_exp_run<4, 2, 2>/32768 12344 ns 12303 ns 55458 0.0167514 56.6832k 118.794k
BM_simd_exp_run<4, 2, 2>/65536 24929 ns 24857 ns 27757 0.0105199 115.089k 237.578k
BM_simd_exp_run<4, 2, 2>/131072 52014 ns 51836 ns 13863 0.0626848 235.588k 475.146k
BM_simd_exp_run<4, 2, 2>/262144 102648 ns 102271 ns 6847 0.0452753 467.016k 950.282k
BM_simd_exp_run<4, 2, 2>/524288 207424 ns 206626 ns 3413 1.01904 938.475k 1.90055M
BM_simd_exp_run<4, 2, 2>/1048576 424958 ns 423366 ns 1613 239.133 1.88394M 3.8011M
BM_simd_exp_run<4, 4, 2>/128 39.3 ns 39.2 ns 17845328 5.54767u 178.602 450
BM_simd_exp_run<4, 4, 2>/256 78.6 ns 78.4 ns 9070283 11.5763u 357.765 890
BM_simd_exp_run<4, 4, 2>/512 156 ns 156 ns 4446127 899.659n 717.863 1.77k
BM_simd_exp_run<4, 4, 2>/1024 335 ns 334 ns 2104534 2.85099u 1.49258k 3.53k
BM_simd_exp_run<4, 4, 2>/2048 686 ns 684 ns 1008900 6.93825u 3.10244k 7.05k
BM_simd_exp_run<4, 4, 2>/4096 1378 ns 1374 ns 516918 245.687u 6.19019k 14.09k
BM_simd_exp_run<4, 4, 2>/8192 2696 ns 2689 ns 256725 11.6857u 12.3724k 28.17k
BM_simd_exp_run<4, 4, 2>/16384 5441 ns 5427 ns 128562 54.4484u 24.6721k 56.33k
BM_simd_exp_run<4, 4, 2>/32768 10765 ns 10738 ns 65743 15.2107u 49.2549k 112.65k
BM_simd_exp_run<4, 4, 2>/65536 21799 ns 21736 ns 32358 8.25144m 98.8428k 225.29k
BM_simd_exp_run<4, 4, 2>/131072 44172 ns 44018 ns 15951 0.0384302 200.628k 450.57k
BM_simd_exp_run<4, 4, 2>/262144 95730 ns 95364 ns 7309 0.114653 433.23k 901.13k
BM_simd_exp_run<4, 4, 2>/524288 192679 ns 191915 ns 3709 1.33082 862.543k 1.80225M
BM_simd_exp_run<4, 4, 2>/1048576 385876 ns 384214 ns 1830 63.0399 1.72514M 3.60449M
BM_simd_exp_run<8, 1, 2>/128 29.8 ns 29.7 ns 23709286 3.07896u 114.19 243
BM_simd_exp_run<8, 1, 2>/256 58.5 ns 58.3 ns 11848717 15.0227u 224.872 475
BM_simd_exp_run<8, 1, 2>/512 124 ns 122 ns 5660293 42.5773u 470.493 939
BM_simd_exp_run<8, 1, 2>/1024 274 ns 272 ns 2642464 94.2302u 1.06698k 1.867k
BM_simd_exp_run<8, 1, 2>/2048 541 ns 531 ns 1319367 21.2223u 2.10412k 3.723k
BM_simd_exp_run<8, 1, 2>/4096 1098 ns 1079 ns 645020 103.873u 4.22446k 7.435k
BM_simd_exp_run<8, 1, 2>/8192 2267 ns 2260 ns 314756 2.87207m 8.72167k 14.859k
BM_simd_exp_run<8, 1, 2>/16384 4498 ns 4480 ns 150624 9.08886m 17.3452k 29.707k
BM_simd_exp_run<8, 1, 2>/32768 9079 ns 8921 ns 75802 0.0394449 34.8358k 59.403k
BM_simd_exp_run<8, 1, 2>/65536 18014 ns 17740 ns 38694 0.0214245 70.5027k 118.795k
BM_simd_exp_run<8, 1, 2>/131072 37760 ns 37025 ns 18931 7.28963m 147.957k 237.579k
BM_simd_exp_run<8, 1, 2>/262144 93320 ns 91416 ns 7722 0.123155 363.525k 475.147k
BM_simd_exp_run<8, 1, 2>/524288 189044 ns 185196 ns 3804 0.299685 731.758k 950.284k
BM_simd_exp_run<8, 1, 2>/1048576 384647 ns 376508 ns 1817 40.6957 1.48483M 1.90056M
BM_simd_exp_run<8, 2, 2>/128 27.7 ns 27.2 ns 25873867 3.55571u 108.603 242
BM_simd_exp_run<8, 2, 2>/256 52.9 ns 52.2 ns 13665976 7.82966u 205.518 474
BM_simd_exp_run<8, 2, 2>/512 108 ns 108 ns 6348955 31.0287u 415.827 938
BM_simd_exp_run<8, 2, 2>/1024 245 ns 243 ns 2929543 62.4671u 957.748 1.866k
BM_simd_exp_run<8, 2, 2>/2048 493 ns 484 ns 1440370 88.8661u 1.88981k 3.722k
BM_simd_exp_run<8, 2, 2>/4096 991 ns 973 ns 712362 92.6495u 3.81446k 7.434k
BM_simd_exp_run<8, 2, 2>/8192 2027 ns 1991 ns 351851 216.001u 7.84716k 14.858k
BM_simd_exp_run<8, 2, 2>/16384 4015 ns 4004 ns 172124 395.064u 15.749k 29.706k
BM_simd_exp_run<8, 2, 2>/32768 7939 ns 7916 ns 88700 1.14994m 31.4611k 59.402k
BM_simd_exp_run<8, 2, 2>/65536 16183 ns 15912 ns 43231 5.96794m 62.6816k 118.794k
BM_simd_exp_run<8, 2, 2>/131072 34447 ns 34097 ns 21021 1.47077 133.248k 237.578k
BM_simd_exp_run<8, 2, 2>/262144 84583 ns 84233 ns 7665 0.638878 327.039k 475.146k
BM_simd_exp_run<8, 2, 2>/524288 179550 ns 177192 ns 3983 0.57419 689.523k 950.282k
BM_simd_exp_run<8, 2, 2>/1048576 345493 ns 343834 ns 1951 16.3911 1.3321M 1.90055M
BM_simd_exp_run<8, 4, 2>/128 28.7 ns 28.6 ns 24105744 2.94536u 111.092 230
BM_simd_exp_run<8, 4, 2>/256 49.0 ns 48.9 ns 13873951 6.12659u 189.506 450
BM_simd_exp_run<8, 4, 2>/512 100 ns 99.8 ns 7042937 567.945n 381.8 890
BM_simd_exp_run<8, 4, 2>/1024 207 ns 206 ns 3397339 44.4466u 785.18 1.77k
BM_simd_exp_run<8, 4, 2>/2048 399 ns 398 ns 1743355 1.72082u 1.55715k 3.53k
BM_simd_exp_run<8, 4, 2>/4096 806 ns 804 ns 871059 3.44408u 3.15473k 7.05k
BM_simd_exp_run<8, 4, 2>/8192 1650 ns 1645 ns 436800 199.176u 6.36097k 14.09k
BM_simd_exp_run<8, 4, 2>/16384 3342 ns 3332 ns 213608 791.169u 12.7082k 28.17k
BM_simd_exp_run<8, 4, 2>/32768 6631 ns 6611 ns 106432 450.992u 25.3881k 56.33k
BM_simd_exp_run<8, 4, 2>/65536 13124 ns 13082 ns 53164 7.3546m 51.3158k 112.65k
BM_simd_exp_run<8, 4, 2>/131072 29777 ns 29654 ns 23150 0.0109719 117.212k 225.29k
BM_simd_exp_run<8, 4, 2>/262144 81641 ns 81269 ns 8564 0.0367819 323.096k 450.57k
BM_simd_exp_run<8, 4, 2>/524288 164046 ns 163308 ns 4269 0.277348 650.824k 901.13k
BM_simd_exp_run<8, 4, 2>/1048576 328410 ns 326806 ns 2147 11.2473 1.30313M 1.80225M
BM_simd_exp_run<16, 1, 2>/128 16.0 ns 15.9 ns 44600224 627.8n 63.2223 134
BM_simd_exp_run<16, 1, 2>/256 29.3 ns 29.2 ns 23299640 8.15463u 114.554 262
BM_simd_exp_run<16, 1, 2>/512 65.3 ns 65.1 ns 11320391 25.3525u 247.789 518
BM_simd_exp_run<16, 1, 2>/1024 139 ns 139 ns 4854883 10.7109u 547.607 1.03k
BM_simd_exp_run<16, 1, 2>/2048 281 ns 280 ns 2510128 40.6354u 1.08696k 2.054k
BM_simd_exp_run<16, 1, 2>/4096 558 ns 557 ns 1226551 1.63059u 2.18541k 4.102k
BM_simd_exp_run<16, 1, 2>/8192 1377 ns 1373 ns 509880 49.0311u 5.35157k 8.198k
BM_simd_exp_run<16, 1, 2>/16384 2769 ns 2761 ns 256111 331.887u 10.6964k 16.39k
BM_simd_exp_run<16, 1, 2>/32768 6365 ns 6272 ns 107630 0.0203568 24.6493k 32.774k
BM_simd_exp_run<16, 1, 2>/65536 11735 ns 11600 ns 62068 0.0763517 45.2171k 65.542k
BM_simd_exp_run<16, 1, 2>/131072 26277 ns 26194 ns 26848 4.76758m 102.177k 131.078k
BM_simd_exp_run<16, 1, 2>/262144 77662 ns 77363 ns 9010 0.334739 299.845k 262.15k
BM_simd_exp_run<16, 1, 2>/524288 157369 ns 156760 ns 4451 0.560099 606.199k 524.294k
BM_simd_exp_run<16, 1, 2>/1048576 300813 ns 297529 ns 2224 45.8719 1.15376M 1.04858M
BM_simd_exp_run<16, 2, 2>/128 16.1 ns 15.8 ns 44394584 2.07232u 62.7249 129
BM_simd_exp_run<16, 2, 2>/256 28.3 ns 27.8 ns 25062974 3.19196u 108.503 245
BM_simd_exp_run<16, 2, 2>/512 56.7 ns 56.0 ns 12663007 7.10732u 216.32 477
BM_simd_exp_run<16, 2, 2>/1024 120 ns 119 ns 5898343 37.1291u 460.186 941
BM_simd_exp_run<16, 2, 2>/2048 240 ns 239 ns 2924456 101.899u 918.72 1.869k
BM_simd_exp_run<16, 2, 2>/4096 499 ns 497 ns 1424139 111.646u 1.89902k 3.725k
BM_simd_exp_run<16, 2, 2>/8192 1178 ns 1174 ns 594421 146.361u 4.50889k 7.437k
BM_simd_exp_run<16, 2, 2>/16384 2329 ns 2321 ns 300434 4.35703m 8.96247k 14.861k
BM_simd_exp_run<16, 2, 2>/32768 4695 ns 4680 ns 149530 555.073u 17.9555k 29.709k
BM_simd_exp_run<16, 2, 2>/65536 9412 ns 9383 ns 73425 0.142145 36.2299k 59.405k
BM_simd_exp_run<16, 2, 2>/131072 22341 ns 22251 ns 31736 0.086999 84.6989k 118.797k
BM_simd_exp_run<16, 2, 2>/262144 77772 ns 77471 ns 8969 0.156428 298.395k 237.581k
BM_simd_exp_run<16, 2, 2>/524288 156712 ns 156059 ns 4498 1.4731 598.642k 475.149k
BM_simd_exp_run<16, 2, 2>/1048576 312543 ns 311209 ns 2238 23.2051 1.21998M 950.285k
BM_simd_exp_run<16, 4, 2>/128 15.3 ns 15.2 ns 45963847 87.0249n 59.5339 123
BM_simd_exp_run<16, 4, 2>/256 25.7 ns 25.6 ns 27032023 36.9932n 99.9058 233
BM_simd_exp_run<16, 4, 2>/512 52.3 ns 52.1 ns 13372896 149.556n 200.577 453
BM_simd_exp_run<16, 4, 2>/1024 109 ns 109 ns 6443652 620.766n 424.463 893
BM_simd_exp_run<16, 4, 2>/2048 218 ns 218 ns 3204169 936.28n 843.409 1.773k
BM_simd_exp_run<16, 4, 2>/4096 435 ns 434 ns 1620470 2.46842u 1.68415k 3.533k
BM_simd_exp_run<16, 4, 2>/8192 932 ns 929 ns 755122 115.213u 3.59165k 7.053k
BM_simd_exp_run<16, 4, 2>/16384 1867 ns 1862 ns 361749 69.1087u 7.16785k 14.093k
BM_simd_exp_run<16, 4, 2>/32768 3744 ns 3732 ns 186731 380.226u 14.3383k 28.173k
BM_simd_exp_run<16, 4, 2>/65536 7601 ns 7581 ns 92008 336.927u 29.7274k 56.333k
BM_simd_exp_run<16, 4, 2>/131072 19898 ns 19836 ns 35677 2.04614m 77.2103k 112.653k
BM_simd_exp_run<16, 4, 2>/262144 77364 ns 77064 ns 9077 0.0208219 299.152k 225.293k
BM_simd_exp_run<16, 4, 2>/524288 156707 ns 156104 ns 4466 0.326243 602.699k 450.573k
BM_simd_exp_run<16, 4, 2>/1048576 322397 ns 321058 ns 2180 7.89771 1.24357M 901.133k
As sizes increase, we become memory bottlenecked. For smaller arrays, e.g. of length 1024, larger vectors significantly improve throughput.
While there is no dependency between iterations, exp kernel has a large dependency chain. A CPU should be able to speculate across loop iterations, but in practice this CPU benefits, e.g. going from no unrolling in exp<16,1> to unrolling by exp<16,4> with 1024-element vectors, we get a roughly 15% improvement in IPC (instructions per clock) on top of a roughly 12% decease in the number of instructions required.
exp2, on top of needing significantly fewer instructions, achieved much better instructions per clock cycle on this computer.