AutocorrelationBenchmark.cs

using System;
using System.Numerics;
using System.Threading.Tasks;
using Accord.Math;
using Accord.Math.Transforms;
using BenchmarkDotNet.Attributes;
using BenchmarkDotNet.Running;

namespace ConsoleApp6
{
    class Program
    {
        static void Main(string[] args)
        {
            BenchmarkRunner.Run<AutocorrelationBenchmark>();
        }
    }

    public class AutocorrelationBenchmark
    {
        private readonly float[] input = { 0.007629395f, 0.06253052f, 0.1296692f, 0.1662903f, 0.146698f, 0.08401489f, 0.02523804f, 0.02484131f, 0.08493042f, 0.1667175f, 0.2186279f, 0.2028503f, 0.1319885f, 0.05505371f, 0.02154541f, 0.06213379f, 0.1493835f, 0.2144165f, 0.2076721f, 0.1312256f, 0.03387451f, -0.01351929f, 0.005279541f, 0.07574463f, 0.1403503f, 0.1398621f, 0.07754517f, -0.02001953f, -0.08612061f, -0.0743103f, -0.0133667f, 0.04589844f, 0.05606079f, 0.0006408691f, -0.07116699f, -0.1292725f, -0.1333313f, -0.09152222f, -0.0461731f, -0.03390503f, -0.0670166f, -0.1152039f, -0.142334f, -0.1343384f, -0.09707642f, -0.06118774f, -0.0496521f, -0.07254028f, -0.106842f, -0.1308899f, -0.1236267f, -0.09387207f, -0.06741333f, -0.05633545f, -0.07669067f, -0.09552002f, -0.1016846f, -0.08355713f, -0.05236816f, -0.02648926f, -0.02047729f, -0.0352478f, -0.06549072f, -0.08349609f, -0.08508301f, -0.0664978f, -0.04782104f, -0.04937744f, -0.06341553f, -0.08822632f, -0.1074219f, -0.1167603f, -0.10672f, -0.09075928f, -0.08215332f, -0.0925293f, -0.1109314f, -0.1309509f, -0.1457214f, -0.147522f, -0.1384888f, -0.1256104f, -0.1268921f, -0.13974f, -0.1642761f, -0.1875305f, -0.1957092f, -0.1843872f, -0.1651001f, -0.152832f, -0.1507568f, -0.1670532f, -0.1907959f, -0.208313f, -0.2009888f, -0.176178f, -0.1485596f, -0.132019f, -0.1403809f, -0.1661682f, -0.1936035f, -0.2076721f, -0.2030334f, -0.1800842f, -0.1570129f, -0.1469116f, -0.1627808f, -0.1892395f, -0.2131348f, -0.2286682f, -0.2267456f, -0.2115173f, -0.1941833f, -0.1913452f, -0.2104492f, -0.2414246f, -0.2727966f, -0.2919617f, -0.2852173f, -0.2657776f, -0.2441406f, -0.2423706f, -0.2662048f, -0.3065796f, -0.3460083f, -0.354126f, -0.330719f, -0.2875977f, -0.2571411f, -0.2582397f, -0.2882385f, -0.339325f, -0.3658447f, -0.3483582f, -0.2980042f, -0.2441406f, -0.2210693f, -0.2410278f, -0.2765198f, -0.2955933f, -0.2717285f, -0.2203369f, -0.1534424f, -0.1130066f, -0.1089478f, -0.1026917f, -0.06954956f, -0.009979248f, 0.04690552f, 0.1034546f, 0.12677f, 0.1435852f, 0.1743164f, 0.2394714f, 0.3059387f, 0.360321f, 0.3834534f, 0.3927612f, 0.3995972f, 0.4477234f, 0.5361328f, 0.6405945f, 0.7354431f, 0.7948608f, 0.8247375f, 0.8282471f, 0.8216858f, 0.8125305f, 0.8186646f, 0.8394165f, 0.8719788f, 0.8868408f, 0.8814697f, 0.8225403f, 0.7244263f, 0.6174622f, 0.5501099f, 0.5533447f, 0.6033936f, 0.6427612f, 0.6040649f, 0.4812317f, 0.2955627f, 0.1337585f, 0.05447388f, 0.06820679f, 0.1108398f, 0.09375f, -0.02676392f, -0.2302856f, -0.4369202f, -0.5551147f, -0.5558472f, -0.4759521f, -0.3867798f, -0.3710327f, -0.4436646f, -0.5588379f, -0.6387024f, -0.6355896f, -0.5627136f, -0.4681091f, -0.4104004f, -0.4189453f, -0.4650879f, -0.5182495f, -0.5274048f, -0.4816284f, -0.3877563f, -0.2749329f, -0.1738586f, -0.1031799f, -0.07592773f, -0.07391357f, -0.07592773f, -0.0513916f, 0.00491333f, 0.09457397f, 0.1882629f, 0.2475281f, 0.2489319f, 0.2037964f, 0.1489258f, 0.125f, 0.1509705f, 0.2204285f, 0.2934265f, 0.3310547f, 0.3183899f, 0.2691956f, 0.2246704f, 0.2098694f, 0.2341003f, 0.2851257f, 0.3298035f, 0.3408508f, 0.3061218f, 0.2328186f, 0.1559753f, 0.1078491f, 0.1076965f, 0.151001f, 0.2138367f, 0.2606201f, 0.2637024f, 0.2256165f, 0.1660461f, 0.1217041f, 0.1238098f, 0.1664429f, 0.216156f, 0.2301636f, 0.1837158f, 0.09158325f, -0.009613037f, -0.06677246f, -0.05923462f, -0.004302979f, 0.04681396f, 0.04507446f, -0.01776123f, -0.1192322f, -0.2052612f, -0.2399292f, -0.2157593f, -0.1645203f, -0.1377869f, -0.1659241f, -0.2453613f, -0.3443604f, -0.4140015f, -0.4295349f, -0.3958435f, -0.3484192f, -0.3210754f, -0.3308105f, -0.3670044f, -0.3996887f, -0.3980408f, -0.3506165f, -0.269989f, -0.184967f, -0.1280823f, -0.1157532f, -0.1317444f, -0.1495667f, -0.1385193f, -0.08932495f, -0.01287842f, 0.06555176f, 0.1159973f, 0.1350708f, 0.1342163f, 0.1384583f, 0.1710815f, 0.2312012f, 0.3011475f, 0.3554382f, 0.3777466f, 0.3649597f, 0.3308105f, 0.3023376f, 0.2938843f, 0.3092041f, 0.3274841f, 0.3363953f, 0.3199463f, 0.2784729f, 0.2259216f, 0.180542f, 0.1573792f, 0.1557312f, 0.1663208f, 0.1681519f, 0.1468811f, 0.1031799f, 0.04605103f, -0.003997803f, -0.03387451f, -0.0418396f, -0.03448486f, -0.03427124f, -0.0496521f, -0.08499146f, -0.1274414f, -0.1574707f, -0.1618042f, -0.1386108f, -0.1062317f, -0.08041382f, -0.08041382f, -0.1070557f, -0.1385498f, -0.1583557f, -0.1523438f, -0.1160278f, -0.06939697f, -0.04016113f, -0.0380249f, -0.0696106f, -0.1192322f, -0.1460266f, -0.1200256f, -0.04376221f, 0.05789185f, 0.133606f, 0.1341858f, 0.05966187f, -0.05548096f, -0.1183777f, -0.08099365f, 0.05169678f, 0.2058411f, 0.2800293f, 0.2211914f, 0.05853271f, -0.1073914f, -0.14328f, -0.006988525f, 0.223877f, 0.39151f, 0.3774414f, 0.1931763f, -0.04199219f, -0.1671448f, -0.07244873f, 0.1820679f, 0.4091492f, 0.4461365f, 0.250061f, -0.03720093f, -0.2227783f, -0.1776123f, 0.05780029f, 0.3069763f, 0.3891907f, 0.2434387f, -0.04690552f, -0.2641296f, -0.260376f, -0.06091309f, 0.1838989f, 0.2834167f, 0.1655884f, -0.08010864f, -0.2942505f, -0.3279419f, -0.1801758f, 0.02612305f, 0.1367188f, 0.05935669f, -0.127533f, -0.283783f, -0.3074951f, -0.1924133f, -0.02954102f, 0.05593872f, 0.01498413f, -0.1230164f, -0.2405396f, -0.2528381f, -0.1612244f, -0.03234863f, 0.03030396f, -0.004180908f, -0.09936523f, -0.1833191f, -0.1928101f, -0.1196289f, -0.02481079f, 0.0302124f, 0.007141113f, -0.06726074f, -0.1365662f, -0.1530457f, -0.1091614f, -0.0411377f, -0.006896973f, -0.0234375f, -0.08096313f, -0.1434021f, -0.1633301f, -0.1369019f, -0.07974243f, -0.03598022f, -0.03741455f, -0.08441162f, -0.1477661f, -0.1871338f, -0.1827393f, -0.1424561f, -0.09320068f, -0.07540894f, -0.1075439f, -0.1714172f, -0.2275391f, -0.238678f, -0.1995239f, -0.1411438f, -0.1029053f, -0.1165771f, -0.170166f, -0.2270203f, -0.2476501f, -0.2208862f, -0.1610718f, -0.1107178f, -0.1054993f, -0.1488647f, -0.2062683f, -0.2363892f, -0.2279053f, -0.1867065f, -0.143158f, -0.1290894f, -0.1552429f, -0.2019043f, -0.2436218f, -0.2523499f, -0.2330017f, -0.203125f, -0.1812439f, -0.1783142f, -0.1994019f, -0.236084f, -0.2703857f, -0.2895508f, -0.2817383f, -0.2622681f, -0.2427673f, -0.2480469f, -0.2844543f, -0.336853f, -0.3838196f, -0.3946533f, -0.3616638f, -0.3071594f, -0.2702332f, -0.281311f, -0.3294067f, -0.3888855f, -0.4133606f, -0.3835144f, -0.3093262f, -0.2521057f, -0.2425537f, -0.289856f, -0.3701782f, -0.407074f, -0.361145f, -0.2438354f, -0.1081238f, -0.02554321f, -0.02856445f, -0.08810425f, -0.1381836f, -0.1072693f, 0.01791382f, 0.1600647f, 0.2745056f, 0.308136f, 0.2700806f, 0.2111511f, 0.1901245f, 0.2591553f, 0.3933716f, 0.5361938f, 0.6325378f, 0.6679382f, 0.653656f, 0.6477661f, 0.6885681f, 0.7729492f, 0.8518677f, 0.8882446f, 0.8711853f, 0.828125f, 0.7943726f, 0.8014832f, 0.8099976f, 0.7939453f, 0.7319641f, 0.6359558f, 0.5609436f, 0.5406189f, 0.5710449f, 0.5880737f, 0.5593872f, 0.4519348f, 0.2987671f, 0.1664734f, 0.1044312f, 0.1049194f, 0.108551f, 0.06182861f, -0.07354736f, -0.2618408f, -0.4258118f, -0.5065918f, -0.4897156f, -0.4189758f, -0.3650513f, -0.3829346f, -0.4683838f, -0.5640259f, -0.614563f, -0.5853271f, -0.4966736f, -0.4098511f, -0.3828735f, -0.4172974f, -0.4908752f, -0.5513306f, -0.5429993f, -0.4605713f, -0.3373718f, -0.2217407f, -0.1454773f, -0.1268616f, -0.1459961f, -0.1599731f, -0.1347961f, -0.06234741f, 0.04449463f, 0.1480103f, 0.2027893f, 0.2010803f, 0.1593628f, 0.1062317f, 0.09143066f, 0.1277771f, 0.1974182f, 0.2639771f, 0.2907715f, 0.2709656f, 0.2156677f, 0.1734619f, 0.1735535f, 0.2232971f, 0.2918701f, 0.3468018f, 0.3529663f, 0.3063354f, 0.2350769f, 0.1674194f, 0.1393433f, 0.1549377f, 0.2003479f, 0.2416687f, 0.2557373f, 0.2399597f, 0.2039795f, 0.1752625f, 0.1745605f, 0.2004089f, 0.2398987f, 0.2642212f, 0.2494507f, 0.1938171f, 0.1218262f, 0.05859375f, 0.02792358f, 0.03259277f, 0.05712891f, 0.06695557f, 0.04388428f, -0.00894165f, -0.07702637f, -0.1291809f, -0.1546631f, -0.1494446f, -0.1426086f, -0.1457825f, -0.1774292f, -0.234375f, -0.2958374f, -0.3461609f, -0.3697815f, -0.3721619f, -0.3593445f, -0.3530579f, -0.3618774f, -0.3840027f, -0.4004211f, -0.4029846f, -0.3739319f, -0.3199768f, -0.2573853f, -0.2027588f, -0.1689453f, -0.1610107f, -0.1655579f, -0.155426f, -0.1257019f, -0.07214355f, -0.01013184f, 0.04211426f, 0.07302856f, 0.0836792f, 0.09234619f, 0.1158752f, 0.1660156f, 0.2322998f, 0.2927856f, 0.3306274f, 0.3384705f, 0.3241882f, 0.303009f, 0.2973328f, 0.3082886f, 0.3237915f, 0.3317261f, 0.3192444f, 0.2861328f, 0.2418823f, 0.2065735f, 0.1870117f, 0.1828613f, 0.1888123f, 0.1888428f, 0.1712952f, 0.1392822f, 0.09613037f, 0.05517578f, 0.02935791f, 0.01785278f, 0.01242065f, 0.003051758f, -0.01672363f, -0.04641724f, -0.07730103f, -0.097229f, -0.1000061f, -0.09100342f, -0.07678223f, -0.0697937f, -0.07366943f, -0.0852356f, -0.09744263f, -0.1062012f, -0.1058044f, -0.09573364f, -0.08404541f, -0.07592773f, -0.07455444f, -0.0758667f, -0.07611084f, -0.07318115f, -0.05728149f, -0.04040527f, -0.01986694f, -0.001953125f, 0.003875732f, 0.003417969f, 0.01412964f, 0.03622437f, 0.0574646f, 0.0663147f, 0.05441284f, 0.02438354f, -0.01449585f, -0.02047729f, 0.01516724f, 0.07315063f, 0.1184692f, 0.1237183f, 0.09414673f, 0.06015015f, 0.04693604f, 0.07415771f, 0.1259766f, 0.1627808f, 0.1609497f, 0.1225281f, 0.07287598f, 0.04428101f, 0.04321289f, 0.05847168f, 0.07952881f, 0.07720947f, 0.0609436f, 0.02813721f, 0.006347656f, 0.005218506f, 0.02084351f, 0.04058838f, 0.0526123f, 0.04458618f, 0.02664185f, -0.003601074f, -0.02807617f, -0.04119873f, -0.04708862f, -0.04846191f, -0.05703735f, -0.06945801f, -0.08395386f, -0.09823608f, -0.1064148f, -0.09918213f, -0.07974243f, -0.04846191f, -0.03201294f, -0.03100586f, -0.0423584f, -0.06350708f, -0.07949829f, -0.07891846f, -0.06491089f, -0.0475769f, -0.04370117f, -0.05767822f, -0.07470703f, -0.08569336f, -0.07962036f, -0.05773926f, -0.04321289f, -0.03851318f, -0.05197144f, -0.0748291f, -0.08224487f, -0.07620239f, -0.05963135f, -0.05422974f, -0.06762695f, -0.09887695f, -0.1289673f, -0.1437073f, -0.1385193f, -0.1225891f, -0.1134644f, -0.1167908f, -0.1309814f, -0.1417542f, -0.1418152f, -0.1290283f, -0.1171265f, -0.1176147f, -0.1313782f, -0.1489868f, -0.1603394f, -0.1604004f, -0.1494751f, -0.1410522f, -0.1437378f, -0.1547852f, -0.1612244f, -0.1563416f, -0.1392517f, -0.1141052f, -0.1000977f, -0.1014709f, -0.1166992f, -0.134491f, -0.148407f, -0.1489868f, -0.1412964f, -0.1351624f, -0.1375427f, -0.150177f, -0.1678772f, -0.1852112f, -0.1913757f, -0.1889343f, -0.1817322f, -0.176178f, -0.1731567f, -0.1852112f, -0.2082214f, -0.2327271f, -0.2525024f, -0.2587891f, -0.2564697f, -0.2503967f, -0.2589111f, -0.2862549f, -0.3128357f, -0.3366089f, -0.3412781f, -0.3271484f, -0.3086853f, -0.3025818f, -0.3192749f, -0.3366699f, -0.3449402f, -0.3385315f, -0.3138733f, -0.2946777f, -0.2963562f, -0.3079224f, -0.3240356f, -0.3340759f, -0.321991f, -0.293396f, -0.2711487f, -0.2580261f, -0.2351074f, -0.1953735f, -0.1487427f, -0.09555054f, -0.04418945f, -0.01922607f, -0.008544922f, 0.01403809f, 0.05807495f, 0.1296387f, 0.2088623f, 0.2555237f, 0.2653809f, 0.2540283f, 0.2631226f, 0.3218079f, 0.4179077f, 0.5349121f, 0.6333618f, 0.6751099f, 0.6892395f, 0.7080994f, 0.7521362f, 0.8150024f, 0.8694763f, 0.8848877f, 0.8597412f, 0.8311768f, 0.8171997f, 0.823822f, 0.8348389f, 0.8188477f, 0.7499695f, 0.6585388f, 0.5975647f, 0.5901489f, 0.6186218f, 0.631073f, 0.5842896f, 0.4572754f, 0.3001099f, 0.1703491f, 0.1055298f, 0.09594727f, 0.09020996f, 0.02127075f, -0.118988f, -0.2954712f, -0.4364319f, -0.4966736f, -0.4828186f, -0.4279785f, -0.3999023f, -0.4240723f, -0.4923401f, -0.5636292f, -0.5982971f, -0.5750427f, -0.5264587f, -0.4816895f, -0.4699097f, -0.4920349f, -0.5281982f, -0.548645f, -0.5257263f, -0.4669189f, -0.3730164f, -0.2714844f, -0.1916504f, -0.1409912f, -0.1167908f, -0.1053772f, -0.08944702f, -0.04293823f, 0.02664185f, 0.1060486f, 0.1697998f, 0.1960754f, 0.1781006f, 0.1385498f, 0.121521f, 0.1354065f, 0.1861877f, 0.246582f, 0.2852478f, 0.2869873f, 0.255127f, 0.2213745f, 0.2099304f, 0.2344666f, 0.2791138f, 0.3187866f, 0.3281555f, 0.3053589f, 0.2550964f, 0.1982727f, 0.1618958f, 0.1592102f, 0.1847229f, 0.2174072f, 0.2445679f, 0.2500305f, 0.2336121f, 0.2073669f, 0.1904907f, 0.1922302f, 0.2133484f, 0.2331848f, 0.2330933f, 0.2049255f, 0.1461792f, 0.08197021f, 0.03631592f, 0.0211792f, 0.0305481f, 0.04568481f, 0.04672241f, 0.01821899f, -0.03634644f, -0.09783936f, -0.1465149f, -0.1693726f, -0.1693115f, -0.1680908f, -0.1819153f, -0.2213135f, -0.2826233f, -0.3468933f, -0.3913269f, -0.4068909f, -0.3947449f, -0.3740845f, -0.3609619f, -0.364502f, -0.3813477f, -0.3930359f, -0.3836975f, -0.3450623f, -0.2845764f, -0.2202148f, -0.1774292f, -0.1631775f, -0.1672974f, -0.1698608f, -0.1522217f, -0.1065063f, -0.03814697f, 0.03109741f, 0.0803833f, 0.1037598f, 0.1139221f, 0.1317444f, 0.1683655f, 0.2269897f, 0.2927856f, 0.3408203f, 0.3582458f, 0.3459167f, 0.3179626f, 0.2978516f, 0.2965698f, 0.312561f, 0.3279419f, 0.3291016f, 0.3074646f, 0.2671204f, 0.2246094f, 0.1974182f, 0.1865234f, 0.1903687f, 0.1966858f, 0.1855469f, 0.1551514f, 0.1123047f, 0.06729126f, 0.03170776f, 0.01242065f, 0.006256104f, 0.003295898f, -0.009277344f, -0.03604126f, -0.06903076f, -0.09829712f, -0.1103516f, -0.1018677f, -0.07931519f, -0.05749512f, -0.050354f };

        [Benchmark]
        public float[] AcfType2()
        {
            var output = new float[input.Length];
            for (var t = 0; t < output.Length; t++)
            {
                var result = 0f;
                for (var j = 0; j < input.Length - t; j++)
                    result += input[j] * input[j + t];
                output[t] = result;
            }
            return output;
        }

        [Benchmark]
        public float[] AcfType2Parallel()
        {
            var output = new float[input.Length];

            Parallel.For(0, output.Length, t =>
            {
                var result = 0f;
                for (var j = 0; j < input.Length - t; j++)
                    result += input[j] * input[j + t];
                output[t] = result;
            });

            return output;
        }

        [Benchmark]
        public float[] AcfType2ParallelSimd()
        {
            var input2x = new float[input.Length * 2];
            Array.Copy(input, input2x, input.Length);

            var output = new float[input.Length];

            Parallel.For(0, output.Length, t =>
            {
                var sum = Vector<float>.Zero;
                for (var j = 0; j < input.Length - t; j += Vector<float>.Count)
                    sum += new Vector<float>(input2x, j) * new Vector<float>(input2x, j + t);

                var result = 0f;
                for (var i = 0; i < Vector<float>.Count; i++)
                    result += sum[i];

                output[t] = result;
            });

            return output;
        }

        [Benchmark]
        public Complex[] AcfWithFftAccord()
        {
            var output = new Complex[input.Length * 2];

            for (var i = 0; i < input.Length; i++)
                output[i] = input[i];

            FourierTransform2.FFT(output, FourierTransform.Direction.Forward);

            for (var i = 0; i < output.Length; i++)
            {
                var x = output[i];
                output[i] = x.Real * x.Real + x.Imaginary * x.Imaginary;
            }

            FourierTransform2.FFT(output, FourierTransform.Direction.Backward);

            return output;
        }
    }
}

ConsoleApp6.AutocorrelationBenchmark-report-github.md

BenchmarkDotNet=v0.10.12, OS=Windows 10.0.17093
Intel Core i7-3770 CPU 3.40GHz (Ivy Bridge), 1 CPU, 8 logical cores and 4 physical cores
.NET Core SDK=2.1.4
  [Host]     : .NET Core 2.0.5 (Framework 4.6.26020.03), 64bit RyuJIT
  DefaultJob : .NET Core 2.0.5 (Framework 4.6.26020.03), 64bit RyuJIT

Method	Mean	Error	StdDev	Median
AcfType2	610.74 us	11.962 us	23.613 us	612.8 us
AcfType2Parallel	198.85 us	1.831 us	1.713 us	199.0 us
AcfType2ParallelSimd	99.54 us	1.989 us	5.309 us	100.9 us
AcfWithFftAccord	187.65 us	3.746 us	10.192 us	181.2 us