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// Copyright Yahoo. Licensed under the terms of the Apache 2.0 license. See LICENSE in the project root.
package com.yahoo.search.dispatch;
import org.junit.jupiter.api.Test;
import java.util.Locale;
import static org.junit.jupiter.api.Assertions.assertEquals;
public class TopKEstimatorTest {
@Test
void requireHitsAreEstimatedAccordingToPartitionsAndProbability() {
TopKEstimator estimator = new TopKEstimator(30, 0.999);
assertEquals(91.97368471911312, estimator.estimateExactK(200, 3), 0.0);
assertEquals(92, estimator.estimateK(200, 3));
assertEquals(37.96328109101396, estimator.estimateExactK(200, 10), 0.0);
assertEquals(38, estimator.estimateK(200, 10));
assertEquals(23.815737601023095, estimator.estimateExactK(200, 20), 0.0);
assertEquals(24, estimator.estimateK(200, 20));
assertEquals(37.96328109101396, estimator.estimateExactK(200, 10, 0.999), 0.0);
assertEquals(38, estimator.estimateK(200, 10, 0.999));
assertEquals(34.36212304875885, estimator.estimateExactK(200, 10, 0.99), 0.0);
assertEquals(35, estimator.estimateK(200, 10, 0.99));
assertEquals(41.44244358524574, estimator.estimateExactK(200, 10, 0.9999), 0.0);
assertEquals(42, estimator.estimateK(200, 10, 0.9999));
assertEquals(44.909040374464155, estimator.estimateExactK(200, 10, 0.99999), 0.0);
assertEquals(45, estimator.estimateK(200, 10, 0.99999));
}
@Test
void requireHitsAreEstimatedAccordingToPartitionsAndProbabilityForVaryingN_K200() {
TopKEstimator estimator = new TopKEstimator(30, 0.99999);
assertEquals(200, estimator.estimateExactK(200, 1), 0.0);
assertEquals(200, estimator.estimateK(200, 1));
assertEquals(137.4727798056239, estimator.estimateExactK(200, 2), 0.0);
assertEquals(102.95409291533568, estimator.estimateExactK(200, 3), 0.0);
assertEquals(44.909040374464155, estimator.estimateExactK(200, 10), 0.0);
assertEquals(28.86025772029091, estimator.estimateExactK(200, 20), 0.0);
}
@Test
void requireHitsAreEstimatedAccordingToPartitionsAndProbabilityForVaryingN_K20() {
TopKEstimator estimator = new TopKEstimator(30, 0.99999);
assertEquals(20, estimator.estimateExactK(20, 1), 0.0);
assertEquals(20, estimator.estimateK(20, 1));
assertEquals(21.849933444373328, estimator.estimateExactK(20, 2), 0.0);
assertEquals(18.14175840378403, estimator.estimateExactK(20, 3), 0.0);
assertEquals(9.87693019124002, estimator.estimateExactK(20, 10), 0.0);
assertEquals(6.964137165389415, estimator.estimateExactK(20, 20), 0.0);
}
@Test
void requireHitsAreEstimatedAccordingToPartitionsAndProbabilityForVaryingN_K10_Five9() {
TopKEstimator estimator = new TopKEstimator(30, 0.99999);
assertEquals(10, estimator.estimateExactK(10, 1), 0.0);
assertEquals(10, estimator.estimateK(10, 1));
assertEquals(13.379168295125641, estimator.estimateExactK(10, 2), 0.0);
assertEquals(11.447448515386741, estimator.estimateExactK(10, 3), 0.0);
assertEquals(6.569830753158866, estimator.estimateExactK(10, 10), 0.0);
assertEquals(4.717281833573569, estimator.estimateExactK(10, 20), 0.0);
}
@Test
void requireHitsAreEstimatedAccordingToPartitionsAndProbabilityForVaryingN_K10_Four9() {
TopKEstimator estimator = new TopKEstimator(30, 0.9999);
assertEquals(10, estimator.estimateExactK(10, 1), 0.0);
assertEquals(10, estimator.estimateK(10, 1));
assertEquals(12.087323848369289, estimator.estimateExactK(10, 2), 0.0);
assertEquals(10.230749855131009, estimator.estimateExactK(10, 3), 0.0);
assertEquals(5.794676146031378, estimator.estimateExactK(10, 10), 0.0);
assertEquals(4.152394782937266, estimator.estimateExactK(10, 20), 0.0);
}
@Test
void requireEstimatesAreRoundeUp() {
TopKEstimator estimator = new TopKEstimator(30, 0.9999);
assertEquals(5.794676146031378, estimator.estimateExactK(10, 10), 0.0);
assertEquals(6, estimator.estimateK(10, 10));
}
@Test
void requireEstimatesAreCappedAtInputK() {
TopKEstimator estimator = new TopKEstimator(30, 0.9999);
assertEquals(12.087323848369289, estimator.estimateExactK(10, 2), 0.0);
assertEquals(10, estimator.estimateK(10, 2));
}
@Test
void requireThatLargeKAreSane() {
System.out.println(dumpProbability(10, 0.05));
TopKEstimator idealEstimator = new TopKEstimator(30, 0.9999);
TopKEstimator skewedEstimator = new TopKEstimator(30, 0.9999, 0.05);
int [] K = {10, 20, 40, 80, 100, 200, 400, 800, 1000, 2000, 4000, 8000, 10000, 20000, 40000, 80000, 100000};
int [] expecedWithZeroSkew = {6, 9, 14, 22, 26, 42, 71, 123, 148, 268, 496, 936, 1152, 2215, 4304, 8429, 10480};
int [] expecedWith5pSkew = {6, 10, 14, 23, 26, 43, 73, 128, 154, 280, 518, 979, 1205, 2319, 4509, 8837, 10989};
for (int i = 0; i < K.length; i++) {
assertEquals(expecedWithZeroSkew[i], idealEstimator.estimateK(K[i], 10));
assertEquals(expecedWith5pSkew[i], skewedEstimator.estimateK(K[i], 10));
}
String expected =
"Prob/Hits: 1.0000000000 0.9999000000 0.9999900000 0.9999990000 0.9999999000 0.9999999900 0.9999999990 0.9999999999\n" +
" 10: 10.000 6.000 7.000 8.000 9.000 10.000 10.000 10.000\n" +
" 20: 10.000 4.500 5.000 5.500 6.500 7.000 7.500 8.000\n" +
" 40: 10.000 3.500 4.000 4.250 4.750 5.250 5.500 6.000\n" +
" 80: 10.000 2.750 3.000 3.250 3.625 3.875 4.250 4.500\n" +
" 100: 10.000 2.600 2.800 3.100 3.300 3.600 3.900 4.200\n" +
" 200: 10.000 2.100 2.250 2.450 2.650 2.800 3.000 3.200\n" +
" 400: 10.000 1.775 1.900 2.025 2.150 2.275 2.425 2.575\n" +
" 800: 10.000 1.538 1.625 1.713 1.813 1.900 2.000 2.100\n" +
" 1000: 10.000 1.480 1.560 1.640 1.720 1.810 1.890 1.990\n" +
" 2000: 10.000 1.340 1.395 1.450 1.510 1.570 1.630 1.695\n" +
" 4000: 10.000 1.240 1.280 1.320 1.360 1.403 1.445 1.493\n" +
" 8000: 10.000 1.170 1.198 1.225 1.254 1.284 1.315 1.348\n" +
" 10000: 10.000 1.152 1.177 1.202 1.227 1.254 1.282 1.311\n" +
" 20000: 10.000 1.108 1.125 1.143 1.161 1.180 1.199 1.220\n" +
" 40000: 10.000 1.076 1.088 1.101 1.114 1.127 1.141 1.156\n" +
" 80000: 10.000 1.054 1.062 1.071 1.080 1.090 1.100 1.110\n" +
" 100000: 10.000 1.048 1.056 1.064 1.072 1.080 1.089 1.098\n";
assertEquals(expected, dumpProbability(10, 0.0));
String expectedSkew =
"Prob/Hits: 1.0000000000 0.9999000000 0.9999900000 0.9999990000 0.9999999000 0.9999999900 0.9999999990 0.9999999999\n" +
" 10: 10.000 6.000 7.000 8.000 9.000 10.000 10.000 10.000\n" +
" 20: 10.000 5.000 5.500 6.000 6.500 7.000 7.500 8.500\n" +
" 40: 10.000 3.500 4.000 4.500 4.750 5.250 5.750 6.250\n" +
" 80: 10.000 2.875 3.125 3.375 3.750 4.000 4.375 4.625\n" +
" 100: 10.000 2.600 2.900 3.100 3.400 3.700 4.000 4.300\n" +
" 200: 10.000 2.150 2.350 2.500 2.700 2.900 3.100 3.300\n" +
" 400: 10.000 1.825 1.950 2.075 2.225 2.350 2.500 2.650\n" +
" 800: 10.000 1.600 1.688 1.775 1.875 1.975 2.075 2.175\n" +
" 1000: 10.000 1.540 1.620 1.700 1.790 1.870 1.960 2.060\n" +
" 2000: 10.000 1.400 1.455 1.510 1.570 1.630 1.695 1.760\n" +
" 4000: 10.000 1.295 1.335 1.375 1.418 1.460 1.505 1.553\n" +
" 8000: 10.000 1.224 1.251 1.280 1.309 1.340 1.371 1.405\n" +
" 10000: 10.000 1.205 1.230 1.255 1.282 1.309 1.337 1.367\n" +
" 20000: 10.000 1.160 1.177 1.195 1.214 1.233 1.253 1.275\n" +
" 40000: 10.000 1.127 1.140 1.153 1.166 1.179 1.194 1.209\n" +
" 80000: 10.000 1.105 1.114 1.123 1.132 1.141 1.152 1.162\n" +
" 100000: 10.000 1.099 1.107 1.115 1.123 1.132 1.141 1.150\n";
assertEquals(expectedSkew, dumpProbability(10, 0.05));
}
/**
* This make a table showing how many more hits will be fetched as a factor of hits requested.
* It shows how it varies with probability and hits requested for a given number of partitions.
*/
private String dumpProbability(int numPartitions, double skewFactor) {
TopKEstimator estimator = new TopKEstimator(30, 0.9999, skewFactor);
int [] K = {10, 20, 40, 80, 100, 200, 400, 800, 1000, 2000, 4000, 8000, 10000, 20000, 40000, 80000, 100000};
double [] P = {1.0, 0.9999, 0.99999, 0.999999, 0.9999999, 0.99999999, 0.999999999, 0.9999999999};
int n = numPartitions;
StringBuilder sb = new StringBuilder();
sb.append(String.format("Prob/Hits:"));
for (double p : P) {
sb.append(String.format(Locale.ENGLISH, " %1.10f", p));
}
sb.append("\n");
for (int k : K) {
sb.append(String.format(Locale.ENGLISH, "%9d:", k));
for (double p : P) {
sb.append(String.format(Locale.ENGLISH, "%13.3f", (double)(estimator.estimateK(k, n, p)*n) / k));
}
sb.append("\n");
}
return sb.toString();
}
}
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