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biases.go
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biases.go
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package hll
import (
"fmt"
"sort"
)
// NOTE: maxTick is just ticks[len(ticks)-1], but is copied out since it _should_ get loaded into CPU
// cache more frequently if it's not a fn() that has an array lookup.
type biases struct {
ticks []int
maxTick uint64
store map[int]float64
}
// getInterpolatedBias returns the average bias for the 4 nearest neighbors to estimate.
func (b *biases) getInterpolatedBias(estimate int) float64 {
sum := 0.0
neighbourTicks := b.getNeighbourTicks(estimate)
for _, neighbourTick := range neighbourTicks {
sum += b.store[neighbourTick]
}
return sum / float64(len(neighbourTicks))
}
func (b *biases) getNeighbourTicks(estimate int) []int {
// If estimate <= biasTicks[1], return first 4 to prevent underflow.
if estimate <= b.ticks[2] {
return b.ticks[0:4]
}
// If estimate >= biasTicks[MAX-3], return final 4 to prevent overflow.
if estimate >= b.ticks[len(b.ticks)-2] {
l := len(b.ticks)
return b.ticks[l-4 : l]
}
// Find the point we tip over the estimate, return the 2 points higher and the 2 lower.
i := 2
for ; i < len(b.ticks); i++ {
if b.ticks[i] > estimate {
break
}
}
return b.ticks[i-2 : i+2]
}
func createBiases(bs map[int]float64) *biases {
ticks := make([]int, len(bs))
i := 0
for tick := range bs {
ticks[i] = tick
i += 1
}
sort.Ints(ticks)
return &biases{
ticks: ticks,
maxTick: uint64(ticks[len(ticks)-1]),
store: bs,
}
}
var defaultBiases = createBiases(defaultGeneratedBiases)
// Package level store for custom generated rawEstimate -> bias maps. Allows for use of a single
// *biases across multiple Sketch instances, whilst ensuring that both the given map remains immutable
// (from our perspective) and we don't have to complicate the API by having to expose biases or a
// builder externally.
var biasStore = map[string]*biases{}
// RegisterBiases allows a custom set of biases to be registered for use in NewCustomSketch.
func RegisterBiases(key string, biases map[int]float64) error {
if key == "" {
return fmt.Errorf("invalid bias key given for registration")
}
if len(biases) < 4 {
return fmt.Errorf("invalid biases: valid biases must contain at least 4 interpolation points")
}
// Copy biases to stop any chance of sneaky external changes to biases having an effect on this package.
ourCopy := make(map[int]float64)
for tick, bias := range biases {
ourCopy[tick] = bias
}
biasStore[key] = createBiases(ourCopy)
return nil
}
// (Discussed in generate.go)
var defaultGeneratedBiases = map[int]float64{
108: 0.463815,
216: 0.463931,
323: 0.464059,
431: 0.464616,
538: 0.465083,
645: 0.465417,
751: 0.465897,
858: 0.466404,
964: 0.466929,
1070: 0.467412,
1176: 0.467875,
1281: 0.468398,
1387: 0.468855,
1492: 0.469315,
1597: 0.46978,
1701: 0.470271,
1806: 0.470776,
1910: 0.471305,
2014: 0.471771,
2118: 0.472282,
2221: 0.472774,
2324: 0.473325,
2427: 0.47382,
2530: 0.474315,
2633: 0.474827,
2735: 0.475332,
2837: 0.475847,
2939: 0.476335,
3041: 0.476825,
3143: 0.477332,
3244: 0.477839,
3345: 0.478324,
3446: 0.478836,
3547: 0.479364,
3647: 0.479848,
3747: 0.48035,
3847: 0.480861,
3947: 0.481369,
4047: 0.481873,
4146: 0.482397,
4245: 0.482891,
4345: 0.483388,
4443: 0.483886,
4542: 0.484405,
4640: 0.484921,
4738: 0.485453,
4836: 0.485937,
4934: 0.486432,
5032: 0.486943,
5129: 0.487428,
5226: 0.487931,
5323: 0.488442,
5420: 0.488945,
5517: 0.489432,
5613: 0.489927,
5710: 0.490403,
5806: 0.49091,
5902: 0.491412,
5997: 0.491919,
6093: 0.492425,
6188: 0.492938,
6283: 0.493454,
6377: 0.49399,
6471: 0.494508,
6566: 0.495004,
6660: 0.495505,
6754: 0.496021,
6848: 0.496521,
6942: 0.497009,
7035: 0.49753,
7128: 0.498039,
7221: 0.498538,
7314: 0.499034,
7407: 0.499543,
7500: 0.500042,
7592: 0.500548,
7684: 0.501055,
7776: 0.501567,
7868: 0.502073,
7959: 0.502587,
8051: 0.503084,
8142: 0.503601,
8233: 0.504104,
8324: 0.504603,
8414: 0.505108,
8505: 0.505621,
8595: 0.506128,
8685: 0.506623,
8775: 0.507123,
8865: 0.50762,
8955: 0.508126,
9044: 0.508618,
9134: 0.509108,
9223: 0.509619,
9311: 0.510144,
9400: 0.510659,
9489: 0.511156,
9577: 0.511664,
9665: 0.512158,
9753: 0.51267,
9841: 0.513171,
9929: 0.513689,
10016: 0.51419,
10103: 0.514699,
10190: 0.515219,
10277: 0.51573,
10364: 0.516232,
10451: 0.516735,
10537: 0.517236,
10623: 0.51774,
10710: 0.518241,
10796: 0.518745,
10881: 0.519257,
10967: 0.519763,
11052: 0.52027,
11137: 0.52078,
11223: 0.52129,
11307: 0.521799,
11392: 0.522315,
11477: 0.522817,
11561: 0.523322,
11645: 0.523825,
11730: 0.524327,
11814: 0.524833,
11898: 0.525326,
11981: 0.525831,
12065: 0.526335,
12148: 0.526843,
12231: 0.527345,
12315: 0.527848,
12397: 0.528352,
12480: 0.528857,
12563: 0.529351,
12645: 0.52986,
12727: 0.53037,
12809: 0.530873,
12891: 0.531382,
12973: 0.531885,
13055: 0.532387,
13136: 0.532884,
13218: 0.533387,
13299: 0.533889,
13380: 0.534385,
13461: 0.53488,
13542: 0.535375,
13623: 0.535878,
13703: 0.536377,
13784: 0.536868,
13864: 0.537369,
13944: 0.537873,
14024: 0.538368,
14104: 0.538866,
14184: 0.539365,
14263: 0.539866,
14342: 0.540377,
14421: 0.540882,
14500: 0.541376,
14579: 0.541875,
14658: 0.542369,
14737: 0.542872,
14815: 0.543371,
14894: 0.543874,
14972: 0.544374,
15049: 0.544884,
15127: 0.545379,
15205: 0.545882,
15283: 0.546382,
15360: 0.546883,
15438: 0.547382,
15514: 0.547889,
15591: 0.54839,
15669: 0.548886,
15745: 0.549382,
15822: 0.549882,
15898: 0.550382,
15975: 0.550881,
16051: 0.551379,
16127: 0.551876,
16203: 0.552375,
16279: 0.552873,
16354: 0.553381,
16430: 0.55388,
16505: 0.554377,
16581: 0.554875,
16656: 0.555377,
16731: 0.555869,
16806: 0.556372,
16881: 0.556863,
16955: 0.557364,
17029: 0.55787,
17104: 0.55836,
17178: 0.558862,
17252: 0.559355,
17326: 0.55986,
17400: 0.560362,
17474: 0.56086,
17547: 0.561358,
17620: 0.561861,
17694: 0.562359,
17767: 0.562855,
17840: 0.563347,
17913: 0.563846,
17986: 0.564343,
18059: 0.564837,
18131: 0.565339,
18204: 0.565827,
18276: 0.56632,
18348: 0.566823,
18421: 0.567315,
18493: 0.567807,
18564: 0.568303,
18636: 0.56881,
18707: 0.569311,
18778: 0.569815,
18850: 0.570309,
18921: 0.570806,
18992: 0.571305,
19063: 0.571807,
19134: 0.572296,
19205: 0.572795,
19276: 0.57328,
19346: 0.57378,
19416: 0.574274,
19487: 0.574769,
19557: 0.575265,
19627: 0.575759,
19696: 0.57626,
19766: 0.576758,
19836: 0.577261,
19905: 0.57775,
19991: 0.578367,
20077: 0.578984,
20163: 0.579597,
20248: 0.580205,
20334: 0.580817,
20419: 0.581419,
20504: 0.582035,
20590: 0.582638,
20674: 0.58325,
20759: 0.58385,
20844: 0.584459,
20928: 0.585071,
21012: 0.585679,
21097: 0.58627,
21180: 0.586874,
21264: 0.587474,
21348: 0.588078,
21431: 0.588687,
21515: 0.589285,
21598: 0.589891,
21680: 0.5905,
21763: 0.591107,
21845: 0.591714,
21928: 0.592313,
22010: 0.592918,
22092: 0.593524,
22174: 0.594125,
22256: 0.594737,
22337: 0.595347,
22418: 0.595958,
22499: 0.596569,
22580: 0.597176,
22661: 0.597783,
22742: 0.598386,
22823: 0.598983,
22903: 0.599591,
22983: 0.600194,
23063: 0.600795,
23143: 0.601397,
23223: 0.601997,
23303: 0.602596,
23383: 0.603191,
23462: 0.603789,
23542: 0.604392,
23621: 0.604996,
23699: 0.605596,
23778: 0.606202,
23857: 0.606803,
23935: 0.607408,
24014: 0.608003,
24092: 0.608604,
24170: 0.609204,
24248: 0.609799,
24326: 0.610394,
24404: 0.61099,
24481: 0.611592,
24558: 0.612196,
24635: 0.612799,
24712: 0.613396,
24789: 0.613992,
24866: 0.614584,
24943: 0.615179,
25019: 0.615774,
25096: 0.616365,
25172: 0.616963,
25249: 0.617554,
25325: 0.618144,
25401: 0.618734,
25477: 0.619323,
25552: 0.61992,
25628: 0.620516,
25703: 0.621102,
25778: 0.621698,
25854: 0.622287,
25929: 0.622877,
26004: 0.623461,
26079: 0.624052,
26153: 0.624637,
26228: 0.625226,
26302: 0.625814,
26377: 0.626401,
26451: 0.62699,
26525: 0.627568,
26599: 0.628153,
26673: 0.628738,
26747: 0.629326,
26820: 0.629914,
26893: 0.630504,
26967: 0.631092,
27039: 0.631684,
27113: 0.632267,
27185: 0.632852,
27258: 0.633432,
27331: 0.634014,
27404: 0.63459,
27476: 0.635175,
27549: 0.635755,
27621: 0.63634,
27693: 0.63693,
27764: 0.637521,
27836: 0.6381,
27908: 0.638678,
27980: 0.639267,
28051: 0.639852,
28122: 0.640435,
28193: 0.641017,
28265: 0.641593,
28336: 0.64217,
28407: 0.642749,
28477: 0.643329,
28548: 0.643911,
28618: 0.644496,
28689: 0.645077,
28759: 0.645654,
28829: 0.646233,
28900: 0.646805,
28970: 0.647376,
29040: 0.647946,
29110: 0.64852,
29180: 0.649099,
29249: 0.649674,
29319: 0.650244,
29388: 0.650816,
29458: 0.651386,
29527: 0.651955,
29596: 0.652526,
29665: 0.653099,
29734: 0.653678,
29803: 0.654242,
29872: 0.654817,
29940: 0.655385,
30009: 0.655953,
30077: 0.656525,
30146: 0.657093,
30214: 0.657656,
30282: 0.658227,
30350: 0.658791,
30418: 0.659355,
30486: 0.659925,
30554: 0.660487,
30621: 0.661056,
30689: 0.661625,
30756: 0.662191,
30824: 0.662751,
30891: 0.663319,
30958: 0.66388,
31025: 0.664438,
31092: 0.665002,
31159: 0.665573,
31226: 0.666135,
31292: 0.666698,
31359: 0.667254,
31425: 0.667821,
31492: 0.668377,
31558: 0.668938,
31624: 0.669497,
31691: 0.670048,
31757: 0.670608,
31823: 0.671162,
31889: 0.671714,
31955: 0.672274,
32021: 0.672829,
32087: 0.673381,
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