81 lines
2.5 KiB
Python
81 lines
2.5 KiB
Python
#!/usr/bin/env python3
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#
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# ddsketch_calc.py
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#
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# This source file is part of the FoundationDB open source project
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#
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# Copyright 2013-2022 Apple Inc. and the FoundationDB project authors
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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#
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import numpy as np
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import math as m
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# Implements a DDSketch class as desrcibed in:
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# https://arxiv.org/pdf/1908.10693.pdf
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# This class has methods that use cubic interpolation to quickly compute log
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# and inverse log. The coefficients A,B,C as well as correctingFactor are
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# all constants used for interpolating.
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# The implementation for interpolation was originally seen here in:
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# https://github.com/DataDog/sketches-java/
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# in the file CubicallyInterpolatedMapping.java
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class DDSketch(object):
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A = 6.0 / 35.0
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B = -3.0 / 5.0
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C = 10.0 / 7.0
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EPS = 1e-18
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correctingFactor = 1.00988652862227438516
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offset = 0
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multiplier = 0
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gamma = 0
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def __init__(self, errorGuarantee):
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self.gamma = (1 + errorGuarantee) / (1 - errorGuarantee)
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self.multiplier = (self.correctingFactor * m.log(2)) / m.log(self.gamma)
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self.offset = self.getIndex(1.0 / self.EPS)
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def fastlog(self, value):
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s = np.frexp(value)
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e = s[1]
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s = s[0]
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s = s * 2 - 1
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return ((self.A * s + self.B) * s + self.C) * s + e - 1
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def reverseLog(self, index):
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exponent = m.floor(index)
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d0 = self.B * self.B - 3 * self.A * self.C
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d1 = (
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2 * self.B * self.B * self.B
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- 9 * self.A * self.B * self.C
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- 27 * self.A * self.A * (index - exponent)
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)
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p = np.cbrt((d1 - np.sqrt(d1 * d1 - 4 * d0 * d0 * d0)) / 2)
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significandPlusOne = -(self.B + p + d0 / p) / (3 * self.A) + 1
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return np.ldexp(significandPlusOne / 2, exponent + 1)
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def getIndex(self, sample):
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return m.ceil(self.fastlog(sample) * self.multiplier) + self.offset
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def getValue(self, idx):
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return (
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self.reverseLog((idx - self.offset) / self.multiplier)
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* 2.0
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/ (1 + self.gamma)
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)
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