Hi,
I ran into an issue where issuing the same query without cache on the same
dataset would yield slightly different hyperLogLog result.
I narrowed it down to an issue in the commutativity of the fold
```
byte[] b1 = { 0x01, 0x00, 0x07, (byte)0xfe, 0x12, 0x03,
(byte)0xb4, 0x35, 0x22, 0x42, 0x32, 0x32, 0x63, 0x32, 0x36, 0x3a, 0x53, 0x46,
0x74, 0x23, 0x33, 0x13, 0x22, 0x46, 0x33, 0x44, 0x32, 0x44, 0x24, 0x43, 0x44,
0x23, (byte)0x84, 0x43, 0x42, 0x33, 0x48, 0x43, (byte)0x93, 0x52, 0x44, 0x33,
0x54, 0x53, 0x56, 0x38, (byte)0x86, 0x37, 0x23, 0x32, 0x3b, 0x76, 0x33, 0x44,
0x63, 0x46, 0x55, 0x62, 0x43, 0x43, 0x74, 0x24, 0x43, 0x45, 0x62, 0x15, 0x34,
(byte)0x84, 0x66, 0x25, 0x54, 0x31, 0x45, 0x73, 0x64, 0x62, 0x33, 0x38, 0x62,
0x43, 0x32, 0x43, 0x14, 0x44, 0x46, 0x32, 0x31, 0x34, 0x14, 0x73, 0x23, 0x25,
(byte)0xa5, 0x67, 0x45, 0x34, 0x29, 0x43, 0x34, 0x35, (byte)0x92, 0x27, 0x53,
0x63, 0x74, 0x55, 0x54, 0x6b, 0x54, 0x3a, 0x44, 0x42, 0x44, 0x42, 0x43, 0x46,
0x63, 0x62, 0x58, 0x1b, 0x74, 0x26, 0x46, 0x33, 0x56, 0x62, 0x52, 0x28,
(byte)0x86, 0x34, 0x34, 0x35, 0x49, 0x42, 0x22, 0x46, 0x24, 0x54, 0x56, 0x35,
0x23, 0x35, 0x43, 0x54, 0x34, 0x58, 0x35, 0x34, 0x62, 0x62, 0x22, 0x14, 0x77
, 0x73, 0x45, 0x43, 0x45, 0x53, 0x23, 0x22, 0x31, 0x15, 0x14, 0x65, 0x54,
0x23, 0x43, (byte)0x95, 0x52, 0x22, 0x53, 0x73, 0x22, 0x27, 0x24, 0x26, 0x23,
0x35, 0x34, 0x36, 0x46, 0x63, 0x43, 0x14, 0x13, 0x53, 0x32, 0x43, 0x64, 0x34,
0x64, 0x43, (byte)0x84, 0x35, 0x76, 0x28, 0x51, 0x63, 0x32, 0x15, 0x32, 0x21,
0x55, 0x76, 0x42, 0x33, 0x23, 0x34, 0x32, 0x24, 0x23, 0x24, 0x27, 0x54, 0x23,
0x34, 0x43, 0x35, 0x36, 0x55, 0x44, 0x45, 0x26, 0x23, 0x55, 0x63, 0x55, 0x46,
0x33, 0x33, 0x54, 0x51, 0x22, 0x34, 0x43, 0x72, 0x5a, 0x3c, 0x74, 0x22, 0x62,
0x29, 0x57, 0x33, 0x25, 0x66, 0x36, (byte)0x92, 0x64, 0x23, 0x41, 0x65, 0x53,
0x79, 0x43, 0x44, 0x21, 0x41, 0x78, 0x44, 0x37, 0x33, 0x52, 0x34, 0x25, 0x42,
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0x34, 0x55, (byte)0xa7, 0x65, 0x34, 0x33, 0x44, 0x11, 0x49, 0x33, 0x43, 0x55,
0x43, 0x37, 0x34, 0x53, 0x74, 0x34, 0x25, 0x42, 0x63, 0x43, 0x35, 0x43, 0x32,
0x32, 0x14, 0x23, 0x45, 0x42, (byte)0xa5, 0x42, 0x68, 0x53, 0x52,
0x53, 0x33, 0x44, 0x25, 0x33, 0x32, 0x37, 0x63, 0x33, 0x63, (byte)0x83, 0x45,
0x76, 0x46, 0x14, 0x41, 0x34, 0x55, 0x74, 0x37, 0x34, (byte)0xa2, 0x53, 0x45,
0x34, 0x53, 0x33, 0x45, 0x43, 0x24, 0x65, 0x46, 0x64, 0x46, 0x48, 0x54, 0x75,
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0x33, 0x52, 0x35, 0x53, 0x32, 0x65, 0x43, 0x22, 0x43, 0x15, 0x23, 0x25, 0x64,
0x54, 0x34, 0x46, 0x45, 0x38, 0x31, 0x63, 0x33, 0x35, 0x72, 0x14, 0x35, 0x75,
0x23, 0x44, 0x42, 0x62, 0x32, 0x64, 0x72, (byte)0x94, 0x33, 0x43, 0x44, 0x43,
0x26, 0x25, 0x55, 0x42, 0x72, 0x13, 0x34, 0x24, 0x12, 0x73, 0x25, 0x42, 0x33,
0x23, 0x32, 0x54, 0x33, 0x31, 0x35, 0x5a, 0x54, 0x42, 0x14, 0x63, 0x28, 0x13,
0x63, 0x32, 0x54, 0x14, 0x44, (byte)0x82, 0x46, 0x35, 0x48, 0x43, 0x68, 0x31,
(byte)0x96, 0x54, 0x45, (byte)0x84, 0x44, 0x24, 0x22, 0x44, 0x55, 0x14, 0x42,
0x24, 0x72, 0x33, 0x34, 0x26, 0x23, 0x53, 0x52, 0x54, 0x35, 0x41, 0x32, 0x23,
0x53, 0x35, 0x33, 0x34, (byte)0xb5, 0x44, 0x54, 0x23, 0x43,
0x32, 0x14, 0x13, 0x54, (byte)0x85, 0x46, 0x45, 0x64, 0x54, 0x50, 0x42, 0x63,
0x43, 0x24, 0x25, 0x36, 0x45, 0x22, 0x52, 0x54, 0x35, 0x22, 0x23, 0x45, 0x76,
0x34, 0x24, 0x44, 0x35, 0x24, 0x36, (byte)0x88, 0x42, 0x25, 0x42, 0x22, 0x31,
0x25, 0x44, 0x44, 0x44, 0x13, 0x23, 0x52, 0x32, 0x31, 0x43, 0x63, 0x14, 0x43,
0x43, (byte)0x83, 0x46, 0x65, 0x44, 0x34, 0x33, 0x62, 0x61, 0x33, 0x21, 0x46,
0x32, 0x25, 0x32, 0x25, 0x34, 0x32, 0x34, 0x45, 0x24, 0x44, 0x33, 0x74, 0x22,
0x74, 0x32, 0x55, 0x56, 0x72, 0x52, 0x54, 0x45, 0x43, 0x42, 0x34, 0x34, 0x56,
0x65, 0x42, 0x43, 0x33, 0x44, 0x43, 0x14, 0x25, 0x31, 0x33, 0x23, 0x45, 0x72,
0x31, 0x44, 0x23, 0x47, 0x62, 0x76, 0x54, 0x64, 0x44, 0x22, 0x65, 0x38, 0x43,
(byte)0xb6, 0x77, 0x34, 0x13, 0x74, 0x25, 0x44, 0x65, 0x38, 0x45, 0x44, 0x35,
0x32, 0x28, 0x55, 0x45, (byte)0x85, (byte)0xa2, 0x46, 0x61, 0x16, 0x34, 0x43,
0x74, 0x44, 0x33, 0x25, 0x66, 0x32, 0x35, 0x65, 0x26, 0x45, 0x33, 0x44, 0x15,
0x14, 0x52, 0x64, 0x44, 0x36, (byte)0x96, 0x35, 0x35, 0x36, (
byte)0x85, 0x23, 0x55, 0x63, 0x45, 0x41, 0x72, 0x53, 0x23, 0x11, 0x71, 0x33,
0x23, 0x34, 0x63, 0x35, 0x44, 0x33, 0x42, 0x44, 0x46, (byte)0xb3, 0x13, 0x63,
0x41, 0x42, 0x43, 0x34, 0x33, 0x33, 0x54, 0x24, 0x26, 0x34, 0x26, 0x31, 0x53,
0x43, 0x44, 0x53, 0x54, 0x33, 0x23, 0x33, 0x24, 0x34, 0x52, 0x62, 0x43, 0x43,
0x33, 0x42, 0x41, 0x54, 0x22, 0x64, 0x44, (byte)0x84, 0x43, 0x32, 0x33, 0x54,
0x14, (byte)0x83, 0x34, 0x54, 0x47, 0x25, 0x53, 0x44, 0x43, 0x24, 0x53, 0x41,
0x65, 0x13, 0x26, 0x56, 0x76, 0x42, 0x15, 0x47, 0x45, 0x43, 0x53, 0x23, 0x35,
0x34, 0x23, 0x43, 0x52, 0x3c, 0x75, (byte)0xa4, 0x23, 0x72, 0x36, 0x21,
(byte)0x83, 0x34, 0x24, 0x43, 0x42, 0x23, 0x34, 0x44, 0x23, 0x36, 0x63, 0x23,
0x22, 0x13, 0x38, 0x44, 0x52, 0x43, 0x23, 0x24, 0x51, 0x53, 0x24, 0x23, 0x53,
0x35, 0x27, 0x53, 0x34, 0x74, (byte)0x86, 0x44, 0x53, 0x23, 0x55, 0x73, 0x33,
0x35, 0x45, 0x45, 0x43, 0x33, 0x14, 0x35, 0x25, 0x38, 0x63, 0x43, 0x34, 0x53,
0x24, 0x76, 0x42, 0x37, 0x42, 0x54, 0x44, 0x26, 0x52, 0x44, (byte)0x
83, 0x33, 0x36, 0x23, 0x35, 0x35, 0x32, 0x35, 0x73, 0x53, 0x24, 0x56, 0x26,
0x32, 0x23, (byte)0x93, 0x47, 0x22, 0x42, 0x74, 0x33, (byte)0x85, 0x53, 0x44,
0x44, 0x33, (byte)0x82, 0x13, 0x53, 0x53, 0x15, (byte)0x83, 0x22, 0x32,
(byte)0x85, 0x50, 0x22, 0x52, 0x53, 0x44, 0x64, 0x74, 0x35, 0x66, 0x32, 0x44,
0x57, 0x33, 0x71, 0x65, 0x53, 0x37, 0x12, 0x54, 0x52, 0x33, 0x23, 0x31, 0x55,
0x59, 0x45, 0x44, 0x38, 0x78, 0x34, (byte)0x83, 0x25, 0x22, 0x35, 0x2b, 0x36,
0x75, (byte)0x83, 0x46, 0x26, 0x61, (byte)0x85, 0x44, 0x23, 0x72, 0x62, 0x74,
0x21, 0x28, 0x52, 0x52, (byte)0x85, 0x41, 0x44, 0x34, 0x34, 0x52, 0x2e, 0x34,
0x53, 0x23, 0x23, 0x27, 0x32, 0x35, (byte)0x98, 0x34, 0x53, 0x14, 0x52, 0x62,
0x55, 0x54, 0x21, 0x73, 0x22, 0x35, 0x72, 0x54, 0x42, 0x33, 0x31, 0x27, 0x27,
0x34, 0x44, 0x13, 0x43, 0x23, (byte)0x82, 0x32, 0x35, 0x42, 0x28, 0x64, 0x44,
0x55, 0x33, 0x68, 0x33, 0x55, 0x45, 0x53, (byte)0x95, 0x45, 0x34,(byte)0xb4,
(byte)0x92, 0x24, 0x22, 0x33, 0x51, 0x32, 0x66, 0x33, 0x31, 0x53, 0x24
, 0x51, 0x36, 0x33, 0x53, 0x23, 0x32, 0x43, 0x42, 0x54, 0x24, 0x34, 0x43,
0x25, 0x65, 0x12, 0x33, 0x72, 0x44, 0x42, 0x15, 0x34, 0x22, 0x24, 0x34, 0x36,
0x15, 0x23, 0x31, 0x65, 0x14, 0x38, 0x32, 0x33, 0x24, (byte)0x84, 0x34, 0x44,
0x63, (byte)0x84, 0x44, (byte)0x85, (byte)0xa2, 0x35, 0x35, 0x47, 0x28, 0x44,
0x46, 0x43, 0x33, 0x23, 0x75, 0x56, 0x53, 0x43, 0x47, 0x56, 0x14, 0x23, 0x13,
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0x35, 0x34, 0x45, 0x25, 0x45, 0x32, 0x56, 0x22, (byte)0x94, 0x14, 0x43, 0x47,
0x63, 0x44, 0x22, (byte)0x92};
byte[] b2 = { 0x01, 0x00, 0x04, 0x2d, 0x12, 0x01, 0x76, 0x02,
0x01, 0x00, 0x00, 0x10, 0x00, 0x01, 0x02, 0x01, 0x02, 0x33, 0x2a, 0x21, 0x10,
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0x34, 0x12, (byte)0x80, 0x00, 0x11, 0x02, 0x26, 0x11, 0x12, 0x10, 0x20, 0x01,
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0x01, 0x13, 0x20, 0x42, 0x12, 0x20, 0x04, 0x04, 0x10, 0x10, 0x41
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(byte)0x81, 0x01, 0x05, 0x02, 0x07, 0x50, 0x00, 0x17, 0x20, 0x30, 0x01, 0x22,
0x00, 0x00, 0x31, 0x30, 0x20, 0x05, 0x03, 0x21, 0x31, 0x40, 0x00, 0x10, 0x14,
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0x00, 0x20, 0x21, 0x10, 0x42, 0x02, 0x00, 0x00, 0x01, 0x23, 0x00, 0x12, 0x0d,
0x03, 0x01, 0x26, 0x31, 0x31, 0x00, 0x00, 0x04, 0x40, 0x21, 0x01, 0x12, 0x00,
0x01, 0x34, 0x44, 0x01, 0x00, 0x20, 0x00, 0x33, 0x20, 0x13, 0x00, 0x
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0x23, 0x20, 0x00, 0x03, 0x10, 0x10, 0x01, 0x14, 0x03, 0x00, 0x01, 0x12, 0x50,
0x03, 0x10, 0x00, 0x60, 0x01, 0x1a, 0x22, 0x00, 0x20, 0x10, 0x17, 0x20, 0x00,
0x11, 0x10, 0x00, 0x24, 0x11, 0x00, 0x30, 0x10, 0x01, 0x31, 0x00, 0x20, 0x00,
0x02, 0x30, 0x01, 0x10, 0x02, 0x00, 0x00, 0x21, 0x20, 0x05, 0x31, 0x10, 0x01,
0x10, 0x20, 0x00, 0x37, 0x02, 0x00, 0x10, 0x51, 0x30, (byte)0xd0, 0x00, 0x01,
0x20, 0x12, 0x23, 0x00, 0x02, 0x50, 0x02, 0x05, 0x00, 0x01, 0x00, 0x02, 0x04,
0x30, 0x00, 0x00, 0x00, 0x01, 0x03, 0x10, 0x03, 0x10, 0x11, 0x02, 0x72, 0x10,
0x24, 0x00, 0x01, 0x00, 0x2b, 0x00, 0x10, 0x11, 0x24, 0x10, 0x01, 0x02, 0x01,
0x20, 0x31, 0x40, 0x10, 0x02, 0x10, 0x15, 0x00, 0x00, 0x10, 0x34, 0x00, 0x00,
0x00, 0x01, 0x00, 0x40, 0x31, 0x00, 0x11, 0x02, 0x30, 0x10, 0x20, 0x01, 0x01,
0x23, 0x01, 0x02, 0x2b, 0x03, 0x02, 0x00, 0x20, 0x12, 0x00, 0x0
1, 0x15, (byte)0x91, 0x03, 0x02, 0x10, 0x01, 0x01, 0x20, 0x11, 0x10, 0x10,
0x01, 0x41, 0x30, 0x00, 0x20, 0x00, 0x20, 0x32, 0x22, 0x04, 0x20, 0x20, 0x22,
0x20, 0x00, 0x03, 0x12, 0x00, 0x61, 0x21, 0x30, 0x41, 0x13, 0x00, 0x02, 0x20,
0x12, 0x01, 0x00, 0x22, 0x10, 0x01, 0x20, 0x00, 0x23};
HyperLogLogCollector col =
HyperLogLogCollector.makeLatestCollector();
col.fold(ByteBuffer.wrap(b1));
col.fold(ByteBuffer.wrap(b2));
double d = col.estimateCardinality();
HyperLogLogCollector col2 =
HyperLogLogCollector.makeLatestCollector();
col2.fold(ByteBuffer.wrap(b2));
col2.fold(ByteBuffer.wrap(b1));
double e = col2.estimateCardinality();
```
```
d == 14272.367304840394
e == 14270.788573667869
```
I understand both of those values or correct probabilistically, but the
unstable results brings confusion to end users.
[ Full content available at:
https://github.com/apache/incubator-druid/issues/6412 ]
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