The indicator t/v data in prometheus is saved in block/chunks, and the label data is saved in block/index.
For t/v data, prometheus adopts the compression method of Facebook Gorilla paper:
- Timestamp: compress the time value of the timing point in delta of delta mode;
- Value: compress the value of the timing point in XOR mode;
According to the above compression method, a 16byte timing point can be compressed into 1.37byte, and the compression rate is very high.
Compression of time sequence point t/v
1)timestamp compression
In terms of timing, the timestamp difference between two adjacent points is generally fixed. If you pull every 60s, the timestamp difference is generally 60s, for example
- p1: 10:00:00，p2: 10:01:00，p3: 10:01:59，p4: 10:03:00，p5: 10:04:00，p6: 10:05:00
- The difference of time stamp is: 60s, 59s, 61s, 60s, 60s;
Gorilla's paper uses delta of delta compression to compress timestamp:
- The timestamp t0 of the first timing point is completely stored;
- The timestamp T1 of the second timing point stores delta=t1-t0;
For the subsequent timestamp TN, first calculate the dod value: delta=(tn - tn-1) - (tn-1 - tn-2);
- If dod=0, use 1bit = "0" to store the timestamp;
- If dod=[-8191, 8192], first store "10" as the identification, and then store the dod value in 14bit;
- If dod=[-65535, 65536], first store "110" as the identification, and then store the dod value in 17bit;
- If dod=[-524287, 524288], first store "1110" as the identification, and then store the dod value in 20bit;
- If dod > 524288, first store "1111" as the identification, and then store the dod value in 64bit;
In practice, it is found that 95% of timestamp s can be stored according to the case of dod=0.
2)value compression
Gorilla's paper compresses the timing point value based on:
- The value value of adjacent timing points will not change significantly;
- value is mostly a floating-point number. When two values are very close, the sign bit, exponential bit and the first few bits of the mantissa of the two floating-point numbers are the same;
Compression algorithm for value:
- The value value of the first timing point is not compressed and is saved directly;
Starting from the second point, XOR its value with the previous value;
- If the XOR operation result is "0", it means that the two values are the same, and only the "0" value of 1 bit can be stored;
Otherwise, store the 1bit value "1";
- If the non-0 part of the XOR result is included in the previous XOR result, write the 1bit value "0" and store it in the non-0 part of the XOR;
- Otherwise, write the 1bit value "1", use 5bit to store the number of the first value 0 in XOR, 6bit to store the length of the middle non-0, and finally store the middle non-0 bit;
The data shows that about 60% of the value values are stored in only 1 bit, 30% of the value values fall into the "10" range, and the remaining 10% of the value values fall into the "11" range.
3) Compression example
Input sequence value
10:00:00 3.1 10:01:01 3.2 10:02:00 3.0 10:02:59 3.2 10:03:00 3.1
Then deposit
10:00:00 3.1 61 3.2 xor 3.1 -2(59-61) 3.0 xor 3.2 0(59-59) 3.2 xor 3.0 2(61-59) 3.1 xor 3.2
Source code analysis of writing t/v
xorAppender is responsible for writing the value of t/v, t=int64, v=float64
// tsdb/chunkenc/xor.go
func (a *xorAppender) Append(t int64, v float64) {
var tDelta uint64
num := binary.BigEndian.Uint16(a.b.bytes())
//At the first point, the values of t1 and v1 are fully recorded
if num == 0 {
buf := make([]byte, binary.MaxVarintLen64)
for _, b := range buf[:binary.PutVarint(buf, t)] {
a.b.writeByte(b) //Write the value of t1
}
a.b.writeBits(math.Float64bits(v), 64) //Write value of v1
} else if num == 1 { //Second point
tDelta = uint64(t - a.t)
buf := make([]byte, binary.MaxVarintLen64)
for _, b := range buf[:binary.PutUvarint(buf, tDelta)] {
a.b.writeByte(b) //Write tDeleta=t2-t1
}
a.writeVDelta(v) //Write the value of v2^v1
} else { //Third and subsequent points
tDelta = uint64(t - a.t)
dod := int64(tDelta - a.tDelta) //Calculate dod
// Gorilla has a max resolution of seconds, Prometheus milliseconds.
// Thus we use higher value range steps with larger bit size.
switch {
case dod == 0:
a.b.writeBit(zero) //Write 0
case bitRange(dod, 14): //dod = [- 81918192], first store 10 as the identification, and then store the value of dod in 14bit
a.b.writeBits(0x02, 2) // '10'
a.b.writeBits(uint64(dod), 14)
case bitRange(dod, 17): //dod = [- 6553565536], first store 110 as the identification, and then store the value of the dod in 17bit
a.b.writeBits(0x06, 3) // '110'
a.b.writeBits(uint64(dod), 17)
case bitRange(dod, 20): //dod = [- 524287524288], first store 1110 as the identification, and then store the value of the dod in 20bit
a.b.writeBits(0x0e, 4) // '1110'
a.b.writeBits(uint64(dod), 20)
default: //dod > 524288, first store 1111 as the identification, and then store the value of the dod in 64bit
a.b.writeBits(0x0f, 4) // '1111'
a.b.writeBits(uint64(dod), 64)
}
a.writeVDelta(v) //Write vn^vn-1
}
a.t = t //Last t written
a.v = v //Last v written
binary.BigEndian.PutUint16(a.b.bytes(), num+1)
a.tDelta = tDelta //Last tDelta written
}Take another look at the source code of writing VDelta using xor:
// tsdb/chunkenc/xor.go
func (a *xorAppender) writeVDelta(v float64) {
vDelta := math.Float64bits(v) ^ math.Float64bits(a.v) //The current value is xor compared with the previous value
if vDelta == 0 { //xor=0, just store it in 1bit'0 '
a.b.writeBit(zero)
return
}
a.b.writeBit(one) //Store control bit '1' first
leading := uint8(bits.LeadingZeros64(vDelta)) //Calculate the number of leading zeros of vdelta
trailing := uint8(bits.TrailingZeros64(vDelta)) //Calculate the number of zeros after vdelta
// Clamp number of leading zeros to avoid overflow when encoding.
if leading >= 32 {
leading = 31
}
if a.leading != 0xff && leading >= a.leading && trailing >= a.trailing {
a.b.writeBit(zero)
a.b.writeBits(vDelta>>a.trailing, 64-int(a.leading)-int(a.trailing))
} else {
a.leading, a.trailing = leading, trailing
a.b.writeBit(one)
a.b.writeBits(uint64(leading), 5)
// Note that if leading == trailing == 0, then sigbits == 64. But that value doesn't actually fit into the 6 bits we have.
// Luckily, we never need to encode 0 significant bits, since that would put us in the other case (vdelta == 0).
// So instead we write out a 0 and adjust it back to 64 on unpacking.
sigbits := 64 - leading - trailing
a.b.writeBits(uint64(sigbits), 6)
a.b.writeBits(vDelta>>trailing, int(sigbits))
}
}Read t/v source code analysis
xorIterator is responsible for reading t/v data: basically, it is the reverse process of the write process
// tsdb/chunkenc/xor.go
func (it *xorIterator) Next() bool {
if it.err != nil || it.numRead == it.numTotal {
return false
}
//Read the first point
if it.numRead == 0 {
t, err := binary.ReadVarint(&it.br) //time original value reading
if err != nil {
it.err = err
return false
}
v, err := it.br.readBits(64) //Value original value reading
if err != nil {
it.err = err
return false
}
it.t = t
it.val = math.Float64frombits(v)
it.numRead++ //Read quantity + 1
return true
}
//Read the second point
if it.numRead == 1 {
tDelta, err := binary.ReadUvarint(&it.br) //Read tDelta
if err != nil {
it.err = err
return false
}
it.tDelta = tDelta
it.t = it.t + int64(it.tDelta) //Calculate time
return it.readValue() //Read xor and calculate the original value
}
//Read point 3 and beyond
var d byte
//Read prefix, up to 4bit
// read delta-of-delta
for i := 0; i < 4; i++ {
d <<= 1
bit, err := it.br.readBit()
if err != nil {
it.err = err
return false
}
if bit == zero {
break
}
d |= 1
}
var sz uint8
var dod int64
switch d {
case 0x00:
// dod == 0 / / prefix = 0
case 0x02:
sz = 14 //Prefix = 10, save dod with 14bit
case 0x06: //Prefix = 110, save dod with 17bit
sz = 17
case 0x0e: //Prefix = 1110, save dod with 20bit
sz = 20
case 0x0f: //Prefix = 1111, save dod with 64bit
bits, err := it.br.readBits(64)
if err != nil {
it.err = err
return false
}
dod = int64(bits)
}
if sz != 0 {
bits, err := it.br.readBits(int(sz))
if err != nil {
it.err = err
return false
}
if bits > (1 << (sz - 1)) {
// or something
bits = bits - (1 << sz)
}
dod = int64(bits) //Read and calculate the value of dod
}
it.tDelta = uint64(int64(it.tDelta) + dod) //Calculate tdelta
it.t = it.t + int64(it.tDelta) //Calculate time
return it.readValue() //Read the value of xor
}Take another look at the process of reading xor value: xor the previous value with the value of xor
// tsdb/chunkenc/xor.go
func (it *xorIterator) readValue() bool {
bit, err := it.br.readBit() //Read the first bit
if err != nil {
it.err = err
return false
}
if bit == zero { //If the first bit=0, the value remains unchanged (so it does not need to be updated)
// it.val = it.val
} else {
bit, err := it.br.readBit()
if err != nil {
it.err = err
return false
}
if bit == zero {
// reuse leading/trailing zero bits
// it.leading, it.trailing = it.leading, it.trailing
} else {
bits, err := it.br.readBits(5)
if err != nil {
it.err = err
return false
}
it.leading = uint8(bits)
bits, err = it.br.readBits(6)
if err != nil {
it.err = err
return false
}
mbits := uint8(bits)
// 0 significant bits here means we overflowed and we actually need 64; see comment in encoder
if mbits == 0 {
mbits = 64
}
it.trailing = 64 - it.leading - mbits
}
mbits := int(64 - it.leading - it.trailing)
bits, err := it.br.readBits(mbits)
if err != nil {
it.err = err
return false
}
vbits := math.Float64bits(it.val) //Get the last value
vbits ^= (bits << it.trailing) //xor with the value of xor to obtain the local value
it.val = math.Float64frombits(vbits) // v1^v2=xor, then v2=v1^xor
}
it.numRead++
return true
}