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| package floats | |
| import ( | |
| "fmt" | |
| "math" | |
| "math/bits" | |
| "github.com/klauspost/compress/fse" | |
| ) | |
| const blockSize = 1024 | |
| type block struct { | |
| signExpHi [blockSize]byte // Contains sign and 2 high bits of exponent | |
| expLow [blockSize]byte // Contains lowest exponent bits | |
| mantissa [blockSize]uint64 // Contains the mantissa remainder | |
| manBits [blockSize]byte // mantissa bits saved from top | |
| tzManBits [blockSize]byte // TZ bits of mantissa to remove at bottom | |
| mantissaBits [blockSize]byte // Actual bits to output (not encoded). | |
| signEnc *fse.Scratch | |
| expEnc *fse.Scratch | |
| manBitsEnc *fse.Scratch | |
| manTzBitsEnc *fse.Scratch | |
| pred predictor | |
| pred32 predictor32 | |
| } | |
| func (b *block) encode() int { | |
| if b.signEnc == nil { | |
| b.signEnc = &fse.Scratch{MaxSymbolValue: 1 << 3} | |
| b.expEnc = &fse.Scratch{MaxSymbolValue: 255} | |
| b.manBitsEnc = &fse.Scratch{MaxSymbolValue: 52} | |
| b.manTzBitsEnc = &fse.Scratch{MaxSymbolValue: 52} | |
| } | |
| checkZero := func(b []byte) []byte { | |
| if len(b) == 0 { | |
| b = make([]byte, 1) // RLE, use 1 bytes. Assume we can store the RLE info somewhere else | |
| } | |
| return b | |
| } | |
| signs, _ := fse.Compress(b.signExpHi[:], b.signEnc) | |
| signs = checkZero(signs) | |
| exp, _ := fse.Compress(b.expLow[:], b.expEnc) | |
| exp = checkZero(exp) | |
| mans, _ := fse.Compress(b.manBits[:], b.manBitsEnc) | |
| mans = checkZero(mans) | |
| mantz, _ := fse.Compress(b.tzManBits[:], b.manTzBitsEnc) | |
| mantz = checkZero(mantz) | |
| mantissas := 0 | |
| for _, v := range b.mantissaBits[:] { | |
| mantissas += int(v) | |
| } | |
| tzSaved := 0 | |
| for i, v := range b.manTzBitsEnc.Histogram()[:b.manTzBitsEnc.MaxSymbolValue] { | |
| tzSaved += i * int(v) | |
| } | |
| bitsSaved := 0 | |
| for i, v := range b.manBitsEnc.Histogram()[:b.manBitsEnc.MaxSymbolValue] { | |
| bitsSaved += i * int(v) | |
| } | |
| const printDetails = true | |
| if printDetails { | |
| fmt.Println("signs:", b.signEnc.Histogram()[:8]) | |
| fmt.Println("exps:", b.expEnc.Histogram()[:256]) | |
| fmt.Println("bits:", b.manBitsEnc.Histogram()[:53], "saves", bitsSaved/8, "bytes") | |
| fmt.Println("TZ:", b.manTzBitsEnc.Histogram()[:53], "saves", tzSaved/8, "bytes") | |
| } | |
| // If storing TZ info takes more space than it saves, ditch it. | |
| if len(mantz)*8 >= tzSaved { | |
| if printDetails { | |
| fmt.Println("TZ is worse", tzSaved/8, "<=", len(mantz)) | |
| } | |
| mantz = nil | |
| mantissas += tzSaved | |
| } else { | |
| if printDetails { | |
| fmt.Println("TZ saved", tzSaved-len(mantz)*8, "bits") | |
| } | |
| } | |
| // If storing TZ info takes more space than it saves, ditch it. | |
| if len(mans)*8 >= bitsSaved { | |
| if printDetails { | |
| fmt.Println("Individual bits is worse") | |
| } | |
| mans = nil | |
| mantissas += bitsSaved | |
| } else { | |
| if printDetails { | |
| fmt.Println("Individual bits saved", bitsSaved-len(mans)*8, "bits") | |
| } | |
| } | |
| size := len(signs) + len(exp) + len(mans) + len(mantz) + (mantissas+7)/8 | |
| if printDetails { | |
| fmt.Println("Sizes in whole bytes; Signs:", len(signs), "Exponents:", len(exp), "ManBits:", len(mans), "ManTz:", len(mantz), "Mantissas:", (mantissas+7)/8, "Total:", size, "-", float64(size*8)/blockSize, "bits/element") | |
| } | |
| return size | |
| } | |
| func (b *block) addFloat64(f float64, idx int) { | |
| fb := b.pred.predict(math.Float64bits(f)) | |
| if false { | |
| fmt.Printf("after pred: 0x%016x, input 0x%016x\n", b.pred.predict(math.Float64bits(f)), math.Float64bits(f)) | |
| } | |
| b.pred.update(math.Float64bits(f)) | |
| sign := byte(fb >> 63) | |
| exp := uint16((fb>>(63-11) + 2) & 2047) | |
| remain := fb & (1<<53 - 1) | |
| if false { | |
| fmt.Printf("full: %08x, sign: %x, exp:%x, remain: 0x%08x\n", fb, sign, exp, remain) | |
| } | |
| // Zigzag exp into expU | |
| trail := bits.TrailingZeros64(remain) | |
| // Trimming only a few bits can be more expensive than leaving them. | |
| // This can be done dynamically at the encoding stage | |
| if trail < 3 { | |
| trail = 0 | |
| } | |
| const tzMod = 3 | |
| // Round down | |
| trail -= trail % tzMod | |
| b.tzManBits[idx] = byte(trail) | |
| remain >>= trail | |
| b.signExpHi[idx] = sign | byte(exp>>8) | |
| b.expLow[idx] = byte(exp) | |
| b.mantissa[idx] = remain | |
| remainBits := byte(53 - bits.Len64(remain)) | |
| b.mantissaBits[idx] = 53 - remainBits | |
| // Again, reduce resolution of bits. | |
| // Optimal value depends on input, but does not need to be communicated. | |
| // This can be done dynamically at the encoding stage | |
| const remainMod = 3 | |
| if m := remainBits % remainMod; m != 0 { | |
| remainBits += remainMod - m | |
| } | |
| b.manBits[idx] = remainBits | |
| } | |
| func (b *block) addFloat32(f float32, idx int) { | |
| fb := b.pred32.predict32(math.Float32bits(f)) | |
| if false { | |
| fmt.Printf("after pred: 0x%08x, input 0x%08x\n", b.pred32.predict32(math.Float32bits(f)), math.Float32bits(f)) | |
| } | |
| b.pred32.update32(math.Float32bits(f)) | |
| sign := byte(fb >> 31) | |
| exp := uint8((fb >> 23) & (1<<8 - 1)) | |
| remain := fb & (1<<24 - 1) | |
| // Zigzag exp into expU | |
| expU := uint16(exp << 1) | |
| if exp < 0 { | |
| expU = ^expU | |
| } | |
| b.signExpHi[idx] = sign | |
| b.expLow[idx] = 128 - exp | |
| trail := bits.TrailingZeros32(remain) | |
| // Trimming only a few bits can be more expensive than leaving them. | |
| // This can be done dynamically at the encoding stage. | |
| if trail < 3 { | |
| trail = 0 | |
| } | |
| const tzMod = 3 | |
| // Round down | |
| trail -= trail % tzMod | |
| b.tzManBits[idx] = byte(trail) | |
| remain >>= trail | |
| b.mantissa[idx] = uint64(remain) | |
| remainBits := byte(24 - bits.Len32(remain)) | |
| b.mantissaBits[idx] = 24 - remainBits | |
| // Again, reduce resolution of bits. | |
| // Optimal value depends on input, but does not need to be communicated. | |
| // This can be done dynamically at the encoding stage. | |
| const remainMod = 3 | |
| if m := remainBits % remainMod; m != 0 { | |
| remainBits += remainMod - m | |
| } | |
| b.manBits[idx] = remainBits | |
| } |
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| package floats | |
| import ( | |
| "bytes" | |
| "fmt" | |
| "testing" | |
| "github.com/spenczar/fpc" | |
| ) | |
| var testsets = [][]float64{numbers, numbers2, numbers3, numbers4} | |
| func Test_block_encode32(t *testing.T) { | |
| predictors := []predictor32{predNone{}, &predDelta{}, &predXor{}, newFCM(512, false), newFCM(512, true), newDFCM(512), newPredDeltaOffset(18), &predSecondOrder{}} | |
| for i, toTest := range testsets { | |
| t.Run(fmt.Sprint(i), func(t *testing.T) { | |
| for _, pred := range predictors { | |
| t.Run(pred.String(), func(t *testing.T) { | |
| toTest := toTest | |
| sz, elems := 0, 0 | |
| for len(toTest) >= blockSize { | |
| var b block | |
| pred.reset() | |
| b.pred32 = pred | |
| for i := 0; i < blockSize; i++ { | |
| b.addFloat32(float32(toTest[i]), i) | |
| } | |
| sz += b.encode() | |
| toTest = toTest[blockSize:] | |
| elems += blockSize | |
| } | |
| t.Logf("Test %d, %9s: %.02f bits/element", i, pred.String(), float64(sz)*8/float64(elems)) | |
| }) | |
| } | |
| }) | |
| } | |
| } | |
| func Test_block_encode64(t *testing.T) { | |
| predictors := []predictor{predNone{}, &predDelta{}, &predXor{}, newFCM(512, false), newFCM(512, true), newDFCM(512), newPredDeltaOffset(18), &predSecondOrder{}} | |
| for i, toTest := range testsets { | |
| t.Run(fmt.Sprint(i), func(t *testing.T) { | |
| for _, pred := range predictors { | |
| t.Run(pred.String(), func(t *testing.T) { | |
| toTest := toTest | |
| sz, elems := 0, 0 | |
| for len(toTest) >= blockSize { | |
| var b block | |
| pred.reset() | |
| b.pred = pred | |
| for i := 0; i < blockSize; i++ { | |
| b.addFloat64(toTest[i], i) | |
| } | |
| sz += b.encode() | |
| toTest = toTest[blockSize:] | |
| elems += blockSize | |
| } | |
| t.Logf("Test %d, %9s: %.02f bits/element", i, pred.String(), float64(sz)*8/float64(elems)) | |
| }) | |
| } | |
| t.Run("fpc", func(t *testing.T) { | |
| var buf bytes.Buffer | |
| f, err := fpc.NewWriterLevel(&buf, fpc.DefaultCompression) | |
| if err != nil { | |
| t.Fatal(err) | |
| } | |
| for i := range toTest { | |
| f.WriteFloat(toTest[i]) | |
| } | |
| f.Close() | |
| t.Logf("Test %d, %9s: %.02f bits/element", i, "fpc", float64(buf.Len())*8/float64(len(toTest))) | |
| }) | |
| }) | |
| } | |
| } |
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| module floats | |
| go 1.19 | |
| require ( | |
| github.com/klauspost/compress v1.16.3 // indirect | |
| github.com/spenczar/fpc v1.0.0 // indirect | |
| ) |
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| package floats | |
| import ( | |
| "fmt" | |
| "math" | |
| ) | |
| type predictor interface { | |
| reset() | |
| predict(n uint64) (predicted uint64) | |
| update(actual uint64) | |
| String() string | |
| } | |
| type predictor32 interface { | |
| reset() | |
| predict32(n uint32) (predicted uint32) | |
| update32(actual uint32) | |
| String() string | |
| } | |
| type fcm struct { | |
| table []uint64 | |
| size uint64 | |
| lastHash uint64 | |
| delta bool // use float subtraction instead of xor | |
| } | |
| func newFCM(size uint, delta bool) *fcm { | |
| // size must be a power of two | |
| d := &fcm{ | |
| table: make([]uint64, size, size), | |
| size: uint64(size), | |
| delta: delta, | |
| } | |
| return d | |
| } | |
| func (f *fcm) reset() { | |
| for i := range f.table { | |
| f.table[i] = 0x3fe0000000000000 | |
| } | |
| f.lastHash = 0 | |
| } | |
| func (f *fcm) hash(actual uint64) uint64 { | |
| return ((f.lastHash << 6) ^ (actual >> 48)) & (f.size - 1) | |
| } | |
| func (f *fcm) predict(n uint64) uint64 { | |
| if f.delta { | |
| return math.Float64bits(math.Float64frombits(n) - math.Float64frombits(f.table[f.lastHash])) | |
| } | |
| return n ^ f.table[f.lastHash] | |
| } | |
| func (f *fcm) predict32(n uint32) uint32 { | |
| if f.delta { | |
| return math.Float32bits(math.Float32frombits(n) - math.Float32frombits(uint32(f.table[f.lastHash]))) | |
| } | |
| return n ^ uint32(f.table[f.lastHash]) | |
| } | |
| func (f *fcm) update(actual uint64) { | |
| f.table[f.lastHash] = actual | |
| f.lastHash = f.hash(actual) | |
| } | |
| func (f *fcm) update32(actual uint32) { | |
| f.table[f.lastHash] = uint64(actual) | |
| f.lastHash = f.hash(uint64(actual) << 32) | |
| } | |
| func (f *fcm) String() string { | |
| if f.delta { | |
| return "FCM-DELTA" | |
| } | |
| return "FCM" | |
| } | |
| type dfcm struct { | |
| table []uint64 | |
| size uint64 | |
| lastHash uint64 | |
| lastValue uint64 | |
| } | |
| func newDFCM(size uint) *dfcm { | |
| // size must be a power of two | |
| d := &dfcm{ | |
| table: make([]uint64, size, size), | |
| size: uint64(size), | |
| } | |
| return d | |
| } | |
| func (d *dfcm) reset() { | |
| for i := range d.table { | |
| d.table[i] = 0 | |
| } | |
| d.lastHash = 0 | |
| d.lastValue = 0 | |
| } | |
| func (d *dfcm) hash(actual uint64) uint64 { | |
| return ((d.lastHash << 2) ^ ((actual - d.lastValue) >> 40)) & (d.size - 1) | |
| } | |
| func (d *dfcm) predict(n uint64) uint64 { | |
| return (d.table[d.lastHash] + d.lastValue) ^ n | |
| } | |
| func (d *dfcm) update(actual uint64) { | |
| d.table[d.lastHash] = actual - d.lastValue | |
| d.lastHash = d.hash(actual) | |
| d.lastValue = actual | |
| } | |
| func (d *dfcm) predict32(n uint32) uint32 { | |
| return uint32(d.table[d.lastHash]+d.lastValue) ^ n | |
| } | |
| func (d *dfcm) update32(actual uint32) { | |
| d.table[d.lastHash] = uint64(actual) - d.lastValue | |
| d.lastHash = d.hash(uint64(actual) << 32) | |
| d.lastValue = uint64(actual) | |
| } | |
| func (d *dfcm) String() string { | |
| return "DFCM" | |
| } | |
| type predDelta struct { | |
| last float64 | |
| last32 float32 | |
| } | |
| func (d *predDelta) reset() { | |
| d.last = 0 | |
| d.last32 = 0 | |
| } | |
| func (d *predDelta) predict(n uint64) uint64 { | |
| return math.Float64bits(math.Float64frombits(n)-d.last) ^ 0x3fe0000000000000 | |
| } | |
| func (d *predDelta) update(actual uint64) { | |
| d.last = math.Float64frombits(actual) | |
| } | |
| func (d *predDelta) predict32(n uint32) uint32 { | |
| return math.Float32bits(math.Float32frombits(n) - d.last32) | |
| } | |
| func (d *predDelta) update32(actual uint32) { | |
| d.last32 = math.Float32frombits(actual) | |
| } | |
| func (d *predDelta) String() string { | |
| return "DELTA" | |
| } | |
| // Pure second order. | |
| type predSecondOrder struct { | |
| last float64 | |
| last32 float32 | |
| delta float64 | |
| delta32 float32 | |
| } | |
| func (d *predSecondOrder) reset() { | |
| d.last = 0 | |
| d.last32 = 0 | |
| d.delta32 = 0 | |
| d.delta = 0 | |
| } | |
| func (d *predSecondOrder) predict(n uint64) uint64 { | |
| return n ^ math.Float64bits(d.last+d.delta) | |
| } | |
| func (d *predSecondOrder) update(actual uint64) { | |
| updated := math.Float64frombits(actual) | |
| d.delta = updated - d.last | |
| d.last = updated | |
| } | |
| func (d *predSecondOrder) predict32(n uint32) uint32 { | |
| return n ^ math.Float32bits(d.last32+d.delta32) | |
| } | |
| func (d *predSecondOrder) update32(actual uint32) { | |
| updated := math.Float32frombits(actual) | |
| d.delta32 = updated - d.last32 | |
| d.last32 = updated | |
| } | |
| func (d *predSecondOrder) String() string { | |
| return "ORDER2" | |
| } | |
| type predXor struct { | |
| last uint64 | |
| last32 uint32 | |
| } | |
| func (d *predXor) reset() { | |
| d.last = 0x3fe0000000000000 | |
| d.last32 = 0 | |
| } | |
| func (d *predXor) predict(n uint64) uint64 { | |
| return n ^ d.last | |
| } | |
| func (d *predXor) update(actual uint64) { | |
| d.last = actual | |
| } | |
| func (d *predXor) predict32(n uint32) uint32 { | |
| return n ^ d.last32 | |
| } | |
| func (d *predXor) update32(actual uint32) { | |
| d.last32 = actual | |
| } | |
| func (d *predXor) String() string { | |
| return "XOR" | |
| } | |
| type predNone struct { | |
| } | |
| func (d predNone) reset() { | |
| } | |
| func (d predNone) predict(n uint64) uint64 { | |
| return n ^ 0x3fe00000_00000000 | |
| } | |
| func (d predNone) update(actual uint64) { | |
| } | |
| func (d predNone) predict32(n uint32) uint32 { | |
| return n | |
| } | |
| func (d predNone) update32(actual uint32) { | |
| } | |
| func (d predNone) String() string { | |
| return "NONE" | |
| } | |
| type predDeltaOffset struct { | |
| idx, sz int | |
| last []float64 | |
| last32 []float32 | |
| } | |
| func newPredDeltaOffset(n int) *predDeltaOffset { | |
| return &predDeltaOffset{ | |
| sz: n, | |
| last: make([]float64, n), | |
| last32: make([]float32, n), | |
| } | |
| } | |
| func (d *predDeltaOffset) reset() { | |
| for i := range d.last { | |
| d.last[i] = 0 | |
| } | |
| d.last32 = make([]float32, d.sz) | |
| } | |
| func (d *predDeltaOffset) predict(n uint64) uint64 { | |
| return math.Float64bits(math.Float64frombits(n) - d.last[d.idx]) | |
| } | |
| func (d *predDeltaOffset) update(actual uint64) { | |
| d.last[d.idx] = math.Float64frombits(actual) | |
| d.idx = (d.idx + 1) % d.sz | |
| } | |
| func (d *predDeltaOffset) predict32(n uint32) uint32 { | |
| return math.Float32bits(math.Float32frombits(n) - d.last32[d.idx]) | |
| } | |
| func (d *predDeltaOffset) update32(actual uint32) { | |
| d.last32[d.idx] = math.Float32frombits(actual) | |
| d.idx = (d.idx + 1) % d.sz | |
| } | |
| func (d *predDeltaOffset) String() string { | |
| return fmt.Sprintf("DELTA-%d", d.sz) | |
| } |
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| package floats | |
| // Coordinates in 3D. | |
| var numbers = []float64{-0.0636837780476, 2.34647130966, 0.0452156066895, -0.0606756210327, 2.34551143646, 0.0295177698135, -0.0577713251114, 2.35072994232, 0.0302016735077, -0.0611855685711, 2.35236978531, 0.0464453697205, -0.0572466850281, 2.34213256836, 0.0151053667068, -0.0538873374462, 2.34651136398, 0.0153127908707, -0.0500386953354, 2.35005044937, 0.0154707431793, -0.0541608035564, 2.35478925705, 0.0311042070389, -0.0577769577503, 2.35722780228, 0.0477689504623, -0.0491383075714, 2.35714840889, 0.0318441390991, -0.0525485277176, 2.36010742188, 0.0491374731064, -0.0452115237713, 2.35152959824, 0.0158544778824, -0.0398955643177, 2.351749897, 0.016560792923, -0.0434094965458, 2.358907938, 0.032267332077, -0.0464098453522, 2.36276626587, 0.0498303174973, -0.0672268867493, 2.34249258041, 0.0760914087296, -0.0658501386642, 2.34509181976, 0.0610657930374, -0.0636596381664, 2.35148978233, 0.0629088878632, -0.0652514994144, 2.34931063652, 0.0785007476807, -0.0603807270527, 2.35694813728, 0.0647082328796, -0.0620350837708, 2.35528898239, 0.0807291269302, -0.0549257993698, 2.36064720154, 0.066307425499, -0.0563369989395, 2.35968732834, 0.0825264453888, -0.0483827590942, 2.36380624771, 0.067479968071, -0.0493980646133, 2.36344623566, 0.0839664936066, -0.0678191184998, 2.33627438545, 0.10135602951, -0.0678658783436, 2.33937382698, 0.0896501541138, -0.0660189092159, 2.34661126137, 0.0925059318542, -0.066019654274, 2.34397220612, 0.104495167732, -0.0628027915955, 2.3531293869, 0.0950469970703, -0.0627468526363, 2.35096979141, 0.107242465019, -0.0568488836288, 2.35818767548, 0.0969561338425, -0.0565277338028, 2.35656833649, 0.109250426292, -0.0495254695415, 2.3625664711, 0.0984976291656, -0.0488352775574, 2.36146688461, 0.110888957977, -0.0658765137196, 2.32881689072, 0.120658159256, -0.067138761282, 2.33299541473, 0.11143040657, -0.0653115212917, 2.3408331871, 0.115031242371, -0.0639520585537, 2.33665418625, 0.124725461006, -0.0619300603867, 2.34801077843, 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| // Normals - appears to be repeated ~ every 18 elements | |
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0.0416666008532, 1.0, 0.0} | |
| // This seems to be just random numbers 0 -> 1 | |
| var numbers3 = []float64{0.696468466152, 0.23033292891, 0.655561997649, 0.54153630768, 0.951658321017, 0.768290816979, 0.16463213799, 0.866369170116, 0.794479730946, 0.218942959759, 0.802232467968, 0.226686891385, 0.7752034515, 0.597746585285, 0.57257689391, 0.0955351209269, 0.265705658961, 0.885431758535, 0.785688641882, 0.613899253659, 0.564536714006, 0.827742542897, 0.194696002071, 0.238508820058, 0.574814952182, 0.838702286253, 0.832581157595, 0.92732625739, 0.765658984152, 0.519628141663, 0.401633106512, 0.617641951392, 0.954408132297, 0.642235610251, 0.140983477116, 0.64169840229, 0.46712758776, 0.634022918017, 0.970069867033, 0.292972460498, 0.756795541985, 0.996019915094, 0.222651124229, 0.749043635528, 0.854400457584, 0.424680209823, 0.0689686896059, 0.217551422756, 0.159702435691, 0.951451287784, 0.997775247833, 0.707543351099, 0.0187072391708, 0.0928484875682, 0.826992584231, 0.797685770512, 0.527304013728, 0.599118861798, 0.206627589911, 0.291958845907, 0.472912636974, 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0.886284553682, 0.776772425022, 0.531678411031, 0.537230630712, 0.433189015441, 0.217625334698, 0.486618306249, 0.771483623381, 0.308824732361, 0.0973109832436, 0.729733012799, 0.763393189783} | |
| // Almost fully predictable. | |
| // We multiply on purpose, since it will not be a fully fixed offset. | |
| var numbers4 = []float64{10000: 0} | |
| func init() { | |
| for i := range numbers4 { | |
| numbers4[i] = float64(i)/5 - 1000 | |
| } | |
| } |
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