It encodes and decodes floating-point numbers with a width of 3 to 16 bits.
Expected applications:
- file format design,
- lossy compression.
It has:
- exact 0, 1, -1
- no NaN, -Inf, +Inf
- values, that are in range about:
- (-256, +256) for 4-bit exponent
- (-4, +4) for 3-bit exponent
- (-3, +3) for 2-bit exponent
- up to 10^308 (custom settings).
Base 3 in 2-bit exponent provides a higher density of values close to zero and a wider range, at the cost of reduced precision of values greater than one-third.
You can also choose other settings.
Examples:
____ sxxx xmmm mmmm - 12-bit
____ xxxx mmmm mmmm - 12-bit unsigned
___s xxxx mmmm mmmm - 13-bit
__sx xxxm mmmm mmmm - 14-bit
_sxx xmmm mmmm mmmm - 15-bit with 3-bit exponent
package main
import (
"fmt"
"github.com/georgy7/toyfloat"
"math"
"os"
)
func exitOnError(err error) {
if err != nil {
fmt.Println("impossible type")
os.Exit(1)
}
}
func printHeader(header string) {
fmt.Println(header)
for i := 0; i < len(header); i++ {
fmt.Print("-")
}
fmt.Println()
}
func report(t toyfloat.Type, value float64) {
encoded := t.Encode(value)
comparable := t.ToComparable(encoded)
decoded := t.Decode(encoded)
fmt.Printf("Input: %f\n", value)
fmt.Printf("Encoded: 0x%X\n", encoded)
fmt.Printf("Comparable: 0x%X\n", comparable)
fmt.Printf("Decoded: %f\n", decoded)
fmt.Printf("Error: %f\n", math.Abs(value-decoded))
fmt.Printf("Relative: %f\n\n", math.Abs((value-decoded)/value))
}
func main() {
fmt.Println()
toyfloat12, err12 := toyfloat.NewTypeX4(12, true)
toyfloat5x3, err5x3 := toyfloat.NewTypeX3(5, true)
toyfloat3x2u, err3x2u := toyfloat.NewTypeX2(3, false)
d8x3, errD8x3 := toyfloat.NewType(8, 10, 3, -2, true)
exitOnError(err12)
exitOnError(err5x3)
exitOnError(err3x2u)
exitOnError(errD8x3)
const input = 1.567
printHeader("12-bit signed")
report(toyfloat12, input)
printHeader("5-bit signed with 3-bit exponent")
report(toyfloat5x3, input)
printHeader("3-bit unsigned with 2-bit exponent")
report(toyfloat3x2u, input)
printHeader("8-bit with base 10 exponent (-2..5)")
report(d8x3, input/10)
report(d8x3, input)
report(d8x3, 65536)
report(d8x3, -7.5e5)
report(d8x3, 1e6)
fmt.Println()
fmt.Println("Delta encoding (12-bit)")
fmt.Println("-----------------------")
fmt.Println()
series := []float64{
-0.0058, 0.01, -0.0058, 0.01, 0.066, 0.123,
0.134, 0.132, 0.144, 0.145, 0.140}
previous := toyfloat12.Encode(series[0])
cPrevious := toyfloat12.ToComparable(previous)
pDecoded := toyfloat12.Decode(previous)
fmt.Printf(" Int. delta Unsigned Fp delta Value\n")
fmt.Printf(" % 47.6f\n", pDecoded)
for i := 1; i < len(series); i++ {
this := toyfloat12.Encode(series[i])
cThis := toyfloat12.ToComparable(this)
delta := toyfloat12.GetIntegerDelta(previous, this)
unsignedDelta := cThis - cPrevious
x := toyfloat12.Decode(this)
fpDelta := x - pDecoded
fmt.Printf(" %+10d %8d %+.6f % .6f\n",
delta, unsignedDelta, fpDelta, x)
previous = this
cPrevious = toyfloat12.ToComparable(previous)
pDecoded = toyfloat12.Decode(previous)
}
fmt.Println()
}go get -u github.com/georgy7/toyfloat
go run example.go12-bit signed
-------------
Input: 1.567000
Encoded: 0x448
Comparable: 0xC48
Decoded: 1.564706
Error: 0.002294
Relative: 0.001464
5-bit signed with 3-bit exponent
--------------------------------
Input: 1.567000
Encoded: 0xD
Comparable: 0x1D
Decoded: 1.507937
Error: 0.059063
Relative: 0.037692
3-bit unsigned with 2-bit exponent
----------------------------------
Input: 1.567000
Encoded: 0x7
Comparable: 0x7
Decoded: 2.038462
Error: 0.471462
Relative: 0.300869
8-bit with base 10 exponent (-2..5)
-----------------------------------
Input: 0.156700
Encoded: 0x11
Comparable: 0x91
Decoded: 0.147727
Error: 0.008973
Relative: 0.057261
Input: 1.567000
Encoded: 0x21
Comparable: 0xA1
Decoded: 1.568182
Error: 0.001182
Relative: 0.000754
Input: 65536.000000
Encoded: 0x6A
Comparable: 0xEA
Decoded: 66919.181818
Error: 1383.181818
Relative: 0.021106
Input: -750000.000000
Encoded: 0xFB
Comparable: 0x4
Decoded: -726010.090909
Error: 23989.909091
Relative: 0.031987
Input: 1000000.000000
Encoded: 0x7F
Comparable: 0xFF
Decoded: 953282.818182
Error: 46717.181818
Relative: 0.046717
Delta encoding (12-bit)
-----------------------
Int. delta Unsigned Fp delta Value
-0.005821
+387 387 +0.015809 0.009988
-387 65149 -0.015809 -0.005821
+387 387 +0.015809 0.009988
+300 300 +0.056189 0.066176
+114 114 +0.056373 0.122549
+12 12 +0.011765 0.134314
-2 65534 -0.001961 0.132353
+12 12 +0.011765 0.144118
+1 1 +0.000980 0.145098
-5 65531 -0.004902 0.140196
BenchmarkFloat64IncrementAsAReference-8 1000000000 1.09 ns/op
BenchmarkCreateTypeX4-8 3917901 299 ns/op
BenchmarkCreateTypeX3-8 11907438 103 ns/op
BenchmarkCreateTypeX2-8 13006556 92.4 ns/op
BenchmarkEncode-8 90582355 13.2 ns/op
BenchmarkDecode-8 229913229 5.15 ns/op
BenchmarkEncode12X2-8 94929739 12.4 ns/op
BenchmarkDecode12X2-8 236135440 5.40 ns/op
BenchmarkGetDelta-8 540333522 2.19 ns/op
BenchmarkGetDeltaX2-8 603912135 1.86 ns/op
BenchmarkUseDelta-8 263490146 4.53 ns/op
BenchmarkUseDeltaX2-8 249798333 4.54 ns/op