Add utils Float16-BigInt converters

* 16 bits fix encoding

* Types modification

* Rounding loss check

* Clean up a bit and add benchmarks

Unneded usage of big.Int has been removed

Conversion methods are now methods/constructors of Float16 to make the code
more idiomatic.

Co-authored-by: Toni Ramírez <toni@iden3.com>
Co-authored-by: arnaucube <root@arnaucube.com>
Co-authored-by: Eduard S <eduard@iden3.io>

utils/utils.go

@@ -0,0 +1,127 @@
+package utils
+
+import (
+	"errors"
+	"math/big"
+)
+
+var (
+	// ErrRoundingLoss is used when converted big.Int to Float16 causes rounding loss
+	ErrRoundingLoss = errors.New("input value causes rounding loss")
+)
+
+// Float16 represents a float in a 16 bit format
+type Float16 uint16
+
+// BigInt converts the Float16 to a big.Int integer
+func (fl16 *Float16) BigInt() *big.Int {
+
+	fl := int64(*fl16)
+
+	m := big.NewInt(fl & 0x3FF)
+	e := big.NewInt(fl >> 11)
+	e5 := (fl >> 10) & 0x01
+
+	exp := big.NewInt(0).Exp(big.NewInt(10), e, nil)
+	res := m.Mul(m, exp)
+
+	if e5 != 0 && e.Cmp(big.NewInt(0)) != 0 {
+
+		res.Add(res, exp.Div(exp, big.NewInt(2)))
+
+	}
+
+	return res
+
+}
+
+// floorFix2Float converts a fix to a float, always rounding down
+func floorFix2Float(_f *big.Int) Float16 {
+
+	zero := big.NewInt(0)
+	ten := big.NewInt(10)
+	e := int64(0)
+
+	m := big.NewInt(0)
+	m.Set(_f)
+
+	if m.Cmp(zero) == 0 {
+		return 0
+	}
+
+	s := big.NewInt(0).Rsh(m, 10)
+
+	for s.Cmp(zero) != 0 {
+
+		m.Div(m, ten)
+		s.Rsh(m, 10)
+		e++
+
+	}
+
+	return Float16(m.Int64() | e<<11)
+
+}
+
+// NewFloat16 encodes a big.Int integer as a Float16, returning error in case
+// of loss during the encoding.
+func NewFloat16(f *big.Int) (Float16, error) {
+
+	fl1 := floorFix2Float(f)
+	fi1 := fl1.BigInt()
+	fl2 := fl1 | 0x400
+	fi2 := fl2.BigInt()
+
+	m3 := (fl1 & 0x3FF) + 1
+	e3 := fl1 >> 11
+
+	if m3&0x400 == 0 {
+		m3 = 0x66
+		e3++
+	}
+
+	fl3 := m3 + e3<<11
+	fi3 := fl3.BigInt()
+
+	res := fl1
+
+	d := big.NewInt(0).Abs(fi1.Sub(fi1, f))
+	d2 := big.NewInt(0).Abs(fi2.Sub(fi2, f))
+
+	if d.Cmp(d2) == 1 {
+		res = fl2
+		d = d2
+	}
+
+	d3 := big.NewInt(0).Abs(fi3.Sub(fi3, f))
+
+	if d.Cmp(d3) == 1 {
+
+		res = fl3
+	}
+
+	// Do rounding check
+
+	if res.BigInt().Cmp(f) == 0 {
+
+		return res, nil
+	}
+
+	return res, ErrRoundingLoss
+
+}
+
+// NewFloat16Floor encodes a big.Int integer as a Float16, rounding down in
+// case of loss during the encoding.
+func NewFloat16Floor(f *big.Int) Float16 {
+
+	fl1 := floorFix2Float(f)
+	fl2 := fl1 | 0x400
+	fi2 := fl2.BigInt()
+
+	if fi2.Cmp(f) < 1 {
+		return fl2
+	}
+	return fl1
+
+}

utils/utils_test.go

@@ -0,0 +1,140 @@
+package utils
+
+import (
+	"math/big"
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestConversions(t *testing.T) {
+
+	testVector := map[Float16]string{
+		0x307B: "123000000",
+		0x1DC6: "454500",
+		0xFFFF: "10235000000000000000000000000000000",
+		0x0000: "0",
+		0x0400: "0",
+		0x0001: "1",
+		0x0401: "1",
+		0x0800: "0",
+		0x0c00: "5",
+		0x0801: "10",
+		0x0c01: "15",
+	}
+
+	for test := range testVector {
+
+		fix := test.BigInt()
+
+		assert.Equal(t, fix.String(), testVector[test])
+
+		bi := big.NewInt(0)
+		bi.SetString(testVector[test], 10)
+
+		fl, err := NewFloat16(bi)
+		assert.Equal(t, nil, err)
+
+		fx2 := fl.BigInt()
+		assert.Equal(t, fx2.String(), testVector[test])
+
+	}
+
+}
+
+func TestFloorFix2Float(t *testing.T) {
+
+	testVector := map[string]Float16{
+		"87999990000000000": 0x776f,
+		"87950000000000001": 0x776f,
+		"87950000000000000": 0x776f,
+		"87949999999999999": 0x736f,
+	}
+
+	for test := range testVector {
+
+		bi := big.NewInt(0)
+		bi.SetString(test, 10)
+
+		testFloat := NewFloat16Floor(bi)
+
+		assert.Equal(t, testFloat, testVector[test])
+
+	}
+
+}
+
+func TestConversionLosses(t *testing.T) {
+	a := big.NewInt(1000)
+	b, err := NewFloat16(a)
+	assert.Equal(t, nil, err)
+	c := b.BigInt()
+	assert.Equal(t, c, a)
+
+	a = big.NewInt(1024)
+	b, err = NewFloat16(a)
+	assert.Equal(t, ErrRoundingLoss, err)
+	c = b.BigInt()
+	assert.NotEqual(t, c, a)
+
+	a = big.NewInt(32767)
+	b, err = NewFloat16(a)
+	assert.Equal(t, ErrRoundingLoss, err)
+	c = b.BigInt()
+	assert.NotEqual(t, c, a)
+
+	a = big.NewInt(32768)
+	b, err = NewFloat16(a)
+	assert.Equal(t, ErrRoundingLoss, err)
+	c = b.BigInt()
+	assert.NotEqual(t, c, a)
+
+	a = big.NewInt(65536000)
+	b, err = NewFloat16(a)
+	assert.Equal(t, ErrRoundingLoss, err)
+	c = b.BigInt()
+	assert.NotEqual(t, c, a)
+
+}
+
+func BenchmarkFloat16(b *testing.B) {
+	newBigInt := func(s string) *big.Int {
+		bigInt, ok := new(big.Int).SetString(s, 10)
+		if !ok {
+			panic("Bad big int")
+		}
+		return bigInt
+	}
+	type pair struct {
+		Float16 Float16
+		BigInt  *big.Int
+	}
+	testVector := []pair{
+		pair{0x307B, newBigInt("123000000")},
+		pair{0x1DC6, newBigInt("454500")},
+		pair{0xFFFF, newBigInt("10235000000000000000000000000000000")},
+		pair{0x0000, newBigInt("0")},
+		pair{0x0400, newBigInt("0")},
+		pair{0x0001, newBigInt("1")},
+		pair{0x0401, newBigInt("1")},
+		pair{0x0800, newBigInt("0")},
+		pair{0x0c00, newBigInt("5")},
+		pair{0x0801, newBigInt("10")},
+		pair{0x0c01, newBigInt("15")},
+	}
+	b.Run("floorFix2Float()", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			NewFloat16Floor(testVector[i%len(testVector)].BigInt)
+		}
+	})
+	b.Run("NewFloat16()", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			NewFloat16(testVector[i%len(testVector)].BigInt) //nolint:errcheck
+		}
+	})
+	b.Run("Float16.BigInt()", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			testVector[i%len(testVector)].Float16.BigInt()
+		}
+	})
+}