Change endianness to BigEndian :(

Change endianness to BigEndian (ಥ﹏ಥ), spec has been updated to achieve
compatibility with js & smart contracts & circuits implementations.

common/float16.go

@@ -0,0 +1,129 @@
+// Package common Float16 provides methods to work with Hermez custom half float
+// precision, 16 bits, codification internally called Float16 has been adopted
+// to encode large integers. This is done in order to save bits when L2
+// transactions are published.
+//nolint:gomnd
+package common
+
+import (
+	"encoding/binary"
+	"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
+
+// Bytes return a byte array of length 2 with the Float16 value encoded in BigEndian
+func (f16 Float16) Bytes() []byte {
+	var b [2]byte
+	binary.BigEndian.PutUint16(b[:], uint16(f16))
+	return b[:]
+}
+
+// Float16FromBytes returns a Float16 from a byte array of 2 bytes.
+func Float16FromBytes(b []byte) *Float16 {
+	f16 := Float16(binary.BigEndian.Uint16(b[:2]))
+	return &f16
+}
+
+// BigInt converts the Float16 to a *big.Int integer
+func (f16 *Float16) BigInt() *big.Int {
+	fl := int64(*f16)
+
+	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
+}