1// Package common Float40 provides methods to work with Hermez custom half
  2// float precision, 40 bits, codification internally called Float40 has been
  3// adopted to encode large integers. This is done in order to save bits when L2
  4// transactions are published.
  5//nolint:gomnd
  6package common
  7
  8import (
  9	"bytes"
 10	"encoding/binary"
 11	"errors"
 12	"math/big"
 13
 14	"github.com/hermeznetwork/tracerr"
 15)
 16
 17const (
 18	// maxFloat40Value is the maximum value that the Float40 can have
 19	// (40 bits: maxFloat40Value=2**40-1)
 20	maxFloat40Value = 0xffffffffff
 21)
 22
 23var (
 24	// ErrFloat40Overflow is used when a given nonce overflows the maximum
 25	// capacity of the Float40 (2**40-1)
 26	ErrFloat40Overflow = errors.New("Float40 overflow, max value: 2**40 -1")
 27	// ErrFloat40E31 is used when the e > 31 when trying to convert a
 28	// *big.Int to Float40
 29	ErrFloat40E31 = errors.New("Float40 error, e > 31")
 30	// ErrFloat40NotEnoughPrecission is used when the given *big.Int can
 31	// not be represented as Float40 due not enough precission
 32	ErrFloat40NotEnoughPrecission = errors.New("Float40 error, not enough precission")
 33)
 34
 35// Float40 represents a float in a 64 bit format
 36type Float40 uint64
 37
 38// Bytes return a byte array of length 5 with the Float40 value encoded in
 39// BigEndian
 40func (f40 Float40) Bytes() ([]byte, error) {
 41	if f40 > maxFloat40Value {
 42		return []byte{}, tracerr.Wrap(ErrFloat40Overflow)
 43	}
 44
 45	var f40Bytes [8]byte
 46	binary.BigEndian.PutUint64(f40Bytes[:], uint64(f40))
 47	var b [5]byte
 48	copy(b[:], f40Bytes[3:])
 49	return b[:], nil
 50}
 51
 52// Float40FromBytes returns a Float40 from a byte array of 5 bytes in Bigendian
 53// representation.
 54func Float40FromBytes(b []byte) Float40 {
 55	var f40Bytes [8]byte
 56	copy(f40Bytes[3:], b[:])
 57	f40 := binary.BigEndian.Uint64(f40Bytes[:])
 58	return Float40(f40)
 59}
 60
 61// BigInt converts the Float40 to a *big.Int v, where v = m * 10^e, being:
 62// [    e   |    m    ]
 63// [ 5 bits | 35 bits ]
 64func (f40 Float40) BigInt() (*big.Int, error) {
 65	// take the 5 used bytes (FF * 5)
 66	var f40Uint64 uint64 = uint64(f40) & 0x00_00_00_FF_FF_FF_FF_FF
 67	f40Bytes, err := f40.Bytes()
 68	if err != nil {
 69		return nil, err
 70	}
 71
 72	e := f40Bytes[0] & 0xF8 >> 3      // take first 5 bits
 73	m := f40Uint64 & 0x07_FF_FF_FF_FF // take the others 35 bits
 74
 75	exp := new(big.Int).Exp(big.NewInt(10), big.NewInt(int64(e)), nil)
 76	r := new(big.Int).Mul(big.NewInt(int64(m)), exp)
 77	return r, nil
 78}
 79
 80// NewFloat40 encodes a *big.Int integer as a Float40, returning error in case
 81// of loss during the encoding.
 82func NewFloat40(f *big.Int) (Float40, error) {
 83	m := f
 84	e := big.NewInt(0)
 85	zero := big.NewInt(0)
 86	ten := big.NewInt(10)
 87	thres := big.NewInt(0x08_00_00_00_00)
 88	for bytes.Equal(zero.Bytes(), new(big.Int).Mod(m, ten).Bytes()) &&
 89		!bytes.Equal(zero.Bytes(), new(big.Int).Div(m, thres).Bytes()) {
 90		m = new(big.Int).Div(m, ten)
 91		e = new(big.Int).Add(e, big.NewInt(1))
 92	}
 93	if e.Int64() > 31 {
 94		return 0, ErrFloat40E31
 95	}
 96	if !bytes.Equal(zero.Bytes(), new(big.Int).Div(m, thres).Bytes()) {
 97		return 0, ErrFloat40NotEnoughPrecission
 98	}
 99	r := new(big.Int).Add(m,
100		new(big.Int).Mul(e, thres))
101	return Float40(r.Uint64()), nil
102}