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small-rational.go
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small-rational.go
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package small_rational
import (
"crypto/rand"
"fmt"
"math/big"
"strconv"
"strings"
)
const Bytes = 64
type SmallRational struct {
text string //For debugging purposes
numerator big.Int
denominator big.Int // By convention, denominator == 0 also indicates zero
}
var smallPrimes = []*big.Int{
big.NewInt(2), big.NewInt(3), big.NewInt(5),
big.NewInt(7), big.NewInt(11), big.NewInt(13),
}
func bigDivides(p, a *big.Int) bool {
var remainder big.Int
remainder.Mod(a, p)
return remainder.BitLen() == 0
}
func (z *SmallRational) UpdateText() {
z.text = z.Text(10)
}
func (z *SmallRational) simplify() {
if z.numerator.BitLen() == 0 || z.denominator.BitLen() == 0 {
return
}
var num, den big.Int
num.Set(&z.numerator)
den.Set(&z.denominator)
for _, p := range smallPrimes {
for bigDivides(p, &num) && bigDivides(p, &den) {
num.Div(&num, p)
den.Div(&den, p)
}
}
if bigDivides(&den, &num) {
num.Div(&num, &den)
den.SetInt64(1)
}
z.numerator = num
z.denominator = den
}
func (z *SmallRational) Square(x *SmallRational) *SmallRational {
var num, den big.Int
num.Mul(&x.numerator, &x.numerator)
den.Mul(&x.denominator, &x.denominator)
z.numerator = num
z.denominator = den
z.UpdateText()
return z
}
func (z *SmallRational) String() string {
z.text = z.Text(10)
return z.text
}
func (z *SmallRational) Add(x, y *SmallRational) *SmallRational {
if x.denominator.BitLen() == 0 {
*z = *y
} else if y.denominator.BitLen() == 0 {
*z = *x
} else {
//TODO: Exploit cases where one denom divides the other
var numDen, denNum big.Int
numDen.Mul(&x.numerator, &y.denominator)
denNum.Mul(&x.denominator, &y.numerator)
numDen.Add(&denNum, &numDen)
z.numerator = numDen //to avoid shallow copy problems
denNum.Mul(&x.denominator, &y.denominator)
z.denominator = denNum
z.simplify()
}
z.UpdateText()
return z
}
func (z *SmallRational) IsZero() bool {
return z.numerator.BitLen() == 0 || z.denominator.BitLen() == 0
}
func (z *SmallRational) Inverse(x *SmallRational) *SmallRational {
if x.IsZero() {
*z = *x
} else {
*z = SmallRational{numerator: x.denominator, denominator: x.numerator}
z.UpdateText()
}
return z
}
func (z *SmallRational) Neg(x *SmallRational) *SmallRational {
z.numerator.Neg(&x.numerator)
z.denominator = x.denominator
if x.text == "" {
x.UpdateText()
}
if x.text[0] == '-' {
z.text = x.text[1:]
} else {
z.text = "-" + x.text
}
return z
}
func (z *SmallRational) Double(x *SmallRational) *SmallRational {
var y big.Int
if x.denominator.Bit(0) == 0 {
z.numerator = x.numerator
y.Rsh(&x.denominator, 1)
z.denominator = y
} else {
y.Lsh(&x.numerator, 1)
z.numerator = y
z.denominator = x.denominator
}
z.UpdateText()
return z
}
func (z *SmallRational) Sign() int {
return z.numerator.Sign() * z.denominator.Sign()
}
func (z *SmallRational) MarshalJSON() ([]byte, error) {
return []byte(z.String()), nil
}
func (z *SmallRational) UnmarshalJson(data []byte) error {
_, err := z.SetInterface(string(data))
return err
}
func (z *SmallRational) Equal(x *SmallRational) bool {
return z.Cmp(x) == 0
}
func (z *SmallRational) Sub(x, y *SmallRational) *SmallRational {
var yNeg SmallRational
yNeg.Neg(y)
z.Add(x, &yNeg)
z.UpdateText()
return z
}
func (z *SmallRational) Cmp(x *SmallRational) int {
zSign, xSign := z.Sign(), x.Sign()
if zSign > xSign {
return 1
}
if zSign < xSign {
return -1
}
var Z, X big.Int
Z.Mul(&z.numerator, &x.denominator)
X.Mul(&x.numerator, &z.denominator)
Z.Abs(&Z)
X.Abs(&X)
return Z.Cmp(&X) * zSign
}
func BatchInvert(a []SmallRational) []SmallRational {
res := make([]SmallRational, len(a))
for i := range a {
res[i].Inverse(&a[i])
}
return res
}
func (z *SmallRational) Mul(x, y *SmallRational) *SmallRational {
var num, den big.Int
num.Mul(&x.numerator, &y.numerator)
den.Mul(&x.denominator, &y.denominator)
z.numerator = num
z.denominator = den
z.simplify()
z.UpdateText()
return z
}
func (z *SmallRational) SetOne() *SmallRational {
return z.SetInt64(1)
}
func (z *SmallRational) SetZero() *SmallRational {
return z.SetInt64(0)
}
func (z *SmallRational) SetInt64(i int64) *SmallRational {
z.numerator = *big.NewInt(i)
z.denominator = *big.NewInt(1)
z.text = strconv.FormatInt(i, 10)
return z
}
func (z *SmallRational) SetRandom() (*SmallRational, error) {
bytes := make([]byte, 1)
n, err := rand.Read(bytes)
if err != nil {
return nil, err
}
if n != len(bytes) {
return nil, fmt.Errorf("%d bytes read instead of %d", n, len(bytes))
}
z.numerator = *big.NewInt(int64(bytes[0]%16) - 8)
z.denominator = *big.NewInt(int64((bytes[0]) / 16))
z.simplify()
z.UpdateText()
return z, nil
}
func (z *SmallRational) SetUint64(i uint64) {
var num big.Int
num.SetUint64(i)
z.numerator = num
z.denominator = *big.NewInt(1)
z.text = strconv.FormatUint(i, 10)
}
func (z *SmallRational) IsOne() bool {
return z.numerator.Cmp(&z.denominator) == 0 && z.denominator.BitLen() != 0
}
func (z *SmallRational) Text(base int) string {
if z.denominator.BitLen() == 0 {
return "0"
}
if z.denominator.Sign() < 0 {
var num, den big.Int
num.Neg(&z.numerator)
den.Neg(&z.denominator)
z.numerator = num
z.denominator = den
}
if bigDivides(&z.denominator, &z.numerator) {
var num big.Int
num.Div(&z.numerator, &z.denominator)
z.numerator = num
z.denominator = *big.NewInt(1)
}
numerator := z.numerator.Text(base)
if z.denominator.IsInt64() && z.denominator.Int64() == 1 {
return numerator
}
return numerator + "/" + z.denominator.Text(base)
}
func (z *SmallRational) Set(x *SmallRational) *SmallRational {
*z = *x // shallow copy is safe because ops are never in place
return z
}
func (z *SmallRational) SetInterface(x interface{}) (*SmallRational, error) {
switch v := x.(type) {
case *SmallRational:
*z = *v
case SmallRational:
*z = v
case int64:
z.SetInt64(v)
case int:
z.SetInt64(int64(v))
case float64:
asInt := int64(v)
if float64(asInt) != v {
return nil, fmt.Errorf("cannot currently parse float")
}
z.SetInt64(asInt)
case string:
z.text = v
sep := strings.Split(v, "/")
switch len(sep) {
case 1:
if asInt, err := strconv.Atoi(sep[0]); err == nil {
z.SetInt64(int64(asInt))
} else {
return nil, err
}
case 2:
var err error
var num, denom int
num, err = strconv.Atoi(sep[0])
if err != nil {
return nil, err
}
denom, err = strconv.Atoi(sep[1])
if err != nil {
return nil, err
}
z.numerator = *big.NewInt(int64(num))
z.denominator = *big.NewInt(int64(denom))
default:
return nil, fmt.Errorf("cannot parse \"%s\"", v)
}
default:
return nil, fmt.Errorf("cannot parse %T", x)
}
return z, nil
}
func bigIntToBytesSigned(dst []byte, src big.Int) {
src.FillBytes(dst[1:])
dst[0] = 0
if src.Sign() < 0 {
dst[0] = 255
}
}
func (z *SmallRational) Bytes() [Bytes]byte {
var res [Bytes]byte
bigIntToBytesSigned(res[:Bytes/2], z.numerator)
bigIntToBytesSigned(res[Bytes/2:], z.denominator)
return res
}
func bytesToBigIntSigned(src []byte) big.Int {
var res big.Int
res.SetBytes(src[1:])
if src[0] != 0 {
res.Neg(&res)
}
return res
}
// BigInt returns sets dst to the value of z if it is an integer.
// if z is not an integer, nil is returned.
// if the given dst is nil, the address of the numerator is returned.
// if the given dst is non-nil, it is returned.
func (z *SmallRational) BigInt(dst *big.Int) *big.Int {
if z.denominator.Cmp(big.NewInt(1)) != 0 {
return nil
}
if dst == nil {
return &z.numerator
}
dst.Set(&z.numerator)
return dst
}
func (z *SmallRational) SetBytes(b []byte) {
if len(b) > Bytes/2 {
z.numerator = bytesToBigIntSigned(b[:Bytes/2])
z.denominator = bytesToBigIntSigned(b[Bytes/2:])
} else {
z.numerator.SetBytes(b)
z.denominator.SetInt64(1)
}
z.simplify()
z.UpdateText()
}
func Modulus() *big.Int {
res := big.NewInt(1)
res.Lsh(res, 64)
return res
}