// decimalMandE computes and returns the mantissa M and exponent E for d.
//
// The mantissa is a base-100 representation of the value. The exponent E
// determines where to put the decimal point.
//
// Each centimal digit of the mantissa is stored in a byte. If the value of the
// centimal digit is X (hence X>=0 and X<=99) then the byte value will be 2*X+1
// for every byte of the mantissa, except for the last byte which will be
// 2*X+0. The mantissa must be the minimum number of bytes necessary to
// represent the value; trailing X==0 digits are omitted. This means that the
// mantissa will never contain a byte with the value 0x00.
//
// If we assume all digits of the mantissa occur to the right of the decimal
// point, then the exponent E is the power of one hundred by which one must
// multiply the mantissa to recover the original value.
func decimalMandE(d decimal.Decimal, tmp []byte) (int, []byte) {
bs := d.BigInt().String()
if bs[0] == '-' {
bs = bs[1:]
}
// The exponent will be the combination of the decimal's exponent, and the
// number of digits in the big.Int.
e10 := int(d.Exponent()) + len(bs)
// Strip off trailing zeros in big.Int's string representation.
for bs[len(bs)-1] == '0' {
bs = bs[:len(bs)-1]
}
// Make sure b is large enough to hold the smallest even number of bytes
// greater than or equal to the size of bs + 1.
if n := 2 * ((len(bs) + 2) / 2); n <= cap(tmp) {
tmp = tmp[:len(bs)+1]
} else {
tmp = make([]byte, len(bs)+1, n)
}
tmp[0] = '0'
copy(tmp[1:], []byte(bs))
// Convert the power-10 exponent to a power of 100 exponent.
var e100 int
if e10 >= 0 {
e100 = (e10 + 1) / 2
} else {
e100 = e10 / 2
}
// Strip the leading 0 if the conversion to e100 did not add a multiple of
// 10.
if e100*2 == e10 {
tmp = tmp[1:]
}
// Ensure that the number of digits is even.
if len(tmp)%2 != 0 {
tmp = append(tmp, '0')
}
// Convert the base-10 'b' slice to a base-100 'm' slice. We do this
// conversion in place to avoid an allocation.
m := tmp[:len(tmp)/2]
for i := 0; i < len(tmp); i += 2 {
accum := 10*int(tmp[i]-'0') + int(tmp[i+1]-'0')
// The bytes are encoded as 2n+1.
m[i/2] = byte(2*accum + 1)
}
// The last byte is encoded as 2n+0.
m[len(m)-1]--
return e100, m
}
// SetDecimal encodes the specified decimal value into the bytes field of
// the receiver, sets the tag and clears the checksum.
func (v *Value) SetDecimal(d decimal.Decimal) error {
// TODO(nvanbenschoten) Deal with exponent normalization.
bb, err := d.BigInt().GobEncode()
if err != nil {
return fmt.Errorf("failed to Gob encode decimal's big.Int: %v", err)
}
v.RawBytes = make([]byte, headerSize+binary.MaxVarintLen64+len(bb))
n := binary.PutVarint(v.RawBytes[headerSize:], int64(d.Exponent()))
copy(v.RawBytes[headerSize+n:], bb)
v.RawBytes = v.RawBytes[:headerSize+n+len(bb)]
v.setTag(ValueType_DECIMAL)
return nil
}
func encodeDecimal(b []byte, d decimal.Decimal, invert bool) []byte {
// Handle the simplistic cases first.
neg := false
switch d.BigInt().Sign() {
case -1:
neg = true
case 0:
return append(b, floatZero)
}
// TODO(nvanbenschoten) Switch to a base-256 mantissa.
e, m := decimalMandE(d, b[len(b):])
return encodeMandE(b, neg != invert, e, m)
}
// prettyPrintFirstValue returns a string representation of the first decodable
// value in the provided byte slice, along with the remaining byte slice
// after decoding.
func prettyPrintFirstValue(b []byte) ([]byte, string, error) {
var err error
switch PeekType(b) {
case Null:
b, _ = DecodeIfNull(b)
return b, "NULL", nil
case NotNull:
b, _ = DecodeIfNotNull(b)
return b, "#", nil
case Int:
var i int64
b, i, err = DecodeVarintAscending(b)
if err != nil {
return b, "", err
}
return b, strconv.FormatInt(i, 10), nil
case Float:
// Handle float specific values separately.
switch b[0] {
case floatNaN, floatNaNDesc:
return b[1:], strconv.FormatFloat(math.NaN(), 'e', -1, 64), nil
case floatInfinity:
return b[1:], strconv.FormatFloat(math.Inf(1), 'e', -1, 64), nil
case floatNegativeInfinity:
return b[1:], strconv.FormatFloat(math.Inf(-1), 'e', -1, 64), nil
}
// Decode both floats and decimals as decimals to avoid
// overflow.
var d decimal.Decimal
b, d, err = DecodeDecimalAscending(b, nil)
if err != nil {
return b, "", err
}
return b, d.String(), nil
case Bytes:
var s string
b, s, err = DecodeStringAscending(b, nil)
if err != nil {
return b, "", err
}
return b, strconv.Quote(s), nil
case BytesDesc:
var s string
b, s, err = DecodeStringDescending(b, nil)
if err != nil {
return b, "", err
}
return b, strconv.Quote(s), nil
case Time:
var t time.Time
b, t, err = DecodeTimeAscending(b)
if err != nil {
return b, "", err
}
return b, t.UTC().Format(time.UnixDate), nil
case TimeDesc:
var t time.Time
b, t, err = DecodeTimeDescending(b)
if err != nil {
return b, "", err
}
return b, t.UTC().Format(time.UnixDate), nil
default:
// This shouldn't ever happen, but if it does, return an empty slice.
return nil, strconv.Quote(string(b)), nil
}
}
func TestEncodeDecimal(t *testing.T) {
testCases := []struct {
Value decimal.Decimal
Encoding []byte
}{
{decimal.NewFromFloat(-math.MaxFloat64), []byte{0x04, 0x64, 0xfc, 0x60, 0x66, 0x44, 0xe4, 0x9e, 0x82, 0xc0, 0x8d, 0x0}},
{decimal.New(-1, 308), []byte{0x04, 0x64, 0xfd, 0x0}},
// Four duplicates to make sure -1*10^4 <= -10*10^3 <= -100*10^2 <= -1*10^4
{decimal.New(-1, 4), []byte{0x0c, 0xfd, 0x0}},
{decimal.New(-10, 3), []byte{0x0c, 0xfd, 0x0}},
{decimal.New(-100, 2), []byte{0x0c, 0xfd, 0x0}},
{decimal.New(-1, 4), []byte{0x0c, 0xfd, 0x0}},
{decimal.New(-9999, 0), []byte{0x0d, 0x38, 0x39, 0x00}},
{decimal.New(-10, 1), []byte{0x0d, 0xfd, 0x00}},
{decimal.New(-99, 0), []byte{0x0e, 0x39, 0x00}},
{decimal.New(-1, 0), []byte{0x0e, 0xfd, 0x0}},
{decimal.New(-123, -5), []byte{0x10, 0x1, 0xe6, 0xc3, 0x0}},
{decimal.New(-1, -307), []byte{0x10, 0x99, 0xeb, 0x0}},
{decimal.NewFromFloat(-math.SmallestNonzeroFloat64), []byte{0x10, 0xa1, 0xf5, 0x0}},
{decimal.New(0, 0), []byte{0x11}},
{decimal.NewFromFloat(math.SmallestNonzeroFloat64), []byte{0x12, 0x5e, 0xa, 0x0}},
{decimal.New(1, -307), []byte{0x12, 0x66, 0x14, 0x0}},
{decimal.New(123, -5), []byte{0x12, 0xfe, 0x19, 0x3c, 0x0}},
{decimal.New(123, -4), []byte{0x13, 0x03, 0x2e, 0x0}},
{decimal.New(123, -3), []byte{0x13, 0x19, 0x3c, 0x0}},
{decimal.New(1, 0), []byte{0x14, 0x02, 0x0}},
{decimal.New(1, 1), []byte{0x14, 0x14, 0x0}},
{decimal.New(12345, -3), []byte{0x14, 0x19, 0x45, 0x64, 0x0}},
{decimal.New(990, -1), []byte{0x14, 0xc6, 0x0}},
{decimal.New(990001, -4), []byte{0x14, 0xc7, 0x01, 0x02, 0x0}},
{decimal.New(9901, -2), []byte{0x14, 0xc7, 0x02, 0x0}},
{decimal.New(10, 1), []byte{0x15, 0x02, 0x0}},
{decimal.New(10001, -2), []byte{0x15, 0x03, 0x01, 0x02, 0x0}},
{decimal.New(1001, -1), []byte{0x15, 0x03, 0x01, 0x14, 0x0}},
{decimal.New(1234, 0), []byte{0x15, 0x19, 0x44, 0x0}},
{decimal.New(12345, -1), []byte{0x15, 0x19, 0x45, 0x64, 0x0}},
{decimal.New(9999, 0), []byte{0x15, 0xc7, 0xc6, 0x0}},
{decimal.New(9999000001, -6), []byte{0x15, 0xc7, 0xc7, 0x01, 0x01, 0x02, 0x0}},
{decimal.New(9999000009, -6), []byte{0x15, 0xc7, 0xc7, 0x01, 0x01, 0x12, 0x0}},
{decimal.New(9999000010, -6), []byte{0x15, 0xc7, 0xc7, 0x01, 0x01, 0x14, 0x0}},
{decimal.New(9999000090, -6), []byte{0x15, 0xc7, 0xc7, 0x01, 0x01, 0xb4, 0x0}},
{decimal.New(9999000099, -6), []byte{0x15, 0xc7, 0xc7, 0x01, 0x01, 0xc6, 0x0}},
{decimal.New(99990001, -4), []byte{0x15, 0xc7, 0xc7, 0x01, 0x02, 0x0}},
{decimal.New(9999001, -3), []byte{0x15, 0xc7, 0xc7, 0x01, 0x14, 0x0}},
{decimal.New(999901, -2), []byte{0x15, 0xc7, 0xc7, 0x02, 0x0}},
{decimal.New(99991, -1), []byte{0x15, 0xc7, 0xc7, 0x14, 0x0}},
{decimal.New(10000, 0), []byte{0x16, 0x02, 0x0}},
{decimal.New(10001, 0), []byte{0x16, 0x03, 0x01, 0x02, 0x0}},
{decimal.New(12345, 0), []byte{0x16, 0x03, 0x2f, 0x5a, 0x0}},
{decimal.New(123450, 0), []byte{0x16, 0x19, 0x45, 0x64, 0x0}},
{decimal.New(1, 308), []byte{0x1e, 0x9b, 0x2, 0x0}},
{decimal.NewFromFloat(math.MaxFloat64), []byte{0x1e, 0x9b, 0x3, 0x9f, 0x99, 0xbb, 0x1b, 0x61, 0x7d, 0x3f, 0x72, 0x0}},
}
var lastEncoded []byte
for _, dir := range []Direction{Ascending, Descending} {
for i, c := range testCases {
var enc []byte
var err error
var dec decimal.Decimal
if dir == Ascending {
enc = EncodeDecimalAscending(nil, c.Value)
_, dec, err = DecodeDecimalAscending(enc, nil)
} else {
enc = EncodeDecimalDescending(nil, c.Value)
_, dec, err = DecodeDecimalDescending(enc, nil)
}
if dir == Ascending && !bytes.Equal(enc, c.Encoding) {
t.Errorf("unexpected mismatch for %s. expected [% x], got [% x]",
c.Value, c.Encoding, enc)
}
if i > 0 {
if (bytes.Compare(lastEncoded, enc) > 0 && dir == Ascending) ||
(bytes.Compare(lastEncoded, enc) < 0 && dir == Descending) {
t.Errorf("%v: expected [% x] to be less than or equal to [% x]",
c.Value, testCases[i-1].Encoding, enc)
}
}
if err != nil {
t.Error(err)
continue
}
if !dec.Equals(c.Value) {
t.Errorf("%d unexpected mismatch for %v. got %v", i, c.Value, dec)
}
lastEncoded = enc
}
// Test that appending the decimal to an existing buffer works.
var enc []byte
var dec decimal.Decimal
other := decimal.NewFromFloat(1.23)
if dir == Ascending {
enc = EncodeDecimalAscending([]byte("hello"), other)
_, dec, _ = DecodeDecimalAscending(enc[5:], nil)
} else {
enc = EncodeDecimalDescending([]byte("hello"), other)
_, dec, _ = DecodeDecimalDescending(enc[5:], nil)
}
if !dec.Equals(other) {
t.Errorf("unexpected mismatch for %v. got %v", 1.23, other)
}
}
}