What problem does ZigZag encoding solve?

Plain varint encoding stores small unsigned numbers compactly, but a negative number's two's-complement form has all high bits set and would take the maximum number of bytes. ZigZag remaps signed values so small magnitudes, positive or negative, become small unsigned numbers that varint can encode in one byte.

What is the encoding formula?

For an n-bit value the encoding is (value > (n - 1)). The left shift makes room for the sign and the arithmetic right shift spreads the sign bit across all bits, producing 0, 2, 4 for non-negatives and 1, 3, 5 for negatives.

How do I decode a ZigZag value?

Decoding is (encoded >> 1) XOR -(encoded AND 1). The low bit recovers the sign and the right shift recovers the magnitude. This exactly inverts the encoding for every integer in range.

When should I use sint32 versus sint64?

Match the protobuf field type. A field declared sint32 uses 32-bit ZigZag and sint64 uses 64-bit. The width determines the valid input range and how the sign bit is positioned during encoding.

Why does -1 encode to 1 and not a huge number?

That is the whole point of ZigZag. Rather than the all-ones two's-complement representation of -1, ZigZag maps -1 to 1, which a varint stores in a single byte. The mapping interleaves negatives and non-negatives: 0, -1, 1, -2, 2 become 0, 1, 2, 3, 4.

ZigZag Integer Encoder

ZigZag encoding is the trick Protocol Buffers uses to store signed integers efficiently. Negative numbers in two’s complement have all their high bits set, which would waste bytes in a varint. ZigZag remaps the signed range so that small magnitudes — whether positive or negative — become small unsigned values that pack into one or two bytes.

How it works

For an n-bit value the encoding interleaves negatives and non-negatives:

encoded = (value << 1) XOR (value >> (n - 1))

  0 ->  0
 -1 ->  1
  1 ->  2
 -2 ->  3
  2 ->  4

The left shift by one frees the lowest bit to carry the sign, while the arithmetic right shift by n - 1 smears the original sign bit across the whole word so the XOR flips the right bits. Decoding inverts it with (encoded >> 1) XOR -(encoded AND 1): the masked low bit reconstructs the sign and the right shift restores the magnitude.

Tips and notes

Select the width that matches your protobuf field: sint32 uses 32-bit ZigZag, sint64 uses 64-bit. The encoder enforces the signed range for the chosen width, and the decoder expects a non-negative encoded value. ZigZag is usually the first step before varint encoding — encode the signed number here, then feed the resulting unsigned value into the varint tool to get the final wire bytes.