This document specifies the canonical on-disk layout of FLOAT/DOUBLE TS_2DIFF pages, derived from the Java reference implementation (FloatEncoder, FloatDecoder, DeltaBinaryEncoder, BitMap). The Java layout is the cross-language compatibility boundary. Other layouts produced by earlier C++ writers (raw bit-cast, per-block wrapper metadata) are implementation artifacts outside the compatibility scope; the C++ decoder treats them as a format error.

TS_2DIFF encodes integers. Floating-point values go through a wrapper that converts each value to an integer, encodes the integers with IntDeltaEncoder (FLOAT) or LongDeltaEncoder (DOUBLE), and emits page-wide conversion metadata.

Given maxPointNumber = mpn and maxPointValue = 10^mpn (mpn <= 0 implies maxPointValue = 1), each value maps to one of three stored forms:

The three forms are tracked per page as a tri-state flag list (underflowFlags in Java):

• true -> scaled form
• false -> rounded form (scale overflow)
• null -> raw IEEE 754 bits (value overflow or NaN)

round is Java Math.round semantics, floor(x + 0.5) — ties go towards +infinity (-2.5 -> -2), unlike C lround's ties-away-from-zero.

# Form 1: every value stored in scaled form (no bitmap at all)
[maxPointNumber varint]
[TS_2DIFF block 1][TS_2DIFF block 2]...[final block]

# Form 2: at least one value is 'false' (scale overflow), none is 'null'
[Integer.MAX_VALUE varint]                    # 0xFF 0xFF 0xFF 0xFF 0x07
[pageValueCount varint]
[scaled-bitmap, pageValueCount/8+1 bytes]     # marks 'true' entries
[maxPointNumber varint]
[TS_2DIFF block 1]...[final block]

# Form 3: at least one value is 'null' (raw bits)
[Integer.MAX_VALUE-1 varint]                  # 0xFF 0xFF 0xFF 0xFF 0x06
[pageValueCount varint]
[scaled-bitmap, pageValueCount/8+1 bytes]     # marks 'true' entries
[raw-bitmap, pageValueCount/8+1 bytes]        # marks 'null' entries
[maxPointNumber varint]
[TS_2DIFF block 1]...[final block]

Key invariants:

• maxPointNumber appears exactly once per page, before the first integer block (for Forms 2/3 it appears after the bitmaps).
• The bitmaps cover the entire page, not individual TS_2DIFF blocks. The decoder keeps one page-wide position that never resets between blocks; only a page-level reset() clears it.
• Bitmap byte length is always size/8 + 1, even when size % 8 == 0 (BitMap.getSizeOfBytes).
• Bitmap bit order is LSB-first within each byte: position p maps to bits[p / 8] & (1 << (p % 8)).
• pageValueCount counts all values of the page (across blocks).
• A first-page byte of 0x00 is the normal encoding of maxPointNumber = 0 (an explicit max_point_number=0 property on the Java side; reachable but not the default — see Encoder Construction below). It is not a legacy marker.
• NaN handling is writer-dependent: Java floatToIntBits / doubleToLongBits canonicalize any NaN to 0x7fc00000 / 0x7ff8000000000000, while the C++ encoder preserves the payload bits. Both are valid raw-bit entries; readers restore the bits as stored.

Identical to the integer TS_2DIFF format (DeltaBinaryEncoder):

[writeIndex int32 BE]   # number of deltas in this block
[bitWidth  int32 BE]
[block-specific header] # first value; min delta
[packed data]           # writeIndex * bitWidth bits

A block stores writeIndex + 1 values (first value + writeIndex deltas). BLOCK_DEFAULT_SIZE = 128 is only DeltaBinaryEncoder's default buffer size, not a wire-format limit: Java exposes block-size constructors (IntDeltaEncoder(int)), so writeIndex is bounded only by the declared page value count and the packed bytes available. A 300-value page from the default encoder produces blocks of 129, 129, 42 values.

The Java TSEncodingBuilder.Ts2Diff field initializes maxPointNumber = 0, but the standard schema write path (MeasurementSchema.getValueEncoder) always calls initFromProps(), which replaces it with the schema's max_point_number property or, when the property is absent, with TSFileConfig.floatPrecision (current default 2). A writer that explicitly sets max_point_number = 0 produces Form 1 pages starting with 0x00. The C++ FloatTS2DIFFEncoder / DoubleTS2DIFFEncoder default to 2, matching the standard Java schema path. The value stored in the stream is self-describing, so files written with other maxPointNumber values remain readable.

Per page, exactly once, the decoder reads the leading marker:

1. Read varint tag.
2. tag == Integer.MAX_VALUE -> read count varint, count/8+1 bytes scaled-bitmap, then varint maxPointNumber (Form 2).
3. tag == Integer.MAX_VALUE-1 -> additionally read a second count/8+1 bytes raw-bitmap (Form 3).
4. Otherwise tag itself is maxPointNumber (Form 1); mpn <= 0 means maxPointValue = 1.

Then values are decoded from the integer blocks. For value at page position p:

• raw-bitmap (if present) marks p -> intBitsToFloat / longBitsToDouble
• else scaled-bitmap (if present) marks p -> value / 10^mpn
• else -> value / 1

Any input that does not conform to this grammar (for example, an integer TS_2DIFF block header where the page metadata is expected) is a format error.