Compressed Delta (`cMdT`) Format

Binary container for regularly-sampled signed-integer multichannel signal data. A file is a fixed 28-byte header followed by an encoded samples block.

The samples block goes through two optional, independent transforms before storage:

Coding — per-sample delta encoding (1st or 2nd order) followed by zig-zag, mapping signed deltas onto small unsigned integers.
Compression — generic compression (Zstandard or zlib) over the coded bytes.

Both stages are selected per file via header fields.

Wire format

All multi-byte fields are little-endian. The header is packed (no padding) and must be exactly 28 bytes:

Off	Size	Field	C type	Constraint
0	4	`magic`	`uint32`	`0x54644D63` (ASCII `c M d T`)
4	8	`payload_size`	`uint64`	size of samples block in bytes
12	1	`total_channels`	`uint8`	`≥ 1`
13	4	`total_samples`	`uint32`	`≥ 1` per channel; `≥ 2` when `coding = 2`
17	8	`sample_rate`	`float64`	finite, `> 0`
25	1	`bits_per_sample`	`uint8`	`8`, `16`, `24`, or `32`
26	1	`coding`	`uint8`	see Coding
27	1	`compression`	`uint8`	see Compression

The samples block immediately follows the header and spans payload_size bytes.

Sample layout

Samples are stored channel-major (non-interleaved). After full decoding — reversing compression then reversing coding — the layout is:

c0[0]  c0[1]  ...  c0[M-1]   c1[0]  c1[1]  ...  c1[M-1]   ...   c(N-1)[M-1]

where N = total_channels and M = total_samples.

Each sample is a signed integer of bits_per_sample bits, stored little-endian. 24-bit samples occupy three consecutive bytes; readers sign-extend from bit 23 when widening to 32 bits.

The fully-decoded payload size equals total_channels × total_samples × (bits_per_sample / 8) bytes.

Coding

The coding field selects per-sample preprocessing applied independently per channel before cross-channel concatenation.

Value	Symbol	Per-channel transform
0	`TWOS_COMPLEMENT`	none — samples stored as raw signed ints
1	`DELTA_ZIGZAG`	1st-order delta, then zig-zag
2	`DOUBLE_DELTA_ZIGZAG`	2nd-order delta, then zig-zag

Storage is in bits_per_sample-wide slots in all three modes; the bit-width never changes.

Zig-zag

Zig-zag maps signed integers onto unsigned integers placing small absolute values near zero. For an N-bit signed integer:

encode(n) = (n << 1) ^ (n >> (N - 1))     // N = 8/16/24/32, arithmetic right shift
decode(z) = (z >> 1) ^ -(z & 1)           // z is unsigned, logical right shift

`DELTA_ZIGZAG` (1st order)

For a channel with raw samples x[0..M-1], the encoder produces deltas d[0..M-1]:

d[0] = x[0]
d[i] = x[i] - x[i-1]      for i ≥ 1

Then writes y[i] = zigzag(d[i]) to the output slot for sample i. The first sample is the raw seed; subsequent samples are first-order differences.

`DOUBLE_DELTA_ZIGZAG` (2nd order)

Two raw seed samples, then second-order differences:

d[0] = x[0]
d[1] = x[1]
d[i] = (x[i] - x[i-1]) - (x[i-1] - x[i-2])      for i ≥ 2

Then writes y[i] = zigzag(d[i]) for each i. Note both d[0] and d[1] are raw samples — not first-order deltas — because the decoder needs two consecutive raw samples to seed the second-order recurrence. Consequently coding = 2 requires total_samples ≥ 2.

Sample arithmetic is in bits_per_sample-wide signed two’s-complement; overflow wraps modulo 2^bits_per_sample and the inverse transform on decode recovers the original x[i].

Compression

The compression field selects how the coded bytes are stored.

Value	Symbol	Storage
0	`NO_COMPRESSION`	coded bytes stored verbatim
1	`ZSTD`	coded bytes compressed with Zstandard
2	`ZLIB`	coded bytes compressed with zlib (deflate)

For NO_COMPRESSION, payload_size equals the raw size total_channels × total_samples × (bits_per_sample / 8).

For ZSTD and ZLIB, payload_size is the compressor’s output size; the decompressor must yield exactly the raw size.

Validation

A conforming reader must reject inputs that violate any of the following:

Header reads less than 28 bytes.
magic != 0x54644D63.
bits_per_sample is not 8, 16, 24, or 32.
coding > 2.
compression > 2.
total_channels == 0.
total_samples == 0.
total_samples < 2 while coding is DOUBLE_DELTA_ZIGZAG.
sample_rate is NaN, ±Inf, or ≤ 0.
For NO_COMPRESSION: fewer bytes than the raw size remain after the header.
For ZSTD / ZLIB: fewer than payload_size bytes remain after the header.
For ZSTD: payload does not start with a valid Zstandard frame header.
For ZLIB: payload does not start with a valid zlib stream header.
For ZSTD / ZLIB: the decompressed samples block size differs from the raw size.

The validation order is at the reader’s discretion, but cheap checks (header size, magic, enum ranges) should run before stream-position-dependent checks (payload size, frame headers).

Reference encoder (ISO C17)

Single-call encoder for any valid combination of coding, compression, and bits_per_sample. Allocates the result on the heap; caller frees with free. Returns NULL on invalid arguments, compression failure, or allocation failure.

Compile: cc -std=c17 -O3 cmdt_encode.c -lzstd -lz -o cmdt_encode

#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <zstd.h>
#include <zlib.h>

#define CMDT_MAGIC              0x54644D63u
#define CMDT_CODING_TWOS        0
#define CMDT_CODING_DELTA       1
#define CMDT_CODING_DOUBLE      2
#define CMDT_COMPRESS_NONE      0
#define CMDT_COMPRESS_ZSTD      1
#define CMDT_COMPRESS_ZLIB      2

#pragma pack(push, 1)
typedef struct {
    uint32_t magic;
    uint64_t payload_size;
    uint8_t  total_channels;
    uint32_t total_samples;
    double   sample_rate;
    uint8_t  bits_per_sample;
    uint8_t  coding;
    uint8_t  compression;
} CmdtHeader;
#pragma pack(pop)

// Unsigned sign-fill mask keeps every step fully defined; a sign-extended N-bit input yields an N-bit result
static inline uint32_t zigzag_encode(int32_t value) {
    const uint32_t sign_mask = 0u - ((uint32_t)value >> 31);
    return ((uint32_t)value << 1) ^ sign_mask;
}

// Reinterpret the low bits of value as a signed bits-wide integer (modular two's-complement)
static inline int32_t truncate_signed(uint32_t value, uint8_t bits) {
    if (bits == 32) {
        return (value & 0x80000000u) ? (int32_t)(value - 0x80000000u) + INT32_MIN : (int32_t)value;
    }
    const uint32_t sign_bit = 1u << (bits - 1);
    const uint32_t low      = value & ((1u << bits) - 1);
    return (int32_t)(low ^ sign_bit) - (int32_t)sign_bit;
}

// Byte-wise little-endian access: no alignment, aliasing, or host byte-order assumptions
static int32_t read_sample(const uint8_t* src, uint32_t sample_index, uint8_t bits_per_sample) {
    const size_t   bytes_per_sample = bits_per_sample / 8u;
    const uint8_t* sample_data      = src + (size_t)sample_index * bytes_per_sample;
    uint32_t       raw              = 0;

    for (size_t byte_index = 0; byte_index < bytes_per_sample; ++byte_index) {
        raw |= (uint32_t)sample_data[byte_index] << (8u * byte_index);
    }

    return truncate_signed(raw, bits_per_sample);
}

static void write_sample(uint8_t* dst, uint32_t sample_index, uint8_t bits_per_sample, uint32_t value) {
    const size_t bytes_per_sample = bits_per_sample / 8u;
    uint8_t*     sample_data      = dst + (size_t)sample_index * bytes_per_sample;

    for (size_t byte_index = 0; byte_index < bytes_per_sample; ++byte_index) {
        sample_data[byte_index] = (uint8_t)(value >> (8u * byte_index));
    }
}

uint8_t* cmdt_encode(const void* input_samples,
                     uint8_t     total_channels,
                     uint32_t    total_samples,
                     double      sample_rate,
                     uint8_t     bits_per_sample,
                     uint8_t     coding,
                     uint8_t     compression,
                     size_t*     output_size) {
    if (!input_samples || !output_size || !total_channels || !total_samples) {
        return NULL;
    }
    if (!isfinite(sample_rate) || sample_rate <= 0.0) {
        return NULL;
    }
    if (bits_per_sample != 8 && bits_per_sample != 16 && bits_per_sample != 24 && bits_per_sample != 32) {
        return NULL;
    }
    if (coding > CMDT_CODING_DOUBLE || compression > CMDT_COMPRESS_ZLIB) {
        return NULL;
    }
    if (coding == CMDT_CODING_DOUBLE && total_samples < 2) {
        return NULL;
    }

    const size_t bytes_per_sample = bits_per_sample / 8;
    const size_t raw_size         = (size_t)total_channels * total_samples * bytes_per_sample;

    // Apply per-channel coding into a contiguous channel-major buffer
    uint8_t* coded = (uint8_t*)malloc(raw_size);

    if (!coded) {
        return NULL;
    }

    for (uint8_t channel = 0; channel < total_channels; ++channel) {
        const uint8_t* src = (const uint8_t*)input_samples + (size_t)channel * total_samples * bytes_per_sample;
        uint8_t*       dst = coded                         + (size_t)channel * total_samples * bytes_per_sample;

        for (uint32_t sample_index = 0; sample_index < total_samples; ++sample_index) {
            const int32_t x     = read_sample(src, sample_index, bits_per_sample);
            uint32_t      delta = (uint32_t)x;

            // Deltas stay in unsigned arithmetic, so wraparound is fully defined at every sample width
            if (coding == CMDT_CODING_DELTA && sample_index >= 1) {
                const int32_t x_prev = read_sample(src, sample_index - 1, bits_per_sample);
                delta = (uint32_t)x - (uint32_t)x_prev;

            } else if (coding == CMDT_CODING_DOUBLE && sample_index >= 2) {
                const int32_t x_prev1 = read_sample(src, sample_index - 1, bits_per_sample);
                const int32_t x_prev2 = read_sample(src, sample_index - 2, bits_per_sample);
                delta = ((uint32_t)x - (uint32_t)x_prev1) - ((uint32_t)x_prev1 - (uint32_t)x_prev2);
            }

            // Wrap the delta to bits_per_sample width before zigzag
            const int32_t d = truncate_signed(delta, bits_per_sample);

            const uint32_t y = (coding == CMDT_CODING_TWOS) ? (uint32_t)d : zigzag_encode(d);

            write_sample(dst, sample_index, bits_per_sample, y);
        }
    }

    // Optionally compress the coded buffer
    const uint8_t* final_data        = coded;
    size_t         final_size        = raw_size;
    uint8_t*       compressed_buffer = NULL;

    if (compression == CMDT_COMPRESS_ZSTD) {
        const size_t bound = ZSTD_compressBound(raw_size);
        compressed_buffer = (uint8_t*)malloc(bound);

        if (!compressed_buffer) {
            free(coded);
            return NULL;
        }

        const size_t result = ZSTD_compress(compressed_buffer, bound, coded, raw_size, 3);

        if (ZSTD_isError(result)) {
            free(compressed_buffer);
            free(coded);
            return NULL;
        }

        final_data = compressed_buffer;
        final_size = result;

    } else if (compression == CMDT_COMPRESS_ZLIB) {
        uLong bound = compressBound((uLong)raw_size);
        compressed_buffer = (uint8_t*)malloc(bound);

        if (!compressed_buffer) {
            free(coded);
            return NULL;
        }

        if (compress(compressed_buffer, &bound, coded, (uLong)raw_size) != Z_OK) {
            free(compressed_buffer);
            free(coded);
            return NULL;
        }

        final_data = compressed_buffer;
        final_size = (size_t)bound;
    }

    // Build the final blob: header followed by samples block
    const size_t blob_size = sizeof(CmdtHeader) + final_size;
    uint8_t*     blob      = (uint8_t*)malloc(blob_size);

    if (!blob) {
        free(compressed_buffer);
        free(coded);
        return NULL;
    }

    CmdtHeader* header = (CmdtHeader*)blob;
    header->magic           = CMDT_MAGIC;
    header->payload_size    = final_size;
    header->total_channels  = total_channels;
    header->total_samples   = total_samples;
    header->sample_rate     = sample_rate;
    header->bits_per_sample = bits_per_sample;
    header->coding          = coding;
    header->compression     = compression;

    memcpy(blob + sizeof(CmdtHeader), final_data, final_size);

    free(compressed_buffer);
    free(coded);

    *output_size = blob_size;
    return blob;
}

Notes

The encoder stores the header in host byte order. On big-endian platforms the multi-byte header fields must be byte-swapped to little-endian before the bytes are written out. The samples block is assembled byte-wise, so it is little-endian on any host and needs no particular input alignment.
For brevity, this encoder reads each input sample twice when computing deltas. A production encoder would maintain prev1 / prev2 running variables to make the inner loop a single read per sample.