What is a better method for packing 4 bytes into 3 than this?

Question

I have an array of values all well within the range 0 - 63, and decided I could pack every 4 bytes into 3 because the values only require 6 bits and I could use the extra 2bits to store the first 2 bits of the next value and so on.

Having never done this before I used the switch statement and a nextbit variable (a state machine like device) to do the packing and keep track of the starting bit. I'm convinced however, there must be a better way.

Suggestions/clues please, but don't ruin my fun ;-)

Any portability problems regarding big/little endian?

btw: I have verified this code is working, by unpacking it again and comparing with the input. And no it ain't homework, just an exercise I've set myself.

/* build with gcc -std=c99 -Wconversion */
#define ASZ 400
typedef unsigned char uc_;
uc_ data[ASZ];
int i;
for (i = 0; i < ASZ; ++i) {
    data[i] = (uc_)(i % 0x40);
}
size_t dl = sizeof(data);
printf("sizeof(data):%z\n",dl);
float fpl = ((float)dl / 4.0f) * 3.0f;
size_t pl = (size_t)(fpl > (float)((int)fpl) ? fpl + 1 : fpl);
printf("length of packed data:%z\n",pl);

for (i = 0; i < dl; ++i)
    printf("%02d  ", data[i]);
printf("\n");

uc_ * packeddata = calloc(pl, sizeof(uc_));
uc_ * byte = packeddata;
uc_ nextbit = 1;
for (int i = 0; i < dl; ++i) {
    uc_ m = (uc_)(data[i] & 0x3f);
    switch(nextbit) {
    case 1:
        /* all 6 bits of m into first 6 bits of byte: */
        *byte = m;
        nextbit = 7;
        break;
    case 3:
        /* all 6 bits of m into last 6 bits of byte: */
        *byte++ = (uc_)(*byte | (m << 2));
        nextbit = 1;
        break;
    case 5:
        /* 1st 4 bits of m into last 4 bits of byte: */
        *byte++ = (uc_)(*byte | ((m & 0x0f) << 4));
        /* 5th and 6th bits of m into 1st and 2nd bits of byte: */
        *byte = (uc_)(*byte | ((m & 0x30) >> 4));
        nextbit = 3;
        break;
    case 7:
        /* 1st 2 bits of m into last 2 bits of byte: */
        *byte++ = (uc_)(*byte | ((m & 0x03) << 6));
        /* next (last) 4 bits of m into 1st 4 bits of byte: */
        *byte = (uc_)((m & 0x3c) >> 2);
        nextbit = 5;
        break;
    }
}

Answer 1

Check out the IETF RFC 4648 for 'The Base16, Base32 and Base64 Data Encodings'.

Partial code critique:

size_t dl = sizeof(data);
printf("sizeof(data):%d\n",dl);
float fpl = ((float)dl / 4.0f) * 3.0f;
size_t pl = (size_t)(fpl > (float)((int)fpl) ? fpl + 1 : fpl);
printf("length of packed data:%d\n",pl);

Don't use the floating point stuff - just use integers. And use '%z' to print 'size_t' values - assuming you've got a C99 library.

size_t pl = ((dl + 3) / 4) * 3;

I think your loop could be simplified by dealing with 3-byte input units until you've got a partial unit left over, and then dealing with a remainder of 1 or 2 bytes as special cases. I note that the standard referenced says that you use one or two '=' signs to pad at the end.

I have a Base64 encoder and decode which does some of that. You are describing the 'decode' part of Base64 -- where the Base64 code has 4 bytes of data that should be stored in just 3 - as your packing code. The Base64 encoder corresponds to the unpacker you will need.

Base-64 Decoder

Note: base_64_inv is an array of 256 values, one for each possible input byte value; it defines the correct decoded value for each encoded byte. In the Base64 encoding, this is a sparse array - 3/4 zeroes. Similarly, base_64_map is the mapping between a value 0..63 and the corresponding storage value.

enum { DC_PAD = -1, DC_ERR = -2 };

static int decode_b64(int c)
{
    int b64 = base_64_inv[c];

    if (c == base64_pad)
        b64 = DC_PAD;
    else if (b64 == 0 && c != base_64_map[0])
        b64 = DC_ERR;
    return(b64);
}

/* Decode 4 bytes into 3 */
static int decode_quad(const char *b64_data, char *bin_data)
{
    int b0 = decode_b64(b64_data[0]);
    int b1 = decode_b64(b64_data[1]);
    int b2 = decode_b64(b64_data[2]);
    int b3 = decode_b64(b64_data[3]);
    int bytes;

    if (b0 < 0 || b1 < 0 || b2 == DC_ERR || b3 == DC_ERR || (b2 == DC_PAD && b3 != DC_PAD))
        return(B64_ERR_INVALID_ENCODED_DATA);
    if (b2 == DC_PAD && (b1 & 0x0F) != 0)
        /* 3rd byte is '='; 2nd byte must end with 4 zero bits */
        return(B64_ERR_INVALID_TRAILING_BYTE);
    if (b2 >= 0 && b3 == DC_PAD && (b2 & 0x03) != 0)
        /* 4th byte is '='; 3rd byte is not '=' and must end with 2 zero bits */
        return(B64_ERR_INVALID_TRAILING_BYTE);
    bin_data[0] = (b0 << 2) | (b1 >> 4);
    bytes = 1;
    if (b2 >= 0)
    {
        bin_data[1] = ((b1 & 0x0F) << 4) | (b2 >> 2);
        bytes = 2;
    }
    if (b3 >= 0)
    {
        bin_data[2] = ((b2 & 0x03) << 6) | (b3);
        bytes = 3;
    }
    return(bytes);
}

/* Decode input Base-64 string to original data.  Output length returned, or negative error */
int base64_decode(const char *data, size_t datalen, char *buffer, size_t buflen)
{
    size_t outlen = 0;
    if (datalen % 4 != 0)
        return(B64_ERR_INVALID_ENCODED_LENGTH);
    if (BASE64_DECLENGTH(datalen) > buflen)
        return(B64_ERR_OUTPUT_BUFFER_TOO_SMALL);
    while (datalen >= 4)
    {
        int nbytes = decode_quad(data, buffer + outlen);
        if (nbytes < 0)
            return(nbytes);
        outlen += nbytes;
        data += 4;
        datalen -= 4;
    }
    assert(datalen == 0);   /* By virtue of the %4 check earlier */
    return(outlen);
}

Base-64 Encoder

/* Encode 3 bytes of data into 4 */
static void encode_triplet(const char *triplet, char *quad)
{
    quad[0] = base_64_map[(triplet[0] >> 2) & 0x3F];
    quad[1] = base_64_map[((triplet[0] & 0x03) << 4) | ((triplet[1] >> 4) & 0x0F)];
    quad[2] = base_64_map[((triplet[1] & 0x0F) << 2) | ((triplet[2] >> 6) & 0x03)];
    quad[3] = base_64_map[triplet[2] & 0x3F];
}

/* Encode 2 bytes of data into 4 */
static void encode_doublet(const char *doublet, char *quad, char pad)
{
    quad[0] = base_64_map[(doublet[0] >> 2) & 0x3F];
    quad[1] = base_64_map[((doublet[0] & 0x03) << 4) | ((doublet[1] >> 4) & 0x0F)];
    quad[2] = base_64_map[((doublet[1] & 0x0F) << 2)];
    quad[3] = pad;
}

/* Encode 1 byte of data into 4 */
static void encode_singlet(const char *singlet, char *quad, char pad)
{
    quad[0] = base_64_map[(singlet[0] >> 2) & 0x3F];
    quad[1] = base_64_map[((singlet[0] & 0x03) << 4)];
    quad[2] = pad;
    quad[3] = pad;
}

/* Encode input data as Base-64 string.  Output length returned, or negative error */
static int base64_encode_internal(const char *data, size_t datalen, char *buffer, size_t buflen, char pad)
{
    size_t outlen = BASE64_ENCLENGTH(datalen);
    const char *bin_data = (const void *)data;
    char *b64_data = (void *)buffer;

    if (outlen > buflen)
        return(B64_ERR_OUTPUT_BUFFER_TOO_SMALL);
    while (datalen >= 3)
    {
        encode_triplet(bin_data, b64_data);
        bin_data += 3;
        b64_data += 4;
        datalen -= 3;
    }
    b64_data[0] = '\0';

    if (datalen == 2)
        encode_doublet(bin_data, b64_data, pad);
    else if (datalen == 1)
        encode_singlet(bin_data, b64_data, pad);
    b64_data[4] = '\0';
    return((b64_data - buffer) + strlen(b64_data));
}

I complicate life by having to deal with a product that uses a variant alphabet for the Base64 encoding, and also manages not to pad data - hence the 'pad' argument (which can be zero for 'null padding' or '=' for standard padding. The 'base_64_map' array contains the alphabet to use for 6-bit values in the range 0..63.

Answer 2

Instead of using a statemachine you can simply use a counter for how many bits are already used in the current byte, from which you can directly derive the shift-offsets and whether or not you overflow into the next byte. Regarding the endianess: As long as you use only a single datatype (that is you don't reinterpret pointer to types of different size (e.g. int* a =...;short* b=(short*) a;) you shouldn't get problems with endianess in most cases

Answer 3

Another simpler way to do it would be to use bit fields. One of the lesser known corners of C struct syntax is the big field. Let's say you have the following structure:

struct packed_bytes {
    byte chunk1 : 6;
    byte chunk2 : 6;
    byte chunk3 : 6;
    byte chunk4 : 6;
};

This declares chunk1, chunk2, chunk3, and chunk4 to have the type byte but to only take up 6 bits in the structure. The result is that sizeof(struct packed_bytes) == 3. Now all you need is a little function to take your array and dump it into the structure like so:

void
dump_to_struct(byte *in, struct packed_bytes *out, int count)
{
    int i, j;
    for (i = 0; i < (count / 4); ++i) {
        out[i].chunk1 = in[i * 4];
        out[i].chunk2 = in[i * 4 + 1];
        out[i].chunk3 = in[i * 4 + 2];
        out[i].chunk4 = in[i * 4 + 3];
    }
    // Finish up
    switch(struct % 4) {
    case 3:
        out[count / 4].chunk3 = in[(count / 4) * 4 + 2];
    case 2:
        out[count / 4].chunk2 = in[(count / 4) * 4 + 1];
    case 1:
        out[count / 4].chunk1 = in[(count / 4) * 4];
    }
}

There you go, you now have an array of struct packed_bytes that you can easily read by using the above struct.

Answer 4

So, this is kinda like code-golf, right?

---

#include <stdlib.h>
#include <string.h>

static void pack2(unsigned char *r, unsigned char *n) {
  unsigned v = n[0] + (n[1] << 6) + (n[2] << 12) + (n[3] << 18);
  *r++ = v;
  *r++ = v >> 8;
  *r++ = v >> 16;
}

unsigned char *apack(const unsigned char *s, int len) {
  unsigned char *s_end = s + len,
                *r, *result = malloc(len/4*3+3),
                lastones[4] = { 0 };
  if (result == NULL)
    return NULL;
  for(r = result; s + 4 <= s_end; s += 4, r += 3)
    pack2(r, s);
  memcpy(lastones, s, s_end - s);
  pack2(r, lastones);
  return result;
}

Answer 5

Taking elements of DigitalRoss's compact code, Grizzly's suggestion, and my own code, I have written my own answer at last. Although DigitalRoss provides a usable working answer, my usage of it without understanding, would not have provided the same satisfaction as to learning something. For this reason I have chosen to base my answer on my original code.

I have also chosen to ignore the advice Jonathon Leffler gives to avoid using floating point arithmetic for the calculation of the packed data length. Both the recommended method given - the same DigitalRoss also uses, increases the length of the packed data by as much as three bytes. Granted this is not much, but is also avoidable by the use of floating point math.

Here is the code, criticisms welcome:

/* built with gcc -std=c99 */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>

unsigned char *
pack(const unsigned char * data, size_t len, size_t * packedlen)
{
    float fpl = ((float)len / 4.0f) * 3.0f;
    *packedlen = (size_t)(fpl > (float)((int)fpl) ? fpl + 1 : fpl);
    unsigned char * packed = malloc(*packedlen);
    if (!packed)
        return 0;
    const unsigned char * in = data;
    const unsigned char * in_end = in + len;
    unsigned char * out;
    for (out = packed; in + 4 <= in_end; in += 4) {
        *out++ = in[0] | ((in[1] & 0x03) << 6);
        *out++ = ((in[1] & 0x3c) >> 2) | ((in[2] & 0x0f) << 4);
        *out++ = ((in[2] & 0x30) >> 4) | (in[3] << 2);
    }
    size_t lastlen = in_end - in;
    if (lastlen > 0) {
        *out = in[0];
        if (lastlen > 1) {
            *out++ |= ((in[1] & 0x03) << 6);
            *out = ((in[1] & 0x3c) >> 2);
            if (lastlen > 2) {
                *out++ |= ((in[2] & 0x0f) << 4);
                *out = ((in[2] & 0x30) >> 4);
                if (lastlen > 3)
                    *out |= (in[3] << 2);
            }
        }
    }
    return packed;
}

int main()
{
    size_t i;
    unsigned char data[] = {
        12, 15, 40, 18,
        26, 32, 50, 3,
        7,  19, 46, 10,
        25, 37, 2,  39,
        60, 59, 0,  17,
        9,  29, 13, 54,
        5,  6,  47, 32
    };
    size_t datalen = sizeof(data);
    printf("unpacked datalen: %td\nunpacked data\n", datalen);
    for (i = 0; i < datalen; ++i)
        printf("%02d  ", data[i]);
    printf("\n");
    size_t packedlen;
    unsigned char * packed = pack(data, sizeof(data), &packedlen);
    if (!packed) {
        fprintf(stderr, "Packing failed!\n");
        return EXIT_FAILURE;
    }
    printf("packedlen: %td\npacked data\n", packedlen);
    for (i = 0; i < packedlen; ++i)
        printf("0x%02x ", packed[i]);
    printf("\n");
    free(packed);
    return EXIT_SUCCESS;
}