How to calulate CRC of 1 byte using stm32l1 CRC unit

The most efficient way to calculate crcs in software is to use a table and doing the calculations eight bits at a time. Below is a table that allows you to calculate these:

#include <stddef.h>
#include <stdint.h>
#include <stdio.h>

static uint32_t crc32mpeg2_table[] = {
    0x00000000, 0x04c11db7, 0x09823b6e, 0x0d4326d9, 0x130476dc, 0x17c56b6b, 0x1a864db2, 0x1e475005,
    0x2608edb8, 0x22c9f00f, 0x2f8ad6d6, 0x2b4bcb61, 0x350c9b64, 0x31cd86d3, 0x3c8ea00a, 0x384fbdbd,
    0x4c11db70, 0x48d0c6c7, 0x4593e01e, 0x4152fda9, 0x5f15adac, 0x5bd4b01b, 0x569796c2, 0x52568b75,
    0x6a1936c8, 0x6ed82b7f, 0x639b0da6, 0x675a1011, 0x791d4014, 0x7ddc5da3, 0x709f7b7a, 0x745e66cd,
    0x9823b6e0, 0x9ce2ab57, 0x91a18d8e, 0x95609039, 0x8b27c03c, 0x8fe6dd8b, 0x82a5fb52, 0x8664e6e5,
    0xbe2b5b58, 0xbaea46ef, 0xb7a96036, 0xb3687d81, 0xad2f2d84, 0xa9ee3033, 0xa4ad16ea, 0xa06c0b5d,
    0xd4326d90, 0xd0f37027, 0xddb056fe, 0xd9714b49, 0xc7361b4c, 0xc3f706fb, 0xceb42022, 0xca753d95,
    0xf23a8028, 0xf6fb9d9f, 0xfbb8bb46, 0xff79a6f1, 0xe13ef6f4, 0xe5ffeb43, 0xe8bccd9a, 0xec7dd02d,
    0x34867077, 0x30476dc0, 0x3d044b19, 0x39c556ae, 0x278206ab, 0x23431b1c, 0x2e003dc5, 0x2ac12072,
    0x128e9dcf, 0x164f8078, 0x1b0ca6a1, 0x1fcdbb16, 0x018aeb13, 0x054bf6a4, 0x0808d07d, 0x0cc9cdca,
    0x7897ab07, 0x7c56b6b0, 0x71159069, 0x75d48dde, 0x6b93dddb, 0x6f52c06c, 0x6211e6b5, 0x66d0fb02,
    0x5e9f46bf, 0x5a5e5b08, 0x571d7dd1, 0x53dc6066, 0x4d9b3063, 0x495a2dd4, 0x44190b0d, 0x40d816ba,
    0xaca5c697, 0xa864db20, 0xa527fdf9, 0xa1e6e04e, 0xbfa1b04b, 0xbb60adfc, 0xb6238b25, 0xb2e29692,
    0x8aad2b2f, 0x8e6c3698, 0x832f1041, 0x87ee0df6, 0x99a95df3, 0x9d684044, 0x902b669d, 0x94ea7b2a,
    0xe0b41de7, 0xe4750050, 0xe9362689, 0xedf73b3e, 0xf3b06b3b, 0xf771768c, 0xfa325055, 0xfef34de2,
    0xc6bcf05f, 0xc27dede8, 0xcf3ecb31, 0xcbffd686, 0xd5b88683, 0xd1799b34, 0xdc3abded, 0xd8fba05a,
    0x690ce0ee, 0x6dcdfd59, 0x608edb80, 0x644fc637, 0x7a089632, 0x7ec98b85, 0x738aad5c, 0x774bb0eb,
    0x4f040d56, 0x4bc510e1, 0x46863638, 0x42472b8f, 0x5c007b8a, 0x58c1663d, 0x558240e4, 0x51435d53,
    0x251d3b9e, 0x21dc2629, 0x2c9f00f0, 0x285e1d47, 0x36194d42, 0x32d850f5, 0x3f9b762c, 0x3b5a6b9b,
    0x0315d626, 0x07d4cb91, 0x0a97ed48, 0x0e56f0ff, 0x1011a0fa, 0x14d0bd4d, 0x19939b94, 0x1d528623,
    0xf12f560e, 0xf5ee4bb9, 0xf8ad6d60, 0xfc6c70d7, 0xe22b20d2, 0xe6ea3d65, 0xeba91bbc, 0xef68060b,
    0xd727bbb6, 0xd3e6a601, 0xdea580d8, 0xda649d6f, 0xc423cd6a, 0xc0e2d0dd, 0xcda1f604, 0xc960ebb3,
    0xbd3e8d7e, 0xb9ff90c9, 0xb4bcb610, 0xb07daba7, 0xae3afba2, 0xaafbe615, 0xa7b8c0cc, 0xa379dd7b,
    0x9b3660c6, 0x9ff77d71, 0x92b45ba8, 0x9675461f, 0x8832161a, 0x8cf30bad, 0x81b02d74, 0x857130c3,
    0x5d8a9099, 0x594b8d2e, 0x5408abf7, 0x50c9b640, 0x4e8ee645, 0x4a4ffbf2, 0x470cdd2b, 0x43cdc09c,
    0x7b827d21, 0x7f436096, 0x7200464f, 0x76c15bf8, 0x68860bfd, 0x6c47164a, 0x61043093, 0x65c52d24,
    0x119b4be9, 0x155a565e, 0x18197087, 0x1cd86d30, 0x029f3d35, 0x065e2082, 0x0b1d065b, 0x0fdc1bec,
    0x3793a651, 0x3352bbe6, 0x3e119d3f, 0x3ad08088, 0x2497d08d, 0x2056cd3a, 0x2d15ebe3, 0x29d4f654,
    0xc5a92679, 0xc1683bce, 0xcc2b1d17, 0xc8ea00a0, 0xd6ad50a5, 0xd26c4d12, 0xdf2f6bcb, 0xdbee767c,
    0xe3a1cbc1, 0xe760d676, 0xea23f0af, 0xeee2ed18, 0xf0a5bd1d, 0xf464a0aa, 0xf9278673, 0xfde69bc4,
    0x89b8fd09, 0x8d79e0be, 0x803ac667, 0x84fbdbd0, 0x9abc8bd5, 0x9e7d9662, 0x933eb0bb, 0x97ffad0c,
    0xafb010b1, 0xab710d06, 0xa6322bdf, 0xa2f33668, 0xbcb4666d, 0xb8757bda, 0xb5365d03, 0xb1f740b4,
};

uint32_t crc32mpeg2(uint32_t state, uint8_t *buff, size_t buff_sz)
{
    while (buff_sz-- > 0) {
        int index = (state >> 24) ^ *buff++;
        state <<= 8;
        state ^= crc32mpeg2_table[index];
    }
    return state;
}

/* this main() function to demonstrate that the crc 
 * applied to a string with a single space character works */
int main()
{
    uint8_t buff[] = { 0x20 };
    uint32_t crc = crc32mpeg2(0xffffffff, buff, sizeof buff);
    printf("0x%08x\n", crc);
}

As you can see, the result, after aplying it to your input buffer is the expected value:

$ ./crcmpg3 
0xd62b0954
$ _

To generate the table, you can just run the proposed algorithm by Mark Adler (@MarkAdler) in his response, for the full set of possible input bytes (from 0x00 to 0xff) as in:

#include <stddef.h>
#include <stdio.h>
#include <stdint.h>

/* this is the function provided by Mark in his response */
uint32_t crc32mpeg2(uint32_t crc, void const *mem, size_t len) {
    unsigned char const *data = mem;
    if (data == NULL)
        return 0xffffffff;
    while (len--) {
        crc ^= (uint32_t)(*data++) << 24;
        for (unsigned k = 0; k < 8; k++)
            crc = crc & 0x80000000 ? (crc << 1) ^ 0x04c11db7 : crc << 1;
    }
    return crc;
}

int main()
{
    int i;
    char *sep = "uint32_t crc32mpeg2_table[] = {\n\t";
    for (i = 0; i < 256; i++) {
        status = crc32mpeg2(i & 0xff, &ch, sizeof ch);
        printf("%s0x%08x", sep, status);
        sep = i % 8 == 7 ? ",\n\t" : ", ";
    }
    printf("\n};\n");
}

It will produce the table above. Once you have the table, you just need to use this function (far more quick, as you operate one full byte per iteration) to get the result:

uint32_t crc32mpeg2(uint32_t state, uint8_t *buff, size_t buff_sz)
{
    while (buff_sz-- > 0) {
        int index = (state >> 24) ^ *buff++;
        state <<= 8;
        state ^= crc32mpeg2_table[index];
    }
    return state;
}

The correct use of the function is to call it by passing the old state (which is the CRC upto the last byte processed) to get the new state (the new CRC after processing a new bunch of bytes) The first value for the state must be initialized to 0xffffffff, so to calculate the CRC of "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua." you can use this main:

#include <string.h>
#include <stddef.h>
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>

int main()
{
    /* first piece */
    char *s = "Lorem ipsum dolor sit amet, consectetur adipiscing elit, ";
    uint32_t crc = crc32mpeg2(0xffffffff, s, strlen(s)); /* intialize with 0xffffffff */
    printf("CRC(\"%s", s);

    /* second piece */
    s = "sed do eiusmod tempor incididunt ut labore et dolore ";
    crc = crc32mpeg2(crc, s, strlen(s));
    printf("%s", s);

    /* third piece */
    s = "magna aliqua.";
    crc = crc32mpeg2(crc, s, strlen(s));
    printf("%s\") => ", s);

    /* print crc of the whole string */
    printf("0x%08x\n", crc);
}

which should output:

$ crcmpg3.c
CRC("Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.") => 0x81e9201f
$ _