mode_s.c

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// dump1090, a Mode S messages decoder for RTLSDR devices.
//
// Copyright (C) 2012 by Salvatore Sanfilippo <antirez@gmail.com>
//
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
//  *  Redistributions of source code must retain the above copyright
//     notice, this list of conditions and the following disclaimer.
//
//  *  Redistributions in binary form must reproduce the above copyright
//     notice, this list of conditions and the following disclaimer in the
//     documentation and/or other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//

#include "dump1090.h"
#include "aera.h"
//
// ===================== Mode S detection and decoding  ===================
//
// Parity table for MODE S Messages.
// The table contains 112 elements, every element corresponds to a bit set
// in the message, starting from the first bit of actual data after the
// preamble.
//
// For messages of 112 bit, the whole table is used.
// For messages of 56 bits only the last 56 elements are used.
//
// The algorithm is as simple as xoring all the elements in this table
// for which the corresponding bit on the message is set to 1.
//
// The latest 24 elements in this table are set to 0 as the checksum at the
// end of the message should not affect the computation.
//
// Note: this function can be used with DF11 and DF17, other modes have
// the CRC xored with the sender address as they are reply to interrogations,
// but a casual listener can't split the address from the checksum.
//
uint32_t modes_checksum_table[112] = {
0x3935ea, 0x1c9af5, 0xf1b77e, 0x78dbbf, 0xc397db, 0x9e31e9, 0xb0e2f0, 0x587178,
0x2c38bc, 0x161c5e, 0x0b0e2f, 0xfa7d13, 0x82c48d, 0xbe9842, 0x5f4c21, 0xd05c14,
0x682e0a, 0x341705, 0xe5f186, 0x72f8c3, 0xc68665, 0x9cb936, 0x4e5c9b, 0xd8d449,
0x939020, 0x49c810, 0x24e408, 0x127204, 0x093902, 0x049c81, 0xfdb444, 0x7eda22,
0x3f6d11, 0xe04c8c, 0x702646, 0x381323, 0xe3f395, 0x8e03ce, 0x4701e7, 0xdc7af7,
0x91c77f, 0xb719bb, 0xa476d9, 0xadc168, 0x56e0b4, 0x2b705a, 0x15b82d, 0xf52612,
0x7a9309, 0xc2b380, 0x6159c0, 0x30ace0, 0x185670, 0x0c2b38, 0x06159c, 0x030ace,
0x018567, 0xff38b7, 0x80665f, 0xbfc92b, 0xa01e91, 0xaff54c, 0x57faa6, 0x2bfd53,
0xea04ad, 0x8af852, 0x457c29, 0xdd4410, 0x6ea208, 0x375104, 0x1ba882, 0x0dd441,
0xf91024, 0x7c8812, 0x3e4409, 0xe0d800, 0x706c00, 0x383600, 0x1c1b00, 0x0e0d80,
0x0706c0, 0x038360, 0x01c1b0, 0x00e0d8, 0x00706c, 0x003836, 0x001c1b, 0xfff409,
0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000,
0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000,
0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000, 0x000000
};

uint32_t modesChecksum(unsigned char *msg, int bits) {
    uint32_t   crc = 0;
    uint32_t   rem = 0;
    int        offset = (bits == 112) ? 0 : (112-56);
    uint8_t    theByte = *msg;
    uint32_t * pCRCTable = &modes_checksum_table[offset];
    int j;

    // We don't really need to include the checksum itself
    bits -= 24;
    for(j = 0; j < bits; j++) {
        if ((j & 7) == 0)
            theByte = *msg++;

        // If bit is set, xor with corresponding table entry.
        if (theByte & 0x80) {crc ^= *pCRCTable;} 
        pCRCTable++;
        theByte = theByte << 1; 
    }

    rem = (msg[0] << 16) | (msg[1] << 8) | msg[2]; // message checksum
    return ((crc ^ rem) & 0x00FFFFFF); // 24 bit checksum syndrome.
}
//
//=========================================================================
//
// Given the Downlink Format (DF) of the message, return the message length in bits.
//
// All known DF's 16 or greater are long. All known DF's 15 or less are short. 
// There are lots of unused codes in both category, so we can assume ICAO will stick to 
// these rules, meaning that the most significant bit of the DF indicates the length.
//
int modesMessageLenByType(int type) {
    return (type & 0x10) ? MODES_LONG_MSG_BITS : MODES_SHORT_MSG_BITS ;
}
//
//=========================================================================
//
// Try to fix single bit errors using the checksum. On success modifies
// the original buffer with the fixed version, and returns the position
// of the error bit. Otherwise if fixing failed -1 is returned.
/*
int fixSingleBitErrors(unsigned char *msg, int bits) {
    int j;
    unsigned char aux[MODES_LONG_MSG_BYTES];

    memcpy(aux, msg, bits/8);

    // Do not attempt to error correct Bits 0-4. These contain the DF, and must
    // be correct because we can only error correct DF17
    for (j = 5; j < bits; j++) {
        int byte    = j/8;
        int bitmask = 1 << (7 - (j & 7));

        aux[byte] ^= bitmask; // Flip j-th bit

        if (0 == modesChecksum(aux, bits)) {
            // The error is fixed. Overwrite the original buffer with the 
            // corrected sequence, and returns the error bit position
            msg[byte] = aux[byte];
            return (j);
        }

        aux[byte] ^= bitmask; // Flip j-th bit back again
    }
    return (-1);
}
*/
//=========================================================================
//
// Similar to fixSingleBitErrors() but try every possible two bit combination.
// This is very slow and should be tried only against DF17 messages that
// don't pass the checksum, and only in Aggressive Mode.
/*
int fixTwoBitsErrors(unsigned char *msg, int bits) {
    int j, i;
    unsigned char aux[MODES_LONG_MSG_BYTES];

    memcpy(aux, msg, bits/8);

    // Do not attempt to error correct Bits 0-4. These contain the DF, and must
    // be correct because we can only error correct DF17
    for (j = 5; j < bits; j++) {
        int byte1    = j/8;
        int bitmask1 = 1 << (7 - (j & 7));
        aux[byte1] ^= bitmask1; // Flip j-th bit

        // Don't check the same pairs multiple times, so i starts from j+1
        for (i = j+1; i < bits; i++) {
            int byte2    = i/8;
            int bitmask2 = 1 << (7 - (i & 7));

            aux[byte2] ^= bitmask2; // Flip i-th bit

            if (0 == modesChecksum(aux, bits)) {
                // The error is fixed. Overwrite the original buffer with
                // the corrected sequence, and returns the error bit position
                msg[byte1] = aux[byte1];
                msg[byte2] = aux[byte2];

                // We return the two bits as a 16 bit integer by shifting
                // 'i' on the left. This is possible since 'i' will always
                // be non-zero because i starts from j+1
                return (j | (i << 8));

            aux[byte2] ^= bitmask2; // Flip i-th bit back
            }

        aux[byte1] ^= bitmask1; // Flip j-th bit back
        }
    }
    return (-1);
}
*/
//
//=========================================================================
//
// Code for introducing a less CPU-intensive method of correcting
// single bit errors.
//
// Makes use of the fact that the crc checksum is linear with respect to
// the bitwise xor operation, i.e.
//      crc(m^e) = (crc(m)^crc(e)
// where m and e are the message resp. error bit vectors.
//
// Call crc(e) the syndrome.
//
// The code below works by precomputing a table of (crc(e), e) for all
// possible error vectors e (here only single bit and double bit errors),
// search for the syndrome in the table, and correct the then known error.
// The error vector e is represented by one or two bit positions that are
// changed. If a second bit position is not used, it is -1.
//
// Run-time is binary search in a sorted table, plus some constant overhead,
// instead of running through all possible bit positions (resp. pairs of
// bit positions).
//
struct errorinfo {
    uint32_t syndrome;                 // CRC syndrome
    int      bits;                     // Number of bit positions to fix
    int      pos[MODES_MAX_BITERRORS]; // Bit positions corrected by this syndrome
};

#define NERRORINFO \
        (MODES_LONG_MSG_BITS+MODES_LONG_MSG_BITS*(MODES_LONG_MSG_BITS-1)/2)
struct errorinfo bitErrorTable[NERRORINFO];

// Compare function as needed for stdlib's qsort and bsearch functions
int cmpErrorInfo(const void *p0, const void *p1) {
    struct errorinfo *e0 = (struct errorinfo*)p0;
    struct errorinfo *e1 = (struct errorinfo*)p1;
    if (e0->syndrome == e1->syndrome) {
        return 0;
    } else if (e0->syndrome < e1->syndrome) {
        return -1;
    } else {
        return 1;
    }
}
//
//=========================================================================
//
// Compute the table of all syndromes for 1-bit and 2-bit error vectors
void modesInitErrorInfo() {
    unsigned char msg[MODES_LONG_MSG_BYTES];
    int i, j, n;
    uint32_t crc;
    n = 0;
    memset(bitErrorTable, 0, sizeof(bitErrorTable));
    memset(msg, 0, MODES_LONG_MSG_BYTES);
    // Add all possible single and double bit errors
    // don't include errors in first 5 bits (DF type)
    for (i = 5;  i < MODES_LONG_MSG_BITS;  i++) {
        int bytepos0 = (i >> 3);
        int mask0 = 1 << (7 - (i & 7));
        msg[bytepos0] ^= mask0;          // create error0
        crc = modesChecksum(msg, MODES_LONG_MSG_BITS);
        bitErrorTable[n].syndrome = crc;      // single bit error case
        bitErrorTable[n].bits = 1;
        bitErrorTable[n].pos[0] = i;
        bitErrorTable[n].pos[1] = -1;
        n += 1;

        if (Modes.nfix_crc > 1) {
            for (j = i+1;  j < MODES_LONG_MSG_BITS;  j++) {
                int bytepos1 = (j >> 3);
                int mask1 = 1 << (7 - (j & 7));
                msg[bytepos1] ^= mask1;  // create error1
                crc = modesChecksum(msg, MODES_LONG_MSG_BITS);
                if (n >= NERRORINFO) {
                    //fprintf(stderr, "Internal error, too many entries, fix NERRORINFO\n");
                    break;
                }
                bitErrorTable[n].syndrome = crc; // two bit error case
                bitErrorTable[n].bits = 2;
                bitErrorTable[n].pos[0] = i;
                bitErrorTable[n].pos[1] = j;
                n += 1;
                msg[bytepos1] ^= mask1;  // revert error1
            }
        }
        msg[bytepos0] ^= mask0;          // revert error0
    }
    qsort(bitErrorTable, NERRORINFO, sizeof(struct errorinfo), cmpErrorInfo);

    // Test code: report if any syndrome appears at least twice. In this
    // case the correction cannot be done without ambiguity.
    // Tried it, does not happen for 1- and 2-bit errors. 
    /*
    for (i = 1;  i < NERRORINFO;  i++) {
        if (bitErrorTable[i-1].syndrome == bitErrorTable[i].syndrome) {
            fprintf(stderr, "modesInitErrorInfo: Collision for syndrome %06x\n",
                            (int)bitErrorTable[i].syndrome);
        }
    }

    for (i = 0;  i < NERRORINFO;  i++) {
        printf("syndrome %06x    bit0 %3d    bit1 %3d\n",
               bitErrorTable[i].syndrome,
               bitErrorTable[i].pos0, bitErrorTable[i].pos1);
    }
    */
}
//
//=========================================================================
//
// Search for syndrome in table and if an entry is found, flip the necessary
// bits. Make sure the indices fit into the array
// Additional parameter: fix only less than maxcorrected bits, and record
// fixed bit positions in corrected[]. This array can be NULL, otherwise
// must be of length at least maxcorrected.
// Return number of fixed bits.
//
int fixBitErrors(unsigned char *msg, int bits, int maxfix, char *fixedbits) {
    struct errorinfo *pei;
    struct errorinfo ei;
    int bitpos, offset, res, i;
    memset(&ei, 0, sizeof(struct errorinfo));
    ei.syndrome = modesChecksum(msg, bits);
    pei = bsearch(&ei, bitErrorTable, NERRORINFO,
                  sizeof(struct errorinfo), cmpErrorInfo);
    if (pei == NULL) {
        return 0; // No syndrome found
    }

    // Check if the syndrome fixes more bits than we allow
    if (maxfix < pei->bits) {
        return 0;
    }

    // Check that all bit positions lie inside the message length
    offset = MODES_LONG_MSG_BITS-bits;
    for (i = 0;  i < pei->bits;  i++) {
            bitpos = pei->pos[i] - offset;
            if ((bitpos < 0) || (bitpos >= bits)) {
                    return 0;
            }
    }

    // Fix the bits
    for (i = res = 0;  i < pei->bits;  i++) {
            bitpos = pei->pos[i] - offset;
            msg[bitpos >> 3] ^= (1 << (7 - (bitpos & 7)));
            if (fixedbits) {
                    fixedbits[res++] = bitpos;
            }
    }
    return res;
}
//
// ============================== Debugging =================================
//
// Helper function for dumpMagnitudeVector().
// It prints a single bar used to display raw signals.
//
// Since every magnitude sample is between 0-255, the function uses
// up to 63 characters for every bar. Every character represents
// a length of 4, 3, 2, 1, specifically:
//
// "O" is 4
// "o" is 3
// "-" is 2
// "." is 1
//
void dumpMagnitudeBar(int index, int magnitude) {
    char *set = " .-o";
    char buf[256];
    int div = magnitude / 256 / 4;
    int rem = magnitude / 256 % 4;

    memset(buf,'O',div);
    buf[div] = set[rem];
    buf[div+1] = '\0';

    if (index >= 0)
        printf("[%.3d] |%-66s 0x%04X\n", index, buf, magnitude);
    else
        printf("[%.2d] |%-66s 0x%04X\n", index, buf, magnitude);
}
//
//=========================================================================
//
// Display an ASCII-art alike graphical representation of the undecoded
// message as a magnitude signal.
//
// The message starts at the specified offset in the "m" buffer.
// The function will display enough data to cover a short 56 bit message.
//
// If possible a few samples before the start of the messsage are included
// for context.
//
void dumpMagnitudeVector(uint16_t *m, uint32_t offset) {
    uint32_t padding = 5; // Show a few samples before the actual start.
    uint32_t start = (offset < padding) ? 0 : offset-padding;
    uint32_t end = offset + (MODES_PREAMBLE_SAMPLES)+(MODES_SHORT_MSG_SAMPLES) - 1;
    uint32_t j;

    for (j = start; j <= end; j++) {
        dumpMagnitudeBar(j-offset, m[j]);
    }
}
//
//=========================================================================
//
// Produce a raw representation of the message as a Javascript file
// loadable by debug.html.
//
void dumpRawMessageJS(char *descr, unsigned char *msg,
                      uint16_t *m, uint32_t offset, int fixable, char *bitpos)
{
    int padding = 5; // Show a few samples before the actual start.
    int start = offset - padding;
    int end = offset + (MODES_PREAMBLE_SAMPLES)+(MODES_LONG_MSG_SAMPLES) - 1;
    FILE *fp;
    int j;

    MODES_NOTUSED(fixable);
    if ((fp = fopen("frames.js","a")) == NULL) {
        fprintf(stderr, "Error opening frames.js: %s\n", strerror(errno));
        exit(1);
    }

    fprintf(fp,"frames.push({\"descr\": \"%s\", \"mag\": [", descr);
    for (j = start; j <= end; j++) {
        fprintf(fp,"%d", j < 0 ? 0 : m[j]);
        if (j != end) fprintf(fp,",");
    }
    fprintf(fp,"], \"fix1\": %d, \"fix2\": %d, \"bits\": %d, \"hex\": \"",
            bitpos[0], bitpos[1] , modesMessageLenByType(msg[0]>>3));
    for (j = 0; j < MODES_LONG_MSG_BYTES; j++)
        fprintf(fp,"\\x%02x",msg[j]);
    fprintf(fp,"\"});\n");
    fclose(fp);
}
//
//=========================================================================
//
// This is a wrapper for dumpMagnitudeVector() that also show the message
// in hex format with an additional description.
//
// descr  is the additional message to show to describe the dump.
// msg    points to the decoded message
// m      is the original magnitude vector
// offset is the offset where the message starts
//
// The function also produces the Javascript file used by debug.html to
// display packets in a graphical format if the Javascript output was
// enabled.
//
void dumpRawMessage(char *descr, unsigned char *msg, uint16_t *m, uint32_t offset) {
    int  j;
    int  msgtype = msg[0] >> 3;
    int  fixable = 0;
    char bitpos[MODES_MAX_BITERRORS];

    for (j = 0;  j < MODES_MAX_BITERRORS;  j++) {
        bitpos[j] = -1;
    }
    if (msgtype == 17) {
        fixable = fixBitErrors(msg, MODES_LONG_MSG_BITS, MODES_MAX_BITERRORS, bitpos);
    }

    if (Modes.debug & MODES_DEBUG_JS) {
        dumpRawMessageJS(descr, msg, m, offset, fixable, bitpos);
        return;
    }

    printf("\n--- %s\n    ", descr);
    for (j = 0; j < MODES_LONG_MSG_BYTES; j++) {
        printf("%02x",msg[j]);
        if (j == MODES_SHORT_MSG_BYTES-1) printf(" ... ");
    }
    printf(" (DF %d, Fixable: %d)\n", msgtype, fixable);
    dumpMagnitudeVector(m,offset);
    printf("---\n\n");
}
//
//=========================================================================
//
// Code for testing the timing: run all possible 1- and 2-bit error 
// the test message by all 1-bit errors. Run the old code against
// all of them, and new the code.
//
// Example measurements:
// Timing old vs. new crc correction code:
//    Old code: 1-bit errors on 112 msgs: 3934 usecs
//    New code: 1-bit errors on 112 msgs: 104 usecs
//    Old code: 2-bit errors on 6216 msgs: 407743 usecs
//    New code: 2-bit errors on 6216 msgs: 5176 usecs
// indicating a 37-fold resp. 78-fold improvement in speed for 1-bit resp.
// 2-bit error.
/*
unsigned char tmsg0[MODES_LONG_MSG_BYTES] = {
        // Test data: first ADS-B message from testfiles/modes1.bin
        0x8f, 0x4d, 0x20, 0x23, 0x58, 0x7f, 0x34, 0x5e,
        0x35, 0x83, 0x7e, 0x22, 0x18, 0xb2
};
#define NTWOBITS (MODES_LONG_MSG_BITS*(MODES_LONG_MSG_BITS-1)/2)
unsigned char tmsg1[MODES_LONG_MSG_BITS][MODES_LONG_MSG_BYTES];
unsigned char tmsg2[NTWOBITS][MODES_LONG_MSG_BYTES];
// Init an array of cloned messages with all possible 1-bit errors present,
// applied to each message at the respective position
//
void inittmsg1() {
        int i, bytepos, mask;
        for (i = 0;  i < MODES_LONG_MSG_BITS;  i++) {
                bytepos = i >> 3;
                mask = 1 << (7 - (i & 7));
                memcpy(&tmsg1[i][0], tmsg0, MODES_LONG_MSG_BYTES);
                tmsg1[i][bytepos] ^= mask;
        }
}

// Run sanity check on all but first 5 messages / bits, as those bits
// are not corrected.
//
void checktmsg1(FILE *out) {
        int i, k;
        uint32_t crc;
        for (i = 5;  i < MODES_LONG_MSG_BITS;  i++) {
                crc = modesChecksum(&tmsg1[i][0], MODES_LONG_MSG_BITS);
                if (crc != 0) {
                        fprintf(out, "CRC not fixed for "
                                "positon %d\n", i);
                        fprintf(out, "  MSG ");
                        for (k = 0;  k < MODES_LONG_MSG_BYTES;  k++) {
                                fprintf(out, "%02x", tmsg1[i][k]);
                        }
                        fprintf(out, "\n");
                }
        }
}

void inittmsg2() {
        int i, j, n, bytepos0, bytepos1, mask0, mask1;
        n = 0;
        for (i = 0;  i < MODES_LONG_MSG_BITS;  i++) {
                bytepos0 = i >> 3;
                mask0 = 1 << (7 - (i & 7));
                for (j = i+1;  j < MODES_LONG_MSG_BITS;  j++) {
                        bytepos1 = j >> 3;
                        mask1 = 1 << (7 - (j & 7));
                        memcpy(&tmsg2[n][0], tmsg0, MODES_LONG_MSG_BYTES);
                        tmsg2[n][bytepos0] ^= mask0;
                        tmsg2[n][bytepos1] ^= mask1;
                        n += 1;
                }
        }
}

long difftvusec(struct timeval *t0, struct timeval *t1) {
        long res = 0;
        res = t1->tv_usec-t0->tv_usec;
        res += (t1->tv_sec-t0->tv_sec)*1000000L;
        return res;
}

// the actual test code
void testAndTimeBitCorrection() {
        struct timeval starttv, endtv;
        int i;
        // Run timing on 1-bit errors
        printf("Timing old vs. new crc correction code:\n");
        inittmsg1();
        gettimeofday(&starttv, NULL);
        for (i = 0;  i < MODES_LONG_MSG_BITS;  i++) {
            fixSingleBitErrors(&tmsg1[i][0], MODES_LONG_MSG_BITS);
        }
        gettimeofday(&endtv, NULL);
        printf("   Old code: 1-bit errors on %d msgs: %ld usecs\n",
               MODES_LONG_MSG_BITS, difftvusec(&starttv, &endtv));
        checktmsg1(stdout);
        // Re-init
        inittmsg1();
        gettimeofday(&starttv, NULL);
        for (i = 0;  i < MODES_LONG_MSG_BITS;  i++) {
            fixBitErrors(&tmsg1[i][0], MODES_LONG_MSG_BITS, MODES_MAX_BITERRORS, NULL);
        }
        gettimeofday(&endtv, NULL);
        printf("   New code: 1-bit errors on %d msgs: %ld usecs\n",
               MODES_LONG_MSG_BITS, difftvusec(&starttv, &endtv));
        checktmsg1(stdout);
        // Run timing on 2-bit errors
        inittmsg2();
        gettimeofday(&starttv, NULL);
        for (i = 0;  i < NTWOBITS;  i++) {
            fixSingleBitErrors(&tmsg2[i][0], MODES_LONG_MSG_BITS);
        }
        gettimeofday(&endtv, NULL);
        printf("   Old code: 2-bit errors on %d msgs: %ld usecs\n",
               NTWOBITS, difftvusec(&starttv, &endtv));
        // Re-init
        inittmsg2();
        gettimeofday(&starttv, NULL);
        for (i = 0;  i < NTWOBITS;  i++) {
            fixBitErrors(&tmsg2[i][0], MODES_LONG_MSG_BITS, MODES_MAX_BITERRORS, NULL);
        }
        gettimeofday(&endtv, NULL);
        printf("   New code: 2-bit errors on %d msgs: %ld usecs\n",
               NTWOBITS, difftvusec(&starttv, &endtv));
}
*/
//=========================================================================
//
// Hash the ICAO address to index our cache of MODES_ICAO_CACHE_LEN
// elements, that is assumed to be a power of two
//
uint32_t ICAOCacheHashAddress(uint32_t a) {
    // The following three rounds wil make sure that every bit affects
    // every output bit with ~ 50% of probability.
    a = ((a >> 16) ^ a) * 0x45d9f3b;
    a = ((a >> 16) ^ a) * 0x45d9f3b;
    a = ((a >> 16) ^ a);
    return a & (MODES_ICAO_CACHE_LEN-1);
}
//
//=========================================================================
//
// Add the specified entry to the cache of recently seen ICAO addresses.
// Note that we also add a timestamp so that we can make sure that the
// entry is only valid for MODES_ICAO_CACHE_TTL seconds.
//
void addRecentlySeenICAOAddr(uint32_t addr) {
    uint32_t h = ICAOCacheHashAddress(addr);
    Modes.icao_cache[h*2] = addr;
    Modes.icao_cache[h*2+1] = (uint32_t) time(NULL);
}
//
//=========================================================================
//
// Returns 1 if the specified ICAO address was seen in a DF format with
// proper checksum (not xored with address) no more than * MODES_ICAO_CACHE_TTL
// seconds ago. Otherwise returns 0.
//
int ICAOAddressWasRecentlySeen(uint32_t addr) {
    uint32_t h = ICAOCacheHashAddress(addr);
    uint32_t a = Modes.icao_cache[h*2];
    uint32_t t = Modes.icao_cache[h*2+1];
    uint64_t tn = time(NULL);

    return ( (a) && (a == addr) && ( (tn - t) <= MODES_ICAO_CACHE_TTL) );
}
//
//=========================================================================
//
// In the squawk (identity) field bits are interleaved as follows in
// (message bit 20 to bit 32):
//
// C1-A1-C2-A2-C4-A4-ZERO-B1-D1-B2-D2-B4-D4
//
// So every group of three bits A, B, C, D represent an integer from 0 to 7.
//
// The actual meaning is just 4 octal numbers, but we convert it into a hex 
// number tha happens to represent the four octal numbers.
//
// For more info: http://en.wikipedia.org/wiki/Gillham_code
//
int decodeID13Field(int ID13Field) {
    int hexGillham = 0;

    if (ID13Field & 0x1000) {hexGillham |= 0x0010;} // Bit 12 = C1
    if (ID13Field & 0x0800) {hexGillham |= 0x1000;} // Bit 11 = A1
    if (ID13Field & 0x0400) {hexGillham |= 0x0020;} // Bit 10 = C2
    if (ID13Field & 0x0200) {hexGillham |= 0x2000;} // Bit  9 = A2
    if (ID13Field & 0x0100) {hexGillham |= 0x0040;} // Bit  8 = C4
    if (ID13Field & 0x0080) {hexGillham |= 0x4000;} // Bit  7 = A4
  //if (ID13Field & 0x0040) {hexGillham |= 0x0800;} // Bit  6 = X  or M 
    if (ID13Field & 0x0020) {hexGillham |= 0x0100;} // Bit  5 = B1 
    if (ID13Field & 0x0010) {hexGillham |= 0x0001;} // Bit  4 = D1 or Q
    if (ID13Field & 0x0008) {hexGillham |= 0x0200;} // Bit  3 = B2
    if (ID13Field & 0x0004) {hexGillham |= 0x0002;} // Bit  2 = D2
    if (ID13Field & 0x0002) {hexGillham |= 0x0400;} // Bit  1 = B4
    if (ID13Field & 0x0001) {hexGillham |= 0x0004;} // Bit  0 = D4

    return (hexGillham);
    }
//
//=========================================================================
//
// Decode the 13 bit AC altitude field (in DF 20 and others).
// Returns the altitude, and set 'unit' to either MODES_UNIT_METERS or MDOES_UNIT_FEETS.
//
int decodeAC13Field(int AC13Field, int *unit) {
    int m_bit  = AC13Field & 0x0040; // set = meters, clear = feet
    int q_bit  = AC13Field & 0x0010; // set = 25 ft encoding, clear = Gillham Mode C encoding

    if (!m_bit) {
        *unit = MODES_UNIT_FEET;
        if (q_bit) {
            // N is the 11 bit integer resulting from the removal of bit Q and M
            int n = ((AC13Field & 0x1F80) >> 2) |
                    ((AC13Field & 0x0020) >> 1) |
                     (AC13Field & 0x000F);
            // The final altitude is resulting number multiplied by 25, minus 1000.
            return ((n * 25) - 1000);
        } else {
            // N is an 11 bit Gillham coded altitude
            int n = ModeAToModeC(decodeID13Field(AC13Field));
            if (n < -12) {n = 0;}

            return (100 * n);
        }
    } else {
        *unit = MODES_UNIT_METERS;
        // TODO: Implement altitude when meter unit is selected
    }
    return 0;
}
//
//=========================================================================
//
// Decode the 12 bit AC altitude field (in DF 17 and others).
//
int decodeAC12Field(int AC12Field, int *unit) {
    int q_bit  = AC12Field & 0x10; // Bit 48 = Q

    *unit = MODES_UNIT_FEET;
    if (q_bit) {
        int n = ((AC12Field & 0x0FE0) >> 1) | 
                 (AC12Field & 0x000F);
        // The final altitude is the resulting number multiplied by 25, minus 1000.
        return ((n * 25) - 1000);
    } else {
        // Make N a 13 bit Gillham coded altitude by inserting M=0 at bit 6
        int n = ((AC12Field & 0x0FC0) << 1) | 
                 (AC12Field & 0x003F);
        n = ModeAToModeC(decodeID13Field(n));
        if (n < -12) {n = 0;}

        return (100 * n);
    }
}
//
//=========================================================================
//
// Decode the 7 bit ground movement field PWL exponential style scale
//
int decodeMovementField(int movement) {
    int gspeed;

    // Note : movement codes 0,125,126,127 are all invalid, but they are 
    //        trapped for before this function is called.

    if      (movement  > 123) gspeed = 199; // > 175kt
    else if (movement  > 108) gspeed = ((movement - 108)  * 5) + 100;
    else if (movement  >  93) gspeed = ((movement -  93)  * 2) +  70;
    else if (movement  >  38) gspeed = ((movement -  38)     ) +  15;
    else if (movement  >  12) gspeed = ((movement -  11) >> 1) +   2;
    else if (movement  >   8) gspeed = ((movement -   6) >> 2) +   1;
    else                      gspeed = 0;

    return (gspeed);
}
//
//=========================================================================
//
// Capability table
char *ca_str[8] = {
    /* 0 */ "Level 1 (Survillance Only)",
    /* 1 */ "Level 2 (DF0,4,5,11)",
    /* 2 */ "Level 3 (DF0,4,5,11,20,21)",
    /* 3 */ "Level 4 (DF0,4,5,11,20,21,24)",
    /* 4 */ "Level 2+3+4 (DF0,4,5,11,20,21,24,code7 - is on ground)",
    /* 5 */ "Level 2+3+4 (DF0,4,5,11,20,21,24,code7 - is airborne)",
    /* 6 */ "Level 2+3+4 (DF0,4,5,11,20,21,24,code7)",
    /* 7 */ "Level 7 ???"
};

// DF 18 Control field table.
char *cf_str[8] = {
    /* 0 */ "ADS-B ES/NT device with ICAO 24-bit address",
    /* 1 */ "ADS-B ES/NT device with other address",
    /* 2 */ "Fine format TIS-B",
    /* 3 */ "Coarse format TIS-B",
    /* 4 */ "TIS-B managment message",
    /* 5 */ "TIS-B relay of ADS-B message with other address",
    /* 6 */ "ADS-B rebroadcast using DF-17 message format",
    /* 7 */ "Reserved"
};

// Flight status table
char *fs_str[8] = {
    /* 0 */ "Normal, Airborne",
    /* 1 */ "Normal, On the ground",
    /* 2 */ "ALERT,  Airborne",
    /* 3 */ "ALERT,  On the ground",
    /* 4 */ "ALERT & Special Position Identification. Airborne or Ground",
    /* 5 */ "Special Position Identification. Airborne or Ground",
    /* 6 */ "Value 6 is not assigned",
    /* 7 */ "Value 7 is not assigned"
};
//
//=========================================================================
//
char *getMEDescription(int metype, int mesub) {
    char *mename = "Unknown";

    if (metype >= 1 && metype <= 4)
        mename = "Aircraft Identification and Category";
    else if (metype >= 5 && metype <= 8)
        mename = "Surface Position";
    else if (metype >= 9 && metype <= 18)
        mename = "Airborne Position (Baro Altitude)";
    else if (metype == 19 && mesub >=1 && mesub <= 4)
        mename = "Airborne Velocity";
    else if (metype >= 20 && metype <= 22)
        mename = "Airborne Position (GNSS Height)";
    else if (metype == 23 && mesub == 0)
        mename = "Test Message";
    else if (metype == 24 && mesub == 1)
        mename = "Surface System Status";
    else if (metype == 28 && mesub == 1)
        mename = "Extended Squitter Aircraft Status (Emergency)";
    else if (metype == 28 && mesub == 2)
        mename = "Extended Squitter Aircraft Status (1090ES TCAS RA)";
    else if (metype == 29 && (mesub == 0 || mesub == 1))
        mename = "Target State and Status Message";
    else if (metype == 31 && (mesub == 0 || mesub == 1))
        mename = "Aircraft Operational Status Message";
    return mename;
}
//
//=========================================================================
//
// Decode a raw Mode S message demodulated as a stream of bytes by detectModeS(), 
// and split it into fields populating a modesMessage structure.
//
void decodeModesMessage(struct modesMessage *mm, unsigned char *msg) {
    char *ais_charset = "?ABCDEFGHIJKLMNOPQRSTUVWXYZ????? ???????????????0123456789??????";

    // Work on our local copy
    memcpy(mm->msg, msg, MODES_LONG_MSG_BYTES);
    msg = mm->msg;

    // Get the message type ASAP as other operations depend on this
    mm->msgtype         = msg[0] >> 3; // Downlink Format
    mm->msgbits         = modesMessageLenByType(mm->msgtype);
    mm->crc             = modesChecksum(msg, mm->msgbits);

    if ((mm->crc) && (Modes.nfix_crc) && ((mm->msgtype == 17) || (mm->msgtype == 18))) {
//  if ((mm->crc) && (Modes.nfix_crc) && ((mm->msgtype == 11) || (mm->msgtype == 17))) {
        //
        // Fixing single bit errors in DF-11 is a bit dodgy because we have no way to 
        // know for sure if the crc is supposed to be 0 or not - it could be any value 
        // less than 80. Therefore, attempting to fix DF-11 errors can result in a 
        // multitude of possible crc solutions, only one of which is correct.
        // 
        // We should probably perform some sanity checks on corrected DF-11's before 
        // using the results. Perhaps check the ICAO against known aircraft, and check
        // IID against known good IID's. That's a TODO.
        //
        mm->correctedbits = fixBitErrors(msg, mm->msgbits, Modes.nfix_crc, mm->corrected);

        // If we correct, validate ICAO addr to help filter birthday paradox solutions.
        if (mm->correctedbits) {
            uint32_t ulAddr = (msg[1] << 16) | (msg[2] << 8) | (msg[3]); 
            if (!ICAOAddressWasRecentlySeen(ulAddr))
                mm->correctedbits = 0;
        }
    }
    //
    // Note that most of the other computation happens *after* we fix the 
    // single/two bit errors, otherwise we would need to recompute the fields again.
    //
    if (mm->msgtype == 11) { // DF 11
        mm->iid   =  mm->crc;
        mm->addr  = (msg[1] << 16) | (msg[2] << 8) | (msg[3]); 
        mm->ca    = (msg[0] & 0x07); // Responder capabilities

        if ((mm->crcok = (0 == mm->crc))) {
            // DF 11 : if crc == 0 try to populate our ICAO addresses whitelist.
            addRecentlySeenICAOAddr(mm->addr);
        } else if (mm->crc < 80) {
            mm->crcok = ICAOAddressWasRecentlySeen(mm->addr);
            if (mm->crcok) {
                addRecentlySeenICAOAddr(mm->addr);
            }
        }

    } else if (mm->msgtype == 17) { // DF 17
        mm->addr  = (msg[1] << 16) | (msg[2] << 8) | (msg[3]); 
        mm->ca    = (msg[0] & 0x07); // Responder capabilities

        if ((mm->crcok = (0 == mm->crc))) {
            // DF 17 : if crc == 0 try to populate our ICAO addresses whitelist.
            addRecentlySeenICAOAddr(mm->addr);
        }

    } else if (mm->msgtype == 18) { // DF 18
        mm->addr  = (msg[1] << 16) | (msg[2] << 8) | (msg[3]); 
        mm->ca    = (msg[0] & 0x07); // Control Field

        if ((mm->crcok = (0 == mm->crc))) {
            // DF 18 : if crc == 0 try to populate our ICAO addresses whitelist.
            addRecentlySeenICAOAddr(mm->addr);
        }

    } else { // All other DF's
        // Compare the checksum with the whitelist of recently seen ICAO 
        // addresses. If it matches one, then declare the message as valid
        mm->crcok = ICAOAddressWasRecentlySeen(mm->addr = mm->crc);
    }

    // Fields for DF0, DF16
    if (mm->msgtype == 0  || mm->msgtype == 16) {
        if (msg[0] & 0x04) {                       // VS Bit
            mm->bFlags |= MODES_ACFLAGS_AOG_VALID | MODES_ACFLAGS_AOG;
        } else {
            mm->bFlags |= MODES_ACFLAGS_AOG_VALID;
        }
    }

    // Fields for DF11, DF17
    if (mm->msgtype == 11 || mm->msgtype == 17) {
        if (mm->ca == 4) {
            mm->bFlags |= MODES_ACFLAGS_AOG_VALID | MODES_ACFLAGS_AOG;
        } else if (mm->ca == 5) {
            mm->bFlags |= MODES_ACFLAGS_AOG_VALID;
        }
    }
          
    // Fields for DF5, DF21 = Gillham encoded Squawk
    if (mm->msgtype == 5  || mm->msgtype == 21) {
        int ID13Field = ((msg[2] << 8) | msg[3]) & 0x1FFF; 
        if (ID13Field) {
            mm->bFlags |= MODES_ACFLAGS_SQUAWK_VALID;
            mm->modeA   = decodeID13Field(ID13Field);
        }
    }

    // Fields for DF0, DF4, DF16, DF20 13 bit altitude
    if (mm->msgtype == 0  || mm->msgtype == 4 ||
        mm->msgtype == 16 || mm->msgtype == 20) {
        int AC13Field = ((msg[2] << 8) | msg[3]) & 0x1FFF; 
        if (AC13Field) { // Only attempt to decode if a valid (non zero) altitude is present
            mm->bFlags  |= MODES_ACFLAGS_ALTITUDE_VALID;
            mm->altitude = decodeAC13Field(AC13Field, &mm->unit);
        }
    }

    // Fields for DF4, DF5, DF20, DF21
    if ((mm->msgtype == 4) || (mm->msgtype == 20) ||
        (mm->msgtype == 5) || (mm->msgtype == 21)) {
        mm->bFlags  |= MODES_ACFLAGS_FS_VALID;
        mm->fs       = msg[0]  & 7;               // Flight status for DF4,5,20,21
        if (mm->fs <= 3) {
            mm->bFlags |= MODES_ACFLAGS_AOG_VALID;
            if (mm->fs & 1)
                {mm->bFlags |= MODES_ACFLAGS_AOG;}
        }
    }

    // Fields for DF17, DF18_CF0, DF18_CF1, DF18_CF6 squitters
    if (  (mm->msgtype == 17) 
      || ((mm->msgtype == 18) && ((mm->ca == 0) || (mm->ca == 1) || (mm->ca == 6)) )) {
         int metype = mm->metype = msg[4] >> 3;   // Extended squitter message type
         int mesub  = mm->mesub  = msg[4]  & 7;   // Extended squitter message subtype

        // Decode the extended squitter message

        if (metype >= 1 && metype <= 4) { // Aircraft Identification and Category
            uint32_t chars;
            mm->bFlags |= MODES_ACFLAGS_CALLSIGN_VALID;

            chars = (msg[5] << 16) | (msg[6] << 8) | (msg[7]);
            mm->flight[3] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[2] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[1] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[0] = ais_charset[chars & 0x3F];

            chars = (msg[8] << 16) | (msg[9] << 8) | (msg[10]);
            mm->flight[7] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[6] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[5] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[4] = ais_charset[chars & 0x3F];

            mm->flight[8] = '\0';

        } else if (metype >= 5 && metype <= 18) { // Position Message
            mm->raw_latitude  = ((msg[6] & 3) << 15) | (msg[7] << 7) | (msg[8] >> 1);
            mm->raw_longitude = ((msg[8] & 1) << 16) | (msg[9] << 8) | (msg[10]);
            mm->bFlags       |= (mm->msg[6] & 0x04) ? MODES_ACFLAGS_LLODD_VALID 
                                                    : MODES_ACFLAGS_LLEVEN_VALID;
            if (metype >= 9) {        // Airborne
                int AC12Field = ((msg[5] << 4) | (msg[6] >> 4)) & 0x0FFF;
                mm->bFlags |= MODES_ACFLAGS_AOG_VALID;
                if (AC12Field) {// Only attempt to decode if a valid (non zero) altitude is present
                    mm->bFlags |= MODES_ACFLAGS_ALTITUDE_VALID;
                    mm->altitude = decodeAC12Field(AC12Field, &mm->unit);
                }
            } else {                      // Ground
                int movement = ((msg[4] << 4) | (msg[5] >> 4)) & 0x007F;
                mm->bFlags |= MODES_ACFLAGS_AOG_VALID | MODES_ACFLAGS_AOG;
                if ((movement) && (movement < 125)) {
                    mm->bFlags |= MODES_ACFLAGS_SPEED_VALID;
                    mm->velocity = decodeMovementField(movement);
                }

                if (msg[5] & 0x08) {
                    mm->bFlags |= MODES_ACFLAGS_HEADING_VALID;
                    mm->heading = ((((msg[5] << 4) | (msg[6] >> 4)) & 0x007F) * 45) >> 4;
                }
            }

        } else if (metype == 19) { // Airborne Velocity Message

           // Presumably airborne if we get an Airborne Velocity Message
            mm->bFlags |= MODES_ACFLAGS_AOG_VALID; 

            if ( (mesub >= 1) && (mesub <= 4) ) {
                int vert_rate = ((msg[8] & 0x07) << 6) | (msg[9] >> 2);
                if (vert_rate) {
                    --vert_rate;
                    if (msg[8] & 0x08) 
                      {vert_rate = 0 - vert_rate;}
                    mm->vert_rate =  vert_rate * 64;
                    mm->bFlags   |= MODES_ACFLAGS_VERTRATE_VALID;
                }
            }

            if ((mesub == 1) || (mesub == 2)) {
                int ew_raw = ((msg[5] & 0x03) << 8) |  msg[6];
                int ew_vel = ew_raw - 1;
                int ns_raw = ((msg[7] & 0x7F) << 3) | (msg[8] >> 5);
                int ns_vel = ns_raw - 1;

                if (mesub == 2) { // If (supersonic) unit is 4 kts
                   ns_vel = ns_vel << 2;
                   ew_vel = ew_vel << 2;
                }

                if (ew_raw) { // Do East/West  
                    mm->bFlags |= MODES_ACFLAGS_EWSPEED_VALID;
                    if (msg[5] & 0x04)
                        {ew_vel = 0 - ew_vel;}                   
                    mm->ew_velocity = ew_vel;
                }

                if (ns_raw) { // Do North/South
                    mm->bFlags |= MODES_ACFLAGS_NSSPEED_VALID;
                    if (msg[7] & 0x80)
                        {ns_vel = 0 - ns_vel;}                   
                    mm->ns_velocity = ns_vel;
                }

                if (ew_raw && ns_raw) {
                    // Compute velocity and angle from the two speed components
                    mm->bFlags |= (MODES_ACFLAGS_SPEED_VALID | MODES_ACFLAGS_HEADING_VALID | MODES_ACFLAGS_NSEWSPD_VALID);
                    mm->velocity = (int) sqrt((ns_vel * ns_vel) + (ew_vel * ew_vel));

                    if (mm->velocity) {
                        mm->heading = (int) (atan2(ew_vel, ns_vel) * 180.0 / M_PI);
                        // We don't want negative values but a 0-360 scale
                        if (mm->heading < 0) mm->heading += 360;
                    }
                }

            } else if (mesub == 3 || mesub == 4) {
                int airspeed = ((msg[7] & 0x7f) << 3) | (msg[8] >> 5);
                if (airspeed) {
                    mm->bFlags |= MODES_ACFLAGS_SPEED_VALID;
                    --airspeed;
                    if (mesub == 4)  // If (supersonic) unit is 4 kts
                        {airspeed = airspeed << 2;}
                    mm->velocity =  airspeed;
                }

                if (msg[5] & 0x04) {
                    mm->bFlags |= MODES_ACFLAGS_HEADING_VALID;
                    mm->heading = ((((msg[5] & 0x03) << 8) | msg[6]) * 45) >> 7;
                }
            }
        }
    }

    // Fields for DF20, DF21 Comm-B
    if ((mm->msgtype == 20) || (mm->msgtype == 21)){

        if (msg[4] == 0x20) { // Aircraft Identification
            uint32_t chars;
            mm->bFlags |= MODES_ACFLAGS_CALLSIGN_VALID;

            chars = (msg[5] << 16) | (msg[6] << 8) | (msg[7]);
            mm->flight[3] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[2] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[1] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[0] = ais_charset[chars & 0x3F];

            chars = (msg[8] << 16) | (msg[9] << 8) | (msg[10]);
            mm->flight[7] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[6] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[5] = ais_charset[chars & 0x3F]; chars = chars >> 6;
            mm->flight[4] = ais_charset[chars & 0x3F];

            mm->flight[8] = '\0';
        } else {
        }
    }
}
//
//=========================================================================
//
// This function gets a decoded Mode S Message and prints it on the screen
// in a human readable format.
//
void displayModesMessage(struct modesMessage *mm) {
    int j;
    unsigned char * pTimeStamp;

    // Handle only addresses mode first.
    if (Modes.onlyaddr) {
        printf("%06x\n", mm->addr);
        return;         // Enough for --onlyaddr mode
    }

    // output data for AERA
    if (Modes.aera) {
        aera(mm);
//         return;         // Logfile of --aera and --aera-net modes contains not all information. Still write out raw data.
    }

    if (Modes.print_timestamp) {
        printf("%llu ", mstime()); // Print the current timestamp
    }

    // Show the raw message.
    if (Modes.mlat && mm->timestampMsg) {
        printf("@");
        pTimeStamp = (unsigned char *) &mm->timestampMsg;
        for (j=5; j>=0;j--) {
            printf("%02X",pTimeStamp[j]);
        } 
    } else
        printf("*");

    for (j = 0; j < mm->msgbits/8; j++) printf("%02x", mm->msg[j]);
    printf(";\n");

    if (Modes.raw) {
        fflush(stdout); // Provide data to the reader ASAP
        return;         // Enough for --raw and --raw-with-timestamp modes
    }

    if (mm->msgtype < 32)
        printf("CRC: %06x (%s)\n", (int)mm->crc, mm->crcok ? "ok" : "wrong");

    if (mm->correctedbits != 0)
        printf("No. of bit errors fixed: %d\n", mm->correctedbits);

    if (mm->msgtype == 0) { // DF 0
        printf("DF 0: Short Air-Air Surveillance.\n");
        printf("  VS             : %s\n",  (mm->msg[0] & 0x04) ? "Ground" : "Airborne");
        printf("  CC             : %d\n", ((mm->msg[0] & 0x02) >> 1));
        printf("  SL             : %d\n", ((mm->msg[1] & 0xE0) >> 5));
        printf("  Altitude       : %d %s\n", mm->altitude,
            (mm->unit == MODES_UNIT_METERS) ? "meters" : "feet");
        printf("  ICAO Address   : %06x\n", mm->addr);

    } else if (mm->msgtype == 4 || mm->msgtype == 20) {
        printf("DF %d: %s, Altitude Reply.\n", mm->msgtype,
            (mm->msgtype == 4) ? "Surveillance" : "Comm-B");
        printf("  Flight Status  : %s\n", fs_str[mm->fs]);
        printf("  DR             : %d\n", ((mm->msg[1] >> 3) & 0x1F));
        printf("  UM             : %d\n", (((mm->msg[1]  & 7) << 3) | (mm->msg[2] >> 5)));
        printf("  Altitude       : %d %s\n", mm->altitude,
            (mm->unit == MODES_UNIT_METERS) ? "meters" : "feet");
        printf("  ICAO Address   : %06x\n", mm->addr);

        if (mm->msgtype == 20) {
            printf("  Comm-B BDS     : %x\n", mm->msg[4]);

            // Decode the extended squitter message
            if        ( mm->msg[4]       == 0x20) { // BDS 2,0 Aircraft identification
                printf("    BDS 2,0 Aircraft Identification : %s\n", mm->flight);
/*
            } else if ( mm->msg[4]       == 0x10) { // BDS 1,0 Datalink Capability report
                printf("    BDS 1,0 Datalink Capability report\n");

            } else if ( mm->msg[4]       == 0x30) { // BDS 3,0 ACAS Active Resolution Advisory
                printf("    BDS 3,0 ACAS Active Resolution Advisory\n");

            } else if ((mm->msg[4] >> 3) ==   28) { // BDS 6,1 Extended Squitter Emergecy/Priority Status
                printf("    BDS 6,1 Emergecy/Priority Status\n");

            } else if ((mm->msg[4] >> 3) ==   29) { // BDS 6,2 Target State and Status
                printf("    BDS 6,2 Target State and Status\n");

            } else if ((mm->msg[4] >> 3) ==   31) { // BDS 6,5 Extended Squitter Aircraft Operational Status
                printf("    BDS 6,5 Aircraft Operational Status\n");
*/
            }        
        }

    } else if (mm->msgtype == 5 || mm->msgtype == 21) {
        printf("DF %d: %s, Identity Reply.\n", mm->msgtype,
            (mm->msgtype == 5) ? "Surveillance" : "Comm-B");
        printf("  Flight Status  : %s\n", fs_str[mm->fs]);
        printf("  DR             : %d\n", ((mm->msg[1] >> 3) & 0x1F));
        printf("  UM             : %d\n", (((mm->msg[1]  & 7) << 3) | (mm->msg[2] >> 5)));
        printf("  Squawk         : %x\n", mm->modeA);
        printf("  ICAO Address   : %06x\n", mm->addr);

        if (mm->msgtype == 21) {
            printf("  Comm-B BDS     : %x\n", mm->msg[4]);

            // Decode the extended squitter message
            if        ( mm->msg[4]       == 0x20) { // BDS 2,0 Aircraft identification
                printf("    BDS 2,0 Aircraft Identification : %s\n", mm->flight);
/*
            } else if ( mm->msg[4]       == 0x10) { // BDS 1,0 Datalink Capability report
                printf("    BDS 1,0 Datalink Capability report\n");

            } else if ( mm->msg[4]       == 0x30) { // BDS 3,0 ACAS Active Resolution Advisory
                printf("    BDS 3,0 ACAS Active Resolution Advisory\n");

            } else if ((mm->msg[4] >> 3) ==   28) { // BDS 6,1 Extended Squitter Emergecy/Priority Status
                printf("    BDS 6,1 Emergecy/Priority Status\n");

            } else if ((mm->msg[4] >> 3) ==   29) { // BDS 6,2 Target State and Status
                printf("    BDS 6,2 Target State and Status\n");

            } else if ((mm->msg[4] >> 3) ==   31) { // BDS 6,5 Extended Squitter Aircraft Operational Status
                printf("    BDS 6,5 Aircraft Operational Status\n");
*/
            }        
        }

    } else if (mm->msgtype == 11) { // DF 11
        printf("DF 11: All Call Reply.\n");
        printf("  Capability  : %d (%s)\n", mm->ca, ca_str[mm->ca]);
        printf("  ICAO Address: %06x\n", mm->addr);
        if (mm->iid > 16)
            {printf("  IID         : SI-%02d\n", mm->iid-16);}
        else
            {printf("  IID         : II-%02d\n", mm->iid);}

    } else if (mm->msgtype == 16) { // DF 16
        printf("DF 16: Long Air to Air ACAS\n");
        printf("  VS             : %s\n",  (mm->msg[0] & 0x04) ? "Ground" : "Airborne");
        printf("  CC             : %d\n", ((mm->msg[0] & 0x02) >> 1));
        printf("  SL             : %d\n", ((mm->msg[1] & 0xE0) >> 5));
        printf("  Altitude       : %d %s\n", mm->altitude,
            (mm->unit == MODES_UNIT_METERS) ? "meters" : "feet");
        printf("  ICAO Address   : %06x\n", mm->addr);

    } else if (mm->msgtype == 17) { // DF 17
        printf("DF 17: ADS-B message.\n");
        printf("  Capability     : %d (%s)\n", mm->ca, ca_str[mm->ca]);
        printf("  ICAO Address   : %06x\n", mm->addr);
        printf("  Extended Squitter  Type: %d\n", mm->metype);
        printf("  Extended Squitter  Sub : %d\n", mm->mesub);
        printf("  Extended Squitter  Name: %s\n", getMEDescription(mm->metype, mm->mesub));

        // Decode the extended squitter message
        if (mm->metype >= 1 && mm->metype <= 4) { // Aircraft identification
            printf("    Aircraft Type  : %c%d\n", ('A' + 4 - mm->metype), mm->mesub);
            printf("    Identification : %s\n", mm->flight);

      //} else if (mm->metype >= 5 && mm->metype <= 8) { // Surface position

        } else if (mm->metype >= 9 && mm->metype <= 18) { // Airborne position Baro
            printf("    F flag   : %s\n", (mm->msg[6] & 0x04) ? "odd" : "even");
            printf("    T flag   : %s\n", (mm->msg[6] & 0x08) ? "UTC" : "non-UTC");
            printf("    Altitude : %d feet\n", mm->altitude);
            if (mm->bFlags & MODES_ACFLAGS_LATLON_VALID) {
                printf("    Latitude : %f\n", mm->fLat);
                printf("    Longitude: %f\n", mm->fLon);
            } else {
                printf("    Latitude : %d (not decoded)\n", mm->raw_latitude);
                printf("    Longitude: %d (not decoded)\n", mm->raw_longitude);
            }

        } else if (mm->metype == 19) { // Airborne Velocity
            if (mm->mesub == 1 || mm->mesub == 2) {
                printf("    EW status         : %s\n", (mm->bFlags & MODES_ACFLAGS_EWSPEED_VALID)  ? "Valid" : "Unavailable");
                printf("    EW velocity       : %d\n", mm->ew_velocity);
                printf("    NS status         : %s\n", (mm->bFlags & MODES_ACFLAGS_NSSPEED_VALID)  ? "Valid" : "Unavailable");
                printf("    NS velocity       : %d\n", mm->ns_velocity);
                printf("    Vertical status   : %s\n", (mm->bFlags & MODES_ACFLAGS_VERTRATE_VALID) ? "Valid" : "Unavailable");
                printf("    Vertical rate src : %d\n", ((mm->msg[8] >> 4) & 1));
                printf("    Vertical rate     : %d\n", mm->vert_rate);

            } else if (mm->mesub == 3 || mm->mesub == 4) {
                printf("    Heading status    : %s\n", (mm->bFlags & MODES_ACFLAGS_HEADING_VALID)  ? "Valid" : "Unavailable");
                printf("    Heading           : %d\n", mm->heading);
                printf("    Airspeed status   : %s\n", (mm->bFlags & MODES_ACFLAGS_SPEED_VALID)    ? "Valid" : "Unavailable");
                printf("    Airspeed          : %d\n", mm->velocity);
                printf("    Vertical status   : %s\n", (mm->bFlags & MODES_ACFLAGS_VERTRATE_VALID) ? "Valid" : "Unavailable");
                printf("    Vertical rate src : %d\n", ((mm->msg[8] >> 4) & 1));
                printf("    Vertical rate     : %d\n", mm->vert_rate);

            } else {
                printf("    Unrecognized ME subtype: %d subtype: %d\n", mm->metype, mm->mesub);
            }

      //} else if (mm->metype >= 20 && mm->metype <= 22) { // Airborne position GNSS

        } else {
            printf("    Unrecognized ME type: %d subtype: %d\n", mm->metype, mm->mesub);
        }

    } else if (mm->msgtype == 18) { // DF 18 
        printf("DF 18: Extended Squitter.\n");
        printf("  Control Field : %d (%s)\n", mm->ca, cf_str[mm->ca]);
        if ((mm->ca == 0) || (mm->ca == 1) || (mm->ca == 6)) {
            if (mm->ca == 1) {
                printf("  Other Address : %06x\n", mm->addr);
            } else {
                printf("  ICAO Address  : %06x\n", mm->addr);
            }
            printf("  Extended Squitter  Type: %d\n", mm->metype);
            printf("  Extended Squitter  Sub : %d\n", mm->mesub);
            printf("  Extended Squitter  Name: %s\n", getMEDescription(mm->metype, mm->mesub));

            // Decode the extended squitter message
            if (mm->metype >= 1 && mm->metype <= 4) { // Aircraft identification
                printf("    Aircraft Type  : %c%d\n", ('A' + 4 - mm->metype), mm->mesub);
                printf("    Identification : %s\n", mm->flight);

          //} else if (mm->metype >= 5 && mm->metype <= 8) { // Surface position

            } else if (mm->metype >= 9 && mm->metype <= 18) { // Airborne position Baro
                printf("    F flag   : %s\n", (mm->msg[6] & 0x04) ? "odd" : "even");
                printf("    T flag   : %s\n", (mm->msg[6] & 0x08) ? "UTC" : "non-UTC");
                printf("    Altitude : %d feet\n", mm->altitude);
                if (mm->bFlags & MODES_ACFLAGS_LATLON_VALID) {
                    printf("    Latitude : %f\n", mm->fLat);
                    printf("    Longitude: %f\n", mm->fLon);
                } else {
                    printf("    Latitude : %d (not decoded)\n", mm->raw_latitude);
                    printf("    Longitude: %d (not decoded)\n", mm->raw_longitude);
                }

            } else if (mm->metype == 19) { // Airborne Velocity
                if (mm->mesub == 1 || mm->mesub == 2) {
                    printf("    EW status         : %s\n", (mm->bFlags & MODES_ACFLAGS_EWSPEED_VALID)  ? "Valid" : "Unavailable");
                    printf("    EW velocity       : %d\n", mm->ew_velocity);
                    printf("    NS status         : %s\n", (mm->bFlags & MODES_ACFLAGS_NSSPEED_VALID)  ? "Valid" : "Unavailable");
                    printf("    NS velocity       : %d\n", mm->ns_velocity);
                    printf("    Vertical status   : %s\n", (mm->bFlags & MODES_ACFLAGS_VERTRATE_VALID) ? "Valid" : "Unavailable");
                    printf("    Vertical rate src : %d\n", ((mm->msg[8] >> 4) & 1));
                    printf("    Vertical rate     : %d\n", mm->vert_rate);

                } else if (mm->mesub == 3 || mm->mesub == 4) {
                    printf("    Heading status    : %s\n", (mm->bFlags & MODES_ACFLAGS_HEADING_VALID)  ? "Valid" : "Unavailable");
                    printf("    Heading           : %d\n", mm->heading);
                    printf("    Airspeed status   : %s\n", (mm->bFlags & MODES_ACFLAGS_SPEED_VALID)    ? "Valid" : "Unavailable");
                    printf("    Airspeed          : %d\n", mm->velocity);
                    printf("    Vertical status   : %s\n", (mm->bFlags & MODES_ACFLAGS_VERTRATE_VALID) ? "Valid" : "Unavailable");
                    printf("    Vertical rate src : %d\n", ((mm->msg[8] >> 4) & 1));
                    printf("    Vertical rate     : %d\n", mm->vert_rate);

                } else {
                    printf("    Unrecognized ME subtype: %d subtype: %d\n", mm->metype, mm->mesub);
                }

          //} else if (mm->metype >= 20 && mm->metype <= 22) { // Airborne position GNSS

            } else {
                printf("    Unrecognized ME type: %d subtype: %d\n", mm->metype, mm->mesub);
            }
        }             

    } else if (mm->msgtype == 19) { // DF 19
        printf("DF 19: Military Extended Squitter.\n");

    } else if (mm->msgtype == 22) { // DF 22
        printf("DF 22: Military Use.\n");

    } else if (mm->msgtype == 24) { // DF 24
        printf("DF 24: Comm D Extended Length Message.\n");

    } else if (mm->msgtype == 32) { // DF 32 is special code we use for Mode A/C
        printf("SSR : Mode A/C Reply.\n");
        if (mm->fs & 0x0080) {
            printf("  Mode A : %04x IDENT\n", mm->modeA);
        } else {
            printf("  Mode A : %04x\n", mm->modeA);
            if (mm->bFlags & MODES_ACFLAGS_ALTITUDE_VALID)
                {printf("  Mode C : %d feet\n", mm->altitude);}
        }

    } else {
        printf("DF %d: Unknown DF Format.\n", mm->msgtype);
    }

    printf("\n");
}
//
//=========================================================================
//
// Turn I/Q samples pointed by Modes.data into the magnitude vector
// pointed by Modes.magnitude.
//
void computeMagnitudeVector(void) {
    uint16_t *m = &Modes.magnitude[MODES_PREAMBLE_SAMPLES+MODES_LONG_MSG_SAMPLES];
    uint16_t *p = Modes.data;
    uint32_t j;

    memcpy(Modes.magnitude,&Modes.magnitude[MODES_ASYNC_BUF_SAMPLES], MODES_PREAMBLE_SIZE+MODES_LONG_MSG_SIZE);

    // Compute the magnitudo vector. It's just SQRT(I^2 + Q^2), but
    // we rescale to the 0-255 range to exploit the full resolution.
    for (j = 0; j < MODES_ASYNC_BUF_SAMPLES; j ++) {
        *m++ = Modes.maglut[*p++];
    }
}
//
//=========================================================================
//
// Return -1 if the message is out of fase left-side
// Return  1 if the message is out of fase right-size
// Return  0 if the message is not particularly out of phase.
//
// Note: this function will access pPreamble[-1], so the caller should make sure to
// call it only if we are not at the start of the current buffer
//
int detectOutOfPhase(uint16_t *pPreamble) {
    if (pPreamble[ 3] > pPreamble[2]/3) return  1;
    if (pPreamble[10] > pPreamble[9]/3) return  1;
    if (pPreamble[ 6] > pPreamble[7]/3) return -1;
    if (pPreamble[-1] > pPreamble[1]/3) return -1;
    return 0;
}
//
//=========================================================================
//
// This function does not really correct the phase of the message, it just
// applies a transformation to the first sample representing a given bit:
//
// If the previous bit was one, we amplify it a bit.
// If the previous bit was zero, we decrease it a bit.
//
// This simple transformation makes the message a bit more likely to be
// correctly decoded for out of phase messages:
//
// When messages are out of phase there is more uncertainty in
// sequences of the same bit multiple times, since 11111 will be
// transmitted as continuously altering magnitude (high, low, high, low...)
// 
// However because the message is out of phase some part of the high
// is mixed in the low part, so that it is hard to distinguish if it is
// a zero or a one.
//
// However when the message is out of phase passing from 0 to 1 or from
// 1 to 0 happens in a very recognizable way, for instance in the 0 -> 1
// transition, magnitude goes low, high, high, low, and one of of the
// two middle samples the high will be *very* high as part of the previous
// or next high signal will be mixed there.
//
// Applying our simple transformation we make more likely if the current
// bit is a zero, to detect another zero. Symmetrically if it is a one
// it will be more likely to detect a one because of the transformation.
// In this way similar levels will be interpreted more likely in the
// correct way.
//
void applyPhaseCorrection(uint16_t *pPayload) {
    int j;

    for (j = 0; j < MODES_LONG_MSG_SAMPLES; j += 2, pPayload += 2) {
        if (pPayload[0] > pPayload[1]) { // One
            pPayload[2] = (pPayload[2] * 5) / 4;
        } else {                         // Zero
            pPayload[2] = (pPayload[2] * 4) / 5;
        }
    }
}
//
//=========================================================================
//
// Detect a Mode S messages inside the magnitude buffer pointed by 'm' and of
// size 'mlen' bytes. Every detected Mode S message is convert it into a
// stream of bits and passed to the function to display it.
//
void detectModeS(uint16_t *m, uint32_t mlen) {
    struct modesMessage mm;
    unsigned char msg[MODES_LONG_MSG_BYTES], *pMsg;
    uint16_t aux[MODES_LONG_MSG_SAMPLES];
    uint32_t j;
    int use_correction = 0;

    memset(&mm, 0, sizeof(mm));

    // The Mode S preamble is made of impulses of 0.5 microseconds at
    // the following time offsets:
    //
    // 0   - 0.5 usec: first impulse.
    // 1.0 - 1.5 usec: second impulse.
    // 3.5 - 4   usec: third impulse.
    // 4.5 - 5   usec: last impulse.
    // 
    // Since we are sampling at 2 Mhz every sample in our magnitude vector
    // is 0.5 usec, so the preamble will look like this, assuming there is
    // an impulse at offset 0 in the array:
    //
    // 0   -----------------
    // 1   -
    // 2   ------------------
    // 3   --
    // 4   -
    // 5   --
    // 6   -
    // 7   ------------------
    // 8   --
    // 9   -------------------
    //
    for (j = 0; j < mlen; j++) {
        int high, i, errors, errors56, errorsTy; 
        uint16_t *pPreamble, *pPayload, *pPtr;
        uint8_t  theByte, theErrs;
        int msglen, scanlen, sigStrength;

        pPreamble = &m[j];
        pPayload  = &m[j+MODES_PREAMBLE_SAMPLES];

        // Rather than clear the whole mm structure, just clear the parts which are required. The clear
        // is required for every bit of the input stream, and we don't want to be memset-ing the whole
        // modesMessage structure two million times per second if we don't have to..
        mm.bFlags          =
        mm.crcok           = 
        mm.correctedbits   = 0;

        if (!use_correction)  // This is not a re-try with phase correction
            {                 // so try to find a new preamble

            if (Modes.mode_ac) 
                {
                int ModeA = detectModeA(pPreamble, &mm);

                if (ModeA) // We have found a valid ModeA/C in the data                    
                    {
                    mm.timestampMsg = Modes.timestampBlk + ((j+1) * 6);

                    // Decode the received message
                    decodeModeAMessage(&mm, ModeA);

                    // Pass data to the next layer
                    useModesMessage(&mm);

                    j += MODEAC_MSG_SAMPLES;
                    Modes.stat_ModeAC++;
                    continue;
                    }
                }

            // First check of relations between the first 10 samples
            // representing a valid preamble. We don't even investigate further
            // if this simple test is not passed
            if (!(pPreamble[0] > pPreamble[1] &&
                  pPreamble[1] < pPreamble[2] &&
                  pPreamble[2] > pPreamble[3] &&
                  pPreamble[3] < pPreamble[0] &&
                  pPreamble[4] < pPreamble[0] &&
                  pPreamble[5] < pPreamble[0] &&
                  pPreamble[6] < pPreamble[0] &&
                  pPreamble[7] > pPreamble[8] &&
                  pPreamble[8] < pPreamble[9] &&
                  pPreamble[9] > pPreamble[6]))
            {
                if (Modes.debug & MODES_DEBUG_NOPREAMBLE &&
                    *pPreamble  > MODES_DEBUG_NOPREAMBLE_LEVEL)
                    dumpRawMessage("Unexpected ratio among first 10 samples", msg, m, j);
                continue;
            }

            // The samples between the two spikes must be < than the average
            // of the high spikes level. We don't test bits too near to
            // the high levels as signals can be out of phase so part of the
            // energy can be in the near samples
            high = (pPreamble[0] + pPreamble[2] + pPreamble[7] + pPreamble[9]) / 6;
            if (pPreamble[4] >= high ||
                pPreamble[5] >= high)
            {
                if (Modes.debug & MODES_DEBUG_NOPREAMBLE &&
                    *pPreamble  > MODES_DEBUG_NOPREAMBLE_LEVEL)
                    dumpRawMessage("Too high level in samples between 3 and 6", msg, m, j);
                continue;
            }

            // Similarly samples in the range 11-14 must be low, as it is the
            // space between the preamble and real data. Again we don't test
            // bits too near to high levels, see above
            if (pPreamble[11] >= high ||
                pPreamble[12] >= high ||
                pPreamble[13] >= high ||
                pPreamble[14] >= high)
            {
                if (Modes.debug & MODES_DEBUG_NOPREAMBLE &&
                    *pPreamble  > MODES_DEBUG_NOPREAMBLE_LEVEL)
                    dumpRawMessage("Too high level in samples between 10 and 15", msg, m, j);
                continue;
            }
            Modes.stat_valid_preamble++;
        } 

        else {
            // If the previous attempt with this message failed, retry using
            // magnitude correction
            // Make a copy of the Payload, and phase correct the copy
            memcpy(aux, pPayload, sizeof(aux));
            applyPhaseCorrection(aux);
            Modes.stat_out_of_phase++;
            pPayload = aux;
            // TODO ... apply other kind of corrections
            }

        // Decode all the next 112 bits, regardless of the actual message
        // size. We'll check the actual message type later
        pMsg    = &msg[0];
        pPtr    = pPayload;
        theByte = 0;
        theErrs = 0; errorsTy = 0;
        errors  = 0; errors56 = 0;

        // We should have 4 'bits' of 0/1 and 1/0 samples in the preamble, 
        // so include these in the signal strength 
        sigStrength = (pPreamble[0]-pPreamble[1])
                    + (pPreamble[2]-pPreamble[3])
                    + (pPreamble[7]-pPreamble[6])
                    + (pPreamble[9]-pPreamble[8]);

        msglen = scanlen = MODES_LONG_MSG_BITS;
        for (i = 0; i < scanlen; i++) {
            uint32_t a = *pPtr++;
            uint32_t b = *pPtr++;

            if      (a > b) 
                {theByte |= 1; if (i < 56) {sigStrength += (a-b);}} 
            else if (a < b) 
                {/*theByte |= 0;*/ if (i < 56) {sigStrength += (b-a);}} 
            else if (i >= MODES_SHORT_MSG_BITS) //(a == b), and we're in the long part of a frame
                {errors++;  /*theByte |= 0;*/} 
            else if (i >= 5)                    //(a == b), and we're in the short part of a frame
                {scanlen = MODES_LONG_MSG_BITS; errors56 = ++errors;/*theByte |= 0;*/}            
            else if (i)                         //(a == b), and we're in the message type part of a frame
                {errorsTy = errors56 = ++errors; theErrs |= 1; /*theByte |= 0;*/} 
            else                                //(a == b), and we're in the first bit of the message type part of a frame
                {errorsTy = errors56 = ++errors; theErrs |= 1; theByte |= 1;} 

            if ((i & 7) == 7) 
              {*pMsg++ = theByte;}
            else if (i == 4) {
              msglen  = modesMessageLenByType(theByte);
              if (errors == 0)
                  {scanlen = msglen;}
            }

            theByte = theByte << 1;
            if (i < 7)
              {theErrs = theErrs << 1;}

            // If we've exceeded the permissible number of encoding errors, abandon ship now
            if (errors > MODES_MSG_ENCODER_ERRS) {

                if        (i < MODES_SHORT_MSG_BITS) {
                    msglen = 0;

                } else if ((errorsTy == 1) && (theErrs == 0x80)) {
                    // If we only saw one error in the first bit of the byte of the frame, then it's possible 
                    // we guessed wrongly about the value of the bit. We may be able to correct it by guessing
                    // the other way.
                    //
                    // We guessed a '1' at bit 7, which is the DF length bit == 112 Bits.
                    // Inverting bit 7 will change the message type from a long to a short. 
                    // Invert the bit, cross your fingers and carry on.
                    msglen  = MODES_SHORT_MSG_BITS;
                    msg[0] ^= theErrs; errorsTy = 0;
                    errors  = errors56; // revert to the number of errors prior to bit 56
                    Modes.stat_DF_Len_Corrected++;

                } else if (i < MODES_LONG_MSG_BITS) {
                    msglen = MODES_SHORT_MSG_BITS;
                    errors = errors56;

                } else {
                    msglen = MODES_LONG_MSG_BITS;
                }

            break;
            }
        }

        // Ensure msglen is consistent with the DF type
        i = modesMessageLenByType(msg[0] >> 3);
        if      (msglen > i) {msglen = i;}
        else if (msglen < i) {msglen = 0;}

        //
        // If we guessed at any of the bits in the DF type field, then look to see if our guess was sensible.
        // Do this by looking to see if the original guess results in the DF type being one of the ICAO defined
        // message types. If it isn't then toggle the guessed bit and see if this new value is ICAO defined.
        // if the new value is ICAO defined, then update it in our message.
        if ((msglen) && (errorsTy == 1) && (theErrs & 0x78)) {
            // We guessed at one (and only one) of the message type bits. See if our guess is "likely" 
            // to be correct by comparing the DF against a list of known good DF's
            int      thisDF      = ((theByte = msg[0]) >> 3) & 0x1f;
            uint32_t validDFbits = 0x017F0831;   // One bit per 32 possible DF's. Set bits 0,4,5,11,16.17.18.19,20,21,22,24
            uint32_t thisDFbit   = (1 << thisDF);
            if (0 == (validDFbits & thisDFbit)) {
                // The current DF is not ICAO defined, so is probably an errors. 
                // Toggle the bit we guessed at and see if the resultant DF is more likely
                theByte  ^= theErrs;
                thisDF    = (theByte >> 3) & 0x1f;
                thisDFbit = (1 << thisDF);
                // if this DF any more likely?
                if (validDFbits & thisDFbit) {
                    // Yep, more likely, so update the main message 
                    msg[0] = theByte;
                    Modes.stat_DF_Type_Corrected++;
                    errors--; // decrease the error count so we attempt to use the modified DF.
                }
            }
        }

        // We measured signal strength over the first 56 bits. Don't forget to add 4 
        // for the preamble samples, so round up and divide by 60.
        sigStrength = (sigStrength + 29) / 60;

        // When we reach this point, if error is small, and the signal strength is large enough
        // we may have a Mode S message on our hands. It may still be broken and the CRC may not 
        // be correct, but this can be handled by the next layer.
        if ( (msglen) 
          && (sigStrength >  MODES_MSG_SQUELCH_LEVEL) 
          && (errors      <= MODES_MSG_ENCODER_ERRS) ) {

            // Set initial mm structure details
            mm.timestampMsg = Modes.timestampBlk + (j*6);
            sigStrength    = (sigStrength + 0x7F) >> 8;
            mm.signalLevel = ((sigStrength < 255) ? sigStrength : 255);
            mm.phase_corrected = use_correction;

            // Decode the received message
            decodeModesMessage(&mm, msg);

            // Update statistics
            if (Modes.stats) {
                if (mm.crcok || use_correction || mm.correctedbits) {

                    if (use_correction) {
                        switch (errors) {
                            case 0: {Modes.stat_ph_demodulated0++; break;}
                            case 1: {Modes.stat_ph_demodulated1++; break;}
                            case 2: {Modes.stat_ph_demodulated2++; break;}
                            default:{Modes.stat_ph_demodulated3++; break;}
                        }
                    } else {
                        switch (errors) {
                            case 0: {Modes.stat_demodulated0++; break;}
                            case 1: {Modes.stat_demodulated1++; break;}
                            case 2: {Modes.stat_demodulated2++; break;}
                            default:{Modes.stat_demodulated3++; break;}
                        }
                    }

                    if (mm.correctedbits == 0) {
                        if (use_correction) {
                            if (mm.crcok) {Modes.stat_ph_goodcrc++;}
                            else          {Modes.stat_ph_badcrc++;}
                        } else {
                            if (mm.crcok) {Modes.stat_goodcrc++;}
                            else          {Modes.stat_badcrc++;}
                        }

                    } else if (use_correction) {
                        Modes.stat_ph_badcrc++;
                        Modes.stat_ph_fixed++;
                        if ( (mm.correctedbits) 
                          && (mm.correctedbits <= MODES_MAX_BITERRORS) ) {
                            Modes.stat_ph_bit_fix[mm.correctedbits-1] += 1;
                        }

                    } else {
                        Modes.stat_badcrc++;
                        Modes.stat_fixed++;
                        if ( (mm.correctedbits) 
                          && (mm.correctedbits <= MODES_MAX_BITERRORS) ) {
                            Modes.stat_bit_fix[mm.correctedbits-1] += 1;
                        }
                    }
                }
            }

            // Output debug mode info if needed
            if (use_correction) {
                if (Modes.debug & MODES_DEBUG_DEMOD)
                    dumpRawMessage("Demodulated with 0 errors", msg, m, j);
                else if (Modes.debug & MODES_DEBUG_BADCRC &&
                         mm.msgtype == 17 &&
                         (!mm.crcok || mm.correctedbits != 0))
                    dumpRawMessage("Decoded with bad CRC", msg, m, j);
                else if (Modes.debug & MODES_DEBUG_GOODCRC && mm.crcok &&
                         mm.correctedbits == 0)
                    dumpRawMessage("Decoded with good CRC", msg, m, j);
            }

            // Skip this message if we are sure it's fine
            if (mm.crcok) {
                j += (MODES_PREAMBLE_US+msglen)*2;
            }

            // Pass data to the next layer
            useModesMessage(&mm);

        } else {
            if (Modes.debug & MODES_DEBUG_DEMODERR && use_correction) {
                printf("The following message has %d demod errors\n", errors);
                dumpRawMessage("Demodulated with errors", msg, m, j);
            }
        }

        // Retry with phase correction if enabled, necessary and possible.
        if (Modes.phase_enhance && !mm.crcok && !mm.correctedbits && !use_correction && j && detectOutOfPhase(pPreamble)) {
            use_correction = 1; j--;
        } else {
            use_correction = 0; 
        }
    }

    //Send any remaining partial raw buffers now
    if (Modes.rawOutUsed || Modes.beastOutUsed)
      {
      Modes.net_output_raw_rate_count++;
      if (Modes.net_output_raw_rate_count > Modes.net_output_raw_rate)
        {
        if (Modes.rawOutUsed) {
            modesSendAllClients(Modes.ros, Modes.rawOut, Modes.rawOutUsed);
            Modes.rawOutUsed = 0;
        }
        if (Modes.beastOutUsed) {
            modesSendAllClients(Modes.bos, Modes.beastOut, Modes.beastOutUsed);
            Modes.beastOutUsed = 0;
        }
        Modes.net_output_raw_rate_count = 0;
        }
      }
}
//
//=========================================================================
//
// When a new message is available, because it was decoded from the RTL device, 
// file, or received in the TCP input port, or any other way we can receive a 
// decoded message, we call this function in order to use the message.
//
// Basically this function passes a raw message to the upper layers for further
// processing and visualization
//
void useModesMessage(struct modesMessage *mm) {
    if ((Modes.check_crc == 0) || (mm->crcok) || (mm->correctedbits)) { // not checking, ok or fixed

        // Always track aircraft
        interactiveReceiveData(mm);

        // In non-interactive non-quiet mode, display messages on standard output
        if (!Modes.interactive && !Modes.quiet) {
            displayModesMessage(mm);
        }

        // Feed output clients
        if (Modes.net) {modesQueueOutput(mm);}
    }
}
//
//=========================================================================
//
// Always positive MOD operation, used for CPR decoding.
//
int cprModFunction(int a, int b) {
    int res = a % b;
    if (res < 0) res += b;
    return res;
}
//
//=========================================================================
//
// The NL function uses the precomputed table from 1090-WP-9-14
//
int cprNLFunction(double lat) {
    if (lat < 0) lat = -lat; // Table is simmetric about the equator
    if (lat < 10.47047130) return 59;
    if (lat < 14.82817437) return 58;
    if (lat < 18.18626357) return 57;
    if (lat < 21.02939493) return 56;
    if (lat < 23.54504487) return 55;
    if (lat < 25.82924707) return 54;
    if (lat < 27.93898710) return 53;
    if (lat < 29.91135686) return 52;
    if (lat < 31.77209708) return 51;
    if (lat < 33.53993436) return 50;
    if (lat < 35.22899598) return 49;
    if (lat < 36.85025108) return 48;
    if (lat < 38.41241892) return 47;
    if (lat < 39.92256684) return 46;
    if (lat < 41.38651832) return 45;
    if (lat < 42.80914012) return 44;
    if (lat < 44.19454951) return 43;
    if (lat < 45.54626723) return 42;
    if (lat < 46.86733252) return 41;
    if (lat < 48.16039128) return 40;
    if (lat < 49.42776439) return 39;
    if (lat < 50.67150166) return 38;
    if (lat < 51.89342469) return 37;
    if (lat < 53.09516153) return 36;
    if (lat < 54.27817472) return 35;
    if (lat < 55.44378444) return 34;
    if (lat < 56.59318756) return 33;
    if (lat < 57.72747354) return 32;
    if (lat < 58.84763776) return 31;
    if (lat < 59.95459277) return 30;
    if (lat < 61.04917774) return 29;
    if (lat < 62.13216659) return 28;
    if (lat < 63.20427479) return 27;
    if (lat < 64.26616523) return 26;
    if (lat < 65.31845310) return 25;
    if (lat < 66.36171008) return 24;
    if (lat < 67.39646774) return 23;
    if (lat < 68.42322022) return 22;
    if (lat < 69.44242631) return 21;
    if (lat < 70.45451075) return 20;
    if (lat < 71.45986473) return 19;
    if (lat < 72.45884545) return 18;
    if (lat < 73.45177442) return 17;
    if (lat < 74.43893416) return 16;
    if (lat < 75.42056257) return 15;
    if (lat < 76.39684391) return 14;
    if (lat < 77.36789461) return 13;
    if (lat < 78.33374083) return 12;
    if (lat < 79.29428225) return 11;
    if (lat < 80.24923213) return 10;
    if (lat < 81.19801349) return 9;
    if (lat < 82.13956981) return 8;
    if (lat < 83.07199445) return 7;
    if (lat < 83.99173563) return 6;
    if (lat < 84.89166191) return 5;
    if (lat < 85.75541621) return 4;
    if (lat < 86.53536998) return 3;
    if (lat < 87.00000000) return 2;
    else return 1;
}
//
//=========================================================================
//
int cprNFunction(double lat, int fflag) {
    int nl = cprNLFunction(lat) - (fflag ? 1 : 0);
    if (nl < 1) nl = 1;
    return nl;
}
//
//=========================================================================
//
double cprDlonFunction(double lat, int fflag, int surface) {
    return (surface ? 90.0 : 360.0) / cprNFunction(lat, fflag);
}
//
//=========================================================================
//
// This algorithm comes from:
// http://www.lll.lu/~edward/edward/adsb/DecodingADSBposition.html.
//
// A few remarks:
// 1) 131072 is 2^17 since CPR latitude and longitude are encoded in 17 bits.
// 2) We assume that we always received the odd packet as last packet for
//    simplicity. This may provide a position that is less fresh of a few
//    seconds.
//
void decodeCPR(struct aircraft *a, int fflag, int surface) {
    double AirDlat0 = (surface ? 90.0 : 360.0) / 60.0;
    double AirDlat1 = (surface ? 90.0 : 360.0) / 59.0;
    double lat0 = a->even_cprlat;
    double lat1 = a->odd_cprlat;
    double lon0 = a->even_cprlon;
    double lon1 = a->odd_cprlon;

    // Compute the Latitude Index "j"
    int    j     = (int) floor(((59*lat0 - 60*lat1) / 131072) + 0.5);
    double rlat0 = AirDlat0 * (cprModFunction(j,60) + lat0 / 131072);
    double rlat1 = AirDlat1 * (cprModFunction(j,59) + lat1 / 131072);

    if (surface) {
        // If we're on the ground, make sure we have our receiver base station Lat/Lon
        if (0 == (Modes.bUserFlags & MODES_USER_LATLON_VALID))
            {return;}
        rlat0 += floor(Modes.fUserLat / 90.0) * 90.0;  // Move from 1st quadrant to our quadrant
        rlat1 += floor(Modes.fUserLat / 90.0) * 90.0;
    } else {
        if (rlat0 >= 270) rlat0 -= 360;
        if (rlat1 >= 270) rlat1 -= 360;
    }

    // Check that both are in the same latitude zone, or abort.
    if (cprNLFunction(rlat0) != cprNLFunction(rlat1)) return;

    // Compute ni and the Longitude Index "m"
    if (fflag) { // Use odd packet.
        int ni = cprNFunction(rlat1,1);
        int m = (int) floor((((lon0 * (cprNLFunction(rlat1)-1)) -
                              (lon1 * cprNLFunction(rlat1))) / 131072.0) + 0.5);
        a->lon = cprDlonFunction(rlat1, 1, surface) * (cprModFunction(m, ni)+lon1/131072);
        a->lat = rlat1;
    } else {     // Use even packet.
        int ni = cprNFunction(rlat0,0);
        int m = (int) floor((((lon0 * (cprNLFunction(rlat0)-1)) -
                              (lon1 * cprNLFunction(rlat0))) / 131072) + 0.5);
        a->lon = cprDlonFunction(rlat0, 0, surface) * (cprModFunction(m, ni)+lon0/131072);
        a->lat = rlat0;
    }

    if (surface) {
        a->lon += floor(Modes.fUserLon / 90.0) * 90.0;  // Move from 1st quadrant to our quadrant
    } else if (a->lon > 180) {
        a->lon -= 360;
    }

    a->seenLatLon      = a->seen;
    a->timestampLatLon = a->timestamp;
    a->bFlags         |= (MODES_ACFLAGS_LATLON_VALID | MODES_ACFLAGS_LATLON_REL_OK);
}
//
//=========================================================================
//
// This algorithm comes from:
// 1090-WP29-07-Draft_CPR101 (which also defines decodeCPR() )
//
// There is an error in this document related to CPR relative decode.
// Should use trunc() rather than the floor() function in Eq 38 and related for deltaZI.
// floor() returns integer less than argument
// trunc() returns integer closer to zero than argument.
// Note:   text of document describes trunc() functionality for deltaZI calculation
//         but the formulae use floor().
//
int decodeCPRrelative(struct aircraft *a, int fflag, int surface) {
    double AirDlat;
    double AirDlon;
    double lat;
    double lon;
    double lonr, latr;
    double rlon, rlat;
    int j,m;

    if (a->bFlags & MODES_ACFLAGS_LATLON_REL_OK) { // Ok to try aircraft relative first
        latr = a->lat;
        lonr = a->lon;
    } else if (Modes.bUserFlags & MODES_USER_LATLON_VALID) { // Try ground station relative next
        latr = Modes.fUserLat;
        lonr = Modes.fUserLon;
    } else {
        return (-1); // Exit with error - can't do relative if we don't have ref.
    }

    if (fflag) { // odd
        AirDlat = (surface ? 90.0 : 360.0) / 59.0;
        lat = a->odd_cprlat;
        lon = a->odd_cprlon;
    } else {    // even
        AirDlat = (surface ? 90.0 : 360.0) / 60.0;
        lat = a->even_cprlat;
        lon = a->even_cprlon;
    }

    // Compute the Latitude Index "j"
    j = (int) (floor(latr/AirDlat) +
               trunc(0.5 + cprModFunction((int)latr, (int)AirDlat)/AirDlat - lat/131072));
    rlat = AirDlat * (j + lat/131072);
    if (rlat >= 270) rlat -= 360;

    // Check to see that answer is reasonable - ie no more than 1/2 cell away 
    if (fabs(rlat - a->lat) > (AirDlat/2)) {
        a->bFlags &= ~MODES_ACFLAGS_LATLON_REL_OK; // This will cause a quick exit next time if no global has been done
        return (-1);                               // Time to give up - Latitude error 
    }

    // Compute the Longitude Index "m"
    AirDlon = cprDlonFunction(rlat, fflag, surface);
    m = (int) (floor(lonr/AirDlon) +
               trunc(0.5 + cprModFunction((int)lonr, (int)AirDlon)/AirDlon - lon/131072));
    rlon = AirDlon * (m + lon/131072);
    if (rlon > 180) rlon -= 360;

    // Check to see that answer is reasonable - ie no more than 1/2 cell away
    if (fabs(rlon - a->lon) > (AirDlon/2)) {
        a->bFlags &= ~MODES_ACFLAGS_LATLON_REL_OK; // This will cause a quick exit next time if no global has been done
        return (-1);                               // Time to give up - Longitude error
    }

    a->lat = rlat;
    a->lon = rlon;

    a->seenLatLon      = a->seen;
    a->timestampLatLon = a->timestamp;
    a->bFlags         |= (MODES_ACFLAGS_LATLON_VALID | MODES_ACFLAGS_LATLON_REL_OK);
    return (0);
}
//
// ===================== Mode S detection and decoding  ===================
//