Add library build and install

Makefile

@@ -21,3 +21,6 @@ decode_ft8: decode_ft8.o fft/kiss_fftr.o fft/kiss_fft.o ft8/decode.o ft8/encode.
 
 clean:
 	rm -f *.o ft8/*.o common/*.o fft/*.o $(TARGETS)
+install:
+	$(AR) rc libft8.a ft8/constants.o ft8/encode.o ft8/pack.o ft8/text.o common/wave.o 
+	install libft8.a /usr/lib/libft8.a

decode_ft8.cpp

@@ -15,9 +15,6 @@
 
 #define LOG_LEVEL   LOG_INFO
 
-const int kFreq_osr = 2;
-const int kTime_osr = 2;
-
 const int kMin_score = 40;		// Minimum sync score threshold for candidates
 const int kMax_candidates = 120;
 const int kLDPC_iterations = 25;
@@ -25,6 +22,11 @@ const int kLDPC_iterations = 25;
 const int kMax_decoded_messages = 50;
 const int kMax_message_length = 25;
 
+const int kFreq_osr = 2;
+const int kTime_osr = 2;
+
+const float kFSK_dev = 6.25f;    // tone deviation in Hz and symbol rate
+
 void usage() {
     fprintf(stderr, "Decode a 15-second WAV file.\n");
 }
@@ -58,63 +60,10 @@ float blackman_i(int i, int N) {
     return a0 - a1*x1 + a2*x2;
 }
 
-class Monitor : public ft8::Monitor1Base {
-public:
-    Monitor(float sample_rate);
-protected:
-    virtual void fft_forward(const float *in, std::complex<float> *out) override;
-private:
-    kiss_fftr_cfg fft_cfg;
-};
-
-Monitor::Monitor(float sample_rate) : Monitor1Base(sample_rate)
-{
-    window_fn = new float[nfft];   // [nfft]
-    fft_frame = new float[nfft];   // [nfft]
-    last_frame = new float[nfft * 3/4];  // [nfft * 3/4]
-    freqdata = new std::complex<float>[nfft/2 + 1]; // [nfft/2 + 1]
-
-    fft_cfg = kiss_fftr_alloc(nfft, 0, NULL, NULL);
+static float max2(float a, float b) {
+    return (a >= b) ? a : b;
 }
 
-void Monitor::fft_forward(const float *in, std::complex<float> *out) {
-    kiss_fftr(fft_cfg, 
-        reinterpret_cast<const kiss_fft_scalar *>(in), 
-        reinterpret_cast<kiss_fft_cpx *>(out));
-}
-
-// #include <complex>
-
-// class FFT_r2c {
-// public:
-//     // [N] real --> [N/2 + 1] complex
-//     virtual void forward(const float *in, std::complex<float> *out) = 0;
-// };
-
-// class KissFFT_r2c : public FFT_r2c {
-// public:
-//     KissFFT_r2c(int N) {
-//         LOG(LOG_INFO, "N_FFT = %d\n", N);
-//         // size_t  fft_work_size;
-//         // kiss_fftr_alloc(N, 0, 0, &fft_work_size);
-//         // LOG(LOG_INFO, "FFT work area = %lu\n", fft_work_size);
-//         // fft_work = malloc(fft_work_size);
-//         // fft_cfg = kiss_fftr_alloc(N, 0, fft_work, &fft_work_size);
-//         fft_cfg = kiss_fftr_alloc(N, 0, NULL, NULL);
-//     }
-//     ~KissFFT_r2c() {
-//         // free(fft_work);
-//         kiss_fftr_free(fft_cfg);
-//     }
-//     virtual void forward(const float *in, std::complex<float> *out) override {
-//         kiss_fftr(fft_cfg, in, reinterpret_cast<kiss_fft_cpx *>(out));
-//     }
-
-// private:
-//     void        *fft_work;
-//     kiss_fftr_cfg fft_cfg;
-// };
-
 // Compute FFT magnitudes (log power) for each timeslot in the signal
 void extract_power(const float signal[], ft8::MagArray * power) {
     const int block_size = 2 * power->num_bins; // Average over 2 bins per FSK tone
@@ -157,16 +106,17 @@ void extract_power(const float signal[], ft8::MagArray * power) {
             // Compute log magnitude in decibels
             for (int j = 0; j < nfft/2 + 1; ++j) {
                 float mag2 = (freqdata[j].i * freqdata[j].i + freqdata[j].r * freqdata[j].r);
-                mag_db[j] = 10.0f * log10f(1E-12f + mag2 * fft_norm * fft_norm);
+                mag_db[j] = 10.0f * log10f(1E-10f + mag2 * fft_norm * fft_norm);
             }
 
             // Loop over two possible frequency bin offsets (for averaging)
             for (int freq_sub = 0; freq_sub < power->freq_osr; ++freq_sub) {                
                 for (int j = 0; j < power->num_bins; ++j) {
-                    //float db1 = mag_db[j * power->freq_osr + freq_sub];
+                    float db1 = mag_db[j * power->freq_osr + freq_sub];
                     //float db2 = mag_db[j * 2 + freq_sub + 1];
                     //float db = (db1 + db2) / 2;
-                    float db = mag_db[j * power->freq_osr + freq_sub];
+                    float db = db1;
+                    //float db = sqrtf(db1 * db2);
 
                     // Scale decibels to unsigned 8-bit range and clamp the value
                     int scaled = (int)(2 * (db + 120));
@@ -230,7 +180,7 @@ int main(int argc, char **argv) {
     normalize_signal(signal, num_samples);
 
     // Compute DSP parameters that depend on the sample rate
-    const int num_bins = (int)(sample_rate / (2 * ft8::FSK_dev));
+    const int num_bins = (int)(sample_rate / (2 * kFSK_dev));
     const int block_size = 2 * num_bins;
     const int subblock_size = block_size / kTime_osr;
     const int nfft = block_size * kFreq_osr;
@@ -262,8 +212,8 @@ int main(int argc, char **argv) {
         ft8::Candidate &cand = candidate_list[idx];
         if (cand.score < kMin_score) continue;
 
-        float freq_hz  = (cand.freq_offset + (float)cand.freq_sub / kFreq_osr) * ft8::FSK_dev;
-        float time_sec = (cand.time_offset + (float)cand.time_sub / kTime_osr) / ft8::FSK_dev;
+        float freq_hz  = (cand.freq_offset + (float)cand.freq_sub / kFreq_osr) * kFSK_dev;
+        float time_sec = (cand.time_offset + (float)cand.time_sub / kTime_osr) / kFSK_dev;
 
         float   log174[ft8::N];
         ft8::extract_likelihood(&power, cand, ft8::kGray_map, log174);
@@ -272,9 +222,7 @@ int main(int argc, char **argv) {
         uint8_t plain[ft8::N];
         int     n_errors = 0;
         ft8::bp_decode(log174, kLDPC_iterations, plain, &n_errors);
-        if (n_errors > 0) {
-            // ft8::ldpc_decode(log174, kLDPC_iterations, plain, &n_errors);
-        }
+        //ft8::ldpc_decode(log174, kLDPC_iterations, plain, &n_errors);
 
         if (n_errors > 0) {
             LOG(LOG_DEBUG, "ldpc_decode() = %d (%.0f Hz)\n", n_errors, freq_hz);

ft8/constants.h

@@ -3,7 +3,6 @@
 #include <stdint.h>
 
 namespace ft8 {
-    constexpr float FSK_dev = 6.25f;    // tone deviation in Hz and symbol rate
 
     // Define FT8 symbol counts
     constexpr int ND = 58;      // Data symbols

ft8/decode.cpp

@@ -17,57 +17,6 @@ static int get_index(const MagArray *power, int block, int time_sub, int freq_su
     return ((((block * power->time_osr) + time_sub) * power->freq_osr + freq_sub) * power->num_bins) + bin; 
 }
 
-Monitor1Base::Monitor1Base(float sample_rate, int time_osr, int freq_osr, float fmin, float fmax) {
-    int block_size = (int)(0.5f + sample_rate / ft8::FSK_dev); // Samples per FSK tone
-    nfft = block_size * freq_osr; // FFT over symbols with frequency oversampling
-    int bin1 = (block_size * fmin) / sample_rate;
-    int bin2 = (block_size * fmax) / sample_rate;
-
-    power.time_osr = time_osr;
-    power.freq_osr = freq_osr;
-    power.num_bins = bin2 - bin1;
-    power.num_blocks = 0;
-}
-
-void Monitor1Base::feed(const float *frame) {
-    // Fill the first 3/4 of analysis frame
-    for (int i = 0; i < 3 * nfft / 4; ++i) {
-        fft_frame[i] = window_fn[i] * last_frame[i];
-    }
-
-    // Shift the frame history
-    for (int i = 0; i < nfft / 2; ++i) {
-        last_frame[i] = last_frame[i + nfft / 4];
-    }
-
-    // Now fill the last_frame array
-    for (int i = 0; i < nfft / 4; ++i) {
-        last_frame[i + nfft / 2] = frame[i];
-    }
-
-    // Fill the last 1/4 of analysis frame
-    for (int i = 3 * nfft / 4, j = nfft / 2; i < nfft; ++i, ++j) {
-        fft_frame[i] = window_fn[i] * last_frame[j];
-    }
-
-    fft_forward(fft_frame, freqdata);
-
-    for (int freq_sub = 0; freq_sub < power.freq_osr; ++freq_sub) {
-        for (int i = 0; i < power.num_bins; i += power.freq_osr) {
-            float mag2 = std::norm(freqdata[i]);    // re^2 + im^2
-            float mag_db = 10.0f * log10f(1E-12f + mag2);
-            int scaled = (int)(2 * (mag_db + 120));
-            power.mag[offset] = (scaled < 0) ? 0 : ((scaled > 255) ? 255 : scaled);
-            ++offset;
-        }
-    }
-
-    if (++time_sub >= power.time_osr) {
-        time_sub = 0;
-        ++power.num_blocks;
-    }
-}
-
 // Localize top N candidates in frequency and time according to their sync strength (looking at Costas symbols)
 // We treat and organize the candidate list as a min-heap (empty initially).
 int find_sync(const MagArray *power, const uint8_t *sync_map, int num_candidates, Candidate *heap, int min_score) {
@@ -86,14 +35,13 @@ int find_sync(const MagArray *power, const uint8_t *sync_map, int num_candidates
                     // Compute average score over sync symbols (m+k = 0-7, 36-43, 72-79)
                     int num_symbols = 0;
                     for (int m = 0; m <= 72; m += 36) {
-                        // Iterate over 7 Costas synchronisation symbols
                         for (int k = 0; k < 7; ++k) {
-                            int n = time_offset + k + m;
                             // Check for time boundaries
-                            if (n < 0) continue;
-                            if (n >= power->num_blocks) break;
+                            if (time_offset + k + m < 0) continue;
+                            if (time_offset + k + m >= power->num_blocks) break;
 
-                            int offset = get_index(power, n, time_sub, freq_sub, freq_offset);
+                            // int offset = ((time_offset + k + m) * num_alt + alt) * power->num_bins + freq_offset;
+                            int offset = get_index(power, time_offset + k + m, time_sub, freq_sub, freq_offset);
                             const uint8_t *p8 = power->mag + offset;
 
                             // Weighted difference between the expected and all other symbols
@@ -112,18 +60,18 @@ int find_sync(const MagArray *power, const uint8_t *sync_map, int num_candidates
                                 // look at one frequency bin higher
                                 score += p8[sm] - p8[sm + 1];
                             }
-                            if (k > 0 && n - 1 >= 0) {
+                            if (k > 0) {
                                 // look one symbol back in time
                                 score += p8[sm] - p8[sm - num_alt * power->num_bins];
                             }
-                            if (k < 6 && n + 1 < power->num_blocks) {
+                            if (k < 6) {
                                 // look one symbol forward in time
                                 score += p8[sm] - p8[sm + num_alt * power->num_bins];
                             }
+                        
                             ++num_symbols;
                         }
                     }
-                    if (num_symbols > 0)
                     score /= num_symbols;
 
                     if (score < min_score) continue;
@@ -173,11 +121,10 @@ void extract_likelihood(const MagArray *power, const Candidate & cand, const uin
         int sym_idx = (k < ft8::ND / 2) ? (k + 7) : (k + 14);
         int bit_idx = 3 * k;
 
-        // Index of the 8 bins of the current symbol
-        int sym_offset = offset + sym_idx * num_alt * power->num_bins;
+        // Pointer to 8 bins of the current symbol
+        const uint8_t *ps = power->mag + (offset + sym_idx * num_alt * power->num_bins);
 
-        decode_symbol(power->mag + sym_offset, code_map, bit_idx, log174);
-        // decode_multi_symbols(power->mag + sym_offset, power->num_bins, n_syms, code_map, bit_idx, log174);
+        decode_symbol(ps, code_map, bit_idx, log174);
     }
 
     // Compute the variance of log174

ft8/decode.h

@@ -1,7 +1,6 @@
 #pragma once
 
 #include <stdint.h>
-#include <complex>
 
 namespace ft8 {
 
@@ -21,28 +20,6 @@ struct Candidate {
     uint8_t      freq_sub;
 };
 
-class Monitor1Base {
-public:
-    Monitor1Base(float sample_rate, int time_osr = 2, int freq_osr = 2, float fmin = 300, float fmax = 3000);
-
-    void feed(const float *frame);
-    void search();
-    void reset();
-protected:
-    float *window_fn;   // [nfft]
-    float *fft_frame;   // [nfft]
-    float *last_frame;  // [nfft * 3/4]
-    std::complex<float> *freqdata; // [nfft/2 + 1]
-    int nfft;
-
-    int offset;
-    int time_sub;
-    ft8::MagArray power;
-
-    // [N] real --> [N/2 + 1] log magnitudes (decibels)
-    // virtual void fft_forward_mag_db(const float *frame, uint8_t *mag_db) = 0;
-    virtual void fft_forward(const float *in, std::complex<float> *out) = 0;
-};
 
 // Localize top N candidates in frequency and time according to their sync strength (looking at Costas symbols)
 // We treat and organize the candidate list as a min-heap (empty initially).

ft8/ldpc.cpp

@@ -8,11 +8,11 @@
 // from Sarah Johnson's Iterative Error Correction book.
 // codeword[i] = log ( P(x=0) / P(x=1) )
 //
-#include "ldpc.h"
 
 #include <stdio.h>
 #include <math.h>
 #include <stdlib.h>
+#include "constants.h"
 
 namespace ft8 {
 
@@ -47,13 +47,11 @@ void pack_bits(const uint8_t plain[], int num_bits, uint8_t packed[]) {
 // codeword is 174 log-likelihoods.
 // plain is a return value, 174 ints, to be 0 or 1.
 // max_iters is how hard to try.
-// n_errors == 87 means success.
-void ldpc_decode(const float codeword[], int max_iters, uint8_t plain[], int *n_errors) {
+// ok == 87 means success.
+void ldpc_decode(float codeword[], int max_iters, uint8_t plain[], int *ok) {
     float m[ft8::M][ft8::N];       // ~60 kB
     float e[ft8::M][ft8::N];       // ~60 kB
     int min_errors = ft8::M;
-    int n_err_last = 0;
-    int n_cnt = 0;
 
     for (int j = 0; j < ft8::M; j++) {
         for (int i = 0; i < ft8::N; i++) {
@@ -95,22 +93,6 @@ void ldpc_decode(const float codeword[], int max_iters, uint8_t plain[], int *n_
             }
         }
 
-        // Early stopping criterion
-        if (iter > 0) {
-            int nd = errors - n_err_last;
-            if (nd < 0) {
-                n_cnt = 0;
-            }
-            else {
-                ++n_cnt;
-            }
-            if (n_cnt >= 5 && iter >= 10 && errors >= 15) {
-                *n_errors = errors;
-                return;
-            }
-        }
-        n_err_last = errors;
-
         for (int i = 0; i < ft8::N; i++) {
             for (int ji1 = 0; ji1 < 3; ji1++) {
                 int j1 = kMn[i][ji1] - 1;
@@ -126,7 +108,7 @@ void ldpc_decode(const float codeword[], int max_iters, uint8_t plain[], int *n_
         }
     }
 
-    *n_errors = min_errors;
+    *ok = min_errors;
 }
 
 
@@ -151,19 +133,32 @@ static int ldpc_check(uint8_t codeword[]) {
 }
 
 
-void BPDecoderState::reset() {
+void bp_decode(float codeword[], int max_iters, uint8_t plain[], int *ok) {
+    float tov[ft8::N][3];
+    float toc[ft8::M][7];
+
+    int min_errors = ft8::M;
+
+    int nclast = 0;
+    int ncnt = 0;
+
     // initialize messages to checks
+    for (int i = 0; i < ft8::M; ++i) {
+        for (int j = 0; j < kNrw[i]; ++j) {
+            toc[i][j] = codeword[kNm[i][j] - 1];
+        }
+    }
+
     for (int i = 0; i < ft8::N; ++i) {
         for (int j = 0; j < 3; ++j) {
             tov[i][j] = 0;
         }
     }
-}
 
-
-int BPDecoderState::iterate(const float codeword[], uint8_t plain[]) {
-    // Update bit log likelihood ratios (tov=0 in iter 0)
+    for (int iter = 0; iter < max_iters; ++iter) {
         float   zn[ft8::N];
+
+        // Update bit log likelihood ratios (tov=0 in iter 0)
         for (int i = 0; i < ft8::N; ++i) {
             zn[i] = codeword[i] + tov[i][0] + tov[i][1] + tov[i][2];
             plain[i] = (zn[i] > 0) ? 1 : 0;
@@ -172,8 +167,13 @@ int BPDecoderState::iterate(const float codeword[], uint8_t plain[]) {
         // Check to see if we have a codeword (check before we do any iter)
         int errors = ldpc_check(plain);
 
+        if (errors < min_errors) {
+            // we have a better guess - update the result
+            min_errors = errors;
+
             if (errors == 0) {
-        return 0;   // Found a perfect answer
+                break;  // Found a perfect answer
+            }
         }
 
         // Send messages from bits to check nodes 
@@ -209,44 +209,9 @@ int BPDecoderState::iterate(const float codeword[], uint8_t plain[]) {
                 tov[i][j] = 2 * fast_atanh(-Tmn);
             }
         }
-
-    return errors;
-}
-
-
-
-void bp_decode(const float codeword[], int max_iters, uint8_t plain[], int *n_errors) {
-    BPDecoderState state;
-    
-    int n_err_last = 0;
-    int n_cnt = 0;
-
-    state.reset();
-    *n_errors = ft8::M;
-
-    for (int iter = 0; iter < max_iters; ++iter) {
-        int errors = state.iterate(codeword, plain);
-        if (errors < *n_errors) {
-            *n_errors = errors;
     }
-        if (errors == 0) return;
 
-        // Early stopping criterion
-        if (iter > 0) {
-            int nd = errors - n_err_last;
-            if (nd < 0) {
-                n_cnt = 0;
-            }
-            else {
-                ++n_cnt;
-            }
-            if (n_cnt >= 5 && iter >= 10 && errors >= 15) {
-                *n_errors = errors;
-                return;
-            }
-        }
-        n_err_last = errors;
-    }
+    *ok = min_errors;
 }
 
 // https://varietyofsound.wordpress.com/2011/02/14/efficient-tanh-computation-using-lamberts-continued-fraction/

ft8/ldpc.h

@@ -1,26 +1,14 @@
 #pragma once
 
-#include "constants.h"
-
 namespace ft8 {
 
-    class BPDecoderState {
-    public:
-        void reset();
-        int iterate(const float codeword[], uint8_t plain[]);
-
-    private:
-        float tov[ft8::N][3];
-        float toc[ft8::M][7];
-    };
-
     // codeword is 174 log-likelihoods.
     // plain is a return value, 174 ints, to be 0 or 1.
     // iters is how hard to try.
-    // n_errors == 0 means success.
-    void ldpc_decode(const float codeword[], int max_iters, uint8_t plain[], int *n_errors);
+    // ok == 87 means success.
+    void ldpc_decode(float codeword[], int max_iters, uint8_t plain[], int *ok);
 
-    void bp_decode(const float codeword[], int max_iters, uint8_t plain[], int *n_errors);
+    void bp_decode(float codeword[], int max_iters, uint8_t plain[], int *ok);
 
     // Packs a string of bits each represented as a zero/non-zero byte in plain[], 
     // as a string of packed bits starting from the MSB of the first byte of packed[]

ft8/message77.cpp

@@ -1,49 +0,0 @@
-#include "message77.h"
-#include "unpack.h"
-
-#include <string.h>
-
-namespace ft8 {
-
-Message77::Message77() {
-    i3 = n3 = 0;
-    field1[0] = field2[0] = field3[0] = '\0';
-}
-
-int Message77::str(char *buf, int buf_sz) const {
-    // Calculate the available space sans the '\0' terminator
-    int rem_sz = buf_sz - 1;
-    int field1_sz = strlen(field1);
-    int field2_sz = strlen(field2);
-    int field3_sz = strlen(field3);
-    int msg_sz = field1_sz + (field2_sz > 0 ? 1 : 0) + 
-                 field2_sz + (field3_sz > 0 ? 1 : 0) + 
-                 field3_sz;
-
-    if (rem_sz < msg_sz) return -1;
-
-    char *dst = buf;
-
-    dst = stpcpy(dst, field1);
-    *dst++ = ' ';
-    dst = stpcpy(dst, field2);
-    *dst++ = ' ';
-    dst = stpcpy(dst, field3);
-    *dst = '\0';
-
-    return msg_sz;
-}
-
-int Message77::unpack(const uint8_t *a77) {
-    // Extract n3 (bits 71..73) and i3 (bits 74..76)
-    n3 = ((a77[8] << 2) & 0x04) | ((a77[9] >> 6) & 0x03);
-    i3 = (a77[9] >> 3) & 0x07;
-
-    int rc = unpack77_fields(a77, field1, field2, field3);
-    if (rc < 0) {
-        field1[0] = field2[0] = field3[0] = '\0';
-    }
-    return rc;
-}
-
-}   // namespace ft8

ft8/message77.h

@@ -1,48 +0,0 @@
-#pragma once
-
-#include <stdint.h>
-
-namespace ft8 {
-
-class CallsignHasher {
-    virtual void save_callsign(void *obj, const char *callsign) = 0;
-    virtual bool hash10(void *obj, uint16_t hash, char *result) = 0;
-    virtual bool hash12(void *obj, uint16_t hash, char *result) = 0;
-    virtual bool hash22(void *obj, uint32_t hash, char *result) = 0;
-};
-
-class EmptyHasher : public CallsignHasher {
-    virtual void save_callsign(void *obj, const char *callsign) override {
-    }
-    virtual bool hash10(void *obj, uint16_t hash, char *result) override {
-        strcpy(result, "...");
-        return true;
-    }
-    virtual bool hash12(void *obj, uint16_t hash, char *result) override {
-        strcpy(result, "...");
-        return true;
-    }
-    virtual bool hash22(void *obj, uint32_t hash, char *result) override {
-        strcpy(result, "...");
-        return true;
-    }
-};
-
-struct Message77 {
-    uint8_t i3, n3;
-
-    // 11 chars nonstd call + 2 chars <...>
-    // 6 chars for grid/report/courtesy
-    char field1[13 + 1];
-    char field2[13 + 1];
-    char field3[6 + 1];
-
-    Message77();
-    int unpack(const uint8_t *packed77);
-    void pack(uint8_t *packed77);
-    int str(char *buf, int buf_sz) const;
-
-private:
-};
-
-} // namespace ft8

ft8/unpack.cpp

@@ -53,11 +53,11 @@ int unpack28(uint32_t n28, uint8_t ip, uint8_t i3, char *result) {
         // This is a 22-bit hash of a result
         //call hash22(n22,c13)     !Retrieve result from hash table
         // TODO: implement
-        strcpy(result, "<...>");
-        // result[0] = '<';
-        // int_to_dd(result + 1, n28, 7);
-        // result[8] = '>';
-        // result[9] = '\0';
+        // strcpy(result, "<...>");
+        result[0] = '<';
+        int_to_dd(result + 1, n28, 7);
+        result[8] = '>';
+        result[9] = '\0';
         return 0;
     }
 
@@ -181,6 +181,7 @@ int unpack_type1(const uint8_t *a77, uint8_t i3, char *field1, char *field2, cha
 
 
 int unpack_text(const uint8_t *a71, char *text) {
+    // TODO: test
     uint8_t b71[9];
 
     uint8_t carry = 0;
@@ -271,11 +272,11 @@ int unpack_nonstandard(const uint8_t *a77, char *field1, char *field2, char *fie
 
 	char call_3[15];
     // should replace with hash12(n12, call_3);
-    strcpy(call_3, "<...>");
-    // call_3[0] = '<';
-    // int_to_dd(call_3 + 1, n12, 4);
-    // call_3[5] = '>';
-    // call_3[6] = '\0';
+    // strcpy(call_3, "<...>");
+    call_3[0] = '<';
+    int_to_dd(call_3 + 1, n12, 4);
+    call_3[5] = '>';
+    call_3[6] = '\0';
 
 	char * call_1 = (iflip) ? c11 : call_3;
     char * call_2 = (iflip) ? call_3 : c11;
@@ -369,4 +370,4 @@ int unpack77(const uint8_t *a77, char *message) {
     return 0;
 }
 
-} // namespace ft8
+} // namespace