Useful GDB commands for my 3Q test on message https://github.com/barrettotte
x/30ub &msg
30 characters representing `https://github.com/barrettotte`
0x?????: 104 116 116 112 115 58 47 47
0x?????: 103 105 116 104 117 98 46 99
0x?????: 111 109 47 98 97 114 114 101
0x?????: 116 116 111 116 116 101
x/34ub &data_words
34 bytes = mode + char count indicator + encoded message
0x?????: 65 230 135 71 71 7 51 162
0x?????: 242 246 118 151 70 135 86 34
0x?????: 230 54 246 210 246 38 23 39
0x?????: 38 87 71 70 247 71 70 80
0x?????: 236 17
Message length = 34 / 2 blocks = 17 words per block
x/17ub &dw_block
group 1, block 1 = 17 bytes
0x?????: 65 230 135 71 71 7 51 162
0x?????: 242 246 118 151 70 135 86 34
0x?????: 230
x/18ub &msg_poly
byte 1 = 17 terms, bytes 2-18 = terms array
230x^0 + 34x^1 + 86x^2 + 135x^3 + 70x^4 + 151x^5 + 118x^6
+ 246x^7 + 242x^8 + 162x^9 + 51x^10 + 7x^11 + 71x^12 + 71x^13
+ 135x^14 + 230x^15 + 65x^16
0x?????: 17 230 34 86 135 70 151 118
0x?????: 246 242 162 51 7 71 71 135
0x?????: 230 65
Verifying debug outputs from ../jupyter/lunch-and-learn.ipynb
x/20ub &gen_polyx/24ub >mpA_polyx/24ub >mpB_polyx/24ub &prdA_polyx/24ub &prdB_poly
set breakpoint to blt _gpoly_loop and repeat c and x/20ub &gen_poly in GDB
- [x] 00: 2 1 1
- [x] 01: 3 2 3 1
- [x] 02: 4 8 14 7 1
- [x] 03: 5 64 120 54 15 1
- [x] 04: 6 116 147 63 198 31 1
- [x] 05: 7 38 227 32 218 1 63 1
- [x] 06: 8 117 68 11 164 154 122 127 1
- [x] 07: 9 24 200 173 239 54 81 11 255 1
- [x] 08: 10 37 197 232 164 235 245 158 207 226 1
- [x] 09: 11 193 157 113 95 94 199 111 159 194 216 1
- [x] 10: 12 160 116 144 248 162 219 123 50 163 130 172 1
- [x] 11: 13 97 213 127 92 84 7 31 220 118 67 119 68 1
- [x] 12: 14 120 132 83 43 46 13 52 17 177 17 227 73 137 1
- [x] 13: 15 163 234 210 166 127 195 158 43 151 174 70 114 54 14 1
- [x] 14: 16 26 134 32 151 132 139 105 105 10 74 112 163 111 196 29 1
- [x] 15: 17 59 36 50 98 229 41 65 163 8 30 209 68 189 104 13 59 1
- [x] 16: 18 79 99 125 53 85 134 143 41 249 83 197 22 119 120 83 66 119 1
- [x] 17: 19 146 217 67 32 75 173 82 73 220 240 215 199 175 149 113 183 251 239 1
Wooo! I literally struggled on this for over a week ... :^)
x/20ub &gen_poly
byte 1 = 19 terms, bytes 2-20 = terms array
146x^0 + 217x^1 + 67x^2 + 32x^3 + 75x^4 + 173x^5 + 82x^6 + 73x^7
+ 220x^8 + 240x^9 + 215x^10 + 199x^11 + 175x^12 + 149x^13 + 113x^14
+ 183x^15 + 251x^16 + 239x^17 + 1x^18
0x?????: 19 146 217 67 32 75 173 82
0x?????: 73 220 240 215 199 175 149 113
0x?????: 183 251 239 1
Verifying the rest of the Reed-Solomon error correction steps.
x/18ub &msg_polyx/20ub &gen_poly
Ensure lead term doesn't become too small during division.
x/35ub &tmpA_polyx/64ub &tmpB_polyx/18ub &msg_poly
(1x^18) * msg_poly
byte 1 = 35 terms, bytes 2-35 = terms array
0x^0 + 0x^1 + 0x^2 + 0x^3 + 0x^4 + 0x^5 + 0x^6 + 0x^7 + 0x^8 + 0x^9 + 0x^10
+ 0x^11 + 0x^12 + 0x^13 + 0x^14 + 0x^15 + 0x^16 + 0x^17 + 230x^18 + 34x^19
+ 86x^20 + 135x^21 + 70x^22 + 151x^23 + 118x^24 + 246x^25 + 242x^26 + 162x^27
+ 51x^28 + 7x290 + 71x^30 + 71x^31 + 135x^32 + 230x^33 + 65x^34
0x?????: 35 0 0 0 0 0 0 0
0x?????: 0 0 0 0 0 0 0 0
0x?????: 0 0 0 230 34 86 135 70
0x?????: 151 118 246 242 162 51 7 71
0x?????: 71 135 230 65 0 0 0 0
0x?????: 0 0 0 0 0 0 0 0
0x?????: 0 0 0 0 0 0 0 0
0x?????: 0 0 0 0 0 0 0 0
poly_remainder(msg_poly, gen_poly)
x/18ub &msg_polyx/40ub &tmpA_polyx/40ub &tmpB_poly
check divisor = denominator * mono => &tmpC_poly = &gen_poly * &tmp_mono
x/40ub &tmp_monox/20ub &gen_polyx/35ub &tmpC_poly
check remainder = remainder + divisor => &rem_poly = &rem_poly + &tmpC_poly
- Byte one should go down each iteration
x/35ub &rem_polyx/35ub &tmpC_poly
Verify polynomial remainder calculated correctly:
x/19ub &rem_poly
Note: This is for Block 0!
rem_poly = (msg_poly * 1x^18) / (gen_poly)
byte 1 = 18 terms, bytes 2-18 = terms array
202x^0 + 242x^1 + 0x^2 + 131x^3 + 35x^4 + 80x^5 + 198x^6 + 27x^7 + 233x^8
+ 174x^9 + 204x^10 + 245x^11 + 42x^12 + 54x^13 + 168x^14 + 17x^15
+ 51x^16 + 253x^17
0x?????: 18 202 242 0 131 35 80 198
0x?????: 27 233 174 204 245 42 54 168
0x?????: 17 51 253
Verify error correction word block filled correctly.
x/18ub &ecw_blockx/19ub &rem_poly
18 error correction words (max of 28).
0x?????: 253 51 17 168 54 42 245 204
0x?????: 174 233 27 198 80 35 131 0
0x?????: 242 202
Verify ECW block is copied correctly to ECW array.
x/18ub &ecw_blockx/36ub &ecw_blocks
ECW block 0 copied; 18 words
0x?????: 253 51 17 168 54 42 245 204
0x?????: 174 233 27 198 80 35 131 0
0x?????: 242 202 0 0 0 0 0 0
0x?????: 0 0 0 0 0 0 0 0
0x?????: 0 0 0 0
ECW block 1 copied; 36 words
0x?????: 253 51 17 168 54 42 245 204
0x?????: 174 233 27 198 80 35 131 0
0x?????: 242 202 9 107 30 118 21 108
0x?????: 227 15 117 139 15 178 142 79
0x?????: 151 162 200 57
x/70ub &payloadx/36ub &ecw_blocksx/34ub &data_words
interleaved data; 70 words = 2(18 + 17)
0x?????: 65 54 230 246 135 210 71 246
0x?????: 71 38 7 23 51 39 162 38
0x?????: 242 87 246 71 118 70 151 247
0x?????: 70 71 135 70 86 80 34 236
0x?????: 230 17 253 9 51 107 17 30
0x?????: 168 118 54 21 42 108 245 227
0x?????: 204 15 174 117 233 139 27 15
0x?????: 198 178 80 142 35 79 131 151
0x?????: 0 162 242 200 202 57
Add remainder, verify bit size - x/1uh &pyld_bits = 567 = (70 * 8) + 7
x/1ub &qr_width = 29 ... used for 29x29 QR code matrix
Verify PBM width converted to ASCII - x/11ub &ascii_buff
10 bytes representing a ten digit ASCII string, 11th byte for null terminator.
50 = '2'; 57 = '9'; 48='0' => "0000000029"
0x?????: 48 48 48 48 48 48 48 48
0x?????: 50 57 0
Verify PBM length converted to ASCII - x/11ub &ascii_buff
10 bytes representing a ten digit ASCII string, 11th byte for null terminator.
50 = '2'; 57 = '9'; 48='0' => "0000000029"
0x?????: 48 48 48 48 48 48 48 48
0x?????: 50 57 0
Verify PBM header 2nd line - x/6ub &line_buff
6 bytes representing "29 29\n"
0x?????: 50 57 32 50 57 10
Verify ubyte to ASCII binary string worked - x/9ub &bin_string, x/9ub &aub2b_buf
From this point on its a lot of visual checking.
x/567ub &data_bin
x/9ub &fmt_hi
"00110101"
0x?????: 48 48 49 49 48 49 48 49
0x?????: 0
x/9ub &fmt_lo
"01011111"
0x?????: 48 49 48 49 49 49 49 49
0x?????: 0