summaryrefslogtreecommitdiffstats
path: root/panels/network/qrcodegen.c
blob: 7cda9659b83a01548f96fb10bce2cc72942ef24d (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
/*
 * QR Code generator library (C)
 *
 * Copyright (c) Project Nayuki. (MIT License)
 * https://www.nayuki.io/page/qr-code-generator-library
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy of
 * this software and associated documentation files (the "Software"), to deal in
 * the Software without restriction, including without limitation the rights to
 * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
 * the Software, and to permit persons to whom the Software is furnished to do so,
 * subject to the following conditions:
 * - The above copyright notice and this permission notice shall be included in
 *   all copies or substantial portions of the Software.
 * - The Software is provided "as is", without warranty of any kind, express or
 *   implied, including but not limited to the warranties of merchantability,
 *   fitness for a particular purpose and noninfringement. In no event shall the
 *   authors or copyright holders be liable for any claim, damages or other
 *   liability, whether in an action of contract, tort or otherwise, arising from,
 *   out of or in connection with the Software or the use or other dealings in the
 *   Software.
 */

#include <assert.h>
#include <limits.h>
#include <stdlib.h>
#include <string.h>
#include "qrcodegen.h"

#ifndef QRCODEGEN_TEST
	#define testable static  // Keep functions private
#else
	#define testable  // Expose private functions
#endif


/*---- Forward declarations for private functions ----*/

// Regarding all public and private functions defined in this source file:
// - They require all pointer/array arguments to be not null unless the array length is zero.
// - They only read input scalar/array arguments, write to output pointer/array
//   arguments, and return scalar values; they are "pure" functions.
// - They don't read mutable global variables or write to any global variables.
// - They don't perform I/O, read the clock, print to console, etc.
// - They allocate a small and constant amount of stack memory.
// - They don't allocate or free any memory on the heap.
// - They don't recurse or mutually recurse. All the code
//   could be inlined into the top-level public functions.
// - They run in at most quadratic time with respect to input arguments.
//   Most functions run in linear time, and some in constant time.
//   There are no unbounded loops or non-obvious termination conditions.
// - They are completely thread-safe if the caller does not give the
//   same writable buffer to concurrent calls to these functions.

testable void appendBitsToBuffer(unsigned int val, int numBits, uint8_t buffer[], int *bitLen);

testable void addEccAndInterleave(uint8_t data[], int version, enum qrcodegen_Ecc ecl, uint8_t result[]);
testable int getNumDataCodewords(int version, enum qrcodegen_Ecc ecl);
testable int getNumRawDataModules(int ver);

testable void calcReedSolomonGenerator(int degree, uint8_t result[]);
testable void calcReedSolomonRemainder(const uint8_t data[], int dataLen,
	const uint8_t generator[], int degree, uint8_t result[]);
testable uint8_t finiteFieldMultiply(uint8_t x, uint8_t y);

testable void initializeFunctionModules(int version, uint8_t qrcode[]);
static void drawWhiteFunctionModules(uint8_t qrcode[], int version);
static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[]);
testable int getAlignmentPatternPositions(int version, uint8_t result[7]);
static void fillRectangle(int left, int top, int width, int height, uint8_t qrcode[]);

static void drawCodewords(const uint8_t data[], int dataLen, uint8_t qrcode[]);
static void applyMask(const uint8_t functionModules[], uint8_t qrcode[], enum qrcodegen_Mask mask);
static long getPenaltyScore(const uint8_t qrcode[]);
static void addRunToHistory(unsigned char run, unsigned char history[7]);
static bool hasFinderLikePattern(unsigned char runHistory[7]);

testable bool getModule(const uint8_t qrcode[], int x, int y);
testable void setModule(uint8_t qrcode[], int x, int y, bool isBlack);
testable void setModuleBounded(uint8_t qrcode[], int x, int y, bool isBlack);
static bool getBit(int x, int i);

testable int calcSegmentBitLength(enum qrcodegen_Mode mode, size_t numChars);
testable int getTotalBits(const struct qrcodegen_Segment segs[], size_t len, int version);
static int numCharCountBits(enum qrcodegen_Mode mode, int version);



/*---- Private tables of constants ----*/

// The set of all legal characters in alphanumeric mode, where each character
// value maps to the index in the string. For checking text and encoding segments.
static const char *ALPHANUMERIC_CHARSET = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:";

// For generating error correction codes.
testable const int8_t ECC_CODEWORDS_PER_BLOCK[4][41] = {
	// Version: (note that index 0 is for padding, and is set to an illegal value)
	//0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40    Error correction level
	{-1,  7, 10, 15, 20, 26, 18, 20, 24, 30, 18, 20, 24, 26, 30, 22, 24, 28, 30, 28, 28, 28, 28, 30, 30, 26, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30},  // Low
	{-1, 10, 16, 26, 18, 24, 16, 18, 22, 22, 26, 30, 22, 22, 24, 24, 28, 28, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28},  // Medium
	{-1, 13, 22, 18, 26, 18, 24, 18, 22, 20, 24, 28, 26, 24, 20, 30, 24, 28, 28, 26, 30, 28, 30, 30, 30, 30, 28, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30},  // Quartile
	{-1, 17, 28, 22, 16, 22, 28, 26, 26, 24, 28, 24, 28, 22, 24, 24, 30, 28, 28, 26, 28, 30, 24, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30},  // High
};

#define qrcodegen_REED_SOLOMON_DEGREE_MAX 30  // Based on the table above

// For generating error correction codes.
testable const int8_t NUM_ERROR_CORRECTION_BLOCKS[4][41] = {
	// Version: (note that index 0 is for padding, and is set to an illegal value)
	//0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40    Error correction level
	{-1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 4,  4,  4,  4,  4,  6,  6,  6,  6,  7,  8,  8,  9,  9, 10, 12, 12, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 21, 22, 24, 25},  // Low
	{-1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5,  5,  8,  9,  9, 10, 10, 11, 13, 14, 16, 17, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 33, 35, 37, 38, 40, 43, 45, 47, 49},  // Medium
	{-1, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8,  8, 10, 12, 16, 12, 17, 16, 18, 21, 20, 23, 23, 25, 27, 29, 34, 34, 35, 38, 40, 43, 45, 48, 51, 53, 56, 59, 62, 65, 68},  // Quartile
	{-1, 1, 1, 2, 4, 4, 4, 5, 6, 8, 8, 11, 11, 16, 16, 18, 16, 19, 21, 25, 25, 25, 34, 30, 32, 35, 37, 40, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 77, 81},  // High
};

// For automatic mask pattern selection.
static const int PENALTY_N1 =  3;
static const int PENALTY_N2 =  3;
static const int PENALTY_N3 = 40;
static const int PENALTY_N4 = 10;



/*---- High-level QR Code encoding functions ----*/

// Public function - see documentation comment in header file.
bool qrcodegen_encodeText(const char *text, uint8_t tempBuffer[], uint8_t qrcode[],
		enum qrcodegen_Ecc ecl, int minVersion, int maxVersion, enum qrcodegen_Mask mask, bool boostEcl) {

	size_t textLen = strlen(text);
	if (textLen == 0)
		return qrcodegen_encodeSegmentsAdvanced(NULL, 0, ecl, minVersion, maxVersion, mask, boostEcl, tempBuffer, qrcode);
	size_t bufLen = qrcodegen_BUFFER_LEN_FOR_VERSION(maxVersion);

	struct qrcodegen_Segment seg;
	if (qrcodegen_isNumeric(text)) {
		if (qrcodegen_calcSegmentBufferSize(qrcodegen_Mode_NUMERIC, textLen) > bufLen)
			goto fail;
		seg = qrcodegen_makeNumeric(text, tempBuffer);
	} else if (qrcodegen_isAlphanumeric(text)) {
		if (qrcodegen_calcSegmentBufferSize(qrcodegen_Mode_ALPHANUMERIC, textLen) > bufLen)
			goto fail;
		seg = qrcodegen_makeAlphanumeric(text, tempBuffer);
	} else {
		if (textLen > bufLen)
			goto fail;
		for (size_t i = 0; i < textLen; i++)
			tempBuffer[i] = (uint8_t)text[i];
		seg.mode = qrcodegen_Mode_BYTE;
		seg.bitLength = calcSegmentBitLength(seg.mode, textLen);
		if (seg.bitLength == -1)
			goto fail;
		seg.numChars = (int)textLen;
		seg.data = tempBuffer;
	}
	return qrcodegen_encodeSegmentsAdvanced(&seg, 1, ecl, minVersion, maxVersion, mask, boostEcl, tempBuffer, qrcode);

fail:
	qrcode[0] = 0;  // Set size to invalid value for safety
	return false;
}


// Public function - see documentation comment in header file.
bool qrcodegen_encodeBinary(uint8_t dataAndTemp[], size_t dataLen, uint8_t qrcode[],
		enum qrcodegen_Ecc ecl, int minVersion, int maxVersion, enum qrcodegen_Mask mask, bool boostEcl) {

	struct qrcodegen_Segment seg;
	seg.mode = qrcodegen_Mode_BYTE;
	seg.bitLength = calcSegmentBitLength(seg.mode, dataLen);
	if (seg.bitLength == -1) {
		qrcode[0] = 0;  // Set size to invalid value for safety
		return false;
	}
	seg.numChars = (int)dataLen;
	seg.data = dataAndTemp;
	return qrcodegen_encodeSegmentsAdvanced(&seg, 1, ecl, minVersion, maxVersion, mask, boostEcl, dataAndTemp, qrcode);
}


// Appends the given number of low-order bits of the given value to the given byte-based
// bit buffer, increasing the bit length. Requires 0 <= numBits <= 16 and val < 2^numBits.
testable void appendBitsToBuffer(unsigned int val, int numBits, uint8_t buffer[], int *bitLen) {
	assert(0 <= numBits && numBits <= 16 && (unsigned long)val >> numBits == 0);
	for (int i = numBits - 1; i >= 0; i--, (*bitLen)++)
		buffer[*bitLen >> 3] |= ((val >> i) & 1) << (7 - (*bitLen & 7));
}



/*---- Low-level QR Code encoding functions ----*/

// Public function - see documentation comment in header file.
bool qrcodegen_encodeSegments(const struct qrcodegen_Segment segs[], size_t len,
		enum qrcodegen_Ecc ecl, uint8_t tempBuffer[], uint8_t qrcode[]) {
	return qrcodegen_encodeSegmentsAdvanced(segs, len, ecl,
		qrcodegen_VERSION_MIN, qrcodegen_VERSION_MAX, -1, true, tempBuffer, qrcode);
}


// Public function - see documentation comment in header file.
bool qrcodegen_encodeSegmentsAdvanced(const struct qrcodegen_Segment segs[], size_t len, enum qrcodegen_Ecc ecl,
		int minVersion, int maxVersion, int mask, bool boostEcl, uint8_t tempBuffer[], uint8_t qrcode[]) {
	assert(segs != NULL || len == 0);
	assert(qrcodegen_VERSION_MIN <= minVersion && minVersion <= maxVersion && maxVersion <= qrcodegen_VERSION_MAX);
	assert(0 <= (int)ecl && (int)ecl <= 3 && -1 <= (int)mask && (int)mask <= 7);

	// Find the minimal version number to use
	int version, dataUsedBits;
	for (version = minVersion; ; version++) {
		int dataCapacityBits = getNumDataCodewords(version, ecl) * 8;  // Number of data bits available
		dataUsedBits = getTotalBits(segs, len, version);
		if (dataUsedBits != -1 && dataUsedBits <= dataCapacityBits)
			break;  // This version number is found to be suitable
		if (version >= maxVersion) {  // All versions in the range could not fit the given data
			qrcode[0] = 0;  // Set size to invalid value for safety
			return false;
		}
	}
	assert(dataUsedBits != -1);

	// Increase the error correction level while the data still fits in the current version number
	for (int i = (int)qrcodegen_Ecc_MEDIUM; i <= (int)qrcodegen_Ecc_HIGH; i++) {  // From low to high
		if (boostEcl && dataUsedBits <= getNumDataCodewords(version, (enum qrcodegen_Ecc)i) * 8)
			ecl = (enum qrcodegen_Ecc)i;
	}

	// Concatenate all segments to create the data bit string
	memset(qrcode, 0, qrcodegen_BUFFER_LEN_FOR_VERSION(version) * sizeof(qrcode[0]));
	int bitLen = 0;
	for (size_t i = 0; i < len; i++) {
		const struct qrcodegen_Segment *seg = &segs[i];
		appendBitsToBuffer((int)seg->mode, 4, qrcode, &bitLen);
		appendBitsToBuffer(seg->numChars, numCharCountBits(seg->mode, version), qrcode, &bitLen);
		for (int j = 0; j < seg->bitLength; j++)
			appendBitsToBuffer((seg->data[j >> 3] >> (7 - (j & 7))) & 1, 1, qrcode, &bitLen);
	}
	assert(bitLen == dataUsedBits);

	// Add terminator and pad up to a byte if applicable
	int dataCapacityBits = getNumDataCodewords(version, ecl) * 8;
	assert(bitLen <= dataCapacityBits);
	int terminatorBits = dataCapacityBits - bitLen;
	if (terminatorBits > 4)
		terminatorBits = 4;
	appendBitsToBuffer(0, terminatorBits, qrcode, &bitLen);
	appendBitsToBuffer(0, (8 - bitLen % 8) % 8, qrcode, &bitLen);
	assert(bitLen % 8 == 0);

	// Pad with alternating bytes until data capacity is reached
	for (uint8_t padByte = 0xEC; bitLen < dataCapacityBits; padByte ^= 0xEC ^ 0x11)
		appendBitsToBuffer(padByte, 8, qrcode, &bitLen);

	// Draw function and data codeword modules
	addEccAndInterleave(qrcode, version, ecl, tempBuffer);
	initializeFunctionModules(version, qrcode);
	drawCodewords(tempBuffer, getNumRawDataModules(version) / 8, qrcode);
	drawWhiteFunctionModules(qrcode, version);
	initializeFunctionModules(version, tempBuffer);

	// Handle masking
	if (mask == qrcodegen_Mask_AUTO) {  // Automatically choose best mask
		long minPenalty = LONG_MAX;
		for (int i = 0; i < 8; i++) {
			enum qrcodegen_Mask msk = (enum qrcodegen_Mask)i;
			drawFormatBits(ecl, msk, qrcode);
			applyMask(tempBuffer, qrcode, msk);
			long penalty = getPenaltyScore(qrcode);
			if (penalty < minPenalty) {
				mask = msk;
				minPenalty = penalty;
			}
			applyMask(tempBuffer, qrcode, msk);  // Undoes the mask due to XOR
		}
	}
	assert(0 <= (int)mask && (int)mask <= 7);
	drawFormatBits(ecl, mask, qrcode);
	applyMask(tempBuffer, qrcode, mask);
	return true;
}



/*---- Error correction code generation functions ----*/

// Appends error correction bytes to each block of the given data array, then interleaves
// bytes from the blocks and stores them in the result array. data[0 : dataLen] contains
// the input data. data[dataLen : rawCodewords] is used as a temporary work area and will
// be clobbered by this function. The final answer is stored in result[0 : rawCodewords].
testable void addEccAndInterleave(uint8_t data[], int version, enum qrcodegen_Ecc ecl, uint8_t result[]) {
	// Calculate parameter numbers
	assert(0 <= (int)ecl && (int)ecl < 4 && qrcodegen_VERSION_MIN <= version && version <= qrcodegen_VERSION_MAX);
	int numBlocks = NUM_ERROR_CORRECTION_BLOCKS[(int)ecl][version];
	int blockEccLen = ECC_CODEWORDS_PER_BLOCK  [(int)ecl][version];
	int rawCodewords = getNumRawDataModules(version) / 8;
	int dataLen = getNumDataCodewords(version, ecl);
	int numShortBlocks = numBlocks - rawCodewords % numBlocks;
	int shortBlockDataLen = rawCodewords / numBlocks - blockEccLen;

	// Split data into blocks, calculate ECC, and interleave
	// (not concatenate) the bytes into a single sequence
	uint8_t generator[qrcodegen_REED_SOLOMON_DEGREE_MAX];
	calcReedSolomonGenerator(blockEccLen, generator);
	const uint8_t *dat = data;
	for (int i = 0; i < numBlocks; i++) {
		int datLen = shortBlockDataLen + (i < numShortBlocks ? 0 : 1);
		uint8_t *ecc = &data[dataLen];  // Temporary storage
		calcReedSolomonRemainder(dat, datLen, generator, blockEccLen, ecc);
		for (int j = 0, k = i; j < datLen; j++, k += numBlocks) {  // Copy data
			if (j == shortBlockDataLen)
				k -= numShortBlocks;
			result[k] = dat[j];
		}
		for (int j = 0, k = dataLen + i; j < blockEccLen; j++, k += numBlocks)  // Copy ECC
			result[k] = ecc[j];
		dat += datLen;
	}
}


// Returns the number of 8-bit codewords that can be used for storing data (not ECC),
// for the given version number and error correction level. The result is in the range [9, 2956].
testable int getNumDataCodewords(int version, enum qrcodegen_Ecc ecl) {
	int v = version, e = (int)ecl;
	assert(0 <= e && e < 4);
	return getNumRawDataModules(v) / 8
		- ECC_CODEWORDS_PER_BLOCK    [e][v]
		* NUM_ERROR_CORRECTION_BLOCKS[e][v];
}


// Returns the number of data bits that can be stored in a QR Code of the given version number, after
// all function modules are excluded. This includes remainder bits, so it might not be a multiple of 8.
// The result is in the range [208, 29648]. This could be implemented as a 40-entry lookup table.
testable int getNumRawDataModules(int ver) {
	assert(qrcodegen_VERSION_MIN <= ver && ver <= qrcodegen_VERSION_MAX);
	int result = (16 * ver + 128) * ver + 64;
	if (ver >= 2) {
		int numAlign = ver / 7 + 2;
		result -= (25 * numAlign - 10) * numAlign - 55;
		if (ver >= 7)
			result -= 36;
	}
	return result;
}



/*---- Reed-Solomon ECC generator functions ----*/

// Calculates the Reed-Solomon generator polynomial of the given degree, storing in result[0 : degree].
testable void calcReedSolomonGenerator(int degree, uint8_t result[]) {
	// Start with the monomial x^0
	assert(1 <= degree && degree <= qrcodegen_REED_SOLOMON_DEGREE_MAX);
	memset(result, 0, degree * sizeof(result[0]));
	result[degree - 1] = 1;

	// Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}),
	// drop the highest term, and store the rest of the coefficients in order of descending powers.
	// Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D).
	uint8_t root = 1;
	for (int i = 0; i < degree; i++) {
		// Multiply the current product by (x - r^i)
		for (int j = 0; j < degree; j++) {
			result[j] = finiteFieldMultiply(result[j], root);
			if (j + 1 < degree)
				result[j] ^= result[j + 1];
		}
		root = finiteFieldMultiply(root, 0x02);
	}
}


// Calculates the remainder of the polynomial data[0 : dataLen] when divided by the generator[0 : degree], where all
// polynomials are in big endian and the generator has an implicit leading 1 term, storing the result in result[0 : degree].
testable void calcReedSolomonRemainder(const uint8_t data[], int dataLen,
		const uint8_t generator[], int degree, uint8_t result[]) {

	// Perform polynomial division
	assert(1 <= degree && degree <= qrcodegen_REED_SOLOMON_DEGREE_MAX);
	memset(result, 0, degree * sizeof(result[0]));
	for (int i = 0; i < dataLen; i++) {
		uint8_t factor = data[i] ^ result[0];
		memmove(&result[0], &result[1], (degree - 1) * sizeof(result[0]));
		result[degree - 1] = 0;
		for (int j = 0; j < degree; j++)
			result[j] ^= finiteFieldMultiply(generator[j], factor);
	}
}

#undef qrcodegen_REED_SOLOMON_DEGREE_MAX


// Returns the product of the two given field elements modulo GF(2^8/0x11D).
// All inputs are valid. This could be implemented as a 256*256 lookup table.
testable uint8_t finiteFieldMultiply(uint8_t x, uint8_t y) {
	// Russian peasant multiplication
	uint8_t z = 0;
	for (int i = 7; i >= 0; i--) {
		z = (z << 1) ^ ((z >> 7) * 0x11D);
		z ^= ((y >> i) & 1) * x;
	}
	return z;
}



/*---- Drawing function modules ----*/

// Clears the given QR Code grid with white modules for the given
// version's size, then marks every function module as black.
testable void initializeFunctionModules(int version, uint8_t qrcode[]) {
	// Initialize QR Code
	int qrsize = version * 4 + 17;
	memset(qrcode, 0, ((qrsize * qrsize + 7) / 8 + 1) * sizeof(qrcode[0]));
	qrcode[0] = (uint8_t)qrsize;

	// Fill horizontal and vertical timing patterns
	fillRectangle(6, 0, 1, qrsize, qrcode);
	fillRectangle(0, 6, qrsize, 1, qrcode);

	// Fill 3 finder patterns (all corners except bottom right) and format bits
	fillRectangle(0, 0, 9, 9, qrcode);
	fillRectangle(qrsize - 8, 0, 8, 9, qrcode);
	fillRectangle(0, qrsize - 8, 9, 8, qrcode);

	// Fill numerous alignment patterns
	uint8_t alignPatPos[7];
	int numAlign = getAlignmentPatternPositions(version, alignPatPos);
	for (int i = 0; i < numAlign; i++) {
		for (int j = 0; j < numAlign; j++) {
			// Don't draw on the three finder corners
			if (!((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0)))
				fillRectangle(alignPatPos[i] - 2, alignPatPos[j] - 2, 5, 5, qrcode);
		}
	}

	// Fill version blocks
	if (version >= 7) {
		fillRectangle(qrsize - 11, 0, 3, 6, qrcode);
		fillRectangle(0, qrsize - 11, 6, 3, qrcode);
	}
}


// Draws white function modules and possibly some black modules onto the given QR Code, without changing
// non-function modules. This does not draw the format bits. This requires all function modules to be previously
// marked black (namely by initializeFunctionModules()), because this may skip redrawing black function modules.
static void drawWhiteFunctionModules(uint8_t qrcode[], int version) {
	// Draw horizontal and vertical timing patterns
	int qrsize = qrcodegen_getSize(qrcode);
	for (int i = 7; i < qrsize - 7; i += 2) {
		setModule(qrcode, 6, i, false);
		setModule(qrcode, i, 6, false);
	}

	// Draw 3 finder patterns (all corners except bottom right; overwrites some timing modules)
	for (int dy = -4; dy <= 4; dy++) {
		for (int dx = -4; dx <= 4; dx++) {
			int dist = abs(dx);
			if (abs(dy) > dist)
				dist = abs(dy);
			if (dist == 2 || dist == 4) {
				setModuleBounded(qrcode, 3 + dx, 3 + dy, false);
				setModuleBounded(qrcode, qrsize - 4 + dx, 3 + dy, false);
				setModuleBounded(qrcode, 3 + dx, qrsize - 4 + dy, false);
			}
		}
	}

	// Draw numerous alignment patterns
	uint8_t alignPatPos[7];
	int numAlign = getAlignmentPatternPositions(version, alignPatPos);
	for (int i = 0; i < numAlign; i++) {
		for (int j = 0; j < numAlign; j++) {
			if ((i == 0 && j == 0) || (i == 0 && j == numAlign - 1) || (i == numAlign - 1 && j == 0))
				continue;  // Don't draw on the three finder corners
			for (int dy = -1; dy <= 1; dy++) {
				for (int dx = -1; dx <= 1; dx++)
					setModule(qrcode, alignPatPos[i] + dx, alignPatPos[j] + dy, dx == 0 && dy == 0);
			}
		}
	}

	// Draw version blocks
	if (version >= 7) {
		// Calculate error correction code and pack bits
		int rem = version;  // version is uint6, in the range [7, 40]
		for (int i = 0; i < 12; i++)
			rem = (rem << 1) ^ ((rem >> 11) * 0x1F25);
		long bits = (long)version << 12 | rem;  // uint18
		assert(bits >> 18 == 0);

		// Draw two copies
		for (int i = 0; i < 6; i++) {
			for (int j = 0; j < 3; j++) {
				int k = qrsize - 11 + j;
				setModule(qrcode, k, i, (bits & 1) != 0);
				setModule(qrcode, i, k, (bits & 1) != 0);
				bits >>= 1;
			}
		}
	}
}


// Draws two copies of the format bits (with its own error correction code) based
// on the given mask and error correction level. This always draws all modules of
// the format bits, unlike drawWhiteFunctionModules() which might skip black modules.
static void drawFormatBits(enum qrcodegen_Ecc ecl, enum qrcodegen_Mask mask, uint8_t qrcode[]) {
	// Calculate error correction code and pack bits
	assert(0 <= (int)mask && (int)mask <= 7);
	static const int table[] = {1, 0, 3, 2};
	int data = table[(int)ecl] << 3 | (int)mask;  // errCorrLvl is uint2, mask is uint3
	int rem = data;
	for (int i = 0; i < 10; i++)
		rem = (rem << 1) ^ ((rem >> 9) * 0x537);
	int bits = (data << 10 | rem) ^ 0x5412;  // uint15
	assert(bits >> 15 == 0);

	// Draw first copy
	for (int i = 0; i <= 5; i++)
		setModule(qrcode, 8, i, getBit(bits, i));
	setModule(qrcode, 8, 7, getBit(bits, 6));
	setModule(qrcode, 8, 8, getBit(bits, 7));
	setModule(qrcode, 7, 8, getBit(bits, 8));
	for (int i = 9; i < 15; i++)
		setModule(qrcode, 14 - i, 8, getBit(bits, i));

	// Draw second copy
	int qrsize = qrcodegen_getSize(qrcode);
	for (int i = 0; i < 8; i++)
		setModule(qrcode, qrsize - 1 - i, 8, getBit(bits, i));
	for (int i = 8; i < 15; i++)
		setModule(qrcode, 8, qrsize - 15 + i, getBit(bits, i));
	setModule(qrcode, 8, qrsize - 8, true);  // Always black
}


// Calculates and stores an ascending list of positions of alignment patterns
// for this version number, returning the length of the list (in the range [0,7]).
// Each position is in the range [0,177), and are used on both the x and y axes.
// This could be implemented as lookup table of 40 variable-length lists of unsigned bytes.
testable int getAlignmentPatternPositions(int version, uint8_t result[7]) {
	if (version == 1)
		return 0;
	int numAlign = version / 7 + 2;
	int step = (version == 32) ? 26 :
		(version*4 + numAlign*2 + 1) / (numAlign*2 - 2) * 2;
	for (int i = numAlign - 1, pos = version * 4 + 10; i >= 1; i--, pos -= step)
		result[i] = pos;
	result[0] = 6;
	return numAlign;
}


// Sets every pixel in the range [left : left + width] * [top : top + height] to black.
static void fillRectangle(int left, int top, int width, int height, uint8_t qrcode[]) {
	for (int dy = 0; dy < height; dy++) {
		for (int dx = 0; dx < width; dx++)
			setModule(qrcode, left + dx, top + dy, true);
	}
}



/*---- Drawing data modules and masking ----*/

// Draws the raw codewords (including data and ECC) onto the given QR Code. This requires the initial state of
// the QR Code to be black at function modules and white at codeword modules (including unused remainder bits).
static void drawCodewords(const uint8_t data[], int dataLen, uint8_t qrcode[]) {
	int qrsize = qrcodegen_getSize(qrcode);
	int i = 0;  // Bit index into the data
	// Do the funny zigzag scan
	for (int right = qrsize - 1; right >= 1; right -= 2) {  // Index of right column in each column pair
		if (right == 6)
			right = 5;
		for (int vert = 0; vert < qrsize; vert++) {  // Vertical counter
			for (int j = 0; j < 2; j++) {
				int x = right - j;  // Actual x coordinate
				bool upward = ((right + 1) & 2) == 0;
				int y = upward ? qrsize - 1 - vert : vert;  // Actual y coordinate
				if (!getModule(qrcode, x, y) && i < dataLen * 8) {
					bool black = getBit(data[i >> 3], 7 - (i & 7));
					setModule(qrcode, x, y, black);
					i++;
				}
				// If this QR Code has any remainder bits (0 to 7), they were assigned as
				// 0/false/white by the constructor and are left unchanged by this method
			}
		}
	}
	assert(i == dataLen * 8);
}


// XORs the codeword modules in this QR Code with the given mask pattern.
// The function modules must be marked and the codeword bits must be drawn
// before masking. Due to the arithmetic of XOR, calling applyMask() with
// the same mask value a second time will undo the mask. A final well-formed
// QR Code needs exactly one (not zero, two, etc.) mask applied.
static void applyMask(const uint8_t functionModules[], uint8_t qrcode[], enum qrcodegen_Mask mask) {
	assert(0 <= (int)mask && (int)mask <= 7);  // Disallows qrcodegen_Mask_AUTO
	int qrsize = qrcodegen_getSize(qrcode);
	for (int y = 0; y < qrsize; y++) {
		for (int x = 0; x < qrsize; x++) {
			if (getModule(functionModules, x, y))
				continue;
			bool invert;
			switch ((int)mask) {
				case 0:  invert = (x + y) % 2 == 0;                    break;
				case 1:  invert = y % 2 == 0;                          break;
				case 2:  invert = x % 3 == 0;                          break;
				case 3:  invert = (x + y) % 3 == 0;                    break;
				case 4:  invert = (x / 3 + y / 2) % 2 == 0;            break;
				case 5:  invert = x * y % 2 + x * y % 3 == 0;          break;
				case 6:  invert = (x * y % 2 + x * y % 3) % 2 == 0;    break;
				case 7:  invert = ((x + y) % 2 + x * y % 3) % 2 == 0;  break;
				default:  assert(false);  return;
			}
			bool val = getModule(qrcode, x, y);
			setModule(qrcode, x, y, val ^ invert);
		}
	}
}


// Calculates and returns the penalty score based on state of the given QR Code's current modules.
// This is used by the automatic mask choice algorithm to find the mask pattern that yields the lowest score.
static long getPenaltyScore(const uint8_t qrcode[]) {
	int qrsize = qrcodegen_getSize(qrcode);
	long result = 0;

	// Adjacent modules in row having same color, and finder-like patterns
	for (int y = 0; y < qrsize; y++) {
		unsigned char runHistory[7] = {0};
		bool color = false;
		unsigned char runX = 0;
		for (int x = 0; x < qrsize; x++) {
			if (getModule(qrcode, x, y) == color) {
				runX++;
				if (runX == 5)
					result += PENALTY_N1;
				else if (runX > 5)
					result++;
			} else {
				addRunToHistory(runX, runHistory);
				if (!color && hasFinderLikePattern(runHistory))
					result += PENALTY_N3;
				color = getModule(qrcode, x, y);
				runX = 1;
			}
		}
		addRunToHistory(runX, runHistory);
		if (color)
			addRunToHistory(0, runHistory);  // Dummy run of white
		if (hasFinderLikePattern(runHistory))
			result += PENALTY_N3;
	}
	// Adjacent modules in column having same color, and finder-like patterns
	for (int x = 0; x < qrsize; x++) {
		unsigned char runHistory[7] = {0};
		bool color = false;
		unsigned char runY = 0;
		for (int y = 0; y < qrsize; y++) {
			if (getModule(qrcode, x, y) == color) {
				runY++;
				if (runY == 5)
					result += PENALTY_N1;
				else if (runY > 5)
					result++;
			} else {
				addRunToHistory(runY, runHistory);
				if (!color && hasFinderLikePattern(runHistory))
					result += PENALTY_N3;
				color = getModule(qrcode, x, y);
				runY = 1;
			}
		}
		addRunToHistory(runY, runHistory);
		if (color)
			addRunToHistory(0, runHistory);  // Dummy run of white
		if (hasFinderLikePattern(runHistory))
			result += PENALTY_N3;
	}

	// 2*2 blocks of modules having same color
	for (int y = 0; y < qrsize - 1; y++) {
		for (int x = 0; x < qrsize - 1; x++) {
			bool  color = getModule(qrcode, x, y);
			if (  color == getModule(qrcode, x + 1, y) &&
			      color == getModule(qrcode, x, y + 1) &&
			      color == getModule(qrcode, x + 1, y + 1))
				result += PENALTY_N2;
		}
	}

	// Balance of black and white modules
	int black = 0;
	for (int y = 0; y < qrsize; y++) {
		for (int x = 0; x < qrsize; x++) {
			if (getModule(qrcode, x, y))
				black++;
		}
	}
	int total = qrsize * qrsize;  // Note that size is odd, so black/total != 1/2
	// Compute the smallest integer k >= 0 such that (45-5k)% <= black/total <= (55+5k)%
	int k = (int)((labs(black * 20L - total * 10L) + total - 1) / total) - 1;
	result += k * PENALTY_N4;
	return result;
}


// Inserts the given value to the front of the given array, which shifts over the
// existing values and deletes the last value. A helper function for getPenaltyScore().
static void addRunToHistory(unsigned char run, unsigned char history[7]) {
	memmove(&history[1], &history[0], 6 * sizeof(history[0]));
	history[0] = run;
}


// Tests whether the given run history has the pattern of ratio 1:1:3:1:1 in the middle, and
// surrounded by at least 4 on either or both ends. A helper function for getPenaltyScore().
// Must only be called immediately after a run of white modules has ended.
static bool hasFinderLikePattern(unsigned char runHistory[7]) {
	unsigned char n = runHistory[1];
	// The maximum QR Code size is 177, hence the run length n <= 177.
	// Arithmetic is promoted to int, so n*4 will not overflow.
	return n > 0 && runHistory[2] == n && runHistory[4] == n && runHistory[5] == n
		&& runHistory[3] == n * 3 && (runHistory[0] >= n * 4 || runHistory[6] >= n * 4);
}



/*---- Basic QR Code information ----*/

// Public function - see documentation comment in header file.
int qrcodegen_getSize(const uint8_t qrcode[]) {
	assert(qrcode != NULL);
	int result = qrcode[0];
	assert((qrcodegen_VERSION_MIN * 4 + 17) <= result
		&& result <= (qrcodegen_VERSION_MAX * 4 + 17));
	return result;
}


// Public function - see documentation comment in header file.
bool qrcodegen_getModule(const uint8_t qrcode[], int x, int y) {
	assert(qrcode != NULL);
	int qrsize = qrcode[0];
	return (0 <= x && x < qrsize && 0 <= y && y < qrsize) && getModule(qrcode, x, y);
}


// Gets the module at the given coordinates, which must be in bounds.
testable bool getModule(const uint8_t qrcode[], int x, int y) {
	int qrsize = qrcode[0];
	assert(21 <= qrsize && qrsize <= 177 && 0 <= x && x < qrsize && 0 <= y && y < qrsize);
	int index = y * qrsize + x;
	return getBit(qrcode[(index >> 3) + 1], index & 7);
}


// Sets the module at the given coordinates, which must be in bounds.
testable void setModule(uint8_t qrcode[], int x, int y, bool isBlack) {
	int qrsize = qrcode[0];
	assert(21 <= qrsize && qrsize <= 177 && 0 <= x && x < qrsize && 0 <= y && y < qrsize);
	int index = y * qrsize + x;
	int bitIndex = index & 7;
	int byteIndex = (index >> 3) + 1;
	if (isBlack)
		qrcode[byteIndex] |= 1 << bitIndex;
	else
		qrcode[byteIndex] &= (1 << bitIndex) ^ 0xFF;
}


// Sets the module at the given coordinates, doing nothing if out of bounds.
testable void setModuleBounded(uint8_t qrcode[], int x, int y, bool isBlack) {
	int qrsize = qrcode[0];
	if (0 <= x && x < qrsize && 0 <= y && y < qrsize)
		setModule(qrcode, x, y, isBlack);
}


// Returns true iff the i'th bit of x is set to 1. Requires x >= 0 and 0 <= i <= 14.
static bool getBit(int x, int i) {
	return ((x >> i) & 1) != 0;
}



/*---- Segment handling ----*/

// Public function - see documentation comment in header file.
bool qrcodegen_isAlphanumeric(const char *text) {
	assert(text != NULL);
	for (; *text != '\0'; text++) {
		if (strchr(ALPHANUMERIC_CHARSET, *text) == NULL)
			return false;
	}
	return true;
}


// Public function - see documentation comment in header file.
bool qrcodegen_isNumeric(const char *text) {
	assert(text != NULL);
	for (; *text != '\0'; text++) {
		if (*text < '0' || *text > '9')
			return false;
	}
	return true;
}


// Public function - see documentation comment in header file.
size_t qrcodegen_calcSegmentBufferSize(enum qrcodegen_Mode mode, size_t numChars) {
	int temp = calcSegmentBitLength(mode, numChars);
	if (temp == -1)
		return SIZE_MAX;
	assert(0 <= temp && temp <= INT16_MAX);
	return ((size_t)temp + 7) / 8;
}


// Returns the number of data bits needed to represent a segment
// containing the given number of characters using the given mode. Notes:
// - Returns -1 on failure, i.e. numChars > INT16_MAX or
//   the number of needed bits exceeds INT16_MAX (i.e. 32767).
// - Otherwise, all valid results are in the range [0, INT16_MAX].
// - For byte mode, numChars measures the number of bytes, not Unicode code points.
// - For ECI mode, numChars must be 0, and the worst-case number of bits is returned.
//   An actual ECI segment can have shorter data. For non-ECI modes, the result is exact.
testable int calcSegmentBitLength(enum qrcodegen_Mode mode, size_t numChars) {
	// All calculations are designed to avoid overflow on all platforms
	if (numChars > (unsigned int)INT16_MAX)
		return -1;
	long result = (long)numChars;
	if (mode == qrcodegen_Mode_NUMERIC)
		result = (result * 10 + 2) / 3;  // ceil(10/3 * n)
	else if (mode == qrcodegen_Mode_ALPHANUMERIC)
		result = (result * 11 + 1) / 2;  // ceil(11/2 * n)
	else if (mode == qrcodegen_Mode_BYTE)
		result *= 8;
	else if (mode == qrcodegen_Mode_KANJI)
		result *= 13;
	else if (mode == qrcodegen_Mode_ECI && numChars == 0)
		result = 3 * 8;
	else {  // Invalid argument
		assert(false);
		return -1;
	}
	assert(result >= 0);
	if (result > (unsigned int)INT16_MAX)
		return -1;
	return (int)result;
}


// Public function - see documentation comment in header file.
struct qrcodegen_Segment qrcodegen_makeBytes(const uint8_t data[], size_t len, uint8_t buf[]) {
	assert(data != NULL || len == 0);
	struct qrcodegen_Segment result;
	result.mode = qrcodegen_Mode_BYTE;
	result.bitLength = calcSegmentBitLength(result.mode, len);
	assert(result.bitLength != -1);
	result.numChars = (int)len;
	if (len > 0)
		memcpy(buf, data, len * sizeof(buf[0]));
	result.data = buf;
	return result;
}


// Public function - see documentation comment in header file.
struct qrcodegen_Segment qrcodegen_makeNumeric(const char *digits, uint8_t buf[]) {
	assert(digits != NULL);
	struct qrcodegen_Segment result;
	size_t len = strlen(digits);
	result.mode = qrcodegen_Mode_NUMERIC;
	int bitLen = calcSegmentBitLength(result.mode, len);
	assert(bitLen != -1);
	result.numChars = (int)len;
	if (bitLen > 0)
		memset(buf, 0, ((size_t)bitLen + 7) / 8 * sizeof(buf[0]));
	result.bitLength = 0;

	unsigned int accumData = 0;
	int accumCount = 0;
	for (; *digits != '\0'; digits++) {
		char c = *digits;
		assert('0' <= c && c <= '9');
		accumData = accumData * 10 + (unsigned int)(c - '0');
		accumCount++;
		if (accumCount == 3) {
			appendBitsToBuffer(accumData, 10, buf, &result.bitLength);
			accumData = 0;
			accumCount = 0;
		}
	}
	if (accumCount > 0)  // 1 or 2 digits remaining
		appendBitsToBuffer(accumData, accumCount * 3 + 1, buf, &result.bitLength);
	assert(result.bitLength == bitLen);
	result.data = buf;
	return result;
}


// Public function - see documentation comment in header file.
struct qrcodegen_Segment qrcodegen_makeAlphanumeric(const char *text, uint8_t buf[]) {
	assert(text != NULL);
	struct qrcodegen_Segment result;
	size_t len = strlen(text);
	result.mode = qrcodegen_Mode_ALPHANUMERIC;
	int bitLen = calcSegmentBitLength(result.mode, len);
	assert(bitLen != -1);
	result.numChars = (int)len;
	if (bitLen > 0)
		memset(buf, 0, ((size_t)bitLen + 7) / 8 * sizeof(buf[0]));
	result.bitLength = 0;

	unsigned int accumData = 0;
	int accumCount = 0;
	for (; *text != '\0'; text++) {
		const char *temp = strchr(ALPHANUMERIC_CHARSET, *text);
		assert(temp != NULL);
		accumData = accumData * 45 + (unsigned int)(temp - ALPHANUMERIC_CHARSET);
		accumCount++;
		if (accumCount == 2) {
			appendBitsToBuffer(accumData, 11, buf, &result.bitLength);
			accumData = 0;
			accumCount = 0;
		}
	}
	if (accumCount > 0)  // 1 character remaining
		appendBitsToBuffer(accumData, 6, buf, &result.bitLength);
	assert(result.bitLength == bitLen);
	result.data = buf;
	return result;
}


// Public function - see documentation comment in header file.
struct qrcodegen_Segment qrcodegen_makeEci(long assignVal, uint8_t buf[]) {
	struct qrcodegen_Segment result;
	result.mode = qrcodegen_Mode_ECI;
	result.numChars = 0;
	result.bitLength = 0;
	if (assignVal < 0)
		assert(false);
	else if (assignVal < (1 << 7)) {
		memset(buf, 0, 1 * sizeof(buf[0]));
		appendBitsToBuffer(assignVal, 8, buf, &result.bitLength);
	} else if (assignVal < (1 << 14)) {
		memset(buf, 0, 2 * sizeof(buf[0]));
		appendBitsToBuffer(2, 2, buf, &result.bitLength);
		appendBitsToBuffer(assignVal, 14, buf, &result.bitLength);
	} else if (assignVal < 1000000L) {
		memset(buf, 0, 3 * sizeof(buf[0]));
		appendBitsToBuffer(6, 3, buf, &result.bitLength);
		appendBitsToBuffer(assignVal >> 10, 11, buf, &result.bitLength);
		appendBitsToBuffer(assignVal & 0x3FF, 10, buf, &result.bitLength);
	} else
		assert(false);
	result.data = buf;
	return result;
}


// Calculates the number of bits needed to encode the given segments at the given version.
// Returns a non-negative number if successful. Otherwise returns -1 if a segment has too
// many characters to fit its length field, or the total bits exceeds INT16_MAX.
testable int getTotalBits(const struct qrcodegen_Segment segs[], size_t len, int version) {
	assert(segs != NULL || len == 0);
	long result = 0;
	for (size_t i = 0; i < len; i++) {
		int numChars  = segs[i].numChars;
		int bitLength = segs[i].bitLength;
		assert(0 <= numChars  && numChars  <= INT16_MAX);
		assert(0 <= bitLength && bitLength <= INT16_MAX);
		int ccbits = numCharCountBits(segs[i].mode, version);
		assert(0 <= ccbits && ccbits <= 16);
		if (numChars >= (1L << ccbits))
			return -1;  // The segment's length doesn't fit the field's bit width
		result += 4L + ccbits + bitLength;
		if (result > INT16_MAX)
			return -1;  // The sum might overflow an int type
	}
	assert(0 <= result && result <= INT16_MAX);
	return (int)result;
}


// Returns the bit width of the character count field for a segment in the given mode
// in a QR Code at the given version number. The result is in the range [0, 16].
static int numCharCountBits(enum qrcodegen_Mode mode, int version) {
	assert(qrcodegen_VERSION_MIN <= version && version <= qrcodegen_VERSION_MAX);
	int i = (version + 7) / 17;
	switch (mode) {
		case qrcodegen_Mode_NUMERIC     : { static const int temp[] = {10, 12, 14}; return temp[i]; }
		case qrcodegen_Mode_ALPHANUMERIC: { static const int temp[] = { 9, 11, 13}; return temp[i]; }
		case qrcodegen_Mode_BYTE        : { static const int temp[] = { 8, 16, 16}; return temp[i]; }
		case qrcodegen_Mode_KANJI       : { static const int temp[] = { 8, 10, 12}; return temp[i]; }
		case qrcodegen_Mode_ECI         : return 0;
		default:  assert(false);  return -1;  // Dummy value
	}
}