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1.1 root 1: // table of quotients and remainders for [-15...16] / [-15...16]
2:
3: // numerator = -15
4: {1, 0},
5: {1, -1},
6: {1, -2},
7: {1, -3},
8: {1, -4},
9: {1, -5},
10: {1, -6},
11: {1, -7},
12: {2, -1},
13: {2, -3},
14: {3, 0},
15: {3, -3},
16: {5, 0},
17: {7, -1},
18: {15, 0},
19: {0, 0},
20: {-15, 0},
21: {-8, 1},
22: {-5, 0},
23: {-4, 1},
24: {-3, 0},
25: {-3, 3},
26: {-3, 6},
27: {-2, 1},
28: {-2, 3},
29: {-2, 5},
30: {-2, 7},
31: {-2, 9},
32: {-2, 11},
33: {-2, 13},
34: {-1, 0},
35: {-1, 1},
36: // numerator = -14
37: {0, -14},
38: {1, 0},
39: {1, -1},
40: {1, -2},
41: {1, -3},
42: {1, -4},
43: {1, -5},
44: {1, -6},
45: {2, 0},
46: {2, -2},
47: {2, -4},
48: {3, -2},
49: {4, -2},
50: {7, 0},
51: {14, 0},
52: {0, 0},
53: {-14, 0},
54: {-7, 0},
55: {-5, 1},
56: {-4, 2},
57: {-3, 1},
58: {-3, 4},
59: {-2, 0},
60: {-2, 2},
61: {-2, 4},
62: {-2, 6},
63: {-2, 8},
64: {-2, 10},
65: {-2, 12},
66: {-1, 0},
67: {-1, 1},
68: {-1, 2},
69: // numerator = -13
70: {0, -13},
71: {0, -13},
72: {1, 0},
73: {1, -1},
74: {1, -2},
75: {1, -3},
76: {1, -4},
77: {1, -5},
78: {1, -6},
79: {2, -1},
80: {2, -3},
81: {3, -1},
82: {4, -1},
83: {6, -1},
84: {13, 0},
85: {0, 0},
86: {-13, 0},
87: {-7, 1},
88: {-5, 2},
89: {-4, 3},
90: {-3, 2},
91: {-3, 5},
92: {-2, 1},
93: {-2, 3},
94: {-2, 5},
95: {-2, 7},
96: {-2, 9},
97: {-2, 11},
98: {-1, 0},
99: {-1, 1},
100: {-1, 2},
101: {-1, 3},
102: // numerator = -12
103: {0, -12},
104: {0, -12},
105: {0, -12},
106: {1, 0},
107: {1, -1},
108: {1, -2},
109: {1, -3},
110: {1, -4},
111: {1, -5},
112: {2, 0},
113: {2, -2},
114: {3, 0},
115: {4, 0},
116: {6, 0},
117: {12, 0},
118: {0, 0},
119: {-12, 0},
120: {-6, 0},
121: {-4, 0},
122: {-3, 0},
123: {-3, 3},
124: {-2, 0},
125: {-2, 2},
126: {-2, 4},
127: {-2, 6},
128: {-2, 8},
129: {-2, 10},
130: {-1, 0},
131: {-1, 1},
132: {-1, 2},
133: {-1, 3},
134: {-1, 4},
135: // numerator = -11
136: {0, -11},
137: {0, -11},
138: {0, -11},
139: {0, -11},
140: {1, 0},
141: {1, -1},
142: {1, -2},
143: {1, -3},
144: {1, -4},
145: {1, -5},
146: {2, -1},
147: {2, -3},
148: {3, -2},
149: {5, -1},
150: {11, 0},
151: {0, 0},
152: {-11, 0},
153: {-6, 1},
154: {-4, 1},
155: {-3, 1},
156: {-3, 4},
157: {-2, 1},
158: {-2, 3},
159: {-2, 5},
160: {-2, 7},
161: {-2, 9},
162: {-1, 0},
163: {-1, 1},
164: {-1, 2},
165: {-1, 3},
166: {-1, 4},
167: {-1, 5},
168: // numerator = -10
169: {0, -10},
170: {0, -10},
171: {0, -10},
172: {0, -10},
173: {0, -10},
174: {1, 0},
175: {1, -1},
176: {1, -2},
177: {1, -3},
178: {1, -4},
179: {2, 0},
180: {2, -2},
181: {3, -1},
182: {5, 0},
183: {10, 0},
184: {0, 0},
185: {-10, 0},
186: {-5, 0},
187: {-4, 2},
188: {-3, 2},
189: {-2, 0},
190: {-2, 2},
191: {-2, 4},
192: {-2, 6},
193: {-2, 8},
194: {-1, 0},
195: {-1, 1},
196: {-1, 2},
197: {-1, 3},
198: {-1, 4},
199: {-1, 5},
200: {-1, 6},
201: // numerator = -9
202: {0, -9},
203: {0, -9},
204: {0, -9},
205: {0, -9},
206: {0, -9},
207: {0, -9},
208: {1, 0},
209: {1, -1},
210: {1, -2},
211: {1, -3},
212: {1, -4},
213: {2, -1},
214: {3, 0},
215: {4, -1},
216: {9, 0},
217: {0, 0},
218: {-9, 0},
219: {-5, 1},
220: {-3, 0},
221: {-3, 3},
222: {-2, 1},
223: {-2, 3},
224: {-2, 5},
225: {-2, 7},
226: {-1, 0},
227: {-1, 1},
228: {-1, 2},
229: {-1, 3},
230: {-1, 4},
231: {-1, 5},
232: {-1, 6},
233: {-1, 7},
234: // numerator = -8
235: {0, -8},
236: {0, -8},
237: {0, -8},
238: {0, -8},
239: {0, -8},
240: {0, -8},
241: {0, -8},
242: {1, 0},
243: {1, -1},
244: {1, -2},
245: {1, -3},
246: {2, 0},
247: {2, -2},
248: {4, 0},
249: {8, 0},
250: {0, 0},
251: {-8, 0},
252: {-4, 0},
253: {-3, 1},
254: {-2, 0},
255: {-2, 2},
256: {-2, 4},
257: {-2, 6},
258: {-1, 0},
259: {-1, 1},
260: {-1, 2},
261: {-1, 3},
262: {-1, 4},
263: {-1, 5},
264: {-1, 6},
265: {-1, 7},
266: {-1, 8},
267: // numerator = -7
268: {0, -7},
269: {0, -7},
270: {0, -7},
271: {0, -7},
272: {0, -7},
273: {0, -7},
274: {0, -7},
275: {0, -7},
276: {1, 0},
277: {1, -1},
278: {1, -2},
279: {1, -3},
280: {2, -1},
281: {3, -1},
282: {7, 0},
283: {0, 0},
284: {-7, 0},
285: {-4, 1},
286: {-3, 2},
287: {-2, 1},
288: {-2, 3},
289: {-2, 5},
290: {-1, 0},
291: {-1, 1},
292: {-1, 2},
293: {-1, 3},
294: {-1, 4},
295: {-1, 5},
296: {-1, 6},
297: {-1, 7},
298: {-1, 8},
299: {-1, 9},
300: // numerator = -6
301: {0, -6},
302: {0, -6},
303: {0, -6},
304: {0, -6},
305: {0, -6},
306: {0, -6},
307: {0, -6},
308: {0, -6},
309: {0, -6},
310: {1, 0},
311: {1, -1},
312: {1, -2},
313: {2, 0},
314: {3, 0},
315: {6, 0},
316: {0, 0},
317: {-6, 0},
318: {-3, 0},
319: {-2, 0},
320: {-2, 2},
321: {-2, 4},
322: {-1, 0},
323: {-1, 1},
324: {-1, 2},
325: {-1, 3},
326: {-1, 4},
327: {-1, 5},
328: {-1, 6},
329: {-1, 7},
330: {-1, 8},
331: {-1, 9},
332: {-1, 10},
333: // numerator = -5
334: {0, -5},
335: {0, -5},
336: {0, -5},
337: {0, -5},
338: {0, -5},
339: {0, -5},
340: {0, -5},
341: {0, -5},
342: {0, -5},
343: {0, -5},
344: {1, 0},
345: {1, -1},
346: {1, -2},
347: {2, -1},
348: {5, 0},
349: {0, 0},
350: {-5, 0},
351: {-3, 1},
352: {-2, 1},
353: {-2, 3},
354: {-1, 0},
355: {-1, 1},
356: {-1, 2},
357: {-1, 3},
358: {-1, 4},
359: {-1, 5},
360: {-1, 6},
361: {-1, 7},
362: {-1, 8},
363: {-1, 9},
364: {-1, 10},
365: {-1, 11},
366: // numerator = -4
367: {0, -4},
368: {0, -4},
369: {0, -4},
370: {0, -4},
371: {0, -4},
372: {0, -4},
373: {0, -4},
374: {0, -4},
375: {0, -4},
376: {0, -4},
377: {0, -4},
378: {1, 0},
379: {1, -1},
380: {2, 0},
381: {4, 0},
382: {0, 0},
383: {-4, 0},
384: {-2, 0},
385: {-2, 2},
386: {-1, 0},
387: {-1, 1},
388: {-1, 2},
389: {-1, 3},
390: {-1, 4},
391: {-1, 5},
392: {-1, 6},
393: {-1, 7},
394: {-1, 8},
395: {-1, 9},
396: {-1, 10},
397: {-1, 11},
398: {-1, 12},
399: // numerator = -3
400: {0, -3},
401: {0, -3},
402: {0, -3},
403: {0, -3},
404: {0, -3},
405: {0, -3},
406: {0, -3},
407: {0, -3},
408: {0, -3},
409: {0, -3},
410: {0, -3},
411: {0, -3},
412: {1, 0},
413: {1, -1},
414: {3, 0},
415: {0, 0},
416: {-3, 0},
417: {-2, 1},
418: {-1, 0},
419: {-1, 1},
420: {-1, 2},
421: {-1, 3},
422: {-1, 4},
423: {-1, 5},
424: {-1, 6},
425: {-1, 7},
426: {-1, 8},
427: {-1, 9},
428: {-1, 10},
429: {-1, 11},
430: {-1, 12},
431: {-1, 13},
432: // numerator = -2
433: {0, -2},
434: {0, -2},
435: {0, -2},
436: {0, -2},
437: {0, -2},
438: {0, -2},
439: {0, -2},
440: {0, -2},
441: {0, -2},
442: {0, -2},
443: {0, -2},
444: {0, -2},
445: {0, -2},
446: {1, 0},
447: {2, 0},
448: {0, 0},
449: {-2, 0},
450: {-1, 0},
451: {-1, 1},
452: {-1, 2},
453: {-1, 3},
454: {-1, 4},
455: {-1, 5},
456: {-1, 6},
457: {-1, 7},
458: {-1, 8},
459: {-1, 9},
460: {-1, 10},
461: {-1, 11},
462: {-1, 12},
463: {-1, 13},
464: {-1, 14},
465: // numerator = -1
466: {0, -1},
467: {0, -1},
468: {0, -1},
469: {0, -1},
470: {0, -1},
471: {0, -1},
472: {0, -1},
473: {0, -1},
474: {0, -1},
475: {0, -1},
476: {0, -1},
477: {0, -1},
478: {0, -1},
479: {0, -1},
480: {1, 0},
481: {0, 0},
482: {-1, 0},
483: {-1, 1},
484: {-1, 2},
485: {-1, 3},
486: {-1, 4},
487: {-1, 5},
488: {-1, 6},
489: {-1, 7},
490: {-1, 8},
491: {-1, 9},
492: {-1, 10},
493: {-1, 11},
494: {-1, 12},
495: {-1, 13},
496: {-1, 14},
497: {-1, 15},
498: // numerator = 0
499: {0, 0},
500: {0, 0},
501: {0, 0},
502: {0, 0},
503: {0, 0},
504: {0, 0},
505: {0, 0},
506: {0, 0},
507: {0, 0},
508: {0, 0},
509: {0, 0},
510: {0, 0},
511: {0, 0},
512: {0, 0},
513: {0, 0},
514: {0, 0},
515: {0, 0},
516: {0, 0},
517: {0, 0},
518: {0, 0},
519: {0, 0},
520: {0, 0},
521: {0, 0},
522: {0, 0},
523: {0, 0},
524: {0, 0},
525: {0, 0},
526: {0, 0},
527: {0, 0},
528: {0, 0},
529: {0, 0},
530: {0, 0},
531: // numerator = 1
532: {-1, -14},
533: {-1, -13},
534: {-1, -12},
535: {-1, -11},
536: {-1, -10},
537: {-1, -9},
538: {-1, -8},
539: {-1, -7},
540: {-1, -6},
541: {-1, -5},
542: {-1, -4},
543: {-1, -3},
544: {-1, -2},
545: {-1, -1},
546: {-1, 0},
547: {0, 0},
548: {1, 0},
549: {0, 1},
550: {0, 1},
551: {0, 1},
552: {0, 1},
553: {0, 1},
554: {0, 1},
555: {0, 1},
556: {0, 1},
557: {0, 1},
558: {0, 1},
559: {0, 1},
560: {0, 1},
561: {0, 1},
562: {0, 1},
563: {0, 1},
564: // numerator = 2
565: {-1, -13},
566: {-1, -12},
567: {-1, -11},
568: {-1, -10},
569: {-1, -9},
570: {-1, -8},
571: {-1, -7},
572: {-1, -6},
573: {-1, -5},
574: {-1, -4},
575: {-1, -3},
576: {-1, -2},
577: {-1, -1},
578: {-1, 0},
579: {-2, 0},
580: {0, 0},
581: {2, 0},
582: {1, 0},
583: {0, 2},
584: {0, 2},
585: {0, 2},
586: {0, 2},
587: {0, 2},
588: {0, 2},
589: {0, 2},
590: {0, 2},
591: {0, 2},
592: {0, 2},
593: {0, 2},
594: {0, 2},
595: {0, 2},
596: {0, 2},
597: // numerator = 3
598: {-1, -12},
599: {-1, -11},
600: {-1, -10},
601: {-1, -9},
602: {-1, -8},
603: {-1, -7},
604: {-1, -6},
605: {-1, -5},
606: {-1, -4},
607: {-1, -3},
608: {-1, -2},
609: {-1, -1},
610: {-1, 0},
611: {-2, -1},
612: {-3, 0},
613: {0, 0},
614: {3, 0},
615: {1, 1},
616: {1, 0},
617: {0, 3},
618: {0, 3},
619: {0, 3},
620: {0, 3},
621: {0, 3},
622: {0, 3},
623: {0, 3},
624: {0, 3},
625: {0, 3},
626: {0, 3},
627: {0, 3},
628: {0, 3},
629: {0, 3},
630: // numerator = 4
631: {-1, -11},
632: {-1, -10},
633: {-1, -9},
634: {-1, -8},
635: {-1, -7},
636: {-1, -6},
637: {-1, -5},
638: {-1, -4},
639: {-1, -3},
640: {-1, -2},
641: {-1, -1},
642: {-1, 0},
643: {-2, -2},
644: {-2, 0},
645: {-4, 0},
646: {0, 0},
647: {4, 0},
648: {2, 0},
649: {1, 1},
650: {1, 0},
651: {0, 4},
652: {0, 4},
653: {0, 4},
654: {0, 4},
655: {0, 4},
656: {0, 4},
657: {0, 4},
658: {0, 4},
659: {0, 4},
660: {0, 4},
661: {0, 4},
662: {0, 4},
663: // numerator = 5
664: {-1, -10},
665: {-1, -9},
666: {-1, -8},
667: {-1, -7},
668: {-1, -6},
669: {-1, -5},
670: {-1, -4},
671: {-1, -3},
672: {-1, -2},
673: {-1, -1},
674: {-1, 0},
675: {-2, -3},
676: {-2, -1},
677: {-3, -1},
678: {-5, 0},
679: {0, 0},
680: {5, 0},
681: {2, 1},
682: {1, 2},
683: {1, 1},
684: {1, 0},
685: {0, 5},
686: {0, 5},
687: {0, 5},
688: {0, 5},
689: {0, 5},
690: {0, 5},
691: {0, 5},
692: {0, 5},
693: {0, 5},
694: {0, 5},
695: {0, 5},
696: // numerator = 6
697: {-1, -9},
698: {-1, -8},
699: {-1, -7},
700: {-1, -6},
701: {-1, -5},
702: {-1, -4},
703: {-1, -3},
704: {-1, -2},
705: {-1, -1},
706: {-1, 0},
707: {-2, -4},
708: {-2, -2},
709: {-2, 0},
710: {-3, 0},
711: {-6, 0},
712: {0, 0},
713: {6, 0},
714: {3, 0},
715: {2, 0},
716: {1, 2},
717: {1, 1},
718: {1, 0},
719: {0, 6},
720: {0, 6},
721: {0, 6},
722: {0, 6},
723: {0, 6},
724: {0, 6},
725: {0, 6},
726: {0, 6},
727: {0, 6},
728: {0, 6},
729: // numerator = 7
730: {-1, -8},
731: {-1, -7},
732: {-1, -6},
733: {-1, -5},
734: {-1, -4},
735: {-1, -3},
736: {-1, -2},
737: {-1, -1},
738: {-1, 0},
739: {-2, -5},
740: {-2, -3},
741: {-2, -1},
742: {-3, -2},
743: {-4, -1},
744: {-7, 0},
745: {0, 0},
746: {7, 0},
747: {3, 1},
748: {2, 1},
749: {1, 3},
750: {1, 2},
751: {1, 1},
752: {1, 0},
753: {0, 7},
754: {0, 7},
755: {0, 7},
756: {0, 7},
757: {0, 7},
758: {0, 7},
759: {0, 7},
760: {0, 7},
761: {0, 7},
762: // numerator = 8
763: {-1, -7},
764: {-1, -6},
765: {-1, -5},
766: {-1, -4},
767: {-1, -3},
768: {-1, -2},
769: {-1, -1},
770: {-1, 0},
771: {-2, -6},
772: {-2, -4},
773: {-2, -2},
774: {-2, 0},
775: {-3, -1},
776: {-4, 0},
777: {-8, 0},
778: {0, 0},
779: {8, 0},
780: {4, 0},
781: {2, 2},
782: {2, 0},
783: {1, 3},
784: {1, 2},
785: {1, 1},
786: {1, 0},
787: {0, 8},
788: {0, 8},
789: {0, 8},
790: {0, 8},
791: {0, 8},
792: {0, 8},
793: {0, 8},
794: {0, 8},
795: // numerator = 9
796: {-1, -6},
797: {-1, -5},
798: {-1, -4},
799: {-1, -3},
800: {-1, -2},
801: {-1, -1},
802: {-1, 0},
803: {-2, -7},
804: {-2, -5},
805: {-2, -3},
806: {-2, -1},
807: {-3, -3},
808: {-3, 0},
809: {-5, -1},
810: {-9, 0},
811: {0, 0},
812: {9, 0},
813: {4, 1},
814: {3, 0},
815: {2, 1},
816: {1, 4},
817: {1, 3},
818: {1, 2},
819: {1, 1},
820: {1, 0},
821: {0, 9},
822: {0, 9},
823: {0, 9},
824: {0, 9},
825: {0, 9},
826: {0, 9},
827: {0, 9},
828: // numerator = 10
829: {-1, -5},
830: {-1, -4},
831: {-1, -3},
832: {-1, -2},
833: {-1, -1},
834: {-1, 0},
835: {-2, -8},
836: {-2, -6},
837: {-2, -4},
838: {-2, -2},
839: {-2, 0},
840: {-3, -2},
841: {-4, -2},
842: {-5, 0},
843: {-10, 0},
844: {0, 0},
845: {10, 0},
846: {5, 0},
847: {3, 1},
848: {2, 2},
849: {2, 0},
850: {1, 4},
851: {1, 3},
852: {1, 2},
853: {1, 1},
854: {1, 0},
855: {0, 10},
856: {0, 10},
857: {0, 10},
858: {0, 10},
859: {0, 10},
860: {0, 10},
861: // numerator = 11
862: {-1, -4},
863: {-1, -3},
864: {-1, -2},
865: {-1, -1},
866: {-1, 0},
867: {-2, -9},
868: {-2, -7},
869: {-2, -5},
870: {-2, -3},
871: {-2, -1},
872: {-3, -4},
873: {-3, -1},
874: {-4, -1},
875: {-6, -1},
876: {-11, 0},
877: {0, 0},
878: {11, 0},
879: {5, 1},
880: {3, 2},
881: {2, 3},
882: {2, 1},
883: {1, 5},
884: {1, 4},
885: {1, 3},
886: {1, 2},
887: {1, 1},
888: {1, 0},
889: {0, 11},
890: {0, 11},
891: {0, 11},
892: {0, 11},
893: {0, 11},
894: // numerator = 12
895: {-1, -3},
896: {-1, -2},
897: {-1, -1},
898: {-1, 0},
899: {-2, -10},
900: {-2, -8},
901: {-2, -6},
902: {-2, -4},
903: {-2, -2},
904: {-2, 0},
905: {-3, -3},
906: {-3, 0},
907: {-4, 0},
908: {-6, 0},
909: {-12, 0},
910: {0, 0},
911: {12, 0},
912: {6, 0},
913: {4, 0},
914: {3, 0},
915: {2, 2},
916: {2, 0},
917: {1, 5},
918: {1, 4},
919: {1, 3},
920: {1, 2},
921: {1, 1},
922: {1, 0},
923: {0, 12},
924: {0, 12},
925: {0, 12},
926: {0, 12},
927: // numerator = 13
928: {-1, -2},
929: {-1, -1},
930: {-1, 0},
931: {-2, -11},
932: {-2, -9},
933: {-2, -7},
934: {-2, -5},
935: {-2, -3},
936: {-2, -1},
937: {-3, -5},
938: {-3, -2},
939: {-4, -3},
940: {-5, -2},
941: {-7, -1},
942: {-13, 0},
943: {0, 0},
944: {13, 0},
945: {6, 1},
946: {4, 1},
947: {3, 1},
948: {2, 3},
949: {2, 1},
950: {1, 6},
951: {1, 5},
952: {1, 4},
953: {1, 3},
954: {1, 2},
955: {1, 1},
956: {1, 0},
957: {0, 13},
958: {0, 13},
959: {0, 13},
960: // numerator = 14
961: {-1, -1},
962: {-1, 0},
963: {-2, -12},
964: {-2, -10},
965: {-2, -8},
966: {-2, -6},
967: {-2, -4},
968: {-2, -2},
969: {-2, 0},
970: {-3, -4},
971: {-3, -1},
972: {-4, -2},
973: {-5, -1},
974: {-7, 0},
975: {-14, 0},
976: {0, 0},
977: {14, 0},
978: {7, 0},
979: {4, 2},
980: {3, 2},
981: {2, 4},
982: {2, 2},
983: {2, 0},
984: {1, 6},
985: {1, 5},
986: {1, 4},
987: {1, 3},
988: {1, 2},
989: {1, 1},
990: {1, 0},
991: {0, 14},
992: {0, 14},
993: // numerator = 15
994: {-1, 0},
995: {-2, -13},
996: {-2, -11},
997: {-2, -9},
998: {-2, -7},
999: {-2, -5},
1000: {-2, -3},
1001: {-2, -1},
1002: {-3, -6},
1003: {-3, -3},
1004: {-3, 0},
1005: {-4, -1},
1006: {-5, 0},
1007: {-8, -1},
1008: {-15, 0},
1009: {0, 0},
1010: {15, 0},
1011: {7, 1},
1012: {5, 0},
1013: {3, 3},
1014: {3, 0},
1015: {2, 3},
1016: {2, 1},
1017: {1, 7},
1018: {1, 6},
1019: {1, 5},
1020: {1, 4},
1021: {1, 3},
1022: {1, 2},
1023: {1, 1},
1024: {1, 0},
1025: {0, 15},
1026: // numerator = 16
1027: {-2, -14},
1028: {-2, -12},
1029: {-2, -10},
1030: {-2, -8},
1031: {-2, -6},
1032: {-2, -4},
1033: {-2, -2},
1034: {-2, 0},
1035: {-3, -5},
1036: {-3, -2},
1037: {-4, -4},
1038: {-4, 0},
1039: {-6, -2},
1040: {-8, 0},
1041: {-16, 0},
1042: {0, 0},
1043: {16, 0},
1044: {8, 0},
1045: {5, 1},
1046: {4, 0},
1047: {3, 1},
1048: {2, 4},
1049: {2, 2},
1050: {2, 0},
1051: {1, 7},
1052: {1, 6},
1053: {1, 5},
1054: {1, 4},
1055: {1, 3},
1056: {1, 2},
1057: {1, 1},
1058: {1, 0},
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