27 const AllEntities& in,
29 const FF& scaling_factor)
33 using View =
typename Accumulator::View;
35 auto op = View(in.op);
36 const auto lagrange_mini_masking = View(in.lagrange_mini_masking);
37 static const FF minus_three =
FF(-3);
38 static const FF minus_four =
FF(-4);
39 static const FF minus_eight =
FF(-8);
40 static const FF minus_one =
FF(-1);
43 auto tmp_1 = op * (op + minus_three);
44 tmp_1 *= (op + minus_four);
45 tmp_1 *= (op + minus_eight);
46 tmp_1 *= (lagrange_mini_masking + minus_one);
47 tmp_1 *= scaling_factor;
50 const auto lagrange_even_in_minicircuit = View(in.lagrange_even_in_minicircuit);
52 auto accumulators_binary_limbs_0 = View(in.accumulators_binary_limbs_0);
53 auto accumulators_binary_limbs_1 = View(in.accumulators_binary_limbs_1);
54 auto accumulators_binary_limbs_2 = View(in.accumulators_binary_limbs_2);
55 auto accumulators_binary_limbs_3 = View(in.accumulators_binary_limbs_3);
56 auto accumulators_binary_limbs_0_shift = View(in.accumulators_binary_limbs_0_shift);
57 auto accumulators_binary_limbs_1_shift = View(in.accumulators_binary_limbs_1_shift);
58 auto accumulators_binary_limbs_2_shift = View(in.accumulators_binary_limbs_2_shift);
59 auto accumulators_binary_limbs_3_shift = View(in.accumulators_binary_limbs_3_shift);
63 auto tmp_2 = (accumulators_binary_limbs_0 - accumulators_binary_limbs_0_shift);
64 tmp_2 *= (op + minus_three);
65 tmp_2 *= (op + minus_four);
66 tmp_2 *= (op + minus_eight);
67 tmp_2 *= lagrange_even_in_minicircuit;
68 tmp_2 *= scaling_factor;
72 auto tmp_3 = (accumulators_binary_limbs_1 - accumulators_binary_limbs_1_shift);
73 tmp_3 *= (op + minus_three);
74 tmp_3 *= (op + minus_four);
75 tmp_3 *= (op + minus_eight);
76 tmp_3 *= lagrange_even_in_minicircuit;
77 tmp_3 *= scaling_factor;
81 auto tmp_4 = (accumulators_binary_limbs_2 - accumulators_binary_limbs_2_shift);
82 tmp_4 *= (op + minus_three);
83 tmp_4 *= (op + minus_four);
84 tmp_4 *= (op + minus_eight);
85 tmp_4 *= lagrange_even_in_minicircuit;
86 tmp_4 *= scaling_factor;
90 auto tmp_5 = (accumulators_binary_limbs_3 - accumulators_binary_limbs_3_shift);
91 tmp_5 *= (op + minus_three);
92 tmp_5 *= (op + minus_four);
93 tmp_5 *= (op + minus_eight);
94 tmp_5 *= lagrange_even_in_minicircuit;
95 tmp_5 *= scaling_factor;
116 const AllEntities& in,
117 const Parameters& params,
118 const FF& scaling_factor)
121 using View =
typename Accumulator::View;
124 using ShorterView =
typename ShorterAccumulator::View;
126 const auto lagrange_odd_in_minicircuit = View(in.lagrange_odd_in_minicircuit);
129 const auto lagrange_result_row_shorter = ShorterView(in.lagrange_result_row);
133 const auto lagrange_last_in_minicircuit = View(in.lagrange_last_in_minicircuit);
134 const auto lagrange_last_in_minicircuit_shorter = ShorterView(in.lagrange_last_in_minicircuit);
136 auto accumulators_binary_limbs_0 = View(in.accumulators_binary_limbs_0);
137 auto accumulators_binary_limbs_1 = View(in.accumulators_binary_limbs_1);
138 auto accumulators_binary_limbs_2 = View(in.accumulators_binary_limbs_2);
139 auto accumulators_binary_limbs_3 = View(in.accumulators_binary_limbs_3);
140 auto accumulators_binary_limbs_0_shift = View(in.accumulators_binary_limbs_0_shift);
141 auto accumulators_binary_limbs_1_shift = View(in.accumulators_binary_limbs_1_shift);
142 auto accumulators_binary_limbs_2_shift = View(in.accumulators_binary_limbs_2_shift);
143 auto accumulators_binary_limbs_3_shift = View(in.accumulators_binary_limbs_3_shift);
145 auto accumulators_binary_limbs_0_shorter = ShorterView(in.accumulators_binary_limbs_0);
146 auto accumulators_binary_limbs_1_shorter = ShorterView(in.accumulators_binary_limbs_1);
147 auto accumulators_binary_limbs_2_shorter = ShorterView(in.accumulators_binary_limbs_2);
148 auto accumulators_binary_limbs_3_shorter = ShorterView(in.accumulators_binary_limbs_3);
150 const FF minus_one =
FF(-1);
153 const auto is_row_odd_except_last = lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
154 auto tmp_1 = accumulators_binary_limbs_0 - accumulators_binary_limbs_0_shift;
155 tmp_1 *= is_row_odd_except_last;
156 tmp_1 *= scaling_factor;
160 auto tmp_2 = accumulators_binary_limbs_1 - accumulators_binary_limbs_1_shift;
161 tmp_2 *= is_row_odd_except_last;
162 tmp_2 *= scaling_factor;
165 auto tmp_3 = accumulators_binary_limbs_2 - accumulators_binary_limbs_2_shift;
166 tmp_3 *= is_row_odd_except_last;
167 tmp_3 *= scaling_factor;
170 auto tmp_4 = accumulators_binary_limbs_3 - accumulators_binary_limbs_3_shift;
171 tmp_4 *= is_row_odd_except_last;
172 tmp_4 *= scaling_factor;
176 const auto lagrange_last_in_minicircuit_by_scaling_factor = lagrange_last_in_minicircuit_shorter * scaling_factor;
177 auto tmp_5 = accumulators_binary_limbs_0_shorter * lagrange_last_in_minicircuit_by_scaling_factor;
181 auto tmp_6 = accumulators_binary_limbs_1_shorter * lagrange_last_in_minicircuit_by_scaling_factor;
185 auto tmp_7 = accumulators_binary_limbs_2_shorter * lagrange_last_in_minicircuit_by_scaling_factor;
189 auto tmp_8 = accumulators_binary_limbs_3_shorter * lagrange_last_in_minicircuit_by_scaling_factor;
194 const auto lagrange_result_row_by_scaling_factor = lagrange_result_row_shorter * scaling_factor;
196 (accumulators_binary_limbs_0_shorter - params.accumulated_result[0]) * lagrange_result_row_by_scaling_factor;
201 (accumulators_binary_limbs_1_shorter - params.accumulated_result[1]) * lagrange_result_row_by_scaling_factor;
206 (accumulators_binary_limbs_2_shorter - params.accumulated_result[2]) * lagrange_result_row_by_scaling_factor;
211 (accumulators_binary_limbs_3_shorter - params.accumulated_result[3]) * lagrange_result_row_by_scaling_factor;
226 const AllEntities& in,
228 const FF& scaling_factor)
231 using View =
typename Accumulator::View;
234 static const auto minus_one = -
FF(1);
235 const auto lagrange_even_in_minicircuit = View(in.lagrange_even_in_minicircuit);
236 const auto lagrange_odd_in_minicircuit = View(in.lagrange_odd_in_minicircuit);
238 auto p_x_low_limbs_range_constraint_0 = View(in.p_x_low_limbs_range_constraint_0);
239 auto p_x_low_limbs_range_constraint_1 = View(in.p_x_low_limbs_range_constraint_1);
240 auto p_x_low_limbs_range_constraint_2 = View(in.p_x_low_limbs_range_constraint_2);
241 auto p_x_low_limbs_range_constraint_3 = View(in.p_x_low_limbs_range_constraint_3);
242 auto p_x_low_limbs_range_constraint_4 = View(in.p_x_low_limbs_range_constraint_4);
243 auto p_x_high_limbs_range_constraint_0 = View(in.p_x_high_limbs_range_constraint_0);
244 auto p_x_high_limbs_range_constraint_1 = View(in.p_x_high_limbs_range_constraint_1);
245 auto p_x_high_limbs_range_constraint_2 = View(in.p_x_high_limbs_range_constraint_2);
246 auto p_x_high_limbs_range_constraint_3 = View(in.p_x_high_limbs_range_constraint_3);
247 auto p_x_high_limbs_range_constraint_4 = View(in.p_x_high_limbs_range_constraint_4);
248 auto p_y_low_limbs_range_constraint_0 = View(in.p_y_low_limbs_range_constraint_0);
249 auto p_y_low_limbs_range_constraint_1 = View(in.p_y_low_limbs_range_constraint_1);
250 auto p_y_low_limbs_range_constraint_2 = View(in.p_y_low_limbs_range_constraint_2);
251 auto p_y_low_limbs_range_constraint_3 = View(in.p_y_low_limbs_range_constraint_3);
252 auto p_y_low_limbs_range_constraint_4 = View(in.p_y_low_limbs_range_constraint_4);
253 auto p_y_high_limbs_range_constraint_0 = View(in.p_y_high_limbs_range_constraint_0);
254 auto p_y_high_limbs_range_constraint_1 = View(in.p_y_high_limbs_range_constraint_1);
255 auto p_y_high_limbs_range_constraint_2 = View(in.p_y_high_limbs_range_constraint_2);
256 auto p_y_high_limbs_range_constraint_3 = View(in.p_y_high_limbs_range_constraint_3);
257 auto p_y_high_limbs_range_constraint_4 = View(in.p_y_high_limbs_range_constraint_4);
258 auto z_low_limbs_range_constraint_0 = View(in.z_low_limbs_range_constraint_0);
259 auto z_low_limbs_range_constraint_1 = View(in.z_low_limbs_range_constraint_1);
260 auto z_low_limbs_range_constraint_2 = View(in.z_low_limbs_range_constraint_2);
261 auto z_low_limbs_range_constraint_3 = View(in.z_low_limbs_range_constraint_3);
262 auto z_low_limbs_range_constraint_4 = View(in.z_low_limbs_range_constraint_4);
263 auto z_high_limbs_range_constraint_0 = View(in.z_high_limbs_range_constraint_0);
264 auto z_high_limbs_range_constraint_1 = View(in.z_high_limbs_range_constraint_1);
265 auto z_high_limbs_range_constraint_2 = View(in.z_high_limbs_range_constraint_2);
266 auto z_high_limbs_range_constraint_3 = View(in.z_high_limbs_range_constraint_3);
267 auto z_high_limbs_range_constraint_4 = View(in.z_high_limbs_range_constraint_4);
268 auto accumulator_low_limbs_range_constraint_0 = View(in.accumulator_low_limbs_range_constraint_0);
269 auto accumulator_low_limbs_range_constraint_1 = View(in.accumulator_low_limbs_range_constraint_1);
270 auto accumulator_low_limbs_range_constraint_2 = View(in.accumulator_low_limbs_range_constraint_2);
271 auto accumulator_low_limbs_range_constraint_3 = View(in.accumulator_low_limbs_range_constraint_3);
272 auto accumulator_low_limbs_range_constraint_4 = View(in.accumulator_low_limbs_range_constraint_4);
273 auto accumulator_high_limbs_range_constraint_0 = View(in.accumulator_high_limbs_range_constraint_0);
274 auto accumulator_high_limbs_range_constraint_1 = View(in.accumulator_high_limbs_range_constraint_1);
275 auto accumulator_high_limbs_range_constraint_2 = View(in.accumulator_high_limbs_range_constraint_2);
276 auto accumulator_high_limbs_range_constraint_3 = View(in.accumulator_high_limbs_range_constraint_3);
277 auto accumulator_high_limbs_range_constraint_4 = View(in.accumulator_high_limbs_range_constraint_4);
278 auto quotient_low_limbs_range_constraint_0 = View(in.quotient_low_limbs_range_constraint_0);
279 auto quotient_low_limbs_range_constraint_1 = View(in.quotient_low_limbs_range_constraint_1);
280 auto quotient_low_limbs_range_constraint_2 = View(in.quotient_low_limbs_range_constraint_2);
281 auto quotient_low_limbs_range_constraint_3 = View(in.quotient_low_limbs_range_constraint_3);
282 auto quotient_low_limbs_range_constraint_4 = View(in.quotient_low_limbs_range_constraint_4);
283 auto quotient_high_limbs_range_constraint_0 = View(in.quotient_high_limbs_range_constraint_0);
284 auto quotient_high_limbs_range_constraint_1 = View(in.quotient_high_limbs_range_constraint_1);
285 auto quotient_high_limbs_range_constraint_2 = View(in.quotient_high_limbs_range_constraint_2);
286 auto quotient_high_limbs_range_constraint_3 = View(in.quotient_high_limbs_range_constraint_3);
287 auto quotient_high_limbs_range_constraint_4 = View(in.quotient_high_limbs_range_constraint_4);
288 auto relation_wide_limbs_range_constraint_0 = View(in.relation_wide_limbs_range_constraint_0);
289 auto relation_wide_limbs_range_constraint_1 = View(in.relation_wide_limbs_range_constraint_1);
290 auto relation_wide_limbs_range_constraint_2 = View(in.relation_wide_limbs_range_constraint_2);
291 auto relation_wide_limbs_range_constraint_3 = View(in.relation_wide_limbs_range_constraint_3);
292 auto p_x_low_limbs_range_constraint_tail = View(in.p_x_low_limbs_range_constraint_tail);
293 auto p_x_high_limbs_range_constraint_tail = View(in.p_x_high_limbs_range_constraint_tail);
294 auto p_y_low_limbs_range_constraint_tail = View(in.p_y_low_limbs_range_constraint_tail);
295 auto p_y_high_limbs_range_constraint_tail = View(in.p_y_high_limbs_range_constraint_tail);
296 auto z_low_limbs_range_constraint_tail = View(in.z_low_limbs_range_constraint_tail);
297 auto z_high_limbs_range_constraint_tail = View(in.z_high_limbs_range_constraint_tail);
298 auto accumulator_low_limbs_range_constraint_tail = View(in.accumulator_low_limbs_range_constraint_tail);
299 auto accumulator_high_limbs_range_constraint_tail = View(in.accumulator_high_limbs_range_constraint_tail);
300 auto quotient_low_limbs_range_constraint_tail = View(in.quotient_low_limbs_range_constraint_tail);
301 auto quotient_high_limbs_range_constraint_tail = View(in.quotient_high_limbs_range_constraint_tail);
302 auto op = View(in.op);
303 auto x_lo_y_hi = View(in.x_lo_y_hi);
304 auto x_hi_z_1 = View(in.x_hi_z_1);
305 auto y_lo_z_2 = View(in.y_lo_z_2);
306 const auto lagrange_mini_masking = View(in.lagrange_mini_masking);
309 const auto not_in_mininicircuit_or_masked =
310 (lagrange_odd_in_minicircuit + lagrange_even_in_minicircuit + lagrange_mini_masking + minus_one) *
314 std::get<0>(accumulators) += p_x_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
317 std::get<1>(accumulators) += p_x_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
320 std::get<2>(accumulators) += p_x_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
323 std::get<3>(accumulators) += p_x_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
326 std::get<4>(accumulators) += p_x_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
329 std::get<5>(accumulators) += p_x_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
332 std::get<6>(accumulators) += p_x_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
335 std::get<7>(accumulators) += p_x_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
338 std::get<8>(accumulators) += p_x_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
341 std::get<9>(accumulators) += p_x_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
344 std::get<10>(accumulators) += p_y_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
347 std::get<11>(accumulators) += p_y_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
350 std::get<12>(accumulators) += p_y_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
353 std::get<13>(accumulators) += p_y_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
356 std::get<14>(accumulators) += p_y_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
359 std::get<15>(accumulators) += p_y_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
362 std::get<16>(accumulators) += p_y_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
365 std::get<17>(accumulators) += p_y_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
368 std::get<18>(accumulators) += p_y_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
371 std::get<19>(accumulators) += p_y_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
374 std::get<20>(accumulators) += z_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
377 std::get<21>(accumulators) += z_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
380 std::get<22>(accumulators) += z_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
383 std::get<23>(accumulators) += z_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
386 std::get<24>(accumulators) += z_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
389 std::get<25>(accumulators) += z_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
392 std::get<26>(accumulators) += z_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
395 std::get<27>(accumulators) += z_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
398 std::get<28>(accumulators) += z_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
401 std::get<29>(accumulators) += z_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
404 std::get<30>(accumulators) += accumulator_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
407 std::get<31>(accumulators) += accumulator_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
410 std::get<32>(accumulators) += accumulator_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
413 std::get<33>(accumulators) += accumulator_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
416 std::get<34>(accumulators) += accumulator_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
419 std::get<35>(accumulators) += accumulator_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
422 std::get<36>(accumulators) += accumulator_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
425 std::get<37>(accumulators) += accumulator_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
428 std::get<38>(accumulators) += accumulator_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
431 std::get<39>(accumulators) += accumulator_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
434 std::get<40>(accumulators) += quotient_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
437 std::get<41>(accumulators) += quotient_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
440 std::get<42>(accumulators) += quotient_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
443 std::get<43>(accumulators) += quotient_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
446 std::get<44>(accumulators) += quotient_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
449 std::get<45>(accumulators) += quotient_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
452 std::get<46>(accumulators) += quotient_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
455 std::get<47>(accumulators) += quotient_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
458 std::get<48>(accumulators) += quotient_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
461 std::get<49>(accumulators) += quotient_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
464 std::get<50>(accumulators) += relation_wide_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
467 std::get<51>(accumulators) += relation_wide_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
470 std::get<52>(accumulators) += relation_wide_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
473 std::get<53>(accumulators) += relation_wide_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
476 std::get<54>(accumulators) += p_x_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
479 std::get<55>(accumulators) += p_x_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
482 std::get<56>(accumulators) += p_y_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
485 std::get<57>(accumulators) += p_y_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
488 std::get<58>(accumulators) += z_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
491 std::get<59>(accumulators) += z_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
494 std::get<60>(accumulators) += accumulator_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
497 std::get<61>(accumulators) += accumulator_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
500 std::get<62>(accumulators) += quotient_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
503 std::get<63>(accumulators) += quotient_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
506 std::get<64>(accumulators) += op * not_in_mininicircuit_or_masked;
509 std::get<65>(accumulators) += x_lo_y_hi * not_in_mininicircuit_or_masked;
512 std::get<66>(accumulators) += x_hi_z_1 * not_in_mininicircuit_or_masked;
515 std::get<67>(accumulators) += y_lo_z_2 * not_in_mininicircuit_or_masked;