26 const AllEntities& in,
28 const FF& scaling_factor)
32 using View =
typename Accumulator::View;
34 auto op = View(in.op);
35 auto lagrange_mini_masking = View(in.lagrange_mini_masking);
36 static const FF minus_three =
FF(-3);
37 static const FF minus_four =
FF(-4);
38 static const FF minus_eight =
FF(-8);
39 static const FF minus_one =
FF(-1);
42 auto tmp_1 = op * (op + minus_three);
43 tmp_1 *= (op + minus_four);
44 tmp_1 *= (op + minus_eight);
45 tmp_1 *= (lagrange_mini_masking + minus_one);
46 tmp_1 *= scaling_factor;
49 auto lagrange_even_in_minicircuit = View(in.lagrange_even_in_minicircuit);
51 auto accumulators_binary_limbs_0 = View(in.accumulators_binary_limbs_0);
52 auto accumulators_binary_limbs_1 = View(in.accumulators_binary_limbs_1);
53 auto accumulators_binary_limbs_2 = View(in.accumulators_binary_limbs_2);
54 auto accumulators_binary_limbs_3 = View(in.accumulators_binary_limbs_3);
55 auto accumulators_binary_limbs_0_shift = View(in.accumulators_binary_limbs_0_shift);
56 auto accumulators_binary_limbs_1_shift = View(in.accumulators_binary_limbs_1_shift);
57 auto accumulators_binary_limbs_2_shift = View(in.accumulators_binary_limbs_2_shift);
58 auto accumulators_binary_limbs_3_shift = View(in.accumulators_binary_limbs_3_shift);
62 auto tmp_2 = (accumulators_binary_limbs_0 - accumulators_binary_limbs_0_shift);
63 tmp_2 *= (op + minus_three);
64 tmp_2 *= (op + minus_four);
65 tmp_2 *= (op + minus_eight);
66 tmp_2 *= lagrange_even_in_minicircuit;
67 tmp_2 *= scaling_factor;
71 auto tmp_3 = (accumulators_binary_limbs_1 - accumulators_binary_limbs_1_shift);
72 tmp_3 *= (op + minus_three);
73 tmp_3 *= (op + minus_four);
74 tmp_3 *= (op + minus_eight);
75 tmp_3 *= lagrange_even_in_minicircuit;
76 tmp_3 *= scaling_factor;
80 auto tmp_4 = (accumulators_binary_limbs_2 - accumulators_binary_limbs_2_shift);
81 tmp_4 *= (op + minus_three);
82 tmp_4 *= (op + minus_four);
83 tmp_4 *= (op + minus_eight);
84 tmp_4 *= lagrange_even_in_minicircuit;
85 tmp_4 *= scaling_factor;
89 auto tmp_5 = (accumulators_binary_limbs_3 - accumulators_binary_limbs_3_shift);
90 tmp_5 *= (op + minus_three);
91 tmp_5 *= (op + minus_four);
92 tmp_5 *= (op + minus_eight);
93 tmp_5 *= lagrange_even_in_minicircuit;
94 tmp_5 *= scaling_factor;
114 const AllEntities& in,
115 const Parameters& params,
116 const FF& scaling_factor)
119 using View =
typename Accumulator::View;
121 auto lagrange_odd_in_minicircuit = View(in.lagrange_odd_in_minicircuit);
124 auto lagrange_result_row = View(in.lagrange_result_row);
128 auto lagrange_last_in_minicircuit = View(in.lagrange_last_in_minicircuit);
131 auto lagrange_mini_masking = View(in.lagrange_mini_masking);
133 auto accumulators_binary_limbs_0 = View(in.accumulators_binary_limbs_0);
134 auto accumulators_binary_limbs_1 = View(in.accumulators_binary_limbs_1);
135 auto accumulators_binary_limbs_2 = View(in.accumulators_binary_limbs_2);
136 auto accumulators_binary_limbs_3 = View(in.accumulators_binary_limbs_3);
137 auto accumulators_binary_limbs_0_shift = View(in.accumulators_binary_limbs_0_shift);
138 auto accumulators_binary_limbs_1_shift = View(in.accumulators_binary_limbs_1_shift);
139 auto accumulators_binary_limbs_2_shift = View(in.accumulators_binary_limbs_2_shift);
140 auto accumulators_binary_limbs_3_shift = View(in.accumulators_binary_limbs_3_shift);
142 FF minus_one =
FF(-1);
146 auto tmp_1 = accumulators_binary_limbs_0 - accumulators_binary_limbs_0_shift;
147 tmp_1 *= lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
148 tmp_1 *= scaling_factor;
152 auto tmp_2 = accumulators_binary_limbs_1 - accumulators_binary_limbs_1_shift;
153 tmp_2 *= lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
154 tmp_2 *= scaling_factor;
157 auto tmp_3 = accumulators_binary_limbs_2 - accumulators_binary_limbs_2_shift;
158 tmp_3 *= lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
159 tmp_3 *= scaling_factor;
162 auto tmp_4 = accumulators_binary_limbs_3 - accumulators_binary_limbs_3_shift;
163 tmp_4 *= lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
164 tmp_4 *= scaling_factor;
168 auto tmp_5 = accumulators_binary_limbs_0 * lagrange_last_in_minicircuit;
169 tmp_5 *= (lagrange_mini_masking + minus_one) * scaling_factor;
173 auto tmp_6 = accumulators_binary_limbs_1 * lagrange_last_in_minicircuit;
174 tmp_6 *= (lagrange_mini_masking + minus_one) * scaling_factor;
178 auto tmp_7 = accumulators_binary_limbs_2 * lagrange_last_in_minicircuit;
179 tmp_7 *= (lagrange_mini_masking + minus_one) * scaling_factor;
183 auto tmp_8 = accumulators_binary_limbs_3 * lagrange_last_in_minicircuit;
184 tmp_8 *= (lagrange_mini_masking + minus_one) * scaling_factor;
189 auto tmp_9 = (accumulators_binary_limbs_0 - params.accumulated_result[0]) * lagrange_result_row;
190 tmp_9 *= (lagrange_mini_masking + minus_one) * scaling_factor;
194 auto tmp_10 = (accumulators_binary_limbs_1 - params.accumulated_result[1]) * lagrange_result_row;
195 tmp_10 *= (lagrange_mini_masking + minus_one) * scaling_factor;
199 auto tmp_11 = (accumulators_binary_limbs_2 - params.accumulated_result[2]) * lagrange_result_row;
200 tmp_11 *= (lagrange_mini_masking + minus_one) * scaling_factor;
204 auto tmp_12 = (accumulators_binary_limbs_3 - params.accumulated_result[3]) * lagrange_result_row;
205 tmp_12 *= (lagrange_mini_masking + minus_one) * scaling_factor;
220 const AllEntities& in,
222 const FF& scaling_factor)
225 using View =
typename Accumulator::View;
228 static auto minus_one = -
FF(1);
230 auto lagrange_even_in_minicircuit = View(in.lagrange_even_in_minicircuit);
231 auto lagrange_odd_in_minicircuit = View(in.lagrange_odd_in_minicircuit);
233 auto p_x_low_limbs_range_constraint_0 = View(in.p_x_low_limbs_range_constraint_0);
234 auto p_x_low_limbs_range_constraint_1 = View(in.p_x_low_limbs_range_constraint_1);
235 auto p_x_low_limbs_range_constraint_2 = View(in.p_x_low_limbs_range_constraint_2);
236 auto p_x_low_limbs_range_constraint_3 = View(in.p_x_low_limbs_range_constraint_3);
237 auto p_x_low_limbs_range_constraint_4 = View(in.p_x_low_limbs_range_constraint_4);
238 auto p_x_high_limbs_range_constraint_0 = View(in.p_x_high_limbs_range_constraint_0);
239 auto p_x_high_limbs_range_constraint_1 = View(in.p_x_high_limbs_range_constraint_1);
240 auto p_x_high_limbs_range_constraint_2 = View(in.p_x_high_limbs_range_constraint_2);
241 auto p_x_high_limbs_range_constraint_3 = View(in.p_x_high_limbs_range_constraint_3);
242 auto p_x_high_limbs_range_constraint_4 = View(in.p_x_high_limbs_range_constraint_4);
243 auto p_y_low_limbs_range_constraint_0 = View(in.p_y_low_limbs_range_constraint_0);
244 auto p_y_low_limbs_range_constraint_1 = View(in.p_y_low_limbs_range_constraint_1);
245 auto p_y_low_limbs_range_constraint_2 = View(in.p_y_low_limbs_range_constraint_2);
246 auto p_y_low_limbs_range_constraint_3 = View(in.p_y_low_limbs_range_constraint_3);
247 auto p_y_low_limbs_range_constraint_4 = View(in.p_y_low_limbs_range_constraint_4);
248 auto p_y_high_limbs_range_constraint_0 = View(in.p_y_high_limbs_range_constraint_0);
249 auto p_y_high_limbs_range_constraint_1 = View(in.p_y_high_limbs_range_constraint_1);
250 auto p_y_high_limbs_range_constraint_2 = View(in.p_y_high_limbs_range_constraint_2);
251 auto p_y_high_limbs_range_constraint_3 = View(in.p_y_high_limbs_range_constraint_3);
252 auto p_y_high_limbs_range_constraint_4 = View(in.p_y_high_limbs_range_constraint_4);
253 auto z_low_limbs_range_constraint_0 = View(in.z_low_limbs_range_constraint_0);
254 auto z_low_limbs_range_constraint_1 = View(in.z_low_limbs_range_constraint_1);
255 auto z_low_limbs_range_constraint_2 = View(in.z_low_limbs_range_constraint_2);
256 auto z_low_limbs_range_constraint_3 = View(in.z_low_limbs_range_constraint_3);
257 auto z_low_limbs_range_constraint_4 = View(in.z_low_limbs_range_constraint_4);
258 auto z_high_limbs_range_constraint_0 = View(in.z_high_limbs_range_constraint_0);
259 auto z_high_limbs_range_constraint_1 = View(in.z_high_limbs_range_constraint_1);
260 auto z_high_limbs_range_constraint_2 = View(in.z_high_limbs_range_constraint_2);
261 auto z_high_limbs_range_constraint_3 = View(in.z_high_limbs_range_constraint_3);
262 auto z_high_limbs_range_constraint_4 = View(in.z_high_limbs_range_constraint_4);
263 auto accumulator_low_limbs_range_constraint_0 = View(in.accumulator_low_limbs_range_constraint_0);
264 auto accumulator_low_limbs_range_constraint_1 = View(in.accumulator_low_limbs_range_constraint_1);
265 auto accumulator_low_limbs_range_constraint_2 = View(in.accumulator_low_limbs_range_constraint_2);
266 auto accumulator_low_limbs_range_constraint_3 = View(in.accumulator_low_limbs_range_constraint_3);
267 auto accumulator_low_limbs_range_constraint_4 = View(in.accumulator_low_limbs_range_constraint_4);
268 auto accumulator_high_limbs_range_constraint_0 = View(in.accumulator_high_limbs_range_constraint_0);
269 auto accumulator_high_limbs_range_constraint_1 = View(in.accumulator_high_limbs_range_constraint_1);
270 auto accumulator_high_limbs_range_constraint_2 = View(in.accumulator_high_limbs_range_constraint_2);
271 auto accumulator_high_limbs_range_constraint_3 = View(in.accumulator_high_limbs_range_constraint_3);
272 auto accumulator_high_limbs_range_constraint_4 = View(in.accumulator_high_limbs_range_constraint_4);
273 auto quotient_low_limbs_range_constraint_0 = View(in.quotient_low_limbs_range_constraint_0);
274 auto quotient_low_limbs_range_constraint_1 = View(in.quotient_low_limbs_range_constraint_1);
275 auto quotient_low_limbs_range_constraint_2 = View(in.quotient_low_limbs_range_constraint_2);
276 auto quotient_low_limbs_range_constraint_3 = View(in.quotient_low_limbs_range_constraint_3);
277 auto quotient_low_limbs_range_constraint_4 = View(in.quotient_low_limbs_range_constraint_4);
278 auto quotient_high_limbs_range_constraint_0 = View(in.quotient_high_limbs_range_constraint_0);
279 auto quotient_high_limbs_range_constraint_1 = View(in.quotient_high_limbs_range_constraint_1);
280 auto quotient_high_limbs_range_constraint_2 = View(in.quotient_high_limbs_range_constraint_2);
281 auto quotient_high_limbs_range_constraint_3 = View(in.quotient_high_limbs_range_constraint_3);
282 auto quotient_high_limbs_range_constraint_4 = View(in.quotient_high_limbs_range_constraint_4);
283 auto relation_wide_limbs_range_constraint_0 = View(in.relation_wide_limbs_range_constraint_0);
284 auto relation_wide_limbs_range_constraint_1 = View(in.relation_wide_limbs_range_constraint_1);
285 auto relation_wide_limbs_range_constraint_2 = View(in.relation_wide_limbs_range_constraint_2);
286 auto relation_wide_limbs_range_constraint_3 = View(in.relation_wide_limbs_range_constraint_3);
287 auto p_x_low_limbs_range_constraint_tail = View(in.p_x_low_limbs_range_constraint_tail);
288 auto p_x_high_limbs_range_constraint_tail = View(in.p_x_high_limbs_range_constraint_tail);
289 auto p_y_low_limbs_range_constraint_tail = View(in.p_y_low_limbs_range_constraint_tail);
290 auto p_y_high_limbs_range_constraint_tail = View(in.p_y_high_limbs_range_constraint_tail);
291 auto z_low_limbs_range_constraint_tail = View(in.z_low_limbs_range_constraint_tail);
292 auto z_high_limbs_range_constraint_tail = View(in.z_high_limbs_range_constraint_tail);
293 auto accumulator_low_limbs_range_constraint_tail = View(in.accumulator_low_limbs_range_constraint_tail);
294 auto accumulator_high_limbs_range_constraint_tail = View(in.accumulator_high_limbs_range_constraint_tail);
295 auto quotient_low_limbs_range_constraint_tail = View(in.quotient_low_limbs_range_constraint_tail);
296 auto quotient_high_limbs_range_constraint_tail = View(in.quotient_high_limbs_range_constraint_tail);
297 auto op = View(in.op);
298 auto x_lo_y_hi = View(in.x_lo_y_hi);
299 auto x_hi_z_1 = View(in.x_hi_z_1);
300 auto y_lo_z_2 = View(in.y_lo_z_2);
301 auto lagrange_mini_masking = View(in.lagrange_mini_masking);
304 auto not_in_mininicircuit_or_masked = (lagrange_odd_in_minicircuit + lagrange_even_in_minicircuit + minus_one) *
305 (lagrange_mini_masking + minus_one) * scaling_factor;
308 std::get<0>(accumulators) += p_x_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
311 std::get<1>(accumulators) += p_x_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
314 std::get<2>(accumulators) += p_x_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
317 std::get<3>(accumulators) += p_x_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
320 std::get<4>(accumulators) += p_x_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
323 std::get<5>(accumulators) += p_x_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
326 std::get<6>(accumulators) += p_x_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
329 std::get<7>(accumulators) += p_x_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
332 std::get<8>(accumulators) += p_x_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
335 std::get<9>(accumulators) += p_x_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
338 std::get<10>(accumulators) += p_y_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
341 std::get<11>(accumulators) += p_y_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
344 std::get<12>(accumulators) += p_y_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
347 std::get<13>(accumulators) += p_y_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
350 std::get<14>(accumulators) += p_y_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
353 std::get<15>(accumulators) += p_y_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
356 std::get<16>(accumulators) += p_y_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
359 std::get<17>(accumulators) += p_y_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
362 std::get<18>(accumulators) += p_y_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
365 std::get<19>(accumulators) += p_y_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
368 std::get<20>(accumulators) += z_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
371 std::get<21>(accumulators) += z_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
374 std::get<22>(accumulators) += z_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
377 std::get<23>(accumulators) += z_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
380 std::get<24>(accumulators) += z_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
383 std::get<25>(accumulators) += z_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
386 std::get<26>(accumulators) += z_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
389 std::get<27>(accumulators) += z_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
392 std::get<28>(accumulators) += z_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
395 std::get<29>(accumulators) += z_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
398 std::get<30>(accumulators) += accumulator_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
401 std::get<31>(accumulators) += accumulator_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
404 std::get<32>(accumulators) += accumulator_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
407 std::get<33>(accumulators) += accumulator_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
410 std::get<34>(accumulators) += accumulator_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
413 std::get<35>(accumulators) += accumulator_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
416 std::get<36>(accumulators) += accumulator_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
419 std::get<37>(accumulators) += accumulator_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
422 std::get<38>(accumulators) += accumulator_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
425 std::get<39>(accumulators) += accumulator_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
428 std::get<40>(accumulators) += quotient_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
431 std::get<41>(accumulators) += quotient_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
434 std::get<42>(accumulators) += quotient_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
437 std::get<43>(accumulators) += quotient_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
440 std::get<44>(accumulators) += quotient_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
443 std::get<45>(accumulators) += quotient_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
446 std::get<46>(accumulators) += quotient_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
449 std::get<47>(accumulators) += quotient_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
452 std::get<48>(accumulators) += quotient_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
455 std::get<49>(accumulators) += quotient_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
458 std::get<50>(accumulators) += relation_wide_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
461 std::get<51>(accumulators) += relation_wide_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
464 std::get<52>(accumulators) += relation_wide_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
467 std::get<53>(accumulators) += relation_wide_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
470 std::get<54>(accumulators) += p_x_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
473 std::get<55>(accumulators) += p_x_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
476 std::get<56>(accumulators) += p_y_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
479 std::get<57>(accumulators) += p_y_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
482 std::get<58>(accumulators) += z_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
485 std::get<59>(accumulators) += z_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
488 std::get<60>(accumulators) += accumulator_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
491 std::get<61>(accumulators) += accumulator_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
494 std::get<62>(accumulators) += quotient_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
497 std::get<63>(accumulators) += quotient_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
500 std::get<64>(accumulators) += op * not_in_mininicircuit_or_masked;
503 std::get<65>(accumulators) += x_lo_y_hi * not_in_mininicircuit_or_masked;
506 std::get<66>(accumulators) += x_hi_z_1 * not_in_mininicircuit_or_masked;
509 std::get<67>(accumulators) += y_lo_z_2 * not_in_mininicircuit_or_masked;