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;
122 using ShorterView =
typename ShorterAccumulator::View;
124 auto lagrange_odd_in_minicircuit = View(in.lagrange_odd_in_minicircuit);
127 auto lagrange_result_row_shorter = ShorterView(in.lagrange_result_row);
131 auto lagrange_last_in_minicircuit = View(in.lagrange_last_in_minicircuit);
132 auto lagrange_last_in_minicircuit_shorter = ShorterView(in.lagrange_last_in_minicircuit);
134 auto accumulators_binary_limbs_0 = View(in.accumulators_binary_limbs_0);
135 auto accumulators_binary_limbs_1 = View(in.accumulators_binary_limbs_1);
136 auto accumulators_binary_limbs_2 = View(in.accumulators_binary_limbs_2);
137 auto accumulators_binary_limbs_3 = View(in.accumulators_binary_limbs_3);
138 auto accumulators_binary_limbs_0_shift = View(in.accumulators_binary_limbs_0_shift);
139 auto accumulators_binary_limbs_1_shift = View(in.accumulators_binary_limbs_1_shift);
140 auto accumulators_binary_limbs_2_shift = View(in.accumulators_binary_limbs_2_shift);
141 auto accumulators_binary_limbs_3_shift = View(in.accumulators_binary_limbs_3_shift);
143 auto accumulators_binary_limbs_0_shorter = ShorterView(in.accumulators_binary_limbs_0);
144 auto accumulators_binary_limbs_1_shorter = ShorterView(in.accumulators_binary_limbs_1);
145 auto accumulators_binary_limbs_2_shorter = ShorterView(in.accumulators_binary_limbs_2);
146 auto accumulators_binary_limbs_3_shorter = ShorterView(in.accumulators_binary_limbs_3);
148 FF minus_one =
FF(-1);
152 auto tmp_1 = accumulators_binary_limbs_0 - accumulators_binary_limbs_0_shift;
153 tmp_1 *= lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
154 tmp_1 *= scaling_factor;
158 auto tmp_2 = accumulators_binary_limbs_1 - accumulators_binary_limbs_1_shift;
159 tmp_2 *= lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
160 tmp_2 *= scaling_factor;
163 auto tmp_3 = accumulators_binary_limbs_2 - accumulators_binary_limbs_2_shift;
164 tmp_3 *= lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
165 tmp_3 *= scaling_factor;
168 auto tmp_4 = accumulators_binary_limbs_3 - accumulators_binary_limbs_3_shift;
169 tmp_4 *= lagrange_odd_in_minicircuit * (lagrange_last_in_minicircuit + minus_one);
170 tmp_4 *= scaling_factor;
174 auto lagrange_last_in_minicircuit_by_scaling_factor = lagrange_last_in_minicircuit_shorter * scaling_factor;
175 auto tmp_5 = accumulators_binary_limbs_0_shorter * lagrange_last_in_minicircuit_by_scaling_factor;
179 auto tmp_6 = accumulators_binary_limbs_1_shorter * lagrange_last_in_minicircuit_by_scaling_factor;
183 auto tmp_7 = accumulators_binary_limbs_2_shorter * lagrange_last_in_minicircuit_by_scaling_factor;
187 auto tmp_8 = accumulators_binary_limbs_3_shorter * lagrange_last_in_minicircuit_by_scaling_factor;
192 auto lagrange_result_row_by_scaling_factor = lagrange_result_row_shorter * scaling_factor;
194 (accumulators_binary_limbs_0_shorter - params.accumulated_result[0]) * lagrange_result_row_by_scaling_factor;
199 (accumulators_binary_limbs_1_shorter - params.accumulated_result[1]) * lagrange_result_row_by_scaling_factor;
204 (accumulators_binary_limbs_2_shorter - params.accumulated_result[2]) * lagrange_result_row_by_scaling_factor;
209 (accumulators_binary_limbs_3_shorter - params.accumulated_result[3]) * lagrange_result_row_by_scaling_factor;
224 const AllEntities& in,
226 const FF& scaling_factor)
229 using View =
typename Accumulator::View;
232 static auto minus_one = -
FF(1);
234 auto lagrange_even_in_minicircuit = View(in.lagrange_even_in_minicircuit);
235 auto lagrange_odd_in_minicircuit = View(in.lagrange_odd_in_minicircuit);
237 auto p_x_low_limbs_range_constraint_0 = View(in.p_x_low_limbs_range_constraint_0);
238 auto p_x_low_limbs_range_constraint_1 = View(in.p_x_low_limbs_range_constraint_1);
239 auto p_x_low_limbs_range_constraint_2 = View(in.p_x_low_limbs_range_constraint_2);
240 auto p_x_low_limbs_range_constraint_3 = View(in.p_x_low_limbs_range_constraint_3);
241 auto p_x_low_limbs_range_constraint_4 = View(in.p_x_low_limbs_range_constraint_4);
242 auto p_x_high_limbs_range_constraint_0 = View(in.p_x_high_limbs_range_constraint_0);
243 auto p_x_high_limbs_range_constraint_1 = View(in.p_x_high_limbs_range_constraint_1);
244 auto p_x_high_limbs_range_constraint_2 = View(in.p_x_high_limbs_range_constraint_2);
245 auto p_x_high_limbs_range_constraint_3 = View(in.p_x_high_limbs_range_constraint_3);
246 auto p_x_high_limbs_range_constraint_4 = View(in.p_x_high_limbs_range_constraint_4);
247 auto p_y_low_limbs_range_constraint_0 = View(in.p_y_low_limbs_range_constraint_0);
248 auto p_y_low_limbs_range_constraint_1 = View(in.p_y_low_limbs_range_constraint_1);
249 auto p_y_low_limbs_range_constraint_2 = View(in.p_y_low_limbs_range_constraint_2);
250 auto p_y_low_limbs_range_constraint_3 = View(in.p_y_low_limbs_range_constraint_3);
251 auto p_y_low_limbs_range_constraint_4 = View(in.p_y_low_limbs_range_constraint_4);
252 auto p_y_high_limbs_range_constraint_0 = View(in.p_y_high_limbs_range_constraint_0);
253 auto p_y_high_limbs_range_constraint_1 = View(in.p_y_high_limbs_range_constraint_1);
254 auto p_y_high_limbs_range_constraint_2 = View(in.p_y_high_limbs_range_constraint_2);
255 auto p_y_high_limbs_range_constraint_3 = View(in.p_y_high_limbs_range_constraint_3);
256 auto p_y_high_limbs_range_constraint_4 = View(in.p_y_high_limbs_range_constraint_4);
257 auto z_low_limbs_range_constraint_0 = View(in.z_low_limbs_range_constraint_0);
258 auto z_low_limbs_range_constraint_1 = View(in.z_low_limbs_range_constraint_1);
259 auto z_low_limbs_range_constraint_2 = View(in.z_low_limbs_range_constraint_2);
260 auto z_low_limbs_range_constraint_3 = View(in.z_low_limbs_range_constraint_3);
261 auto z_low_limbs_range_constraint_4 = View(in.z_low_limbs_range_constraint_4);
262 auto z_high_limbs_range_constraint_0 = View(in.z_high_limbs_range_constraint_0);
263 auto z_high_limbs_range_constraint_1 = View(in.z_high_limbs_range_constraint_1);
264 auto z_high_limbs_range_constraint_2 = View(in.z_high_limbs_range_constraint_2);
265 auto z_high_limbs_range_constraint_3 = View(in.z_high_limbs_range_constraint_3);
266 auto z_high_limbs_range_constraint_4 = View(in.z_high_limbs_range_constraint_4);
267 auto accumulator_low_limbs_range_constraint_0 = View(in.accumulator_low_limbs_range_constraint_0);
268 auto accumulator_low_limbs_range_constraint_1 = View(in.accumulator_low_limbs_range_constraint_1);
269 auto accumulator_low_limbs_range_constraint_2 = View(in.accumulator_low_limbs_range_constraint_2);
270 auto accumulator_low_limbs_range_constraint_3 = View(in.accumulator_low_limbs_range_constraint_3);
271 auto accumulator_low_limbs_range_constraint_4 = View(in.accumulator_low_limbs_range_constraint_4);
272 auto accumulator_high_limbs_range_constraint_0 = View(in.accumulator_high_limbs_range_constraint_0);
273 auto accumulator_high_limbs_range_constraint_1 = View(in.accumulator_high_limbs_range_constraint_1);
274 auto accumulator_high_limbs_range_constraint_2 = View(in.accumulator_high_limbs_range_constraint_2);
275 auto accumulator_high_limbs_range_constraint_3 = View(in.accumulator_high_limbs_range_constraint_3);
276 auto accumulator_high_limbs_range_constraint_4 = View(in.accumulator_high_limbs_range_constraint_4);
277 auto quotient_low_limbs_range_constraint_0 = View(in.quotient_low_limbs_range_constraint_0);
278 auto quotient_low_limbs_range_constraint_1 = View(in.quotient_low_limbs_range_constraint_1);
279 auto quotient_low_limbs_range_constraint_2 = View(in.quotient_low_limbs_range_constraint_2);
280 auto quotient_low_limbs_range_constraint_3 = View(in.quotient_low_limbs_range_constraint_3);
281 auto quotient_low_limbs_range_constraint_4 = View(in.quotient_low_limbs_range_constraint_4);
282 auto quotient_high_limbs_range_constraint_0 = View(in.quotient_high_limbs_range_constraint_0);
283 auto quotient_high_limbs_range_constraint_1 = View(in.quotient_high_limbs_range_constraint_1);
284 auto quotient_high_limbs_range_constraint_2 = View(in.quotient_high_limbs_range_constraint_2);
285 auto quotient_high_limbs_range_constraint_3 = View(in.quotient_high_limbs_range_constraint_3);
286 auto quotient_high_limbs_range_constraint_4 = View(in.quotient_high_limbs_range_constraint_4);
287 auto relation_wide_limbs_range_constraint_0 = View(in.relation_wide_limbs_range_constraint_0);
288 auto relation_wide_limbs_range_constraint_1 = View(in.relation_wide_limbs_range_constraint_1);
289 auto relation_wide_limbs_range_constraint_2 = View(in.relation_wide_limbs_range_constraint_2);
290 auto relation_wide_limbs_range_constraint_3 = View(in.relation_wide_limbs_range_constraint_3);
291 auto p_x_low_limbs_range_constraint_tail = View(in.p_x_low_limbs_range_constraint_tail);
292 auto p_x_high_limbs_range_constraint_tail = View(in.p_x_high_limbs_range_constraint_tail);
293 auto p_y_low_limbs_range_constraint_tail = View(in.p_y_low_limbs_range_constraint_tail);
294 auto p_y_high_limbs_range_constraint_tail = View(in.p_y_high_limbs_range_constraint_tail);
295 auto z_low_limbs_range_constraint_tail = View(in.z_low_limbs_range_constraint_tail);
296 auto z_high_limbs_range_constraint_tail = View(in.z_high_limbs_range_constraint_tail);
297 auto accumulator_low_limbs_range_constraint_tail = View(in.accumulator_low_limbs_range_constraint_tail);
298 auto accumulator_high_limbs_range_constraint_tail = View(in.accumulator_high_limbs_range_constraint_tail);
299 auto quotient_low_limbs_range_constraint_tail = View(in.quotient_low_limbs_range_constraint_tail);
300 auto quotient_high_limbs_range_constraint_tail = View(in.quotient_high_limbs_range_constraint_tail);
301 auto op = View(in.op);
302 auto x_lo_y_hi = View(in.x_lo_y_hi);
303 auto x_hi_z_1 = View(in.x_hi_z_1);
304 auto y_lo_z_2 = View(in.y_lo_z_2);
305 auto lagrange_mini_masking = View(in.lagrange_mini_masking);
308 auto not_in_mininicircuit_or_masked = (lagrange_odd_in_minicircuit + lagrange_even_in_minicircuit + minus_one) *
309 (lagrange_mini_masking + minus_one) * scaling_factor;
312 std::get<0>(accumulators) += p_x_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
315 std::get<1>(accumulators) += p_x_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
318 std::get<2>(accumulators) += p_x_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
321 std::get<3>(accumulators) += p_x_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
324 std::get<4>(accumulators) += p_x_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
327 std::get<5>(accumulators) += p_x_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
330 std::get<6>(accumulators) += p_x_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
333 std::get<7>(accumulators) += p_x_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
336 std::get<8>(accumulators) += p_x_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
339 std::get<9>(accumulators) += p_x_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
342 std::get<10>(accumulators) += p_y_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
345 std::get<11>(accumulators) += p_y_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
348 std::get<12>(accumulators) += p_y_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
351 std::get<13>(accumulators) += p_y_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
354 std::get<14>(accumulators) += p_y_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
357 std::get<15>(accumulators) += p_y_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
360 std::get<16>(accumulators) += p_y_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
363 std::get<17>(accumulators) += p_y_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
366 std::get<18>(accumulators) += p_y_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
369 std::get<19>(accumulators) += p_y_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
372 std::get<20>(accumulators) += z_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
375 std::get<21>(accumulators) += z_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
378 std::get<22>(accumulators) += z_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
381 std::get<23>(accumulators) += z_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
384 std::get<24>(accumulators) += z_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
387 std::get<25>(accumulators) += z_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
390 std::get<26>(accumulators) += z_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
393 std::get<27>(accumulators) += z_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
396 std::get<28>(accumulators) += z_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
399 std::get<29>(accumulators) += z_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
402 std::get<30>(accumulators) += accumulator_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
405 std::get<31>(accumulators) += accumulator_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
408 std::get<32>(accumulators) += accumulator_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
411 std::get<33>(accumulators) += accumulator_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
414 std::get<34>(accumulators) += accumulator_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
417 std::get<35>(accumulators) += accumulator_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
420 std::get<36>(accumulators) += accumulator_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
423 std::get<37>(accumulators) += accumulator_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
426 std::get<38>(accumulators) += accumulator_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
429 std::get<39>(accumulators) += accumulator_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
432 std::get<40>(accumulators) += quotient_low_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
435 std::get<41>(accumulators) += quotient_low_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
438 std::get<42>(accumulators) += quotient_low_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
441 std::get<43>(accumulators) += quotient_low_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
444 std::get<44>(accumulators) += quotient_low_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
447 std::get<45>(accumulators) += quotient_high_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
450 std::get<46>(accumulators) += quotient_high_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
453 std::get<47>(accumulators) += quotient_high_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
456 std::get<48>(accumulators) += quotient_high_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
459 std::get<49>(accumulators) += quotient_high_limbs_range_constraint_4 * not_in_mininicircuit_or_masked;
462 std::get<50>(accumulators) += relation_wide_limbs_range_constraint_0 * not_in_mininicircuit_or_masked;
465 std::get<51>(accumulators) += relation_wide_limbs_range_constraint_1 * not_in_mininicircuit_or_masked;
468 std::get<52>(accumulators) += relation_wide_limbs_range_constraint_2 * not_in_mininicircuit_or_masked;
471 std::get<53>(accumulators) += relation_wide_limbs_range_constraint_3 * not_in_mininicircuit_or_masked;
474 std::get<54>(accumulators) += p_x_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
477 std::get<55>(accumulators) += p_x_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
480 std::get<56>(accumulators) += p_y_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
483 std::get<57>(accumulators) += p_y_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
486 std::get<58>(accumulators) += z_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
489 std::get<59>(accumulators) += z_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
492 std::get<60>(accumulators) += accumulator_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
495 std::get<61>(accumulators) += accumulator_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
498 std::get<62>(accumulators) += quotient_low_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
501 std::get<63>(accumulators) += quotient_high_limbs_range_constraint_tail * not_in_mininicircuit_or_masked;
504 std::get<64>(accumulators) += op * not_in_mininicircuit_or_masked;
507 std::get<65>(accumulators) += x_lo_y_hi * not_in_mininicircuit_or_masked;
510 std::get<66>(accumulators) += x_hi_z_1 * not_in_mininicircuit_or_masked;
513 std::get<67>(accumulators) += y_lo_z_2 * not_in_mininicircuit_or_masked;