-
Notifications
You must be signed in to change notification settings - Fork 8
/
alt_bn128_field.cairo
497 lines (439 loc) · 16.2 KB
/
alt_bn128_field.cairo
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
from starkware.cairo.common.bitwise import bitwise_and
from starkware.cairo.common.cairo_builtins import BitwiseBuiltin
from bigint import BASE, BigInt3, UnreducedBigInt3, UnreducedBigInt5, nondet_bigint3, bigint_mul
from alt_bn128_def import P0, P1, P2
// FIELD STRUCTURES
struct FQ2 {
e0: BigInt3,
e1: BigInt3,
}
struct FQ12 {
e0: BigInt3,
e1: BigInt3,
e2: BigInt3,
e3: BigInt3,
e4: BigInt3,
e5: BigInt3,
e6: BigInt3,
e7: BigInt3,
e8: BigInt3,
e9: BigInt3,
eA: BigInt3,
eB: BigInt3,
}
struct unreducedFQ12 {
e0: UnreducedBigInt5,
e1: UnreducedBigInt5,
e2: UnreducedBigInt5,
e3: UnreducedBigInt5,
e4: UnreducedBigInt5,
e5: UnreducedBigInt5,
e6: UnreducedBigInt5,
e7: UnreducedBigInt5,
e8: UnreducedBigInt5,
e9: UnreducedBigInt5,
eA: UnreducedBigInt5,
eB: UnreducedBigInt5,
}
// FIELD CONSTANTS
func fq_zero() -> (res: BigInt3) {
return (BigInt3(0, 0, 0),);
}
func fq2_zero() -> (res: FQ2) {
return (FQ2(
e0=BigInt3(0, 0, 0),
e1=BigInt3(0, 0, 0),
),);
}
func fq12_zero() -> (res: FQ12) {
return (
FQ12(
e0=BigInt3(0, 0, 0), e1=BigInt3(0, 0, 0), e2=BigInt3(0, 0, 0),
e3=BigInt3(0, 0, 0), e4=BigInt3(0, 0, 0), e5=BigInt3(0, 0, 0),
e6=BigInt3(0, 0, 0), e7=BigInt3(0, 0, 0), e8=BigInt3(0, 0, 0),
e9=BigInt3(0, 0, 0), eA=BigInt3(0, 0, 0), eB=BigInt3(0, 0, 0),
),
);
}
func fq12_one() -> (res: FQ12) {
return (
FQ12(
e0=BigInt3(1, 0, 0), e1=BigInt3(0, 0, 0), e2=BigInt3(0, 0, 0),
e3=BigInt3(0, 0, 0), e4=BigInt3(0, 0, 0), e5=BigInt3(0, 0, 0),
e6=BigInt3(0, 0, 0), e7=BigInt3(0, 0, 0), e8=BigInt3(0, 0, 0),
e9=BigInt3(0, 0, 0), eA=BigInt3(0, 0, 0), eB=BigInt3(0, 0, 0),
),
);
}
func verify_zero3{range_check_ptr}(val: BigInt3) {
alloc_locals;
local flag;
local q;
%{
from starkware.cairo.common.cairo_secp.secp_utils import pack
from starkware.cairo.common.math_utils import as_int
P = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47
v = pack(ids.val, PRIME)
q, r = divmod(v, P)
assert r == 0, f"verify_zero: Invalid input {ids.val.d0, ids.val.d1, ids.val.d2}."
ids.flag = 1 if q > 0 else 0
q = q if q > 0 else 0-q
ids.q = q % PRIME
%}
assert [range_check_ptr] = q + 2 ** 127;
tempvar carry1 = ((2 * flag - 1) * q * P0 - val.d0) / BASE;
assert [range_check_ptr + 1] = carry1 + 2 ** 127;
tempvar carry2 = ((2 * flag - 1) * q * P1 - val.d1 + carry1) / BASE;
assert [range_check_ptr + 2] = carry2 + 2 ** 127;
assert (2 * flag - 1) * q * P2 - val.d2 + carry2 = 0;
let range_check_ptr = range_check_ptr + 3;
return ();
}
func verify_zero5{range_check_ptr}(val: UnreducedBigInt5) {
alloc_locals;
local flag;
local q1;
%{
from starkware.cairo.common.cairo_secp.secp_utils import pack
from starkware.cairo.common.math_utils import as_int
P = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47
v3 = as_int(ids.val.d3, PRIME)
v4 = as_int(ids.val.d4, PRIME)
v = pack(ids.val, PRIME) + v3*2**258 + v4*2**344
q, r = divmod(v, P)
assert r == 0, f"verify_zero: Invalid input {ids.val.d0, ids.val.d1, ids.val.d2, ids.val.d3, ids.val.d4}."
# Since q usually doesn't fit BigInt3, divide it again
ids.flag = 1 if q > 0 else 0
q = q if q > 0 else 0-q
q1, q2 = divmod(q, P)
ids.q1 = q1
value = k = q2
%}
let (k) = nondet_bigint3();
let fullk = BigInt3(q1 * P0 + k.d0, q1 * P1 + k.d1, q1 * P2 + k.d2);
let P = BigInt3(P0, P1, P2);
let (k_n) = bigint_mul(fullk, P);
// val mod n = 0, so val = k_n
tempvar carry1 = ((2 * flag - 1) * k_n.d0 - val.d0) / BASE;
assert [range_check_ptr + 0] = carry1 + 2 ** 127;
tempvar carry2 = ((2 * flag - 1) * k_n.d1 - val.d1 + carry1) / BASE;
assert [range_check_ptr + 1] = carry2 + 2 ** 127;
tempvar carry3 = ((2 * flag - 1) * k_n.d2 - val.d2 + carry2) / BASE;
assert [range_check_ptr + 2] = carry3 + 2 ** 127;
tempvar carry4 = ((2 * flag - 1) * k_n.d3 - val.d3 + carry3) / BASE;
assert [range_check_ptr + 3] = carry4 + 2 ** 127;
assert (2 * flag - 1) * k_n.d4 - val.d4 + carry4 = 0;
let range_check_ptr = range_check_ptr + 4;
return ();
}
// returns 1 if x ==0 mod alt_bn128 prime
func is_zero{range_check_ptr}(x: BigInt3) -> (res: felt) {
%{
from starkware.cairo.common.cairo_secp.secp_utils import pack
P = 0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47
x = pack(ids.x, PRIME) % P
%}
if (nondet %{ x == 0 %} != 0) {
verify_zero3(x);
// verify_zero5(UnreducedBigInt5(d0=x.d0, d1=x.d1, d2=x.d2, d3=0, d4=0))
return (res=1);
}
%{
from starkware.python.math_utils import div_mod
value = x_inv = div_mod(1, x, P)
%}
let (x_inv) = nondet_bigint3();
let (x_x_inv) = bigint_mul(x, x_inv);
// Check that x * x_inv = 1 to verify that x != 0.
verify_zero5(
UnreducedBigInt5(
d0=x_x_inv.d0 - 1,
d1=x_x_inv.d1,
d2=x_x_inv.d2,
d3=x_x_inv.d3,
d4=x_x_inv.d4),
);
return (res=0);
}
// FQ12 verify
func verify_zero_fq12{range_check_ptr}(x: FQ12) {
verify_zero3(x.e0);
verify_zero3(x.e1);
verify_zero3(x.e2);
verify_zero3(x.e3);
verify_zero3(x.e4);
verify_zero3(x.e5);
verify_zero3(x.e6);
verify_zero3(x.e7);
verify_zero3(x.e8);
verify_zero3(x.e9);
verify_zero3(x.eA);
verify_zero3(x.eB);
return ();
}
func fq_eq_zero(x: BigInt3) -> (res: felt) {
if (x.d0 != 0) {
return (res=0);
}
if (x.d1 != 0) {
return (res=0);
}
if (x.d2 != 0) {
return (res=0);
}
return (res=1);
}
func fq12_eq_zero(x: FQ12) -> (res: felt) {
let (e0_is_zero) = fq_eq_zero(x.e0);
if (e0_is_zero == 0) {
return (res=0);
}
let (e1_is_zero) = fq_eq_zero(x.e1);
if (e1_is_zero == 0) {
return (res=0);
}
let (e2_is_zero) = fq_eq_zero(x.e2);
if (e2_is_zero == 0) {
return (res=0);
}
let (e3_is_zero) = fq_eq_zero(x.e3);
if (e3_is_zero == 0) {
return (res=0);
}
let (e4_is_zero) = fq_eq_zero(x.e4);
if (e4_is_zero == 0) {
return (res=0);
}
let (e5_is_zero) = fq_eq_zero(x.e5);
if (e5_is_zero == 0) {
return (res=0);
}
let (e6_is_zero) = fq_eq_zero(x.e6);
if (e6_is_zero == 0) {
return (res=0);
}
let (e7_is_zero) = fq_eq_zero(x.e7);
if (e7_is_zero == 0) {
return (res=0);
}
let (e8_is_zero) = fq_eq_zero(x.e8);
if (e8_is_zero == 0) {
return (res=0);
}
let (e9_is_zero) = fq_eq_zero(x.e9);
if (e9_is_zero == 0) {
return (res=0);
}
let (eA_is_zero) = fq_eq_zero(x.eA);
if (eA_is_zero == 0) {
return (res=0);
}
let (eB_is_zero) = fq_eq_zero(x.eB);
if (eB_is_zero == 0) {
return (res=0);
}
return (res=1);
}
func fq12_is_zero{range_check_ptr}(x: FQ12) -> (res: felt) {
%{
import sys, os
cwd = os.getcwd()
sys.path.append(cwd)
from utils.bn128_field import FQ, FQ12
from utils.bn128_utils import parse_fq12
val = list(map(FQ, parse_fq12(ids.x)))
if FQ12(val) == FQ12([0]*12):
x = 0
else:
x = 1
%}
if (nondet %{ x == 0 %} != 0) {
verify_zero_fq12(x);
return (res=1);
}
%{
val = list(map(FQ, parse_fq12(ids.x)))
val = FQ12(val).inv()
value = list(map(lambda x: x.n, val.coeffs))
%}
let (x_inv) = nondet_fq12();
// TODO VERIF x * x_inv - 1 = 0
return (res=0);
}
// Difference of two FQ12, resulting FQ12 BigInt3 limbs can be negative
func fq12_diff(x: FQ12, y: FQ12) -> (res: FQ12) {
return (
res=FQ12(
BigInt3(d0=x.e0.d0 - y.e0.d0, d1=x.e0.d1 - y.e0.d1, d2=x.e0.d2 - y.e0.d2),
BigInt3(d0=x.e1.d0 - y.e1.d0, d1=x.e1.d1 - y.e1.d1, d2=x.e1.d2 - y.e1.d2),
BigInt3(d0=x.e2.d0 - y.e2.d0, d1=x.e2.d1 - y.e2.d1, d2=x.e2.d2 - y.e2.d2),
BigInt3(d0=x.e3.d0 - y.e3.d0, d1=x.e3.d1 - y.e3.d1, d2=x.e3.d2 - y.e3.d2),
BigInt3(d0=x.e4.d0 - y.e4.d0, d1=x.e4.d1 - y.e4.d1, d2=x.e4.d2 - y.e4.d2),
BigInt3(d0=x.e5.d0 - y.e5.d0, d1=x.e5.d1 - y.e5.d1, d2=x.e5.d2 - y.e5.d2),
BigInt3(d0=x.e6.d0 - y.e6.d0, d1=x.e6.d1 - y.e6.d1, d2=x.e6.d2 - y.e6.d2),
BigInt3(d0=x.e7.d0 - y.e7.d0, d1=x.e7.d1 - y.e7.d1, d2=x.e7.d2 - y.e7.d2),
BigInt3(d0=x.e8.d0 - y.e8.d0, d1=x.e8.d1 - y.e8.d1, d2=x.e8.d2 - y.e8.d2),
BigInt3(d0=x.e9.d0 - y.e9.d0, d1=x.e9.d1 - y.e9.d1, d2=x.e9.d2 - y.e9.d2),
BigInt3(d0=x.eA.d0 - y.eA.d0, d1=x.eA.d1 - y.eA.d1, d2=x.eA.d2 - y.eA.d2),
BigInt3(d0=x.eB.d0 - y.eB.d0, d1=x.eB.d1 - y.eB.d1, d2=x.eB.d2 - y.eB.d2)),
);
}
func fq12_sum(x: FQ12, y: FQ12) -> (res: FQ12) {
return (
res=FQ12(
BigInt3(d0=x.e0.d0 + y.e0.d0, d1=x.e0.d1 + y.e0.d1, d2=x.e0.d2 + y.e0.d2),
BigInt3(d0=x.e1.d0 + y.e1.d0, d1=x.e1.d1 + y.e1.d1, d2=x.e1.d2 + y.e1.d2),
BigInt3(d0=x.e2.d0 + y.e2.d0, d1=x.e2.d1 + y.e2.d1, d2=x.e2.d2 + y.e2.d2),
BigInt3(d0=x.e3.d0 + y.e3.d0, d1=x.e3.d1 + y.e3.d1, d2=x.e3.d2 + y.e3.d2),
BigInt3(d0=x.e4.d0 + y.e4.d0, d1=x.e4.d1 + y.e4.d1, d2=x.e4.d2 + y.e4.d2),
BigInt3(d0=x.e5.d0 + y.e5.d0, d1=x.e5.d1 + y.e5.d1, d2=x.e5.d2 + y.e5.d2),
BigInt3(d0=x.e6.d0 + y.e6.d0, d1=x.e6.d1 + y.e6.d1, d2=x.e6.d2 + y.e6.d2),
BigInt3(d0=x.e7.d0 + y.e7.d0, d1=x.e7.d1 + y.e7.d1, d2=x.e7.d2 + y.e7.d2),
BigInt3(d0=x.e8.d0 + y.e8.d0, d1=x.e8.d1 + y.e8.d1, d2=x.e8.d2 + y.e8.d2),
BigInt3(d0=x.e9.d0 + y.e9.d0, d1=x.e9.d1 + y.e9.d1, d2=x.e9.d2 + y.e9.d2),
BigInt3(d0=x.eA.d0 + y.eA.d0, d1=x.eA.d1 + y.eA.d1, d2=x.eA.d2 + y.eA.d2),
BigInt3(d0=x.eB.d0 + y.eB.d0, d1=x.eB.d1 + y.eB.d1, d2=x.eB.d2 + y.eB.d2)),
);
}
// TODO
// FIELD MULTIPLICATION
// func ufq12_mul{range_check_ptr}(a : FQ12, b : FQ12) -> (res : unreducedFQ12):
// let ab_e0 = bigint_mul(a.e0, b.d0)
// let ab_e0 = bigint_mul(a.e0, b.d0)
// return (
// unreducedFQ12(
// e0=
// end
// TODO deterministic (unreduced FQ12?)
func fq12_mul{range_check_ptr}(a: FQ12, b: FQ12) -> (res: FQ12) {
%{
import sys, os
cwd = os.getcwd()
sys.path.append(cwd)
from utils.bn128_field import FQ, FQ12
from utils.bn128_utils import parse_fq12, print_g12
a = FQ12(list(map(FQ, parse_fq12(ids.a))))
b = FQ12(list(map(FQ, parse_fq12(ids.b))))
value = res = list(map(lambda x: x.n, (a*b).coeffs))
# print("a*b =", value)
%}
let (res) = nondet_fq12();
// TODO CHECKS
return (res=res);
}
func fq12_pow_inner{range_check_ptr}(x: FQ12, n: felt, m: felt) -> (pow2: FQ12, res: FQ12) {
if (m == 0) {
assert n = 0;
let (one) = fq12_one();
return (pow2=x, res=one);
}
alloc_locals;
let (x_sqr) = fq12_mul(x, x);
%{ memory[ap] = (ids.n % PRIME) % 2 %}
jmp odd if [ap] != 0, ap++;
return fq12_pow_inner(x=x_sqr, n=n / 2, m=m - 1);
odd:
let (inner_pow, inner_res) = fq12_pow_inner(x=x_sqr, n=(n - 1) / 2, m=m - 1);
let (res) = fq12_mul(inner_res, x);
return (inner_pow, res);
}
func fq12_pow_3{range_check_ptr}(x: FQ12, n: BigInt3) -> (pow2: FQ12, res: FQ12) {
alloc_locals;
let (pow2_0: FQ12, local res0: FQ12) = fq12_pow_inner(x, n.d0, 86);
let (pow2_1: FQ12, local res1: FQ12) = fq12_pow_inner(pow2_0, n.d1, 86);
let (pow2_2, local res2: FQ12) = fq12_pow_inner(pow2_1, n.d2, 86);
let (res: FQ12) = fq12_mul(res0, res1);
let (res: FQ12) = fq12_mul(res, res2);
return (pow2_2, res);
}
func fq12_pow_12{range_check_ptr}(x: FQ12, n: FQ12) -> (res: FQ12) {
alloc_locals;
let (pow2_0: FQ12, local res0: FQ12) = fq12_pow_3(x, n.e0);
let (pow2_1: FQ12, local res1: FQ12) = fq12_pow_3(pow2_0, n.e1);
let (pow2_2: FQ12, local res2: FQ12) = fq12_pow_3(pow2_1, n.e2);
let (pow2_3: FQ12, local res3: FQ12) = fq12_pow_3(pow2_2, n.e3);
let (pow2_4: FQ12, local res4: FQ12) = fq12_pow_3(pow2_3, n.e4);
let (pow2_5: FQ12, local res5: FQ12) = fq12_pow_3(pow2_4, n.e5);
let (pow2_6: FQ12, local res6: FQ12) = fq12_pow_3(pow2_5, n.e6);
let (pow2_7: FQ12, local res7: FQ12) = fq12_pow_3(pow2_6, n.e7);
let (pow2_8: FQ12, local res8: FQ12) = fq12_pow_3(pow2_7, n.e8);
let (pow2_9: FQ12, local res9: FQ12) = fq12_pow_3(pow2_8, n.e9);
let (pow2_A: FQ12, local resA: FQ12) = fq12_pow_3(pow2_9, n.eA);
// Simplifications since eB = 0
// let (pow2_B : FQ12, local resB : FQ12) = fq12_pow_3(pow2_A, n.eB)
let (local res01: FQ12) = fq12_mul(res0, res1);
let (local res23: FQ12) = fq12_mul(res2, res3);
let (local res45: FQ12) = fq12_mul(res4, res5);
let (local res67: FQ12) = fq12_mul(res6, res7);
let (local res89: FQ12) = fq12_mul(res8, res9);
// let (local resAB : FQ12) = fq12_mul(resA, resB)
let (local res0123: FQ12) = fq12_mul(res01, res23);
let (local res4567: FQ12) = fq12_mul(res45, res67);
// let (local res89AB : FQ12) = fq12_mul(res89, resAB)
let (local res89A: FQ12) = fq12_mul(res89, resA);
let (local res0123: FQ12) = fq12_mul(res01, res23);
let (local res0__7: FQ12) = fq12_mul(res0123, res4567);
let (res: FQ12) = fq12_mul(res0__7, res89A);
return (res,);
}
// Hint argument: value
// a 12 element list of field elements
func nondet_fq12{range_check_ptr}() -> (res: FQ12) {
let res: FQ12 = [cast(ap + 38, FQ12*)];
%{
from starkware.cairo.common.cairo_secp.secp_utils import split
r = ids.res
var_list = [r.e0, r.e1, r.e2, r.e3, r.e4, r.e5,
r.e6, r.e7, r.e8, r.e9, r.eA, r.eB]
#segments.write_arg(ids.res.e0.address_, split(val[0]))
for (var, val) in zip(var_list, value):
segments.write_arg(var.address_, split(val))
%}
const MAX_SUM = 12 * 3 * (2 ** 86 - 1);
// TODO RANGE CHECKS? (WHY THE ASSERT LIKE THS BTW?)
assert [range_check_ptr] = MAX_SUM - (res.e0.d0 + res.e0.d1 + res.e0.d2 + res.e1.d0 + res.e1.d1 + res.e1.d2 +
res.e2.d0 + res.e2.d1 + res.e2.d2 + res.e3.d0 + res.e3.d1 + res.e3.d2 +
res.e4.d0 + res.e4.d1 + res.e4.d2 + res.e5.d0 + res.e5.d1 + res.e5.d2 +
res.e6.d0 + res.e6.d1 + res.e6.d2 + res.e7.d0 + res.e7.d1 + res.e7.d2 +
res.e8.d0 + res.e8.d1 + res.e8.d2 + res.e9.d0 + res.e9.d1 + res.e9.d2 +
res.eA.d0 + res.eA.d1 + res.eA.d2 + res.eB.d0 + res.eB.d1 + res.eB.d2);
tempvar range_check_ptr = range_check_ptr + 37;
[range_check_ptr - 1] = res.e0.d0, ap++;
[range_check_ptr - 2] = res.e0.d1, ap++;
[range_check_ptr - 3] = res.e0.d2, ap++;
[range_check_ptr - 4] = res.e1.d0, ap++;
[range_check_ptr - 5] = res.e1.d1, ap++;
[range_check_ptr - 6] = res.e1.d2, ap++;
[range_check_ptr - 7] = res.e2.d0, ap++;
[range_check_ptr - 8] = res.e2.d1, ap++;
[range_check_ptr - 9] = res.e2.d2, ap++;
[range_check_ptr - 10] = res.e3.d0, ap++;
[range_check_ptr - 11] = res.e3.d1, ap++;
[range_check_ptr - 12] = res.e3.d2, ap++;
[range_check_ptr - 13] = res.e4.d0, ap++;
[range_check_ptr - 14] = res.e4.d1, ap++;
[range_check_ptr - 15] = res.e4.d2, ap++;
[range_check_ptr - 16] = res.e5.d0, ap++;
[range_check_ptr - 17] = res.e5.d1, ap++;
[range_check_ptr - 18] = res.e5.d2, ap++;
[range_check_ptr - 19] = res.e6.d0, ap++;
[range_check_ptr - 20] = res.e6.d1, ap++;
[range_check_ptr - 21] = res.e6.d2, ap++;
[range_check_ptr - 22] = res.e7.d0, ap++;
[range_check_ptr - 23] = res.e7.d1, ap++;
[range_check_ptr - 24] = res.e7.d2, ap++;
[range_check_ptr - 25] = res.e8.d0, ap++;
[range_check_ptr - 26] = res.e8.d1, ap++;
[range_check_ptr - 27] = res.e8.d2, ap++;
[range_check_ptr - 28] = res.e9.d0, ap++;
[range_check_ptr - 29] = res.e9.d1, ap++;
[range_check_ptr - 30] = res.e9.d2, ap++;
[range_check_ptr - 31] = res.eA.d0, ap++;
[range_check_ptr - 32] = res.eA.d1, ap++;
[range_check_ptr - 33] = res.eA.d2, ap++;
[range_check_ptr - 34] = res.eB.d0, ap++;
[range_check_ptr - 35] = res.eB.d1, ap++;
[range_check_ptr - 36] = res.eB.d2, ap++;
static_assert &res + FQ12.SIZE == ap;
return (res=res);
}