Description:
Smart contract deployed on Ethereum with Factory features.
Blockchain: Ethereum
Source Code: View Code On The Blockchain
Solidity Source Code:
{{
"language": "Solidity",
"sources": {
"starkware/solidity/verifier/cpu/layout0/CpuConstraintPoly.sol": {
"content": "/*
Copyright 2019-2023 StarkWare Industries Ltd.
Licensed under the Apache License, Version 2.0 (the "License").
You may not use this file except in compliance with the License.
You may obtain a copy of the License at
https://www.starkware.co/open-source-license/
Unless required by applicable law or agreed to in writing,
software distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions
and limitations under the License.
*/
// ---------- The following code was auto-generated. PLEASE DO NOT EDIT. ----------
// SPDX-License-Identifier: Apache-2.0.
pragma solidity ^0.6.12;
contract CpuConstraintPoly {
// The Memory map during the execution of this contract is as follows:
// [0x0, 0x20) - periodic_column/pedersen/points/x.
// [0x20, 0x40) - periodic_column/pedersen/points/y.
// [0x40, 0x60) - periodic_column/ecdsa/generator_points/x.
// [0x60, 0x80) - periodic_column/ecdsa/generator_points/y.
// [0x80, 0xa0) - trace_length.
// [0xa0, 0xc0) - offset_size.
// [0xc0, 0xe0) - half_offset_size.
// [0xe0, 0x100) - initial_ap.
// [0x100, 0x120) - initial_pc.
// [0x120, 0x140) - final_ap.
// [0x140, 0x160) - final_pc.
// [0x160, 0x180) - memory/multi_column_perm/perm/interaction_elm.
// [0x180, 0x1a0) - memory/multi_column_perm/hash_interaction_elm0.
// [0x1a0, 0x1c0) - memory/multi_column_perm/perm/public_memory_prod.
// [0x1c0, 0x1e0) - range_check16/perm/interaction_elm.
// [0x1e0, 0x200) - range_check16/perm/public_memory_prod.
// [0x200, 0x220) - range_check_min.
// [0x220, 0x240) - range_check_max.
// [0x240, 0x260) - pedersen/shift_point.x.
// [0x260, 0x280) - pedersen/shift_point.y.
// [0x280, 0x2a0) - initial_pedersen_addr.
// [0x2a0, 0x2c0) - initial_range_check_addr.
// [0x2c0, 0x2e0) - ecdsa/sig_config.alpha.
// [0x2e0, 0x300) - ecdsa/sig_config.shift_point.x.
// [0x300, 0x320) - ecdsa/sig_config.shift_point.y.
// [0x320, 0x340) - ecdsa/sig_config.beta.
// [0x340, 0x360) - initial_ecdsa_addr.
// [0x360, 0x380) - trace_generator.
// [0x380, 0x3a0) - oods_point.
// [0x3a0, 0x400) - interaction_elements.
// [0x400, 0x420) - composition_alpha.
// [0x420, 0x1d40) - oods_values.
// ----------------------- end of input data - -------------------------
// [0x1d40, 0x1d60) - intermediate_value/cpu/decode/opcode_range_check/bit_0.
// [0x1d60, 0x1d80) - intermediate_value/cpu/decode/opcode_range_check/bit_2.
// [0x1d80, 0x1da0) - intermediate_value/cpu/decode/opcode_range_check/bit_4.
// [0x1da0, 0x1dc0) - intermediate_value/cpu/decode/opcode_range_check/bit_3.
// [0x1dc0, 0x1de0) - intermediate_value/cpu/decode/flag_op1_base_op0_0.
// [0x1de0, 0x1e00) - intermediate_value/cpu/decode/opcode_range_check/bit_5.
// [0x1e00, 0x1e20) - intermediate_value/cpu/decode/opcode_range_check/bit_6.
// [0x1e20, 0x1e40) - intermediate_value/cpu/decode/opcode_range_check/bit_9.
// [0x1e40, 0x1e60) - intermediate_value/cpu/decode/flag_res_op1_0.
// [0x1e60, 0x1e80) - intermediate_value/cpu/decode/opcode_range_check/bit_7.
// [0x1e80, 0x1ea0) - intermediate_value/cpu/decode/opcode_range_check/bit_8.
// [0x1ea0, 0x1ec0) - intermediate_value/cpu/decode/flag_pc_update_regular_0.
// [0x1ec0, 0x1ee0) - intermediate_value/cpu/decode/opcode_range_check/bit_12.
// [0x1ee0, 0x1f00) - intermediate_value/cpu/decode/opcode_range_check/bit_13.
// [0x1f00, 0x1f20) - intermediate_value/cpu/decode/fp_update_regular_0.
// [0x1f20, 0x1f40) - intermediate_value/cpu/decode/opcode_range_check/bit_1.
// [0x1f40, 0x1f60) - intermediate_value/npc_reg_0.
// [0x1f60, 0x1f80) - intermediate_value/cpu/decode/opcode_range_check/bit_10.
// [0x1f80, 0x1fa0) - intermediate_value/cpu/decode/opcode_range_check/bit_11.
// [0x1fa0, 0x1fc0) - intermediate_value/cpu/decode/opcode_range_check/bit_14.
// [0x1fc0, 0x1fe0) - intermediate_value/memory/address_diff_0.
// [0x1fe0, 0x2000) - intermediate_value/range_check16/diff_0.
// [0x2000, 0x2020) - intermediate_value/pedersen/hash0/ec_subset_sum/bit_0.
// [0x2020, 0x2040) - intermediate_value/pedersen/hash0/ec_subset_sum/bit_neg_0.
// [0x2040, 0x2060) - intermediate_value/pedersen/hash1/ec_subset_sum/bit_0.
// [0x2060, 0x2080) - intermediate_value/pedersen/hash1/ec_subset_sum/bit_neg_0.
// [0x2080, 0x20a0) - intermediate_value/pedersen/hash2/ec_subset_sum/bit_0.
// [0x20a0, 0x20c0) - intermediate_value/pedersen/hash2/ec_subset_sum/bit_neg_0.
// [0x20c0, 0x20e0) - intermediate_value/pedersen/hash3/ec_subset_sum/bit_0.
// [0x20e0, 0x2100) - intermediate_value/pedersen/hash3/ec_subset_sum/bit_neg_0.
// [0x2100, 0x2120) - intermediate_value/range_check_builtin/value0_0.
// [0x2120, 0x2140) - intermediate_value/range_check_builtin/value1_0.
// [0x2140, 0x2160) - intermediate_value/range_check_builtin/value2_0.
// [0x2160, 0x2180) - intermediate_value/range_check_builtin/value3_0.
// [0x2180, 0x21a0) - intermediate_value/range_check_builtin/value4_0.
// [0x21a0, 0x21c0) - intermediate_value/range_check_builtin/value5_0.
// [0x21c0, 0x21e0) - intermediate_value/range_check_builtin/value6_0.
// [0x21e0, 0x2200) - intermediate_value/range_check_builtin/value7_0.
// [0x2200, 0x2220) - intermediate_value/ecdsa/signature0/doubling_key/x_squared.
// [0x2220, 0x2240) - intermediate_value/ecdsa/signature0/exponentiate_generator/bit_0.
// [0x2240, 0x2260) - intermediate_value/ecdsa/signature0/exponentiate_generator/bit_neg_0.
// [0x2260, 0x2280) - intermediate_value/ecdsa/signature0/exponentiate_key/bit_0.
// [0x2280, 0x22a0) - intermediate_value/ecdsa/signature0/exponentiate_key/bit_neg_0.
// [0x22a0, 0x2520) - expmods.
// [0x2520, 0x2820) - domains.
// [0x2820, 0x2ac0) - denominator_invs.
// [0x2ac0, 0x2d60) - denominators.
// [0x2d60, 0x2e20) - expmod_context.
fallback() external {
uint256 res;
assembly {
let PRIME := 0x800000000000011000000000000000000000000000000000000000000000001
// Copy input from calldata to memory.
calldatacopy(0x0, 0x0, /*Input data size*/ 0x1d40)
let point := /*oods_point*/ mload(0x380)
function expmod(base, exponent, modulus) -> result {
let p := /*expmod_context*/ 0x2d60
mstore(p, 0x20) // Length of Base.
mstore(add(p, 0x20), 0x20) // Length of Exponent.
mstore(add(p, 0x40), 0x20) // Length of Modulus.
mstore(add(p, 0x60), base) // Base.
mstore(add(p, 0x80), exponent) // Exponent.
mstore(add(p, 0xa0), modulus) // Modulus.
// Call modexp precompile.
if iszero(staticcall(not(0), 0x05, p, 0xc0, p, 0x20)) {
revert(0, 0)
}
result := mload(p)
}
{
// Prepare expmods for denominators and numerators.
// expmods[0] = point^(trace_length / 8192).
mstore(0x22a0, expmod(point, div(/*trace_length*/ mload(0x80), 8192), PRIME))
// expmods[1] = point^(trace_length / 4096).
mstore(0x22c0, mulmod(
/*point^(trace_length / 8192)*/ mload(0x22a0),
/*point^(trace_length / 8192)*/ mload(0x22a0),
PRIME))
// expmods[2] = point^(trace_length / 512).
mstore(0x22e0, expmod(point, div(/*trace_length*/ mload(0x80), 512), PRIME))
// expmods[3] = point^(trace_length / 256).
mstore(0x2300, mulmod(
/*point^(trace_length / 512)*/ mload(0x22e0),
/*point^(trace_length / 512)*/ mload(0x22e0),
PRIME))
// expmods[4] = point^(trace_length / 128).
mstore(0x2320, mulmod(
/*point^(trace_length / 256)*/ mload(0x2300),
/*point^(trace_length / 256)*/ mload(0x2300),
PRIME))
// expmods[5] = point^(trace_length / 32).
mstore(0x2340, expmod(point, div(/*trace_length*/ mload(0x80), 32), PRIME))
// expmods[6] = point^(trace_length / 16).
mstore(0x2360, mulmod(
/*point^(trace_length / 32)*/ mload(0x2340),
/*point^(trace_length / 32)*/ mload(0x2340),
PRIME))
// expmods[7] = point^(trace_length / 8).
mstore(0x2380, mulmod(
/*point^(trace_length / 16)*/ mload(0x2360),
/*point^(trace_length / 16)*/ mload(0x2360),
PRIME))
// expmods[8] = point^(trace_length / 2).
mstore(0x23a0, expmod(point, div(/*trace_length*/ mload(0x80), 2), PRIME))
// expmods[9] = point^trace_length.
mstore(0x23c0, mulmod(
/*point^(trace_length / 2)*/ mload(0x23a0),
/*point^(trace_length / 2)*/ mload(0x23a0),
PRIME))
// expmods[10] = trace_generator^(trace_length / 2).
mstore(0x23e0, expmod(/*trace_generator*/ mload(0x360), div(/*trace_length*/ mload(0x80), 2), PRIME))
// expmods[11] = trace_generator^(15 * trace_length / 16).
mstore(0x2400, expmod(/*trace_generator*/ mload(0x360), div(mul(15, /*trace_length*/ mload(0x80)), 16), PRIME))
// expmods[12] = trace_generator^(251 * trace_length / 256).
mstore(0x2420, expmod(/*trace_generator*/ mload(0x360), div(mul(251, /*trace_length*/ mload(0x80)), 256), PRIME))
// expmods[13] = trace_generator^(63 * trace_length / 64).
mstore(0x2440, expmod(/*trace_generator*/ mload(0x360), div(mul(63, /*trace_length*/ mload(0x80)), 64), PRIME))
// expmods[14] = trace_generator^(255 * trace_length / 256).
mstore(0x2460, expmod(/*trace_generator*/ mload(0x360), div(mul(255, /*trace_length*/ mload(0x80)), 256), PRIME))
// expmods[15] = trace_generator^(trace_length - 16).
mstore(0x2480, expmod(/*trace_generator*/ mload(0x360), sub(/*trace_length*/ mload(0x80), 16), PRIME))
// expmods[16] = trace_generator^(trace_length - 2).
mstore(0x24a0, expmod(/*trace_generator*/ mload(0x360), sub(/*trace_length*/ mload(0x80), 2), PRIME))
// expmods[17] = trace_generator^(trace_length - 1).
mstore(0x24c0, expmod(/*trace_generator*/ mload(0x360), sub(/*trace_length*/ mload(0x80), 1), PRIME))
// expmods[18] = trace_generator^(trace_length - 128).
mstore(0x24e0, expmod(/*trace_generator*/ mload(0x360), sub(/*trace_length*/ mload(0x80), 128), PRIME))
// expmods[19] = trace_generator^(trace_length - 8192).
mstore(0x2500, expmod(/*trace_generator*/ mload(0x360), sub(/*trace_length*/ mload(0x80), 8192), PRIME))
}
{
// Compute domains.
// Denominator for constraints: 'cpu/decode/opcode_range_check/bit', 'range_check16/perm/step0', 'range_check16/diff_is_bit', 'pedersen/hash0/ec_subset_sum/booleanity_test', 'pedersen/hash0/ec_subset_sum/add_points/slope', 'pedersen/hash0/ec_subset_sum/add_points/x', 'pedersen/hash0/ec_subset_sum/add_points/y', 'pedersen/hash0/ec_subset_sum/copy_point/x', 'pedersen/hash0/ec_subset_sum/copy_point/y', 'pedersen/hash1/ec_subset_sum/booleanity_test', 'pedersen/hash1/ec_subset_sum/add_points/slope', 'pedersen/hash1/ec_subset_sum/add_points/x', 'pedersen/hash1/ec_subset_sum/add_points/y', 'pedersen/hash1/ec_subset_sum/copy_point/x', 'pedersen/hash1/ec_subset_sum/copy_point/y', 'pedersen/hash2/ec_subset_sum/booleanity_test', 'pedersen/hash2/ec_subset_sum/add_points/slope', 'pedersen/hash2/ec_subset_sum/add_points/x', 'pedersen/hash2/ec_subset_sum/add_points/y', 'pedersen/hash2/ec_subset_sum/copy_point/x', 'pedersen/hash2/ec_subset_sum/copy_point/y', 'pedersen/hash3/ec_subset_sum/booleanity_test', 'pedersen/hash3/ec_subset_sum/add_points/slope', 'pedersen/hash3/ec_subset_sum/add_points/x', 'pedersen/hash3/ec_subset_sum/add_points/y', 'pedersen/hash3/ec_subset_sum/copy_point/x', 'pedersen/hash3/ec_subset_sum/copy_point/y'.
// domains[0] = point^trace_length - 1.
mstore(0x2520,
addmod(/*point^trace_length*/ mload(0x23c0), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'memory/multi_column_perm/perm/step0', 'memory/diff_is_bit', 'memory/is_func'.
// domains[1] = point^(trace_length / 2) - 1.
mstore(0x2540,
addmod(/*point^(trace_length / 2)*/ mload(0x23a0), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'public_memory_addr_zero', 'public_memory_value_zero'.
// domains[2] = point^(trace_length / 8) - 1.
mstore(0x2560,
addmod(/*point^(trace_length / 8)*/ mload(0x2380), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'cpu/decode/opcode_range_check/zero'.
// Numerator for constraints: 'cpu/decode/opcode_range_check/bit'.
// domains[3] = point^(trace_length / 16) - trace_generator^(15 * trace_length / 16).
mstore(0x2580,
addmod(
/*point^(trace_length / 16)*/ mload(0x2360),
sub(PRIME, /*trace_generator^(15 * trace_length / 16)*/ mload(0x2400)),
PRIME))
// Denominator for constraints: 'cpu/decode/opcode_range_check_input', 'cpu/decode/flag_op1_base_op0_bit', 'cpu/decode/flag_res_op1_bit', 'cpu/decode/flag_pc_update_regular_bit', 'cpu/decode/fp_update_regular_bit', 'cpu/operands/mem_dst_addr', 'cpu/operands/mem0_addr', 'cpu/operands/mem1_addr', 'cpu/operands/ops_mul', 'cpu/operands/res', 'cpu/update_registers/update_pc/tmp0', 'cpu/update_registers/update_pc/tmp1', 'cpu/update_registers/update_pc/pc_cond_negative', 'cpu/update_registers/update_pc/pc_cond_positive', 'cpu/update_registers/update_ap/ap_update', 'cpu/update_registers/update_fp/fp_update', 'cpu/opcodes/call/push_fp', 'cpu/opcodes/call/push_pc', 'cpu/opcodes/call/off0', 'cpu/opcodes/call/off1', 'cpu/opcodes/call/flags', 'cpu/opcodes/ret/off0', 'cpu/opcodes/ret/off2', 'cpu/opcodes/ret/flags', 'cpu/opcodes/assert_eq/assert_eq', 'ecdsa/signature0/doubling_key/slope', 'ecdsa/signature0/doubling_key/x', 'ecdsa/signature0/doubling_key/y', 'ecdsa/signature0/exponentiate_key/booleanity_test', 'ecdsa/signature0/exponentiate_key/add_points/slope', 'ecdsa/signature0/exponentiate_key/add_points/x', 'ecdsa/signature0/exponentiate_key/add_points/y', 'ecdsa/signature0/exponentiate_key/add_points/x_diff_inv', 'ecdsa/signature0/exponentiate_key/copy_point/x', 'ecdsa/signature0/exponentiate_key/copy_point/y'.
// domains[4] = point^(trace_length / 16) - 1.
mstore(0x25a0,
addmod(/*point^(trace_length / 16)*/ mload(0x2360), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'ecdsa/signature0/exponentiate_generator/booleanity_test', 'ecdsa/signature0/exponentiate_generator/add_points/slope', 'ecdsa/signature0/exponentiate_generator/add_points/x', 'ecdsa/signature0/exponentiate_generator/add_points/y', 'ecdsa/signature0/exponentiate_generator/add_points/x_diff_inv', 'ecdsa/signature0/exponentiate_generator/copy_point/x', 'ecdsa/signature0/exponentiate_generator/copy_point/y'.
// domains[5] = point^(trace_length / 32) - 1.
mstore(0x25c0,
addmod(/*point^(trace_length / 32)*/ mload(0x2340), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'pedersen/input0_addr', 'pedersen/input1_addr', 'pedersen/output_addr', 'range_check_builtin/value', 'range_check_builtin/addr_step'.
// domains[6] = point^(trace_length / 128) - 1.
mstore(0x25e0,
addmod(/*point^(trace_length / 128)*/ mload(0x2320), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'pedersen/hash0/ec_subset_sum/bit_unpacking/last_one_is_zero', 'pedersen/hash0/ec_subset_sum/bit_unpacking/zeroes_between_ones0', 'pedersen/hash0/ec_subset_sum/bit_unpacking/cumulative_bit192', 'pedersen/hash0/ec_subset_sum/bit_unpacking/zeroes_between_ones192', 'pedersen/hash0/ec_subset_sum/bit_unpacking/cumulative_bit196', 'pedersen/hash0/ec_subset_sum/bit_unpacking/zeroes_between_ones196', 'pedersen/hash0/copy_point/x', 'pedersen/hash0/copy_point/y', 'pedersen/hash1/ec_subset_sum/bit_unpacking/last_one_is_zero', 'pedersen/hash1/ec_subset_sum/bit_unpacking/zeroes_between_ones0', 'pedersen/hash1/ec_subset_sum/bit_unpacking/cumulative_bit192', 'pedersen/hash1/ec_subset_sum/bit_unpacking/zeroes_between_ones192', 'pedersen/hash1/ec_subset_sum/bit_unpacking/cumulative_bit196', 'pedersen/hash1/ec_subset_sum/bit_unpacking/zeroes_between_ones196', 'pedersen/hash1/copy_point/x', 'pedersen/hash1/copy_point/y', 'pedersen/hash2/ec_subset_sum/bit_unpacking/last_one_is_zero', 'pedersen/hash2/ec_subset_sum/bit_unpacking/zeroes_between_ones0', 'pedersen/hash2/ec_subset_sum/bit_unpacking/cumulative_bit192', 'pedersen/hash2/ec_subset_sum/bit_unpacking/zeroes_between_ones192', 'pedersen/hash2/ec_subset_sum/bit_unpacking/cumulative_bit196', 'pedersen/hash2/ec_subset_sum/bit_unpacking/zeroes_between_ones196', 'pedersen/hash2/copy_point/x', 'pedersen/hash2/copy_point/y', 'pedersen/hash3/ec_subset_sum/bit_unpacking/last_one_is_zero', 'pedersen/hash3/ec_subset_sum/bit_unpacking/zeroes_between_ones0', 'pedersen/hash3/ec_subset_sum/bit_unpacking/cumulative_bit192', 'pedersen/hash3/ec_subset_sum/bit_unpacking/zeroes_between_ones192', 'pedersen/hash3/ec_subset_sum/bit_unpacking/cumulative_bit196', 'pedersen/hash3/ec_subset_sum/bit_unpacking/zeroes_between_ones196', 'pedersen/hash3/copy_point/x', 'pedersen/hash3/copy_point/y'.
// domains[7] = point^(trace_length / 256) - 1.
mstore(0x2600,
addmod(/*point^(trace_length / 256)*/ mload(0x2300), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'pedersen/hash0/ec_subset_sum/zeros_tail', 'pedersen/hash1/ec_subset_sum/zeros_tail', 'pedersen/hash2/ec_subset_sum/zeros_tail', 'pedersen/hash3/ec_subset_sum/zeros_tail'.
// Numerator for constraints: 'pedersen/hash0/ec_subset_sum/booleanity_test', 'pedersen/hash0/ec_subset_sum/add_points/slope', 'pedersen/hash0/ec_subset_sum/add_points/x', 'pedersen/hash0/ec_subset_sum/add_points/y', 'pedersen/hash0/ec_subset_sum/copy_point/x', 'pedersen/hash0/ec_subset_sum/copy_point/y', 'pedersen/hash1/ec_subset_sum/booleanity_test', 'pedersen/hash1/ec_subset_sum/add_points/slope', 'pedersen/hash1/ec_subset_sum/add_points/x', 'pedersen/hash1/ec_subset_sum/add_points/y', 'pedersen/hash1/ec_subset_sum/copy_point/x', 'pedersen/hash1/ec_subset_sum/copy_point/y', 'pedersen/hash2/ec_subset_sum/booleanity_test', 'pedersen/hash2/ec_subset_sum/add_points/slope', 'pedersen/hash2/ec_subset_sum/add_points/x', 'pedersen/hash2/ec_subset_sum/add_points/y', 'pedersen/hash2/ec_subset_sum/copy_point/x', 'pedersen/hash2/ec_subset_sum/copy_point/y', 'pedersen/hash3/ec_subset_sum/booleanity_test', 'pedersen/hash3/ec_subset_sum/add_points/slope', 'pedersen/hash3/ec_subset_sum/add_points/x', 'pedersen/hash3/ec_subset_sum/add_points/y', 'pedersen/hash3/ec_subset_sum/copy_point/x', 'pedersen/hash3/ec_subset_sum/copy_point/y'.
// domains[8] = point^(trace_length / 256) - trace_generator^(255 * trace_length / 256).
mstore(0x2620,
addmod(
/*point^(trace_length / 256)*/ mload(0x2300),
sub(PRIME, /*trace_generator^(255 * trace_length / 256)*/ mload(0x2460)),
PRIME))
// Denominator for constraints: 'pedersen/hash0/ec_subset_sum/bit_extraction_end', 'pedersen/hash1/ec_subset_sum/bit_extraction_end', 'pedersen/hash2/ec_subset_sum/bit_extraction_end', 'pedersen/hash3/ec_subset_sum/bit_extraction_end'.
// domains[9] = point^(trace_length / 256) - trace_generator^(63 * trace_length / 64).
mstore(0x2640,
addmod(
/*point^(trace_length / 256)*/ mload(0x2300),
sub(PRIME, /*trace_generator^(63 * trace_length / 64)*/ mload(0x2440)),
PRIME))
// Numerator for constraints: 'pedersen/hash0/copy_point/x', 'pedersen/hash0/copy_point/y', 'pedersen/hash1/copy_point/x', 'pedersen/hash1/copy_point/y', 'pedersen/hash2/copy_point/x', 'pedersen/hash2/copy_point/y', 'pedersen/hash3/copy_point/x', 'pedersen/hash3/copy_point/y'.
// domains[10] = point^(trace_length / 512) - trace_generator^(trace_length / 2).
mstore(0x2660,
addmod(
/*point^(trace_length / 512)*/ mload(0x22e0),
sub(PRIME, /*trace_generator^(trace_length / 2)*/ mload(0x23e0)),
PRIME))
// Denominator for constraints: 'pedersen/hash0/init/x', 'pedersen/hash0/init/y', 'pedersen/hash1/init/x', 'pedersen/hash1/init/y', 'pedersen/hash2/init/x', 'pedersen/hash2/init/y', 'pedersen/hash3/init/x', 'pedersen/hash3/init/y', 'pedersen/input0_value0', 'pedersen/input0_value1', 'pedersen/input0_value2', 'pedersen/input0_value3', 'pedersen/input1_value0', 'pedersen/input1_value1', 'pedersen/input1_value2', 'pedersen/input1_value3', 'pedersen/output_value0', 'pedersen/output_value1', 'pedersen/output_value2', 'pedersen/output_value3'.
// domains[11] = point^(trace_length / 512) - 1.
mstore(0x2680,
addmod(/*point^(trace_length / 512)*/ mload(0x22e0), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'ecdsa/signature0/exponentiate_key/zeros_tail'.
// Numerator for constraints: 'ecdsa/signature0/doubling_key/slope', 'ecdsa/signature0/doubling_key/x', 'ecdsa/signature0/doubling_key/y', 'ecdsa/signature0/exponentiate_key/booleanity_test', 'ecdsa/signature0/exponentiate_key/add_points/slope', 'ecdsa/signature0/exponentiate_key/add_points/x', 'ecdsa/signature0/exponentiate_key/add_points/y', 'ecdsa/signature0/exponentiate_key/add_points/x_diff_inv', 'ecdsa/signature0/exponentiate_key/copy_point/x', 'ecdsa/signature0/exponentiate_key/copy_point/y'.
// domains[12] = point^(trace_length / 4096) - trace_generator^(255 * trace_length / 256).
mstore(0x26a0,
addmod(
/*point^(trace_length / 4096)*/ mload(0x22c0),
sub(PRIME, /*trace_generator^(255 * trace_length / 256)*/ mload(0x2460)),
PRIME))
// Denominator for constraints: 'ecdsa/signature0/exponentiate_key/bit_extraction_end'.
// domains[13] = point^(trace_length / 4096) - trace_generator^(251 * trace_length / 256).
mstore(0x26c0,
addmod(
/*point^(trace_length / 4096)*/ mload(0x22c0),
sub(PRIME, /*trace_generator^(251 * trace_length / 256)*/ mload(0x2420)),
PRIME))
// Denominator for constraints: 'ecdsa/signature0/init_key/x', 'ecdsa/signature0/init_key/y', 'ecdsa/signature0/r_and_w_nonzero'.
// domains[14] = point^(trace_length / 4096) - 1.
mstore(0x26e0,
addmod(/*point^(trace_length / 4096)*/ mload(0x22c0), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'ecdsa/signature0/exponentiate_generator/zeros_tail'.
// Numerator for constraints: 'ecdsa/signature0/exponentiate_generator/booleanity_test', 'ecdsa/signature0/exponentiate_generator/add_points/slope', 'ecdsa/signature0/exponentiate_generator/add_points/x', 'ecdsa/signature0/exponentiate_generator/add_points/y', 'ecdsa/signature0/exponentiate_generator/add_points/x_diff_inv', 'ecdsa/signature0/exponentiate_generator/copy_point/x', 'ecdsa/signature0/exponentiate_generator/copy_point/y'.
// domains[15] = point^(trace_length / 8192) - trace_generator^(255 * trace_length / 256).
mstore(0x2700,
addmod(
/*point^(trace_length / 8192)*/ mload(0x22a0),
sub(PRIME, /*trace_generator^(255 * trace_length / 256)*/ mload(0x2460)),
PRIME))
// Denominator for constraints: 'ecdsa/signature0/exponentiate_generator/bit_extraction_end'.
// domains[16] = point^(trace_length / 8192) - trace_generator^(251 * trace_length / 256).
mstore(0x2720,
addmod(
/*point^(trace_length / 8192)*/ mload(0x22a0),
sub(PRIME, /*trace_generator^(251 * trace_length / 256)*/ mload(0x2420)),
PRIME))
// Denominator for constraints: 'ecdsa/signature0/init_gen/x', 'ecdsa/signature0/init_gen/y', 'ecdsa/signature0/add_results/slope', 'ecdsa/signature0/add_results/x', 'ecdsa/signature0/add_results/y', 'ecdsa/signature0/add_results/x_diff_inv', 'ecdsa/signature0/extract_r/slope', 'ecdsa/signature0/extract_r/x', 'ecdsa/signature0/extract_r/x_diff_inv', 'ecdsa/signature0/z_nonzero', 'ecdsa/signature0/q_on_curve/x_squared', 'ecdsa/signature0/q_on_curve/on_curve', 'ecdsa/message_addr', 'ecdsa/pubkey_addr', 'ecdsa/message_value0', 'ecdsa/pubkey_value0'.
// domains[17] = point^(trace_length / 8192) - 1.
mstore(0x2740,
addmod(/*point^(trace_length / 8192)*/ mload(0x22a0), sub(PRIME, 1), PRIME))
// Denominator for constraints: 'final_ap', 'final_fp', 'final_pc'.
// Numerator for constraints: 'cpu/update_registers/update_pc/tmp0', 'cpu/update_registers/update_pc/tmp1', 'cpu/update_registers/update_pc/pc_cond_negative', 'cpu/update_registers/update_pc/pc_cond_positive', 'cpu/update_registers/update_ap/ap_update', 'cpu/update_registers/update_fp/fp_update'.
// domains[18] = point - trace_generator^(trace_length - 16).
mstore(0x2760,
addmod(point, sub(PRIME, /*trace_generator^(trace_length - 16)*/ mload(0x2480)), PRIME))
// Denominator for constraints: 'initial_ap', 'initial_fp', 'initial_pc', 'memory/multi_column_perm/perm/init0', 'memory/initial_addr', 'range_check16/perm/init0', 'range_check16/minimum', 'pedersen/init_addr', 'range_check_builtin/init_addr', 'ecdsa/init_addr'.
// domains[19] = point - 1.
mstore(0x2780,
addmod(point, sub(PRIME, 1), PRIME))
// Denominator for constraints: 'memory/multi_column_perm/perm/last'.
// Numerator for constraints: 'memory/multi_column_perm/perm/step0', 'memory/diff_is_bit', 'memory/is_func'.
// domains[20] = point - trace_generator^(trace_length - 2).
mstore(0x27a0,
addmod(point, sub(PRIME, /*trace_generator^(trace_length - 2)*/ mload(0x24a0)), PRIME))
// Denominator for constraints: 'range_check16/perm/last', 'range_check16/maximum'.
// Numerator for constraints: 'range_check16/perm/step0', 'range_check16/diff_is_bit'.
// domains[21] = point - trace_generator^(trace_length - 1).
mstore(0x27c0,
addmod(point, sub(PRIME, /*trace_generator^(trace_length - 1)*/ mload(0x24c0)), PRIME))
// Numerator for constraints: 'pedersen/input0_addr', 'range_check_builtin/addr_step'.
// domains[22] = point - trace_generator^(trace_length - 128).
mstore(0x27e0,
addmod(point, sub(PRIME, /*trace_generator^(trace_length - 128)*/ mload(0x24e0)), PRIME))
// Numerator for constraints: 'ecdsa/pubkey_addr'.
// domains[23] = point - trace_generator^(trace_length - 8192).
mstore(0x2800,
addmod(point, sub(PRIME, /*trace_generator^(trace_length - 8192)*/ mload(0x2500)), PRIME))
}
{
// Prepare denominators for batch inverse.
// denominators[0] = domains[0].
mstore(0x2ac0, /*domains[0]*/ mload(0x2520))
// denominators[1] = domains[3].
mstore(0x2ae0, /*domains[3]*/ mload(0x2580))
// denominators[2] = domains[4].
mstore(0x2b00, /*domains[4]*/ mload(0x25a0))
// denominators[3] = domains[18].
mstore(0x2b20, /*domains[18]*/ mload(0x2760))
// denominators[4] = domains[19].
mstore(0x2b40, /*domains[19]*/ mload(0x2780))
// denominators[5] = domains[1].
mstore(0x2b60, /*domains[1]*/ mload(0x2540))
// denominators[6] = domains[20].
mstore(0x2b80, /*domains[20]*/ mload(0x27a0))
// denominators[7] = domains[2].
mstore(0x2ba0, /*domains[2]*/ mload(0x2560))
// denominators[8] = domains[21].
mstore(0x2bc0, /*domains[21]*/ mload(0x27c0))
// denominators[9] = domains[7].
mstore(0x2be0, /*domains[7]*/ mload(0x2600))
// denominators[10] = domains[8].
mstore(0x2c00, /*domains[8]*/ mload(0x2620))
// denominators[11] = domains[9].
mstore(0x2c20, /*domains[9]*/ mload(0x2640))
// denominators[12] = domains[11].
mstore(0x2c40, /*domains[11]*/ mload(0x2680))
// denominators[13] = domains[6].
mstore(0x2c60, /*domains[6]*/ mload(0x25e0))
// denominators[14] = domains[12].
mstore(0x2c80, /*domains[12]*/ mload(0x26a0))
// denominators[15] = domains[5].
mstore(0x2ca0, /*domains[5]*/ mload(0x25c0))
// denominators[16] = domains[15].
mstore(0x2cc0, /*domains[15]*/ mload(0x2700))
// denominators[17] = domains[16].
mstore(0x2ce0, /*domains[16]*/ mload(0x2720))
// denominators[18] = domains[13].
mstore(0x2d00, /*domains[13]*/ mload(0x26c0))
// denominators[19] = domains[17].
mstore(0x2d20, /*domains[17]*/ mload(0x2740))
// denominators[20] = domains[14].
mstore(0x2d40, /*domains[14]*/ mload(0x26e0))
}
{
// Compute the inverses of the denominators into denominatorInvs using batch inverse.
// Start by computing the cumulative product.
// Let (d_0, d_1, d_2, ..., d_{n-1}) be the values in denominators. After this loop
// denominatorInvs will be (1, d_0, d_0 * d_1, ...) and prod will contain the value of
// d_0 * ... * d_{n-1}.
// Compute the offset between the partialProducts array and the input values array.
let productsToValuesOffset := 0x2a0
let prod := 1
let partialProductEndPtr := 0x2ac0
for { let partialProductPtr := 0x2820 }
lt(partialProductPtr, partialProductEndPtr)
{ partialProductPtr := add(partialProductPtr, 0x20) } {
mstore(partialProductPtr, prod)
// prod *= d_{i}.
prod := mulmod(prod,
mload(add(partialProductPtr, productsToValuesOffset)),
PRIME)
}
let firstPartialProductPtr := 0x2820
// Compute the inverse of the product.
let prodInv := expmod(prod, sub(PRIME, 2), PRIME)
if eq(prodInv, 0) {
// Solidity generates reverts with reason that look as follows:
// 1. 4 bytes with the constant 0x08c379a0 (== Keccak256(b'Error(string)')[:4]).
// 2. 32 bytes offset bytes (always 0x20 as far as i can tell).
// 3. 32 bytes with the length of the revert reason.
// 4. Revert reason string.
mstore(0, 0x08c379a000000000000000000000000000000000000000000000000000000000)
mstore(0x4, 0x20)
mstore(0x24, 0x1e)
mstore(0x44, "Batch inverse product is zero.")
revert(0, 0x62)
}
// Compute the inverses.
// Loop over denominator_invs in reverse order.
// currentPartialProductPtr is initialized to one past the end.
let currentPartialProductPtr := 0x2ac0
for { } gt(currentPartialProductPtr, firstPartialProductPtr) { } {
currentPartialProductPtr := sub(currentPartialProductPtr, 0x20)
// Store 1/d_{i} = (d_0 * ... * d_{i-1}) * 1/(d_0 * ... * d_{i}).
mstore(currentPartialProductPtr,
mulmod(mload(currentPartialProductPtr), prodInv, PRIME))
// Update prodInv to be 1/(d_0 * ... * d_{i-1}) by multiplying by d_i.
prodInv := mulmod(prodInv,
mload(add(currentPartialProductPtr, productsToValuesOffset)),
PRIME)
}
}
{
// Compute the result of the composition polynomial.
{
// cpu/decode/opcode_range_check/bit_0 = column1_row0 - (column1_row1 + column1_row1).
let val := addmod(
/*column1_row0*/ mload(0x5a0),
sub(
PRIME,
addmod(/*column1_row1*/ mload(0x5c0), /*column1_row1*/ mload(0x5c0), PRIME)),
PRIME)
mstore(0x1d40, val)
}
{
// cpu/decode/opcode_range_check/bit_2 = column1_row2 - (column1_row3 + column1_row3).
let val := addmod(
/*column1_row2*/ mload(0x5e0),
sub(
PRIME,
addmod(/*column1_row3*/ mload(0x600), /*column1_row3*/ mload(0x600), PRIME)),
PRIME)
mstore(0x1d60, val)
}
{
// cpu/decode/opcode_range_check/bit_4 = column1_row4 - (column1_row5 + column1_row5).
let val := addmod(
/*column1_row4*/ mload(0x620),
sub(
PRIME,
addmod(/*column1_row5*/ mload(0x640), /*column1_row5*/ mload(0x640), PRIME)),
PRIME)
mstore(0x1d80, val)
}
{
// cpu/decode/opcode_range_check/bit_3 = column1_row3 - (column1_row4 + column1_row4).
let val := addmod(
/*column1_row3*/ mload(0x600),
sub(
PRIME,
addmod(/*column1_row4*/ mload(0x620), /*column1_row4*/ mload(0x620), PRIME)),
PRIME)
mstore(0x1da0, val)
}
{
// cpu/decode/flag_op1_base_op0_0 = 1 - (cpu__decode__opcode_range_check__bit_2 + cpu__decode__opcode_range_check__bit_4 + cpu__decode__opcode_range_check__bit_3).
let val := addmod(
1,
sub(
PRIME,
addmod(
addmod(
/*intermediate_value/cpu/decode/opcode_range_check/bit_2*/ mload(0x1d60),
/*intermediate_value/cpu/decode/opcode_range_check/bit_4*/ mload(0x1d80),
PRIME),
/*intermediate_value/cpu/decode/opcode_range_check/bit_3*/ mload(0x1da0),
PRIME)),
PRIME)
mstore(0x1dc0, val)
}
{
// cpu/decode/opcode_range_check/bit_5 = column1_row5 - (column1_row6 + column1_row6).
let val := addmod(
/*column1_row5*/ mload(0x640),
sub(
PRIME,
addmod(/*column1_row6*/ mload(0x660), /*column1_row6*/ mload(0x660), PRIME)),
PRIME)
mstore(0x1de0, val)
}
{
// cpu/decode/opcode_range_check/bit_6 = column1_row6 - (column1_row7 + column1_row7).
let val := addmod(
/*column1_row6*/ mload(0x660),
sub(
PRIME,
addmod(/*column1_row7*/ mload(0x680), /*column1_row7*/ mload(0x680), PRIME)),
PRIME)
mstore(0x1e00, val)
}
{
// cpu/decode/opcode_range_check/bit_9 = column1_row9 - (column1_row10 + column1_row10).
let val := addmod(
/*column1_row9*/ mload(0x6c0),
sub(
PRIME,
addmod(/*column1_row10*/ mload(0x6e0), /*column1_row10*/ mload(0x6e0), PRIME)),
PRIME)
mstore(0x1e20, val)
}
{
// cpu/decode/flag_res_op1_0 = 1 - (cpu__decode__opcode_range_check__bit_5 + cpu__decode__opcode_range_check__bit_6 + cpu__decode__opcode_range_check__bit_9).
let val := addmod(
1,
sub(
PRIME,
addmod(
addmod(
/*intermediate_value/cpu/decode/opcode_range_check/bit_5*/ mload(0x1de0),
/*intermediate_value/cpu/decode/opcode_range_check/bit_6*/ mload(0x1e00),
PRIME),
/*intermediate_value/cpu/decode/opcode_range_check/bit_9*/ mload(0x1e20),
PRIME)),
PRIME)
mstore(0x1e40, val)
}
{
// cpu/decode/opcode_range_check/bit_7 = column1_row7 - (column1_row8 + column1_row8).
let val := addmod(
/*column1_row7*/ mload(0x680),
sub(
PRIME,
addmod(/*column1_row8*/ mload(0x6a0), /*column1_row8*/ mload(0x6a0), PRIME)),
PRIME)
mstore(0x1e60, val)
}
{
// cpu/decode/opcode_range_check/bit_8 = column1_row8 - (column1_row9 + column1_row9).
let val := addmod(
/*column1_row8*/ mload(0x6a0),
sub(
PRIME,
addmod(/*column1_row9*/ mload(0x6c0), /*column1_row9*/ mload(0x6c0), PRIME)),
PRIME)
mstore(0x1e80, val)
}
{
// cpu/decode/flag_pc_update_regular_0 = 1 - (cpu__decode__opcode_range_check__bit_7 + cpu__decode__opcode_range_check__bit_8 + cpu__decode__opcode_range_check__bit_9).
let val := addmod(
1,
sub(
PRIME,
addmod(
addmod(
/*intermediate_value/cpu/decode/opcode_range_check/bit_7*/ mload(0x1e60),
/*intermediate_value/cpu/decode/opcode_range_check/bit_8*/ mload(0x1e80),
PRIME),
/*intermediate_value/cpu/decode/opcode_range_check/bit_9*/ mload(0x1e20),
PRIME)),
PRIME)
mstore(0x1ea0, val)
}
{
// cpu/decode/opcode_range_check/bit_12 = column1_row12 - (column1_row13 + column1_row13).
let val := addmod(
/*column1_row12*/ mload(0x720),
sub(
PRIME,
addmod(/*column1_row13*/ mload(0x740), /*column1_row13*/ mload(0x740), PRIME)),
PRIME)
mstore(0x1ec0, val)
}
{
// cpu/decode/opcode_range_check/bit_13 = column1_row13 - (column1_row14 + column1_row14).
let val := addmod(
/*column1_row13*/ mload(0x740),
sub(
PRIME,
addmod(/*column1_row14*/ mload(0x760), /*column1_row14*/ mload(0x760), PRIME)),
PRIME)
mstore(0x1ee0, val)
}
{
// cpu/decode/fp_update_regular_0 = 1 - (cpu__decode__opcode_range_check__bit_12 + cpu__decode__opcode_range_check__bit_13).
let val := addmod(
1,
sub(
PRIME,
addmod(
/*intermediate_value/cpu/decode/opcode_range_check/bit_12*/ mload(0x1ec0),
/*intermediate_value/cpu/decode/opcode_range_check/bit_13*/ mload(0x1ee0),
PRIME)),
PRIME)
mstore(0x1f00, val)
}
{
// cpu/decode/opcode_range_check/bit_1 = column1_row1 - (column1_row2 + column1_row2).
let val := addmod(
/*column1_row1*/ mload(0x5c0),
sub(
PRIME,
addmod(/*column1_row2*/ mload(0x5e0), /*column1_row2*/ mload(0x5e0), PRIME)),
PRIME)
mstore(0x1f20, val)
}
{
// npc_reg_0 = column19_row0 + cpu__decode__opcode_range_check__bit_2 + 1.
let val := addmod(
addmod(
/*column19_row0*/ mload(0x11e0),
/*intermediate_value/cpu/decode/opcode_range_check/bit_2*/ mload(0x1d60),
PRIME),
1,
PRIME)
mstore(0x1f40, val)
}
{
// cpu/decode/opcode_range_check/bit_10 = column1_row10 - (column1_row11 + column1_row11).
let val := addmod(
/*column1_row10*/ mload(0x6e0),
sub(
PRIME,
addmod(/*column1_row11*/ mload(0x700), /*column1_row11*/ mload(0x700), PRIME)),
PRIME)
mstore(0x1f60, val)
}
{
// cpu/decode/opcode_range_check/bit_11 = column1_row11 - (column1_row12 + column1_row12).
let val := addmod(
/*column1_row11*/ mload(0x700),
sub(
PRIME,
addmod(/*column1_row12*/ mload(0x720), /*column1_row12*/ mload(0x720), PRIME)),
PRIME)
mstore(0x1f80, val)
}
{
// cpu/decode/opcode_range_check/bit_14 = column1_row14 - (column1_row15 + column1_row15).
let val := addmod(
/*column1_row14*/ mload(0x760),
sub(
PRIME,
addmod(/*column1_row15*/ mload(0x780), /*column1_row15*/ mload(0x780), PRIME)),
PRIME)
mstore(0x1fa0, val)
}
{
// memory/address_diff_0 = column20_row2 - column20_row0.
let val := addmod(/*column20_row2*/ mload(0x1680), sub(PRIME, /*column20_row0*/ mload(0x1640)), PRIME)
mstore(0x1fc0, val)
}
{
// range_check16/diff_0 = column2_row1 - column2_row0.
let val := addmod(/*column2_row1*/ mload(0x7c0), sub(PRIME, /*column2_row0*/ mload(0x7a0)), PRIME)
mstore(0x1fe0, val)
}
{
// pedersen/hash0/ec_subset_sum/bit_0 = column5_row0 - (column5_row1 + column5_row1).
let val := addmod(
/*column5_row0*/ mload(0x900),
sub(
PRIME,
addmod(/*column5_row1*/ mload(0x920), /*column5_row1*/ mload(0x920), PRIME)),
PRIME)
mstore(0x2000, val)
}
{
// pedersen/hash0/ec_subset_sum/bit_neg_0 = 1 - pedersen__hash0__ec_subset_sum__bit_0.
let val := addmod(
1,
sub(PRIME, /*intermediate_value/pedersen/hash0/ec_subset_sum/bit_0*/ mload(0x2000)),
PRIME)
mstore(0x2020, val)
}
{
// pedersen/hash1/ec_subset_sum/bit_0 = column8_row0 - (column8_row1 + column8_row1).
let val := addmod(
/*column8_row0*/ mload(0xb40),
sub(
PRIME,
addmod(/*column8_row1*/ mload(0xb60), /*column8_row1*/ mload(0xb60), PRIME)),
PRIME)
mstore(0x2040, val)
}
{
// pedersen/hash1/ec_subset_sum/bit_neg_0 = 1 - pedersen__hash1__ec_subset_sum__bit_0.
let val := addmod(
1,
sub(PRIME, /*intermediate_value/pedersen/hash1/ec_subset_sum/bit_0*/ mload(0x2040)),
PRIME)
mstore(0x2060, val)
}
{
// pedersen/hash2/ec_subset_sum/bit_0 = column11_row0 - (column11_row1 + column11_row1).
let val := addmod(
/*column11_row0*/ mload(0xd80),
sub(
PRIME,
addmod(/*column11_row1*/ mload(0xda0), /*column11_row1*/ mload(0xda0), PRIME)),
PRIME)
mstore(0x2080, val)
}
{
// pedersen/hash2/ec_subset_sum/bit_neg_0 = 1 - pedersen__hash2__ec_subset_sum__bit_0.
let val := addmod(
1,
sub(PRIME, /*intermediate_value/pedersen/hash2/ec_subset_sum/bit_0*/ mload(0x2080)),
PRIME)
mstore(0x20a0, val)
}
{
// pedersen/hash3/ec_subset_sum/bit_0 = column14_row0 - (column14_row1 + column14_row1).
let val := addmod(
/*column14_row0*/ mload(0xfc0),
sub(
PRIME,
addmod(/*column14_row1*/ mload(0xfe0), /*column14_row1*/ mload(0xfe0), PRIME)),
PRIME)
mstore(0x20c0, val)
}
{
// pedersen/hash3/ec_subset_sum/bit_neg_0 = 1 - pedersen__hash3__ec_subset_sum__bit_0.
let val := addmod(
1,
sub(PRIME, /*intermediate_value/pedersen/hash3/ec_subset_sum/bit_0*/ mload(0x20c0)),
PRIME)
mstore(0x20e0, val)
}
{
// range_check_builtin/value0_0 = column0_row12.
let val := /*column0_row12*/ mload(0x4a0)
mstore(0x2100, val)
}
{
// range_check_builtin/value1_0 = range_check_builtin__value0_0 * offset_size + column0_row28.
let val := addmod(
mulmod(
/*intermediate_value/range_check_builtin/value0_0*/ mload(0x2100),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row28*/ mload(0x4c0),
PRIME)
mstore(0x2120, val)
}
{
// range_check_builtin/value2_0 = range_check_builtin__value1_0 * offset_size + column0_row44.
let val := addmod(
mulmod(
/*intermediate_value/range_check_builtin/value1_0*/ mload(0x2120),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row44*/ mload(0x4e0),
PRIME)
mstore(0x2140, val)
}
{
// range_check_builtin/value3_0 = range_check_builtin__value2_0 * offset_size + column0_row60.
let val := addmod(
mulmod(
/*intermediate_value/range_check_builtin/value2_0*/ mload(0x2140),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row60*/ mload(0x500),
PRIME)
mstore(0x2160, val)
}
{
// range_check_builtin/value4_0 = range_check_builtin__value3_0 * offset_size + column0_row76.
let val := addmod(
mulmod(
/*intermediate_value/range_check_builtin/value3_0*/ mload(0x2160),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row76*/ mload(0x520),
PRIME)
mstore(0x2180, val)
}
{
// range_check_builtin/value5_0 = range_check_builtin__value4_0 * offset_size + column0_row92.
let val := addmod(
mulmod(
/*intermediate_value/range_check_builtin/value4_0*/ mload(0x2180),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row92*/ mload(0x540),
PRIME)
mstore(0x21a0, val)
}
{
// range_check_builtin/value6_0 = range_check_builtin__value5_0 * offset_size + column0_row108.
let val := addmod(
mulmod(
/*intermediate_value/range_check_builtin/value5_0*/ mload(0x21a0),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row108*/ mload(0x560),
PRIME)
mstore(0x21c0, val)
}
{
// range_check_builtin/value7_0 = range_check_builtin__value6_0 * offset_size + column0_row124.
let val := addmod(
mulmod(
/*intermediate_value/range_check_builtin/value6_0*/ mload(0x21c0),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row124*/ mload(0x580),
PRIME)
mstore(0x21e0, val)
}
{
// ecdsa/signature0/doubling_key/x_squared = column21_row6 * column21_row6.
let val := mulmod(/*column21_row6*/ mload(0x1780), /*column21_row6*/ mload(0x1780), PRIME)
mstore(0x2200, val)
}
{
// ecdsa/signature0/exponentiate_generator/bit_0 = column21_row15 - (column21_row47 + column21_row47).
let val := addmod(
/*column21_row15*/ mload(0x18a0),
sub(
PRIME,
addmod(/*column21_row47*/ mload(0x1a00), /*column21_row47*/ mload(0x1a00), PRIME)),
PRIME)
mstore(0x2220, val)
}
{
// ecdsa/signature0/exponentiate_generator/bit_neg_0 = 1 - ecdsa__signature0__exponentiate_generator__bit_0.
let val := addmod(
1,
sub(
PRIME,
/*intermediate_value/ecdsa/signature0/exponentiate_generator/bit_0*/ mload(0x2220)),
PRIME)
mstore(0x2240, val)
}
{
// ecdsa/signature0/exponentiate_key/bit_0 = column21_row5 - (column21_row21 + column21_row21).
let val := addmod(
/*column21_row5*/ mload(0x1760),
sub(
PRIME,
addmod(/*column21_row21*/ mload(0x1900), /*column21_row21*/ mload(0x1900), PRIME)),
PRIME)
mstore(0x2260, val)
}
{
// ecdsa/signature0/exponentiate_key/bit_neg_0 = 1 - ecdsa__signature0__exponentiate_key__bit_0.
let val := addmod(
1,
sub(
PRIME,
/*intermediate_value/ecdsa/signature0/exponentiate_key/bit_0*/ mload(0x2260)),
PRIME)
mstore(0x2280, val)
}
let composition_alpha_pow := 1
let composition_alpha := /*composition_alpha*/ mload(0x400)
{
// Constraint expression for cpu/decode/opcode_range_check/bit: cpu__decode__opcode_range_check__bit_0 * cpu__decode__opcode_range_check__bit_0 - cpu__decode__opcode_range_check__bit_0.
let val := addmod(
mulmod(
/*intermediate_value/cpu/decode/opcode_range_check/bit_0*/ mload(0x1d40),
/*intermediate_value/cpu/decode/opcode_range_check/bit_0*/ mload(0x1d40),
PRIME),
sub(PRIME, /*intermediate_value/cpu/decode/opcode_range_check/bit_0*/ mload(0x1d40)),
PRIME)
// Numerator: point^(trace_length / 16) - trace_generator^(15 * trace_length / 16).
// val *= domains[3].
val := mulmod(val, /*domains[3]*/ mload(0x2580), PRIME)
// Denominator: point^trace_length - 1.
// val *= denominator_invs[0].
val := mulmod(val, /*denominator_invs[0]*/ mload(0x2820), PRIME)
// res += val * alpha ** 0.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/decode/opcode_range_check/zero: column1_row0.
let val := /*column1_row0*/ mload(0x5a0)
// Numerator: 1.
// val *= 1.
// Denominator: point^(trace_length / 16) - trace_generator^(15 * trace_length / 16).
// val *= denominator_invs[1].
val := mulmod(val, /*denominator_invs[1]*/ mload(0x2840), PRIME)
// res += val * alpha ** 1.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/decode/opcode_range_check_input: column19_row1 - (((column1_row0 * offset_size + column0_row4) * offset_size + column0_row8) * offset_size + column0_row0).
let val := addmod(
/*column19_row1*/ mload(0x1200),
sub(
PRIME,
addmod(
mulmod(
addmod(
mulmod(
addmod(
mulmod(/*column1_row0*/ mload(0x5a0), /*offset_size*/ mload(0xa0), PRIME),
/*column0_row4*/ mload(0x460),
PRIME),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row8*/ mload(0x480),
PRIME),
/*offset_size*/ mload(0xa0),
PRIME),
/*column0_row0*/ mload(0x420),
PRIME)),
PRIME)
// Numerator: 1.
// val *= 1.
// Denominator: point^(trace_length / 16) - 1.
// val *= denominator_invs[2].
val := mulmod(val, /*denominator_invs[2]*/ mload(0x2860), PRIME)
// res += val * alpha ** 2.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/decode/flag_op1_base_op0_bit: cpu__decode__flag_op1_base_op0_0 * cpu__decode__flag_op1_base_op0_0 - cpu__decode__flag_op1_base_op0_0.
let val := addmod(
mulmod(
/*intermediate_value/cpu/decode/flag_op1_base_op0_0*/ mload(0x1dc0),
/*intermediate_value/cpu/decode/flag_op1_base_op0_0*/ mload(0x1dc0),
PRIME),
sub(PRIME, /*intermediate_value/cpu/decode/flag_op1_base_op0_0*/ mload(0x1dc0)),
PRIME)
// Numerator: 1.
// val *= 1.
// Denominator: point^(trace_length / 16) - 1.
// val *= denominator_invs[2].
val := mulmod(val, /*denominator_invs[2]*/ mload(0x2860), PRIME)
// res += val * alpha ** 3.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/decode/flag_res_op1_bit: cpu__decode__flag_res_op1_0 * cpu__decode__flag_res_op1_0 - cpu__decode__flag_res_op1_0.
let val := addmod(
mulmod(
/*intermediate_value/cpu/decode/flag_res_op1_0*/ mload(0x1e40),
/*intermediate_value/cpu/decode/flag_res_op1_0*/ mload(0x1e40),
PRIME),
sub(PRIME, /*intermediate_value/cpu/decode/flag_res_op1_0*/ mload(0x1e40)),
PRIME)
// Numerator: 1.
// val *= 1.
// Denominator: point^(trace_length / 16) - 1.
// val *= denominator_invs[2].
val := mulmod(val, /*denominator_invs[2]*/ mload(0x2860), PRIME)
// res += val * alpha ** 4.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/decode/flag_pc_update_regular_bit: cpu__decode__flag_pc_update_regular_0 * cpu__decode__flag_pc_update_regular_0 - cpu__decode__flag_pc_update_regular_0.
let val := addmod(
mulmod(
/*intermediate_value/cpu/decode/flag_pc_update_regular_0*/ mload(0x1ea0),
/*intermediate_value/cpu/decode/flag_pc_update_regular_0*/ mload(0x1ea0),
PRIME),
sub(PRIME, /*intermediate_value/cpu/decode/flag_pc_update_regular_0*/ mload(0x1ea0)),
PRIME)
// Numerator: 1.
// val *= 1.
// Denominator: point^(trace_length / 16) - 1.
// val *= denominator_invs[2].
val := mulmod(val, /*denominator_invs[2]*/ mload(0x2860), PRIME)
// res += val * alpha ** 5.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/decode/fp_update_regular_bit: cpu__decode__fp_update_regular_0 * cpu__decode__fp_update_regular_0 - cpu__decode__fp_update_regular_0.
let val := addmod(
mulmod(
/*intermediate_value/cpu/decode/fp_update_regular_0*/ mload(0x1f00),
/*intermediate_value/cpu/decode/fp_update_regular_0*/ mload(0x1f00),
PRIME),
sub(PRIME, /*intermediate_value/cpu/decode/fp_update_regular_0*/ mload(0x1f00)),
PRIME)
// Numerator: 1.
// val *= 1.
// Denominator: point^(trace_length / 16) - 1.
// val *= denominator_invs[2].
val := mulmod(val, /*denominator_invs[2]*/ mload(0x2860), PRIME)
// res += val * alpha ** 6.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/operands/mem_dst_addr: column19_row8 + half_offset_size - (cpu__decode__opcode_range_check__bit_0 * column21_row8 + (1 - cpu__decode__opcode_range_check__bit_0) * column21_row0 + column0_row0).
let val := addmod(
addmod(/*column19_row8*/ mload(0x12e0), /*half_offset_size*/ mload(0xc0), PRIME),
sub(
PRIME,
addmod(
addmod(
mulmod(
/*intermediate_value/cpu/decode/opcode_range_check/bit_0*/ mload(0x1d40),
/*column21_row8*/ mload(0x17c0),
PRIME),
mulmod(
addmod(
1,
sub(PRIME, /*intermediate_value/cpu/decode/opcode_range_check/bit_0*/ mload(0x1d40)),
PRIME),
/*column21_row0*/ mload(0x16c0),
PRIME),
PRIME),
/*column0_row0*/ mload(0x420),
PRIME)),
PRIME)
// Numerator: 1.
// val *= 1.
// Denominator: point^(trace_length / 16) - 1.
// val *= denominator_invs[2].
val := mulmod(val, /*denominator_invs[2]*/ mload(0x2860), PRIME)
// res += val * alpha ** 7.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/operands/mem0_addr: column19_row4 + half_offset_size - (cpu__decode__opcode_range_check__bit_1 * column21_row8 + (1 - cpu__decode__opcode_range_check__bit_1) * column21_row0 + column0_row8).
let val := addmod(
addmod(/*column19_row4*/ mload(0x1260), /*half_offset_size*/ mload(0xc0), PRIME),
sub(
PRIME,
addmod(
addmod(
mulmod(
/*intermediate_value/cpu/decode/opcode_range_check/bit_1*/ mload(0x1f20),
/*column21_row8*/ mload(0x17c0),
PRIME),
mulmod(
addmod(
1,
sub(PRIME, /*intermediate_value/cpu/decode/opcode_range_check/bit_1*/ mload(0x1f20)),
PRIME),
/*column21_row0*/ mload(0x16c0),
PRIME),
PRIME),
/*column0_row8*/ mload(0x480),
PRIME)),
PRIME)
// Numerator: 1.
// val *= 1.
// Denominator: point^(trace_length / 16) - 1.
// val *= denominator_invs[2].
val := mulmod(val, /*denominator_invs[2]*/ mload(0x2860), PRIME)
// res += val * alpha ** 8.
res := addmod(res, mulmod(val, composition_alpha_pow, PRIME), PRIME)
composition_alpha_pow := mulmod(composition_alpha_pow, composition_alpha, PRIME)
}
{
// Constraint expression for cpu/operands/mem1_addr: column19_row12 + half_offset_size - (cpu__decode__opcode_range_check__bit_2 * column19_row0 + cpu__decode__opcode_range_check__bit_4 * column21_row0 + cpu__decode__opcode_range_check__bit_3 * column21_row8 + cpu__decode__flag_op1_base_op0_0 * column19_row5 + column0_row4).
let val := addmod(
addmod(/*column19_row12*/ mload(0x1320), /*half_offset_size*/ mload(0xc0), PRIME),
sub(
PRIME,
addmod(
addmod(
addmod(
addmod(
mulmod(
/*intermediate_value/cpu/decode/opcode_rSubmitted on: 2025-10-08 10:52:16
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