├── AUTHORS
├── src
    ├── proof_system
    │   ├── naive_evaluation.hpp
    │   ├── naive_evaluation.tcc
    │   ├── domain.tcc
    │   ├── prover.hpp
    │   ├── prover.tcc
    │   ├── common.tcc
    │   ├── verifier.tcc
    │   ├── common.hpp
    │   ├── verifier.hpp
    │   └── domain.hpp
    ├── CMakeLists.txt
    ├── profiling
    │   ├── plot
    │   │   └── runtime_plot.gp
    │   ├── logs
    │   │   └── 08-17_01:43
    │   │   │   ├── prover-8-thread.csv
    │   │   │   ├── prover-4-thread.csv
    │   │   │   ├── prover-2-thread.csv
    │   │   │   ├── naive-2-thread.csv
    │   │   │   ├── naive-4-thread.csv
    │   │   │   ├── prover-1-thread.csv
    │   │   │   ├── naive-1-thread.csv
    │   │   │   ├── naive-8-thread.csv
    │   │   │   ├── verifier-1-thread.csv
    │   │   │   ├── verifier-8-thread.csv
    │   │   │   ├── verifier-2-thread.csv
    │   │   │   ├── verifier-4-thread.csv
    │   │   │   ├── naive-prover-1.ps
    │   │   │   ├── naive-prover-8.ps
    │   │   │   └── naive-prover-2.ps
    │   └── profile.cpp
    ├── test
    │   ├── test_verifier.cpp
    │   └── test_circuit.cpp
    └── arithmetic_circuit
    │   ├── arithmetic_circuit.hpp
    │   └── arithmetic_circuit.tcc
├── LICENSE
├── CMakeLists.txt
└── README.md


/AUTHORS:
--------------------------------------------------------------------------------
1 | SCIPR Lab:
2 |     Alessandro Chiesa
3 |     Howard Wu
4 | 
5 | External contributors:
6 | 


--------------------------------------------------------------------------------
/src/proof_system/naive_evaluation.hpp:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Declaration of interfaces for naive evaluation.
 4 |  
 5 |  *****************************************************************************
 6 |  * @author     This file is part of bace, developed by SCIPR Lab
 7 |  *             and contributors (see AUTHORS).
 8 |  * @copyright  MIT license (see LICENSE file)
 9 |  *****************************************************************************/
10 | 
11 | #ifndef NAIVE_EVALUATION_HPP_
12 | #define NAIVE_EVALUATION_HPP_
13 | 
14 | #include "src/proof_system/common.hpp"
15 | 
16 | namespace bace {
17 | 
18 | /*
19 |  * Performs the direct circuit evaluation of an input batch.
20 |  *
21 |  * Given a batch of inputs, all of equal length and matching the
22 |  * circuit's input size, the circuit will evaluate the batch of inputs
23 |  * and construct an ordered batch of outputs.
24 |  */
25 | template<typename FieldT>
26 | void naive_evaluate(const arithmetic_circuit_t<FieldT> &circuit,
27 |                     const input_batch_t<FieldT> &input_batch,
28 |                     output_batch_t<FieldT> &output_batch);
29 | 
30 | } // bace
31 | 
32 | #include "naive_evaluation.tcc"
33 | 
34 | #endif // NAIVE_EVALUATION_HPP_
35 | 


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
 1 | The bace library is developed by SCIPR Lab (http://scipr-lab.org)
 2 | and contributors.
 3 | 
 4 | Copyright (c) 2016 SCIPR Lab and contributors (see AUTHORS file).
 5 | 
 6 | All files, with the exceptions below, are released under the MIT License:
 7 | 
 8 |   Permission is hereby granted, free of charge, to any person obtaining a copy
 9 |   of this software and associated documentation files (the "Software"), to deal
10 |   in the Software without restriction, including without limitation the rights
11 |   to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
12 |   copies of the Software, and to permit persons to whom the Software is
13 |   furnished to do so, subject to the following conditions:
14 | 
15 |   The above copyright notice and this permission notice shall be included in
16 |   all copies or substantial portions of the Software.
17 | 
18 |   THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
19 |   IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
20 |   FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
21 |   AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
22 |   LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
23 |   OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
24 |   THE SOFTWARE.


--------------------------------------------------------------------------------
/src/CMakeLists.txt:
--------------------------------------------------------------------------------
 1 | include_directories(.)
 2 | 
 3 | # Profiling
 4 | add_executable(
 5 |   profile
 6 | 
 7 |   profiling/profile.cpp
 8 | )
 9 | target_link_libraries(
10 |   profile
11 | 
12 |   ${LIBFF_LIBRARIES}
13 |   ${GMP_LIBRARIES}
14 |   ${GMPXX_LIBRARIES}
15 |   ${PROCPS_LIBRARIES}
16 | )
17 | set_target_properties(
18 |   profile
19 | 
20 |   PROPERTIES
21 |   COMPILE_FLAGS "-fopenmp"
22 |   LINK_FLAGS "-fopenmp"
23 |   RUNTIME_OUTPUT_DIRECTORY ${CMAKE_HOME_DIRECTORY}
24 | )
25 | target_compile_definitions(
26 |   profile
27 | 
28 |   PUBLIC
29 |   -DMULTICORE
30 | )
31 | 
32 | # Tests
33 | add_executable(
34 |   test_circuit
35 |   EXCLUDE_FROM_ALL
36 | 
37 |   test/test_circuit.cpp
38 | )
39 | target_link_libraries(
40 |   test_circuit
41 | 
42 |   ${LIBFF_LIBRARIES}
43 |   ${GMP_LIBRARIES}
44 |   ${GMPXX_LIBRARIES}
45 |   ${PROCPS_LIBRARIES}
46 | )
47 | 
48 | add_executable(
49 |   test_verifier
50 |   EXCLUDE_FROM_ALL
51 | 
52 |   test/test_verifier.cpp
53 | )
54 | target_link_libraries(
55 |   test_verifier
56 | 
57 |   ${LIBFF_LIBRARIES}
58 |   ${GMP_LIBRARIES}
59 |   ${GMPXX_LIBRARIES}
60 |   ${PROCPS_LIBRARIES}
61 | )
62 | 
63 | include(CTest)
64 | add_test(
65 |   NAME test_circuit
66 |   COMMAND test_circuit
67 | )
68 | add_test(
69 |   NAME test_verifier
70 |   COMMAND test_verifier
71 | )
72 | 
73 | add_dependencies(check test_circuit)
74 | add_dependencies(check test_verifier)


--------------------------------------------------------------------------------
/src/proof_system/naive_evaluation.tcc:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Implementation of interfaces for naive evaluation.
 4 |  
 5 |  See naive_evaluation.hpp .
 6 | 
 7 |  *****************************************************************************
 8 |  * @author     This file is part of bace, developed by SCIPR Lab
 9 |  *             and contributors (see AUTHORS).
10 |  * @copyright  MIT license (see LICENSE file)
11 |  *****************************************************************************/
12 | 
13 | #ifndef NAIVE_EVALUATION_TCC_
14 | #define NAIVE_EVALUATION_TCC_
15 | 
16 | #include <cassert>
17 | #include <vector>
18 | 
19 | #include "evaluation_domain/evaluation_domain.hpp"
20 | #include "polynomial_arithmetic/naive_evaluate.hpp"
21 | 
22 | #include "src/arithmetic_circuit/arithmetic_circuit.hpp"
23 | 
24 | namespace bace {
25 | 
26 | template<typename FieldT>
27 | void naive_evaluate(const arithmetic_circuit_t<FieldT> &circuit,
28 |                     const input_batch_t<FieldT> &input_batch,
29 |                     output_batch_t<FieldT> &output_batch)
30 | {
31 |     const size_t batch_size = input_batch.size();
32 | 
33 |     output_batch.resize(batch_size);
34 |     for (size_t i = 0; i < batch_size; i++)
35 |     {
36 |         output_batch[i] = circuit.evaluate(input_batch[i]);
37 |     }
38 | }
39 | 
40 | } // bace
41 | 
42 | #endif // NAIVE_EVALUATION_TCC_
43 | 


--------------------------------------------------------------------------------
/src/proof_system/domain.tcc:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Implementation of interfaces for domain.
 4 | 
 5 |  See domain.hpp .
 6 |  
 7 |  *****************************************************************************
 8 |  * @author     This file is part of bace, developed by SCIPR Lab
 9 |  *             and contributors (see AUTHORS).
10 |  * @copyright  MIT license (see LICENSE file)
11 |  *****************************************************************************/
12 | 
13 | #ifndef DOMAIN_TCC_
14 | #define DOMAIN_TCC_
15 | 
16 | namespace bace {
17 | 
18 | template<typename FieldT>
19 | domain_t<FieldT> get_evaluation_domain(const size_t &domain_size)
20 | {
21 |     return domain_t<FieldT>(new libfqfft::basic_radix2_domain<FieldT>(domain_size));
22 | }
23 | 
24 | unsigned int get_previous_power_of_two(const unsigned int &n)
25 | {
26 |     uint32_t p = n;
27 | 
28 |     p |= (p >> 1);
29 |     p |= (p >> 2);
30 |     p |= (p >> 4);
31 |     p |= (p >> 8);
32 |     p |= (p >> 16);
33 |     p = p - (p >> 1);
34 | 
35 |     return p;
36 | }
37 | 
38 | unsigned int get_embedded_index(const size_t &index,
39 |                                 const size_t &small_domain_size,
40 |                                 const size_t &large_domain_size)
41 | {
42 |     const unsigned int embedding_factor = large_domain_size / small_domain_size;
43 |     const unsigned int jump = get_previous_power_of_two(embedding_factor);
44 |     return index * jump;
45 | }
46 | 
47 | size_t get_column_size(const size_t &batch_size)
48 | {
49 |     return libff::get_power_of_two(batch_size);
50 | }
51 | 
52 | size_t get_large_degree(const size_t &column_size, const size_t &degree)
53 | {
54 |     return libff::get_power_of_two(column_size * degree);
55 | }
56 | 
57 | } // bace
58 | 
59 | #endif // DOMAIN_TCC_
60 | 


--------------------------------------------------------------------------------
/src/profiling/plot/runtime_plot.gp:
--------------------------------------------------------------------------------
 1 | ## Initialization ##
 2 | cd input_directory
 3 | set datafile separator ","
 4 | 
 5 | ## Graph Formatting ##
 6 | set title 'Runtime'
 7 | set xlabel 'Batch Size'
 8 | set ylabel 'Input Size'
 9 | set zlabel 'Time (in seconds)' offset 0,-8
10 | 
11 | set hidden3d
12 | set grid x y z
13 | set size ratio -1
14 | set logscale xyz 2
15 | set format x "2^{%L}"
16 | set format y "2^{%L}"
17 | set format z "2^{%L}"
18 | set xtics offset 0, -.4
19 | set ytics offset 0, -.4
20 | set key autotitle columnhead
21 | set term postscript enhanced color solid
22 | 
23 | ## Plotting ##
24 | do for [i=0:5] {
25 | 	t = 2**i
26 | 	list = system(sprintf('ls *-%d-thread.csv 2>/dev/null', t))
27 | 	if (words(list) == 3) {
28 | 		set output sprintf("naive-verifier-%d.ps", t)
29 | 		splot sprintf('naive-%d-thread.csv', t) using 1:2:5 with lines title sprintf('naive (%d-thread)', t),\
30 | 		sprintf('verifier-%d-thread.csv', t) using 1:2:5 with lines title sprintf('verifier (%d-thread)', t)
31 | 
32 | 		set output sprintf("naive-prover-%d.ps", t)
33 | 		splot sprintf('naive-%d-thread.csv', t) using 1:2:5 with lines title sprintf('naive (%d-thread)', t),\
34 | 		sprintf('prover-%d-thread.csv', t) using 1:2:5 with lines title sprintf('prover (%d-thread)', t)
35 | 	}
36 | }
37 | 
38 | list = system('ls naive-*.csv 2>/dev/null')
39 | if (words(list) > 1) {
40 | 	set output "naive.ps"
41 | 	splot for [i=1:words(list)] word(list,i) using 1:2:5 with lines title word(list,i)
42 | }
43 | 
44 | list = system('ls prover-*.csv 2>/dev/null')
45 | if (words(list) > 1) {
46 | 	set output "prover.ps"
47 | 	splot for [i=1:words(list)] word(list,i) using 1:2:5 with lines title word(list,i)
48 | }
49 | 
50 | list = system('ls verifier-*.csv 2>/dev/null')
51 | if (words(list) > 1) {
52 | 	set output "verifier.ps"
53 | 	splot for [i=1:words(list)] word(list,i) using 1:2:5 with lines title word(list,i)
54 | }
55 | 


--------------------------------------------------------------------------------
/src/proof_system/prover.hpp:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Declaration of interfaces for the prover.
 4 |  
 5 |  *****************************************************************************
 6 |  * @author     This file is part of bace, developed by SCIPR Lab
 7 |  *             and contributors (see AUTHORS).
 8 |  * @copyright  MIT license (see LICENSE file)
 9 |  *****************************************************************************/
10 | 
11 | #ifndef PROVER_HPP_
12 | #define PROVER_HPP_
13 | 
14 | #include "src/arithmetic_circuit/arithmetic_circuit.hpp"
15 | #include "src/proof_system/common.hpp"
16 | 
17 | namespace bace {
18 | 
19 | /*
20 |  * Returns a proof for the verifier, given an arithmetic circuit and
21 |  * a batch of inputs.
22 |  *
23 |  * The prover constructs a proof by using the input batch to compose a
24 |  * column_lde_t and extend it to a large degree. The prover takes the FFT
25 |  * of the each column_lde_t and evaluates the columns index-wise on the
26 |  * provided circuit, then takes the inverse FFT of this vector construction.
27 |  * This results in a large degree sized vector of circuit evaluations, which
28 |  * serves as the basis for the proof that is provided to the verifier.
29 |  *
30 |  * proof = circuit.evaluate(column_lde[1][i], ... , column_lde[input_size][i])
31 |  *
32 |  * In the case that there is a size mismatch among the batch of inputs,
33 |  * the prover will return a proof composed of a vector of zeros, or error if
34 |  * the input size fails to match the circuit's defined input size.
35 |  */
36 | template<typename FieldT>
37 | void prover(const arithmetic_circuit_t<FieldT> &circuit,
38 |             const input_batch_t<FieldT> &input_batch,
39 |             proof_t<FieldT> &proof);
40 | 
41 | } // bace
42 | 
43 | #include "prover.tcc"
44 | 
45 | #endif // PROVER_HPP_
46 | 


--------------------------------------------------------------------------------
/src/proof_system/prover.tcc:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Implementation of interfaces for the prover.
 4 | 
 5 |  See prover.hpp .
 6 |  
 7 |  *****************************************************************************
 8 |  * @author     This file is part of bace, developed by SCIPR Lab
 9 |  *             and contributors (see AUTHORS).
10 |  * @copyright  MIT license (see LICENSE file)
11 |  *****************************************************************************/
12 | 
13 | #ifndef PROVER_TCC_
14 | #define PROVER_TCC_
15 | 
16 | namespace bace {
17 | 
18 | template<typename FieldT>
19 | void prover(const arithmetic_circuit_t<FieldT> &circuit,
20 |             const input_batch_t<FieldT> &input_batch,
21 |             proof_t<FieldT> &proof)
22 | {
23 |     const size_t batch_size = input_batch.size();
24 |     const size_t input_size = get_input_size(input_batch);
25 |     const size_t column_size = get_column_size(batch_size);
26 |     const size_t large_degree = get_large_degree(column_size, circuit.degree());
27 |     const domain_t<FieldT> domain = get_evaluation_domain<FieldT>(large_degree);
28 | 
29 |     column_lde_t<FieldT> column_lde = compute_column_lde(input_batch, column_size);
30 | 
31 |     for (size_t i = 0; i < input_size; i++)
32 |     {
33 |         column_lde[i].resize(large_degree, FieldT::zero());
34 |         domain->FFT(column_lde[i]);
35 |     }
36 | 
37 |     proof.resize(large_degree);
38 |     std::vector<FieldT> input_column(input_size);
39 |     for (size_t i = 0; i < large_degree; i++)
40 |     {
41 |         for (size_t j = 0; j < input_size; j++)
42 |         {
43 |             input_column[j] = column_lde[j][i];
44 |         }
45 |         
46 |         proof[i] = circuit.evaluate(input_column);
47 |     }
48 |     domain->iFFT(proof);
49 | }
50 | 
51 | } // bace
52 | 
53 | #endif // PROVER_TCC_
54 | 


--------------------------------------------------------------------------------
/src/proof_system/common.tcc:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Implementation of interfaces for common utilities.
 4 |  
 5 |  See common.hpp .
 6 | 
 7 |  *****************************************************************************
 8 |  * @author     This file is part of bace, developed by SCIPR Lab
 9 |  *             and contributors (see AUTHORS).
10 |  * @copyright  MIT license (see LICENSE file)
11 |  *****************************************************************************/
12 | 
13 | #ifndef COMMON_TCC_
14 | #define COMMON_TCC_
15 | 
16 | namespace bace {
17 | 
18 | template<typename FieldT>
19 | size_t get_input_size(const input_batch_t<FieldT> &input_batch)
20 | {
21 |     const size_t input_size = input_batch[0].size();
22 |     const bool match = std::all_of(begin(input_batch), end(input_batch),
23 |                         [input_size](const input_t<FieldT>& input){ return input.size() == input_size; });
24 |     return match ? input_size : 0;
25 | }
26 | 
27 | template<typename FieldT>
28 | column_lde_t<FieldT> compute_column_lde(const input_batch_t<FieldT> &input_batch,
29 |                                         const size_t &column_size)
30 | {
31 |     const size_t batch_size = input_batch.size();
32 |     const size_t input_size = get_input_size(input_batch);
33 |     const domain_t<FieldT> domain = get_evaluation_domain<FieldT>(column_size);
34 | 
35 |     column_lde_t<FieldT> column_lde(input_size);
36 |     for (size_t i = 0; i < input_size; i++)
37 |     {
38 |         column_lde[i] = std::vector<FieldT>(column_size);
39 |         for (size_t j = 0; j < batch_size; j++) // Only fill up to batch_size
40 |         {
41 |             column_lde[i][j] = input_batch[j][i];
42 |         }
43 |         domain->iFFT(column_lde[i]);
44 |     }
45 | 
46 |     return column_lde;
47 | }
48 | 
49 | } // bace
50 | 
51 | #endif // COMMON_TCC_
52 | 


--------------------------------------------------------------------------------
/src/proof_system/verifier.tcc:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Implementation of interfaces for the verifier.
 4 | 
 5 |  See verifier.hpp .
 6 |  
 7 |  *****************************************************************************
 8 |  * @author     This file is part of bace, developed by SCIPR Lab
 9 |  *             and contributors (see AUTHORS).
10 |  * @copyright  MIT license (see LICENSE file)
11 |  *****************************************************************************/
12 | 
13 | #ifndef VERIFIER_TCC_
14 | #define VERIFIER_TCC_
15 | 
16 | #include "polynomial_arithmetic/naive_evaluate.hpp"
17 | 
18 | namespace bace {
19 | 
20 | template<typename FieldT>
21 | void verifier(const arithmetic_circuit_t<FieldT> &circuit,
22 |               const input_batch_t<FieldT> &input_batch,
23 |               output_batch_t<FieldT> &output_batch,
24 |               const proof_t<FieldT> &proof)
25 | {
26 |     const size_t batch_size = input_batch.size();
27 |     const size_t input_size = get_input_size(input_batch);
28 |     const size_t column_size = get_column_size(batch_size);
29 |     const size_t large_degree = get_large_degree(column_size, circuit.degree());
30 |     const domain_t<FieldT> domain = get_evaluation_domain<FieldT>(large_degree);
31 | 
32 |     const column_lde_t<FieldT> column_lde = compute_column_lde(input_batch, column_size);
33 | 
34 |     const FieldT random_element = FieldT::random_element();
35 |     std::vector<FieldT> random_input(input_size);
36 |     for (size_t i = 0; i < input_size; i++)
37 |     {
38 |         random_input[i] = libfqfft::evaluate_polynomial(column_size, column_lde[i], random_element);
39 |     }
40 |     
41 |     output_batch.clear();
42 |     const FieldT output_mine = circuit.evaluate(random_input);
43 |     const FieldT output_proof = libfqfft::evaluate_polynomial(large_degree, proof, random_element);
44 |     if (output_mine == output_proof)
45 |     {
46 |         output_batch = proof;
47 |         domain->FFT(output_batch);
48 |         
49 |         for (size_t i = 0; i < batch_size; i++)
50 |         {
51 |             output_batch[i] = output_batch[get_embedded_index(i, column_size, large_degree)];
52 |         }
53 |         output_batch.resize(batch_size);
54 |     }
55 | }
56 | 
57 | } // bace
58 | 
59 | #endif // VERIFIER_TCC_
60 | 


--------------------------------------------------------------------------------
/CMakeLists.txt:
--------------------------------------------------------------------------------
  1 | cmake_minimum_required(VERSION 2.8)
  2 | 
  3 | project(bace)
  4 | 
  5 | option(
  6 |   MULTICORE
  7 |   "Enable parallelized execution, using OpenMP"
  8 |   OFF
  9 | )
 10 | 
 11 | option(
 12 |   WITH_PROCPS
 13 |   "Use procps for memory profiling"
 14 |   ON
 15 | )
 16 | 
 17 | set(
 18 |   OPT_FLAGS
 19 |   ""
 20 |   CACHE
 21 |   STRING
 22 |   "Override C++ compiler optimization flags"
 23 | )
 24 | 
 25 | option(
 26 |   VERBOSE
 27 |   "Print internal messages"
 28 |   OFF
 29 | )
 30 | 
 31 | if(CMAKE_COMPILER_IS_GNUCXX OR "${CMAKE_CXX_COMPILER_ID}" STREQUAL "Clang")
 32 |   # Common compilation flags and warning configuration
 33 |   set(
 34 |     CMAKE_CXX_FLAGS
 35 | 
 36 |     "${CMAKE_CXX_FLAGS} -std=c++11 -Wall -Wextra -Wfatal-errors -pthread"
 37 |   )
 38 | 
 39 |   if("${MULTICORE}")
 40 |     set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -fopenmp")
 41 |   endif()
 42 | 
 43 |    # Default optimizations flags (to override, use -DOPT_FLAGS=...)
 44 |   if("${OPT_FLAGS}" STREQUAL "")
 45 |     set(
 46 |       OPT_FLAGS
 47 |       "-ggdb3 -O2 -march=native -mtune=native"
 48 |     )
 49 |   endif()
 50 | endif()
 51 | 
 52 | if("${VERBOSE}")
 53 |   add_definitions(-DVERBOSE=1)
 54 | endif()
 55 | 
 56 | if("${MULTICORE}")
 57 |   add_definitions(-DMULTICORE=1)
 58 | endif()
 59 | 
 60 | set(
 61 |   CMAKE_CXX_FLAGS
 62 |   "${CMAKE_CXX_FLAGS} ${OPT_FLAGS}"
 63 | )
 64 | 
 65 | include(FindPkgConfig)
 66 | if("${WITH_PROCPS}")
 67 |   pkg_check_modules(
 68 |     PROCPS
 69 |     REQUIRED
 70 | 
 71 |     libprocps
 72 |   )
 73 | else()
 74 |   add_definitions(
 75 |     -DNO_PROCPS
 76 |   )
 77 | endif()
 78 | 
 79 | # GMP
 80 | find_path(GMP_INCLUDE_DIR NAMES gmp.h)
 81 | find_library(GMP_LIBRARIES NAMES gmp libgmp)
 82 | find_library(GMPXX_LIBRARIES NAMES gmpxx libgmpxx)
 83 | 
 84 | # libfqfft
 85 | find_path(LIBFQFFT_INCLUDE_DIR NAMES libfqfft)
 86 | set(LIBFQFFT_DIRECTORY ${LIBFQFFT_INCLUDE_DIR}/libfqfft)
 87 | include_directories(${LIBFQFFT_DIRECTORY})
 88 | 
 89 | # libff
 90 | find_path(LIBFF_INCLUDE_DIR NAMES libff)
 91 | include_directories(${LIBFF_INCLUDE_DIR}/libff)
 92 | find_library(LIBFF_LIBRARIES NAMES ff libff)
 93 | 
 94 | enable_testing()
 95 | 
 96 | # Add a `make check` target that builds and tests
 97 | add_custom_target(check COMMAND ${CMAKE_CTEST_COMMAND})
 98 | 
 99 | include_directories(.)
100 | add_subdirectory(src)


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/prover-8-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,6.7964e-05
 3 | 2,4,13,3,9.144e-05
 4 | 2,8,33,3,0.000109379
 5 | 2,16,97,3,0.00017604
 6 | 2,32,321,3,0.000387608
 7 | 2,64,1153,3,0.00104733
 8 | 2,128,4353,3,0.00341244
 9 | 2,256,16897,3,0.0124403
10 | 2,512,66561,3,0.0491973
11 | 2,1024,264193,3,0.183652
12 | 2,2048,1052673,3,0.719106
13 | 2,4096,4202497,3,2.92123
14 | ,,,,
15 | 4,2,6,3,0.0082571
16 | 4,4,13,3,0.000141136
17 | 4,8,33,3,0.000288553
18 | 4,16,97,3,0.00143704
19 | 4,32,321,3,0.00121539
20 | 4,64,1153,3,0.00327977
21 | 4,128,4353,3,0.0212136
22 | 4,256,16897,3,0.0273173
23 | 4,512,66561,3,0.106079
24 | 4,1024,264193,3,0.360661
25 | 4,2048,1052673,3,1.38047
26 | 4,4096,4202497,3,5.60262
27 | ,,,,
28 | 8,2,6,3,0.0254364
29 | 8,4,13,3,0.0108566
30 | 8,8,33,3,0.000420488
31 | 8,16,97,3,0.000872772
32 | 8,32,321,3,0.00223891
33 | 8,64,1153,3,0.0053292
34 | 8,128,4353,3,0.0275113
35 | 8,256,16897,3,0.0662912
36 | 8,512,66561,3,0.196229
37 | 8,1024,264193,3,0.683043
38 | 8,2048,1052673,3,2.717
39 | 8,4096,4202497,3,10.911
40 | ,,,,
41 | 16,2,6,3,0.0128155
42 | 16,4,13,3,0.000811754
43 | 16,8,33,3,0.000640991
44 | 16,16,97,3,0.00140458
45 | 16,32,321,3,0.0066276
46 | 16,64,1153,3,0.0309965
47 | 16,128,4353,3,0.0398716
48 | 16,256,16897,3,0.0954096
49 | 16,512,66561,3,0.358115
50 | 16,1024,264193,3,1.31782
51 | 16,2048,1052673,3,5.51628
52 | 16,4096,4202497,3,21.1438
53 | ,,,,
54 | 32,2,6,3,0.0124429
55 | 32,4,13,3,0.000525348
56 | 32,8,33,3,0.00106704
57 | 32,16,97,3,0.00250024
58 | 32,32,321,3,0.0224196
59 | 32,64,1153,3,0.015358
60 | 32,128,4353,3,0.0578228
61 | 32,256,16897,3,0.179974
62 | 32,512,66561,3,0.687894
63 | 32,1024,264193,3,2.70938
64 | 32,2048,1052673,3,10.976
65 | 32,4096,4202497,3,43.1632
66 | ,,,,
67 | 64,2,6,3,0.0129042
68 | 64,4,13,3,0.00092581
69 | 64,8,33,3,0.0018941
70 | 64,16,97,3,0.0058795
71 | 64,32,321,3,0.0277163
72 | 64,64,1153,3,0.0478477
73 | 64,128,4353,3,0.098126
74 | 64,256,16897,3,0.361591
75 | 64,512,66561,3,1.36875
76 | 64,1024,264193,3,5.17776
77 | 64,2048,1052673,3,21.0047
78 | 64,4096,4202497,3,85.9163
79 | ,,,,
80 | 128,2,6,3,0.016503
81 | 128,4,13,3,0.00167238
82 | 128,8,33,3,0.018081
83 | 128,16,97,3,0.00757026
84 | 128,32,321,3,0.0347152
85 | 128,64,1153,3,0.0571891
86 | 128,128,4353,3,0.210017
87 | 128,256,16897,3,0.723424
88 | 128,512,66561,3,2.74015
89 | 128,1024,264193,3,10.2986
90 | 128,2048,1052673,3,42.8436
91 | 128,4096,4202497,3,172.913
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/prover-4-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,0.00664736
 3 | 2,4,13,3,0.000102888
 4 | 2,8,33,3,0.000167462
 5 | 2,16,97,3,0.000311685
 6 | 2,32,321,3,0.000697072
 7 | 2,64,1153,3,0.00188999
 8 | 2,128,4353,3,0.00623035
 9 | 2,256,16897,3,0.01498
10 | 2,512,66561,3,0.0545319
11 | 2,1024,264193,3,0.187745
12 | 2,2048,1052673,3,0.74155
13 | 2,4096,4202497,3,2.98178
14 | ,,,,
15 | 4,2,6,3,0.00134005
16 | 4,4,13,3,0.000152508
17 | 4,8,33,3,0.000274383
18 | 4,16,97,3,0.000536742
19 | 4,32,321,3,0.00126397
20 | 4,64,1153,3,0.00339415
21 | 4,128,4353,3,0.00779619
22 | 4,256,16897,3,0.0261175
23 | 4,512,66561,3,0.096522
24 | 4,1024,264193,3,0.360375
25 | 4,2048,1052673,3,1.43505
26 | 4,4096,4202497,3,5.65839
27 | ,,,,
28 | 8,2,6,3,0.0129065
29 | 8,4,13,3,0.000303027
30 | 8,8,33,3,0.000410286
31 | 8,16,97,3,0.000834458
32 | 8,32,321,3,0.00209932
33 | 8,64,1153,3,0.00519294
34 | 8,128,4353,3,0.0140015
35 | 8,256,16897,3,0.0494543
36 | 8,512,66561,3,0.182368
37 | 8,1024,264193,3,0.688061
38 | 8,2048,1052673,3,2.70801
39 | 8,4096,4202497,3,10.7193
40 | ,,,,
41 | 16,2,6,3,0.0130356
42 | 16,4,13,3,0.000431156
43 | 16,8,33,3,0.000628409
44 | 16,16,97,3,0.0013927
45 | 16,32,321,3,0.00348247
46 | 16,64,1153,3,0.00870293
47 | 16,128,4353,3,0.0269116
48 | 16,256,16897,3,0.0927836
49 | 16,512,66561,3,0.347045
50 | 16,1024,264193,3,1.35355
51 | 16,2048,1052673,3,5.36106
52 | 16,4096,4202497,3,21.8742
53 | ,,,,
54 | 32,2,6,3,0.0135859
55 | 32,4,13,3,0.000539487
56 | 32,8,33,3,0.00110389
57 | 32,16,97,3,0.00257184
58 | 32,32,321,3,0.00574612
59 | 32,64,1153,3,0.0155934
60 | 32,128,4353,3,0.0501281
61 | 32,256,16897,3,0.173612
62 | 32,512,66561,3,0.689706
63 | 32,1024,264193,3,2.67852
64 | 32,2048,1052673,3,10.5963
65 | 32,4096,4202497,3,43.3852
66 | ,,,,
67 | 64,2,6,3,0.0138003
68 | 64,4,13,3,0.000979557
69 | 64,8,33,3,0.00205983
70 | 64,16,97,3,0.0044466
71 | 64,32,321,3,0.0104222
72 | 64,64,1153,3,0.0297183
73 | 64,128,4353,3,0.0959137
74 | 64,256,16897,3,0.34615
75 | 64,512,66561,3,1.34921
76 | 64,1024,264193,3,5.33647
77 | 64,2048,1052673,3,21.2584
78 | 64,4096,4202497,3,85.7326
79 | ,,,,
80 | 128,2,6,3,0.0146312
81 | 128,4,13,3,0.00189772
82 | 128,8,33,3,0.00396394
83 | 128,16,97,3,0.0080712
84 | 128,32,321,3,0.0200628
85 | 128,64,1153,3,0.051902
86 | 128,128,4353,3,0.192766
87 | 128,256,16897,3,0.683072
88 | 128,512,66561,3,2.67944
89 | 128,1024,264193,3,10.5961
90 | 128,2048,1052673,3,43.1343
91 | 128,4096,4202497,3,172.393
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/prover-2-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,0.000182655
 3 | 2,4,13,3,9.4881e-05
 4 | 2,8,33,3,0.000137811
 5 | 2,16,97,3,0.000262945
 6 | 2,32,321,3,0.000569824
 7 | 2,64,1153,3,0.00149464
 8 | 2,128,4353,3,0.00420589
 9 | 2,256,16897,3,0.0143626
10 | 2,512,66561,3,0.052121
11 | 2,1024,264193,3,0.189838
12 | 2,2048,1052673,3,0.75316
13 | 2,4096,4202497,3,2.95166
14 | ,,,,
15 | 4,2,6,3,0.000178614
16 | 4,4,13,3,0.000107708
17 | 4,8,33,3,0.000179555
18 | 4,16,97,3,0.00036138
19 | 4,32,321,3,0.000828152
20 | 4,64,1153,3,0.00228296
21 | 4,128,4353,3,0.0071285
22 | 4,256,16897,3,0.0256372
23 | 4,512,66561,3,0.0915323
24 | 4,1024,264193,3,0.346048
25 | 4,2048,1052673,3,1.38083
26 | 4,4096,4202497,3,5.43982
27 | ,,,,
28 | 8,2,6,3,0.01223
29 | 8,4,13,3,0.000216815
30 | 8,8,33,3,0.000441658
31 | 8,16,97,3,0.000865483
32 | 8,32,321,3,0.00214061
33 | 8,64,1153,3,0.00527952
34 | 8,128,4353,3,0.0129564
35 | 8,256,16897,3,0.0466944
36 | 8,512,66561,3,0.170581
37 | 8,1024,264193,3,0.664755
38 | 8,2048,1052673,3,2.69289
39 | 8,4096,4202497,3,10.6515
40 | ,,,,
41 | 16,2,6,3,0.0123886
42 | 16,4,13,3,0.000220248
43 | 16,8,33,3,0.00042414
44 | 16,16,97,3,0.000918767
45 | 16,32,321,3,0.00241935
46 | 16,64,1153,3,0.00726913
47 | 16,128,4353,3,0.0245439
48 | 16,256,16897,3,0.087202
49 | 16,512,66561,3,0.332004
50 | 16,1024,264193,3,1.30962
51 | 16,2048,1052673,3,5.31614
52 | 16,4096,4202497,3,21.2561
53 | ,,,,
54 | 32,2,6,3,0.0125502
55 | 32,4,13,3,0.000371507
56 | 32,8,33,3,0.000742072
57 | 32,16,97,3,0.00166563
58 | 32,32,321,3,0.0045108
59 | 32,64,1153,3,0.0139596
60 | 32,128,4353,3,0.047028
61 | 32,256,16897,3,0.169254
62 | 32,512,66561,3,0.658793
63 | 32,1024,264193,3,2.59564
64 | 32,2048,1052673,3,10.7211
65 | 32,4096,4202497,3,42.4351
66 | ,,,,
67 | 64,2,6,3,0.0131123
68 | 64,4,13,3,0.000696471
69 | 64,8,33,3,0.00141018
70 | 64,16,97,3,0.00327275
71 | 64,32,321,3,0.00875437
72 | 64,64,1153,3,0.0271506
73 | 64,128,4353,3,0.0919453
74 | 64,256,16897,3,0.333441
75 | 64,512,66561,3,1.29862
76 | 64,1024,264193,3,5.14828
77 | 64,2048,1052673,3,21.0029
78 | 64,4096,4202497,3,85.8915
79 | ,,,,
80 | 128,2,6,3,0.0138698
81 | 128,4,13,3,0.00137436
82 | 128,8,33,3,0.00278936
83 | 128,16,97,3,0.00645959
84 | 128,32,321,3,0.0233698
85 | 128,64,1153,3,0.0544769
86 | 128,128,4353,3,0.185363
87 | 128,256,16897,3,0.685997
88 | 128,512,66561,3,2.68983
89 | 128,1024,264193,3,10.6753
90 | 128,2048,1052673,3,42.1215
91 | 128,4096,4202497,3,169.419
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/naive-2-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,1.865e-06
 3 | 2,4,13,3,2.232e-06
 4 | 2,8,33,3,4.708e-06
 5 | 2,16,97,3,1.227e-05
 6 | 2,32,321,3,4.0766e-05
 7 | 2,64,1153,3,0.000160732
 8 | 2,128,4353,3,0.000666413
 9 | 2,256,16897,3,0.00274308
10 | 2,512,66561,3,0.0113727
11 | 2,1024,264193,3,0.0448322
12 | 2,2048,1052673,3,0.180207
13 | 2,4096,4202497,3,0.716541
14 | ,,,,
15 | 4,2,6,3,4.101e-06
16 | 4,4,13,3,3.963e-06
17 | 4,8,33,3,8.405e-06
18 | 4,16,97,3,2.4011e-05
19 | 4,32,321,3,9.8034e-05
20 | 4,64,1153,3,0.000322573
21 | 4,128,4353,3,0.00132723
22 | 4,256,16897,3,0.00538443
23 | 4,512,66561,3,0.0235848
24 | 4,1024,264193,3,0.0881839
25 | 4,2048,1052673,3,0.351345
26 | 4,4096,4202497,3,1.38174
27 | ,,,,
28 | 8,2,6,3,5.355e-06
29 | 8,4,13,3,6.744e-06
30 | 8,8,33,3,1.6412e-05
31 | 8,16,97,3,5.5942e-05
32 | 8,32,321,3,0.000166204
33 | 8,64,1153,3,0.000662042
34 | 8,128,4353,3,0.00256799
35 | 8,256,16897,3,0.0107684
36 | 8,512,66561,3,0.0448995
37 | 8,1024,264193,3,0.171752
38 | 8,2048,1052673,3,0.694237
39 | 8,4096,4202497,3,2.87031
40 | ,,,,
41 | 16,2,6,3,7.961e-06
42 | 16,4,13,3,1.1547e-05
43 | 16,8,33,3,3.0981e-05
44 | 16,16,97,3,0.000147579
45 | 16,32,321,3,0.00036279
46 | 16,64,1153,3,0.00141445
47 | 16,128,4353,3,0.00528051
48 | 16,256,16897,3,0.0216662
49 | 16,512,66561,3,0.0886633
50 | 16,1024,264193,3,0.348374
51 | 16,2048,1052673,3,1.43444
52 | 16,4096,4202497,3,5.58145
53 | ,,,,
54 | 32,2,6,3,1.2931e-05
55 | 32,4,13,3,2.195e-05
56 | 32,8,33,3,8.1744e-05
57 | 32,16,97,3,0.000193397
58 | 32,32,321,3,0.000712639
59 | 32,64,1153,3,0.00254451
60 | 32,128,4353,3,0.0102104
61 | 32,256,16897,3,0.0429879
62 | 32,512,66561,3,0.166981
63 | 32,1024,264193,3,0.673839
64 | 32,2048,1052673,3,2.77435
65 | 32,4096,4202497,3,11.4193
66 | ,,,,
67 | 64,2,6,3,2.4962e-05
68 | 64,4,13,3,4.2477e-05
69 | 64,8,33,3,0.000128719
70 | 64,16,97,3,0.000396049
71 | 64,32,321,3,0.0013773
72 | 64,64,1153,3,0.00538543
73 | 64,128,4353,3,0.0208543
74 | 64,256,16897,3,0.0838799
75 | 64,512,66561,3,0.343107
76 | 64,1024,264193,3,1.39047
77 | 64,2048,1052673,3,5.7578
78 | 64,4096,4202497,3,22.421
79 | ,,,,
80 | 128,2,6,3,4.5555e-05
81 | 128,4,13,3,8.525e-05
82 | 128,8,33,3,0.000254468
83 | 128,16,97,3,0.000751657
84 | 128,32,321,3,0.00260678
85 | 128,64,1153,3,0.0104097
86 | 128,128,4353,3,0.0414101
87 | 128,256,16897,3,0.161508
88 | 128,512,66561,3,0.66227
89 | 128,1024,264193,3,2.66748
90 | 128,2048,1052673,3,11.0805
91 | 128,4096,4202497,3,44.5607
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/naive-4-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,1.714e-06
 3 | 2,4,13,3,2.229e-06
 4 | 2,8,33,3,5.415e-06
 5 | 2,16,97,3,1.5656e-05
 6 | 2,32,321,3,6.594e-05
 7 | 2,64,1153,3,0.000197481
 8 | 2,128,4353,3,0.000829071
 9 | 2,256,16897,3,0.00331541
10 | 2,512,66561,3,0.0145428
11 | 2,1024,264193,3,0.0544543
12 | 2,2048,1052673,3,0.211647
13 | 2,4096,4202497,3,0.881724
14 | ,,,,
15 | 4,2,6,3,3.437e-06
16 | 4,4,13,3,3.673e-06
17 | 4,8,33,3,1.0304e-05
18 | 4,16,97,3,3.003e-05
19 | 4,32,321,3,0.00011798
20 | 4,64,1153,3,0.000436922
21 | 4,128,4353,3,0.00170434
22 | 4,256,16897,3,0.00645083
23 | 4,512,66561,3,0.0281007
24 | 4,1024,264193,3,0.108231
25 | 4,2048,1052673,3,0.422676
26 | 4,4096,4202497,3,1.76792
27 | ,,,,
28 | 8,2,6,3,4.763e-06
29 | 8,4,13,3,6.833e-06
30 | 8,8,33,3,1.9543e-05
31 | 8,16,97,3,5.9313e-05
32 | 8,32,321,3,0.000210022
33 | 8,64,1153,3,0.000837595
34 | 8,128,4353,3,0.0032613
35 | 8,256,16897,3,0.013178
36 | 8,512,66561,3,0.0547784
37 | 8,1024,264193,3,0.218445
38 | 8,2048,1052673,3,0.868623
39 | 8,4096,4202497,3,3.8915
40 | ,,,,
41 | 16,2,6,3,7.694e-06
42 | 16,4,13,3,1.3326e-05
43 | 16,8,33,3,3.8097e-05
44 | 16,16,97,3,0.00011794
45 | 16,32,321,3,0.000423823
46 | 16,64,1153,3,0.00166562
47 | 16,128,4353,3,0.00651927
48 | 16,256,16897,3,0.0277122
49 | 16,512,66561,3,0.108206
50 | 16,1024,264193,3,0.435223
51 | 16,2048,1052673,3,1.72035
52 | 16,4096,4202497,3,7.28557
53 | ,,,,
54 | 32,2,6,3,1.4278e-05
55 | 32,4,13,3,2.6138e-05
56 | 32,8,33,3,9.2062e-05
57 | 32,16,97,3,0.000237356
58 | 32,32,321,3,0.000908386
59 | 32,64,1153,3,0.0033104
60 | 32,128,4353,3,0.0129616
61 | 32,256,16897,3,0.0534217
62 | 32,512,66561,3,0.210283
63 | 32,1024,264193,3,0.843448
64 | 32,2048,1052673,3,3.36025
65 | 32,4096,4202497,3,13.8626
66 | ,,,,
67 | 64,2,6,3,2.5816e-05
68 | 64,4,13,3,5.1026e-05
69 | 64,8,33,3,0.0001483
70 | 64,16,97,3,0.000489398
71 | 64,32,321,3,0.0016859
72 | 64,64,1153,3,0.00671014
73 | 64,128,4353,3,0.0263359
74 | 64,256,16897,3,0.105847
75 | 64,512,66561,3,0.433156
76 | 64,1024,264193,3,1.73245
77 | 64,2048,1052673,3,6.99523
78 | 64,4096,4202497,3,28.196
79 | ,,,,
80 | 128,2,6,3,6.0394e-05
81 | 128,4,13,3,0.000104683
82 | 128,8,33,3,0.000288138
83 | 128,16,97,3,0.000959429
84 | 128,32,321,3,0.00339429
85 | 128,64,1153,3,0.0136193
86 | 128,128,4353,3,0.0523516
87 | 128,256,16897,3,0.211174
88 | 128,512,66561,3,0.857622
89 | 128,1024,264193,3,3.46887
90 | 128,2048,1052673,3,13.9752
91 | 128,4096,4202497,3,56.9118
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/prover-1-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,0.000130745
 3 | 2,4,13,3,5.3805e-05
 4 | 2,8,33,3,9.2191e-05
 5 | 2,16,97,3,0.000176163
 6 | 2,32,321,3,0.000349333
 7 | 2,64,1153,3,0.000843757
 8 | 2,128,4353,3,0.00272879
 9 | 2,256,16897,3,0.00962704
10 | 2,512,66561,3,0.0381697
11 | 2,1024,264193,3,0.143504
12 | 2,2048,1052673,3,0.569187
13 | 2,4096,4202497,3,2.23313
14 | ,,,,
15 | 4,2,6,3,9.5423e-05
16 | 4,4,13,3,8.5048e-05
17 | 4,8,33,3,0.000141254
18 | 4,16,97,3,0.00023018
19 | 4,32,321,3,0.000563244
20 | 4,64,1153,3,0.0015044
21 | 4,128,4353,3,0.00497713
22 | 4,256,16897,3,0.0189012
23 | 4,512,66561,3,0.0722619
24 | 4,1024,264193,3,0.279612
25 | 4,2048,1052673,3,1.1096
26 | 4,4096,4202497,3,4.39304
27 | ,,,,
28 | 8,2,6,3,0.000110253
29 | 8,4,13,3,0.000124495
30 | 8,8,33,3,0.000238462
31 | 8,16,97,3,0.00045558
32 | 8,32,321,3,0.00103207
33 | 8,64,1153,3,0.0029901
34 | 8,128,4353,3,0.00962503
35 | 8,256,16897,3,0.0366498
36 | 8,512,66561,3,0.147368
37 | 8,1024,264193,3,0.537882
38 | 8,2048,1052673,3,2.1869
39 | 8,4096,4202497,3,8.74598
40 | ,,,,
41 | 16,2,6,3,0.000186305
42 | 16,4,13,3,0.000212388
43 | 16,8,33,3,0.000357169
44 | 16,16,97,3,0.000851244
45 | 16,32,321,3,0.00198059
46 | 16,64,1153,3,0.00582306
47 | 16,128,4353,3,0.0191757
48 | 16,256,16897,3,0.0702826
49 | 16,512,66561,3,0.270876
50 | 16,1024,264193,3,1.06817
51 | 16,2048,1052673,3,4.36567
52 | 16,4096,4202497,3,16.7619
53 | ,,,,
54 | 32,2,6,3,0.000261862
55 | 32,4,13,3,0.000383252
56 | 32,8,33,3,0.000716145
57 | 32,16,97,3,0.00152782
58 | 32,32,321,3,0.0038149
59 | 32,64,1153,3,0.0116896
60 | 32,128,4353,3,0.0384061
61 | 32,256,16897,3,0.136559
62 | 32,512,66561,3,0.521055
63 | 32,1024,264193,3,2.04798
64 | 32,2048,1052673,3,8.42214
65 | 32,4096,4202497,3,33.1684
66 | ,,,,
67 | 64,2,6,3,0.000471328
68 | 64,4,13,3,0.000764406
69 | 64,8,33,3,0.00148315
70 | 64,16,97,3,0.0032314
71 | 64,32,321,3,0.00796952
72 | 64,64,1153,3,0.0237558
73 | 64,128,4353,3,0.0773076
74 | 64,256,16897,3,0.269403
75 | 64,512,66561,3,1.03704
76 | 64,1024,264193,3,4.0962
77 | 64,2048,1052673,3,16.9022
78 | 64,4096,4202497,3,68.3729
79 | ,,,,
80 | 128,2,6,3,0.000965935
81 | 128,4,13,3,0.0016068
82 | 128,8,33,3,0.00312274
83 | 128,16,97,3,0.00703498
84 | 128,32,321,3,0.0169001
85 | 128,64,1153,3,0.0487154
86 | 128,128,4353,3,0.157937
87 | 128,256,16897,3,0.560784
88 | 128,512,66561,3,2.08928
89 | 128,1024,264193,3,8.2469
90 | 128,2048,1052673,3,34.7028
91 | 128,4096,4202497,3,135.797
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/naive-1-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,1.981e-06
 3 | 2,4,13,3,2.147e-06
 4 | 2,8,33,3,4.441e-06
 5 | 2,16,97,3,1.3062e-05
 6 | 2,32,321,3,5.7746e-05
 7 | 2,64,1153,3,0.000165669
 8 | 2,128,4353,3,0.000726171
 9 | 2,256,16897,3,0.00292835
10 | 2,512,66561,3,0.0124223
11 | 2,1024,264193,3,0.0461969
12 | 2,2048,1052673,3,0.199169
13 | 2,4096,4202497,3,0.789575
14 | ,,,,
15 | 4,2,6,3,3.567e-06
16 | 4,4,13,3,3.94e-06
17 | 4,8,33,3,8.131e-06
18 | 4,16,97,3,2.4153e-05
19 | 4,32,321,3,0.000118985
20 | 4,64,1153,3,0.000345926
21 | 4,128,4353,3,0.00127994
22 | 4,256,16897,3,0.00497732
23 | 4,512,66561,3,0.0252684
24 | 4,1024,264193,3,0.0865308
25 | 4,2048,1052673,3,0.347153
26 | 4,4096,4202497,3,1.40063
27 | ,,,,
28 | 8,2,6,3,5.113e-06
29 | 8,4,13,3,1.8599e-05
30 | 8,8,33,3,1.6532e-05
31 | 8,16,97,3,4.7262e-05
32 | 8,32,321,3,0.000205686
33 | 8,64,1153,3,0.00063789
34 | 8,128,4353,3,0.0025154
35 | 8,256,16897,3,0.0107923
36 | 8,512,66561,3,0.0453205
37 | 8,1024,264193,3,0.172756
38 | 8,2048,1052673,3,0.696944
39 | 8,4096,4202497,3,2.77742
40 | ,,,,
41 | 16,2,6,3,8.429e-06
42 | 16,4,13,3,1.1657e-05
43 | 16,8,33,3,3.1198e-05
44 | 16,16,97,3,0.000104972
45 | 16,32,321,3,0.000328828
46 | 16,64,1153,3,0.00124726
47 | 16,128,4353,3,0.00501182
48 | 16,256,16897,3,0.0221591
49 | 16,512,66561,3,0.0866601
50 | 16,1024,264193,3,0.336587
51 | 16,2048,1052673,3,1.38775
52 | 16,4096,4202497,3,5.6751
53 | ,,,,
54 | 32,2,6,3,1.3562e-05
55 | 32,4,13,3,2.1732e-05
56 | 32,8,33,3,6.2101e-05
57 | 32,16,97,3,0.000188254
58 | 32,32,321,3,0.000662656
59 | 32,64,1153,3,0.00260167
60 | 32,128,4353,3,0.0102747
61 | 32,256,16897,3,0.0433731
62 | 32,512,66561,3,0.170737
63 | 32,1024,264193,3,0.691771
64 | 32,2048,1052673,3,2.85256
65 | 32,4096,4202497,3,11.2258
66 | ,,,,
67 | 64,2,6,3,2.4197e-05
68 | 64,4,13,3,4.2636e-05
69 | 64,8,33,3,0.000132918
70 | 64,16,97,3,0.000381543
71 | 64,32,321,3,0.00132221
72 | 64,64,1153,3,0.00513081
73 | 64,128,4353,3,0.0206987
74 | 64,256,16897,3,0.0849041
75 | 64,512,66561,3,0.33993
76 | 64,1024,264193,3,1.38016
77 | 64,2048,1052673,3,5.70653
78 | 64,4096,4202497,3,23.0195
79 | ,,,,
80 | 128,2,6,3,4.9206e-05
81 | 128,4,13,3,0.000111267
82 | 128,8,33,3,0.00025218
83 | 128,16,97,3,0.000789735
84 | 128,32,321,3,0.00292809
85 | 128,64,1153,3,0.0127229
86 | 128,128,4353,3,0.0419486
87 | 128,256,16897,3,0.16453
88 | 128,512,66561,3,0.675367
89 | 128,1024,264193,3,2.74952
90 | 128,2048,1052673,3,11.4217
91 | 128,4096,4202497,3,44.6043
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/naive-8-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,1.834e-06
 3 | 2,4,13,3,2.219e-06
 4 | 2,8,33,3,1.8706e-05
 5 | 2,16,97,3,1.5366e-05
 6 | 2,32,321,3,5.3275e-05
 7 | 2,64,1153,3,0.000197957
 8 | 2,128,4353,3,0.000845115
 9 | 2,256,16897,3,0.00337998
10 | 2,512,66561,3,0.0147969
11 | 2,1024,264193,3,0.0555424
12 | 2,2048,1052673,3,0.217976
13 | 2,4096,4202497,3,0.904106
14 | ,,,,
15 | 4,2,6,3,3.105e-06
16 | 4,4,13,3,3.922e-06
17 | 4,8,33,3,1.013e-05
18 | 4,16,97,3,2.9792e-05
19 | 4,32,321,3,0.000106894
20 | 4,64,1153,3,0.000421508
21 | 4,128,4353,3,0.00179171
22 | 4,256,16897,3,0.00679437
23 | 4,512,66561,3,0.0294255
24 | 4,1024,264193,3,0.110915
25 | 4,2048,1052673,3,0.437034
26 | 4,4096,4202497,3,1.80816
27 | ,,,,
28 | 8,2,6,3,4.575e-06
29 | 8,4,13,3,6.891e-06
30 | 8,8,33,3,1.9282e-05
31 | 8,16,97,3,6.6032e-05
32 | 8,32,321,3,0.00020991
33 | 8,64,1153,3,0.000826243
34 | 8,128,4353,3,0.00328252
35 | 8,256,16897,3,0.0135814
36 | 8,512,66561,3,0.0555348
37 | 8,1024,264193,3,0.220409
38 | 8,2048,1052673,3,0.873476
39 | 8,4096,4202497,3,3.61396
40 | ,,,,
41 | 16,2,6,3,7.706e-06
42 | 16,4,13,3,1.3514e-05
43 | 16,8,33,3,4.5434e-05
44 | 16,16,97,3,0.00014168
45 | 16,32,321,3,0.000446564
46 | 16,64,1153,3,0.00174746
47 | 16,128,4353,3,0.00672007
48 | 16,256,16897,3,0.0276901
49 | 16,512,66561,3,0.110651
50 | 16,1024,264193,3,0.436467
51 | 16,2048,1052673,3,1.75899
52 | 16,4096,4202497,3,7.20784
53 | ,,,,
54 | 32,2,6,3,1.4024e-05
55 | 32,4,13,3,2.5958e-05
56 | 32,8,33,3,7.4717e-05
57 | 32,16,97,3,0.000244541
58 | 32,32,321,3,0.000848398
59 | 32,64,1153,3,0.00333074
60 | 32,128,4353,3,0.0133683
61 | 32,256,16897,3,0.055228
62 | 32,512,66561,3,0.219003
63 | 32,1024,264193,3,0.872287
64 | 32,2048,1052673,3,3.51672
65 | 32,4096,4202497,3,14.4273
66 | ,,,,
67 | 64,2,6,3,2.5472e-05
68 | 64,4,13,3,6.3101e-05
69 | 64,8,33,3,0.000158765
70 | 64,16,97,3,0.000510346
71 | 64,32,321,3,0.00172817
72 | 64,64,1153,3,0.00674815
73 | 64,128,4353,3,0.0263946
74 | 64,256,16897,3,0.106578
75 | 64,512,66561,3,0.420253
76 | 64,1024,264193,3,1.68291
77 | 64,2048,1052673,3,6.77581
78 | 64,4096,4202497,3,28.5181
79 | ,,,,
80 | 128,2,6,3,6.6837e-05
81 | 128,4,13,3,0.000112989
82 | 128,8,33,3,0.000324711
83 | 128,16,97,3,0.000974018
84 | 128,32,321,3,0.00342667
85 | 128,64,1153,3,0.0133691
86 | 128,128,4353,3,0.0525576
87 | 128,256,16897,3,0.210441
88 | 128,512,66561,3,0.859662
89 | 128,1024,264193,3,3.49606
90 | 128,2048,1052673,3,13.9386
91 | 128,4096,4202497,3,56.8204
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/verifier-1-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,2.3131e-05
 3 | 2,4,13,3,5.0876e-05
 4 | 2,8,33,3,3.4939e-05
 5 | 2,16,97,3,5.4796e-05
 6 | 2,32,321,3,0.000105586
 7 | 2,64,1153,3,0.000282463
 8 | 2,128,4353,3,0.000759578
 9 | 2,256,16897,3,0.00228021
10 | 2,512,66561,3,0.00815161
11 | 2,1024,264193,3,0.0309956
12 | 2,2048,1052673,3,0.12257
13 | 2,4096,4202497,3,0.46672
14 | ,,,,
15 | 4,2,6,3,3.9465e-05
16 | 4,4,13,3,2.9939e-05
17 | 4,8,33,3,4.9948e-05
18 | 4,16,97,3,7.0724e-05
19 | 4,32,321,3,0.000147639
20 | 4,64,1153,3,0.000339998
21 | 4,128,4353,3,0.000795832
22 | 4,256,16897,3,0.00269241
23 | 4,512,66561,3,0.00853315
24 | 4,1024,264193,3,0.0316484
25 | 4,2048,1052673,3,0.123941
26 | 4,4096,4202497,3,0.481597
27 | ,,,,
28 | 8,2,6,3,4.9941e-05
29 | 8,4,13,3,5.4325e-05
30 | 8,8,33,3,6.1245e-05
31 | 8,16,97,3,9.9307e-05
32 | 8,32,321,3,0.000202581
33 | 8,64,1153,3,0.000442043
34 | 8,128,4353,3,0.00102382
35 | 8,256,16897,3,0.00286994
36 | 8,512,66561,3,0.00958658
37 | 8,1024,264193,3,0.0335338
38 | 8,2048,1052673,3,0.127338
39 | 8,4096,4202497,3,0.490595
40 | ,,,,
41 | 16,2,6,3,5.419e-05
42 | 16,4,13,3,6.6531e-05
43 | 16,8,33,3,9.8503e-05
44 | 16,16,97,3,0.000210793
45 | 16,32,321,3,0.000317629
46 | 16,64,1153,3,0.00065148
47 | 16,128,4353,3,0.00156986
48 | 16,256,16897,3,0.00376793
49 | 16,512,66561,3,0.0112198
50 | 16,1024,264193,3,0.0373658
51 | 16,2048,1052673,3,0.134397
52 | 16,4096,4202497,3,0.484465
53 | ,,,,
54 | 32,2,6,3,9.295e-05
55 | 32,4,13,3,0.000135835
56 | 32,8,33,3,0.000180143
57 | 32,16,97,3,0.00033926
58 | 32,32,321,3,0.000588939
59 | 32,64,1153,3,0.00118399
60 | 32,128,4353,3,0.00249965
61 | 32,256,16897,3,0.00554241
62 | 32,512,66561,3,0.0147427
63 | 32,1024,264193,3,0.0430991
64 | 32,2048,1052673,3,0.145665
65 | 32,4096,4202497,3,0.514738
66 | ,,,,
67 | 64,2,6,3,0.000213171
68 | 64,4,13,3,0.0002414
69 | 64,8,33,3,0.00036914
70 | 64,16,97,3,0.0006486
71 | 64,32,321,3,0.00116718
72 | 64,64,1153,3,0.00228649
73 | 64,128,4353,3,0.00448088
74 | 64,256,16897,3,0.0099335
75 | 64,512,66561,3,0.0234351
76 | 64,1024,264193,3,0.0598246
77 | 64,2048,1052673,3,0.186025
78 | 64,4096,4202497,3,0.612551
79 | ,,,,
80 | 128,2,6,3,0.000392085
81 | 128,4,13,3,0.00055556
82 | 128,8,33,3,0.000804
83 | 128,16,97,3,0.00135661
84 | 128,32,321,3,0.00255472
85 | 128,64,1153,3,0.00489625
86 | 128,128,4353,3,0.00955021
87 | 128,256,16897,3,0.0201971
88 | 128,512,66561,3,0.0415531
89 | 128,1024,264193,3,0.0968295
90 | 128,2048,1052673,3,0.261903
91 | 128,4096,4202497,3,0.751273
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/verifier-8-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,2.3048e-05
 3 | 2,4,13,3,2.709e-05
 4 | 2,8,33,3,3.5118e-05
 5 | 2,16,97,3,9.4505e-05
 6 | 2,32,321,3,0.00011837
 7 | 2,64,1153,3,0.000325701
 8 | 2,128,4353,3,0.000977875
 9 | 2,256,16897,3,0.00350825
10 | 2,512,66561,3,0.0116384
11 | 2,1024,264193,3,0.0433666
12 | 2,2048,1052673,3,0.167957
13 | 2,4096,4202497,3,0.676202
14 | ,,,,
15 | 4,2,6,3,6.0632e-05
16 | 4,4,13,3,5.8935e-05
17 | 4,8,33,3,8.7319e-05
18 | 4,16,97,3,0.000147949
19 | 4,32,321,3,0.000289135
20 | 4,64,1153,3,0.000640126
21 | 4,128,4353,3,0.00170383
22 | 4,256,16897,3,0.00371348
23 | 4,512,66561,3,0.0119029
24 | 4,1024,264193,3,0.0452574
25 | 4,2048,1052673,3,0.165894
26 | 4,4096,4202497,3,0.682788
27 | ,,,,
28 | 8,2,6,3,8.4537e-05
29 | 8,4,13,3,0.00010242
30 | 8,8,33,3,0.000140917
31 | 8,16,97,3,0.000247514
32 | 8,32,321,3,0.000460019
33 | 8,64,1153,3,0.00103376
34 | 8,128,4353,3,0.00244383
35 | 8,256,16897,3,0.00603025
36 | 8,512,66561,3,0.0166512
37 | 8,1024,264193,3,0.0509237
38 | 8,2048,1052673,3,0.184343
39 | 8,4096,4202497,3,0.709591
40 | ,,,,
41 | 16,2,6,3,9.9884e-05
42 | 16,4,13,3,0.000119181
43 | 16,8,33,3,0.000177547
44 | 16,16,97,3,0.000305734
45 | 16,32,321,3,0.000593034
46 | 16,64,1153,3,0.00131712
47 | 16,128,4353,3,0.00849482
48 | 16,256,16897,3,0.00681946
49 | 16,512,66561,3,0.0181581
50 | 16,1024,264193,3,0.0545039
51 | 16,2048,1052673,3,0.195096
52 | 16,4096,4202497,3,0.696258
53 | ,,,,
54 | 32,2,6,3,0.00060904
55 | 32,4,13,3,0.000167615
56 | 32,8,33,3,0.00025881
57 | 32,16,97,3,0.00044768
58 | 32,32,321,3,0.00345608
59 | 32,64,1153,3,0.00172793
60 | 32,128,4353,3,0.00376578
61 | 32,256,16897,3,0.00854
62 | 32,512,66561,3,0.0211154
63 | 32,1024,264193,3,0.0623028
64 | 32,2048,1052673,3,0.209804
65 | 32,4096,4202497,3,0.748223
66 | ,,,,
67 | 64,2,6,3,0.000210834
68 | 64,4,13,3,0.000281782
69 | 64,8,33,3,0.000407982
70 | 64,16,97,3,0.000720298
71 | 64,32,321,3,0.00132348
72 | 64,64,1153,3,0.0271723
73 | 64,128,4353,3,0.00561181
74 | 64,256,16897,3,0.0117811
75 | 64,512,66561,3,0.0277232
76 | 64,1024,264193,3,0.0744899
77 | 64,2048,1052673,3,0.230022
78 | 64,4096,4202497,3,0.801636
79 | ,,,,
80 | 128,2,6,3,0.000363814
81 | 128,4,13,3,0.000478418
82 | 128,8,33,3,0.0127439
83 | 128,16,97,3,0.00141906
84 | 128,32,321,3,0.00237843
85 | 128,64,1153,3,0.0044941
86 | 128,128,4353,3,0.00896587
87 | 128,256,16897,3,0.0185007
88 | 128,512,66561,3,0.041569
89 | 128,1024,264193,3,0.276371
90 | 128,2048,1052673,3,0.288084
91 | 128,4096,4202497,3,0.893898
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/verifier-2-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,3.4405e-05
 3 | 2,4,13,3,4.0535e-05
 4 | 2,8,33,3,5.8787e-05
 5 | 2,16,97,3,0.000101992
 6 | 2,32,321,3,0.000205463
 7 | 2,64,1153,3,0.000464844
 8 | 2,128,4353,3,0.00117662
 9 | 2,256,16897,3,0.00398863
10 | 2,512,66561,3,0.0124327
11 | 2,1024,264193,3,0.0451397
12 | 2,2048,1052673,3,0.175964
13 | 2,4096,4202497,3,0.685573
14 | ,,,,
15 | 4,2,6,3,3.8621e-05
16 | 4,4,13,3,7.4309e-05
17 | 4,8,33,3,6.8993e-05
18 | 4,16,97,3,0.000117943
19 | 4,32,321,3,0.000229711
20 | 4,64,1153,3,0.000517176
21 | 4,128,4353,3,0.00131012
22 | 4,256,16897,3,0.00391622
23 | 4,512,66561,3,0.0126915
24 | 4,1024,264193,3,0.0443038
25 | 4,2048,1052673,3,0.170578
26 | 4,4096,4202497,3,0.661747
27 | ,,,,
28 | 8,2,6,3,7.87e-05
29 | 8,4,13,3,9.8702e-05
30 | 8,8,33,3,0.000132271
31 | 8,16,97,3,0.000222624
32 | 8,32,321,3,0.000440542
33 | 8,64,1153,3,0.000642418
34 | 8,128,4353,3,0.00152152
35 | 8,256,16897,3,0.00423261
36 | 8,512,66561,3,0.0134547
37 | 8,1024,264193,3,0.0460644
38 | 8,2048,1052673,3,0.173643
39 | 8,4096,4202497,3,0.665901
40 | ,,,,
41 | 16,2,6,3,7.4937e-05
42 | 16,4,13,3,8.0347e-05
43 | 16,8,33,3,0.000132651
44 | 16,16,97,3,0.000209036
45 | 16,32,321,3,0.000401655
46 | 16,64,1153,3,0.00082621
47 | 16,128,4353,3,0.00192219
48 | 16,256,16897,3,0.00501716
49 | 16,512,66561,3,0.0148135
50 | 16,1024,264193,3,0.0499485
51 | 16,2048,1052673,3,0.179889
52 | 16,4096,4202497,3,0.688697
53 | ,,,,
54 | 32,2,6,3,0.000123701
55 | 32,4,13,3,0.000137845
56 | 32,8,33,3,0.000202039
57 | 32,16,97,3,0.00033522
58 | 32,32,321,3,0.000624253
59 | 32,64,1153,3,0.00127131
60 | 32,128,4353,3,0.00276132
61 | 32,256,16897,3,0.00668426
62 | 32,512,66561,3,0.018103
63 | 32,1024,264193,3,0.0575996
64 | 32,2048,1052673,3,0.198625
65 | 32,4096,4202497,3,0.706862
66 | ,,,,
67 | 64,2,6,3,0.000180552
68 | 64,4,13,3,0.000220648
69 | 64,8,33,3,0.000347676
70 | 64,16,97,3,0.000597101
71 | 64,32,321,3,0.00109876
72 | 64,64,1153,3,0.00212524
73 | 64,128,4353,3,0.00443605
74 | 64,256,16897,3,0.0100389
75 | 64,512,66561,3,0.025346
76 | 64,1024,264193,3,0.0694057
77 | 64,2048,1052673,3,0.21954
78 | 64,4096,4202497,3,0.78494
79 | ,,,,
80 | 128,2,6,3,0.00036766
81 | 128,4,13,3,0.000426628
82 | 128,8,33,3,0.000657438
83 | 128,16,97,3,0.00112513
84 | 128,32,321,3,0.00207878
85 | 128,64,1153,3,0.0039871
86 | 128,128,4353,3,0.0080414
87 | 128,256,16897,3,0.0172229
88 | 128,512,66561,3,0.0393264
89 | 128,1024,264193,3,0.0979671
90 | 128,2048,1052673,3,0.282536
91 | 128,4096,4202497,3,0.887477
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/profiling/logs/08-17_01:43/verifier-4-thread.csv:
--------------------------------------------------------------------------------
 1 | batch_size, input_size, circuit_size, degree, time (in sec)
 2 | 2,2,6,3,5.3839e-05
 3 | 2,4,13,3,4.7512e-05
 4 | 2,8,33,3,6.7606e-05
 5 | 2,16,97,3,0.000112353
 6 | 2,32,321,3,0.000238357
 7 | 2,64,1153,3,0.000517255
 8 | 2,128,4353,3,0.00151841
 9 | 2,256,16897,3,0.00369142
10 | 2,512,66561,3,0.0116302
11 | 2,1024,264193,3,0.0430954
12 | 2,2048,1052673,3,0.176606
13 | 2,4096,4202497,3,0.683354
14 | ,,,,
15 | 4,2,6,3,5.9243e-05
16 | 4,4,13,3,6.8266e-05
17 | 4,8,33,3,0.000104129
18 | 4,16,97,3,0.000192884
19 | 4,32,321,3,0.000349642
20 | 4,64,1153,3,0.000538406
21 | 4,128,4353,3,0.00207449
22 | 4,256,16897,3,0.00519722
23 | 4,512,66561,3,0.0130519
24 | 4,1024,264193,3,0.0465827
25 | 4,2048,1052673,3,0.177198
26 | 4,4096,4202497,3,0.690294
27 | ,,,,
28 | 8,2,6,3,8.2205e-05
29 | 8,4,13,3,8.6026e-05
30 | 8,8,33,3,0.000147791
31 | 8,16,97,3,0.000225178
32 | 8,32,321,3,0.000462508
33 | 8,64,1153,3,0.000927299
34 | 8,128,4353,3,0.00223793
35 | 8,256,16897,3,0.00427506
36 | 8,512,66561,3,0.0156107
37 | 8,1024,264193,3,0.047779
38 | 8,2048,1052673,3,0.182579
39 | 8,4096,4202497,3,0.677081
40 | ,,,,
41 | 16,2,6,3,0.000113992
42 | 16,4,13,3,0.000116032
43 | 16,8,33,3,0.000186084
44 | 16,16,97,3,0.000306078
45 | 16,32,321,3,0.000571837
46 | 16,64,1153,3,0.00120589
47 | 16,128,4353,3,0.00178515
48 | 16,256,16897,3,0.00493896
49 | 16,512,66561,3,0.0149692
50 | 16,1024,264193,3,0.0504539
51 | 16,2048,1052673,3,0.190385
52 | 16,4096,4202497,3,0.703268
53 | ,,,,
54 | 32,2,6,3,0.00015046
55 | 32,4,13,3,0.000175527
56 | 32,8,33,3,0.000277581
57 | 32,16,97,3,0.000463356
58 | 32,32,321,3,0.000866356
59 | 32,64,1153,3,0.00178517
60 | 32,128,4353,3,0.00254003
61 | 32,256,16897,3,0.00617187
62 | 32,512,66561,3,0.0174866
63 | 32,1024,264193,3,0.0551472
64 | 32,2048,1052673,3,0.191426
65 | 32,4096,4202497,3,0.696981
66 | ,,,,
67 | 64,2,6,3,0.000241695
68 | 64,4,13,3,0.000294681
69 | 64,8,33,3,0.000450447
70 | 64,16,97,3,0.000787916
71 | 64,32,321,3,0.00158392
72 | 64,64,1153,3,0.00296593
73 | 64,128,4353,3,0.00616482
74 | 64,256,16897,3,0.00868897
75 | 64,512,66561,3,0.0225492
76 | 64,1024,264193,3,0.0654059
77 | 64,2048,1052673,3,0.208555
78 | 64,4096,4202497,3,0.770678
79 | ,,,,
80 | 128,2,6,3,0.000419589
81 | 128,4,13,3,0.000549739
82 | 128,8,33,3,0.000851143
83 | 128,16,97,3,0.00158347
84 | 128,32,321,3,0.00157838
85 | 128,64,1153,3,0.0030849
86 | 128,128,4353,3,0.00638896
87 | 128,256,16897,3,0.016818
88 | 128,512,66561,3,0.0327509
89 | 128,1024,264193,3,0.0853533
90 | 128,2048,1052673,3,0.256377
91 | 128,4096,4202497,3,0.854242
92 | ,,,,
93 | 


--------------------------------------------------------------------------------
/src/proof_system/common.hpp:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Declaration of interfaces for common utilities.
 4 |  
 5 |  *****************************************************************************
 6 |  * @author     This file is part of bace, developed by SCIPR Lab
 7 |  *             and contributors (see AUTHORS).
 8 |  * @copyright  MIT license (see LICENSE file)
 9 |  *****************************************************************************/
10 | 
11 | #ifndef COMMON_HPP_
12 | #define COMMON_HPP_
13 | 
14 | #include "src/proof_system/domain.hpp"
15 | 
16 | namespace bace {
17 | 
18 | /***************************** INPUT / OUTPUT ********************************/
19 | 
20 | template<typename FieldT>
21 | using input_t = std::vector<FieldT>;
22 | 
23 | template<typename FieldT>
24 | using input_batch_t = std::vector<input_t<FieldT> >;
25 | 
26 | template<typename FieldT>
27 | using output_batch_t = std::vector<FieldT>;
28 | 
29 | /**************************** PROVER / VERIFIER ******************************/
30 | 
31 | template<typename FieldT>
32 | using column_lde_t = std::vector<std::vector<FieldT> >;
33 | 
34 | template<typename FieldT>
35 | using proof_t = std::vector<FieldT>;
36 | 
37 | /*
38 |  * Returns the input size of a given batch of inputs, or 0 if there is a
39 |  * mismatch among input sizes in the batch.
40 |  *
41 |  * Given a batch of inputs, the function determines whether all inputs have
42 |  * matching input size. As inputs should have, by definition, at least
43 |  * one element, the function returns 0 in the case that there is a mismatch
44 |  * of input sizes. One can use this return value as a sanity check for
45 |  * input size correctness.
46 |  */
47 | template<typename FieldT>
48 | size_t get_input_size(const input_batch_t<FieldT> &input_batch);
49 | 
50 | /*
51 |  * Returns the column_lde_t of a given input batch in vector form, or an
52 |  * empty vector if there is a mismatch among input sizes.
53 |  *
54 |  * Given a batch of inputs, consider these to be ordered as rows of inputs.
55 |  * The function computes the column-wise low degree extension by taking
56 |  * the inverse FFT of the columns on a column_size domain.
57 |  *
58 |  * column_lde[i] = IFFT([input_batch[1][i], ... , input_batch[batch_size][i]])
59 |  */
60 | template<typename FieldT>
61 | column_lde_t<FieldT> compute_column_lde(const input_batch_t<FieldT> &input_batch,
62 |                                         const size_t &column_size);
63 | 
64 | } // bace
65 | 
66 | #include "common.tcc"
67 | 
68 | #endif // COMMON_HPP_
69 | 


--------------------------------------------------------------------------------
/src/proof_system/verifier.hpp:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Declaration of interfaces for the verifier.
 4 |  
 5 |  *****************************************************************************
 6 |  * @author     This file is part of bace, developed by SCIPR Lab
 7 |  *             and contributors (see AUTHORS).
 8 |  * @copyright  MIT license (see LICENSE file)
 9 |  *****************************************************************************/
10 | 
11 | #ifndef VERIFIER_HPP_
12 | #define VERIFIER_HPP_
13 | 
14 | #include "src/arithmetic_circuit/arithmetic_circuit.hpp"
15 | #include "src/proof_system/common.hpp"
16 | 
17 | namespace bace {
18 | 
19 | /*
20 |  * Returns a batch of outputs, given an arithmetic circuit, batch of inputs,
21 |  * and proof from the prover.
22 |  *
23 |  * The verifier first performs a probabilistic check of the proof provided by
24 |  * the prover. The verifier constructs the column_lde_t and selects a random
25 |  * field element, evaluating the random element on the columns to compose an
26 |  * input vector of input_size. Then, the verifier evaluates this input vector
27 |  * on the given circuit and evaluates the random field element on the proof to
28 |  * verify that the two outputs match.
29 |  *
30 |  * If the two evaluations match, there is a large probability
31 |  * that the proof is correct, and the verifier proceeds to derive
32 |  * the batch of outputs from the proof. After evaluating on a large degree
33 |  * by taking the FFT of the proof, the verifier selects the outputs, seperated
34 |  * approximately degree indices apart by properties of the FFT.
35 |  *
36 |  * random = FieldT::random_element()
37 |  * random_input = [column_lde[1](random), ... , column_lde[input_size](random)]
38 |  * output_mine = circuit.evaluate(random_input)
39 |  * output_proof = proof(random)
40 |  *
41 |  * In the case that the outputs from the evaluation of the random input and
42 |  * proof do not match, the verifier will return an empty vector as output. If
43 |  * there is a size mismatch among the batch of inputs, the verifier will either
44 |  * return an output batch composed of zeros, or error if the input size fails
45 |  * to match the circuit's defined input size.
46 |  */
47 | template<typename FieldT>
48 | void verifier(const arithmetic_circuit_t<FieldT> &circuit,
49 |               const input_batch_t<FieldT> &input_batch,
50 |               output_batch_t<FieldT> &output_batch,
51 |               const proof_t<FieldT> &proof);
52 | 
53 | } // bace
54 | 
55 | #include "verifier.tcc"
56 | 
57 | #endif // VERIFIER_HPP_
58 | 


--------------------------------------------------------------------------------
/src/test/test_verifier.cpp:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  * @author     This file is part of bace, developed by SCIPR Lab
 4 |  *             and contributors (see AUTHORS).
 5 |  * @copyright  MIT license (see LICENSE file)
 6 |  *****************************************************************************/
 7 | 
 8 | #include <cassert>
 9 | #include <stdio.h>
10 | #include <stdlib.h>
11 | #include <vector>
12 | 
13 | #include "algebra/curves/mnt/mnt4/mnt4_pp.hpp"
14 | 
15 | #include "src/arithmetic_circuit/arithmetic_circuit.hpp"
16 | #include "src/proof_system/prover.hpp"
17 | #include "src/proof_system/verifier.hpp"
18 | #include "src/proof_system/naive_evaluation.hpp"
19 | 
20 | using namespace bace;
21 | 
22 | template<typename FieldT>
23 | void test_verifier()
24 | {
25 |     /* Arithmetic circuit over F_q with input_size variables */
26 |     const size_t input_size = 8;
27 | 
28 |     /* Evaluation for batch_size points */
29 |     const size_t batch_size = 8;
30 | 
31 |     /* Input input_batch_1, ... , input_batch_{batch_size} in (F_q)^input_size */
32 |     input_batch_t<FieldT> input_batch(batch_size);
33 |     for (int i = 0; i < batch_size; i++)
34 |     {
35 |         input_batch[i] = std::vector<FieldT>(input_size);
36 |         for (int j = 0; j < input_size; j++)
37 |         {
38 |             input_batch[i][j] = FieldT(rand() % FieldT::s);
39 |         }
40 |     }
41 | 
42 |     /* Arithmetic circuit construction */
43 |     arithmetic_circuit_t<FieldT> circuit = arithmetic_circuit_t<FieldT>(input_size);
44 |     circuit.add_quadratic_inner_product_gates();
45 | 
46 |     /* Proof */
47 |     proof_t<FieldT> proof;
48 |     prover(circuit, input_batch, proof);
49 | 
50 |     /* Output output_batch_1, ... , output_batch_k in F_q, s.t. output_batch_i = circuit(input_batch_i) */
51 |     output_batch_t<FieldT> output_batch;
52 |     output_batch_t<FieldT> output_batch_naive;
53 |     verifier(circuit, input_batch, output_batch, proof);
54 |     naive_evaluate(circuit, input_batch, output_batch_naive);
55 | 
56 |     printf("%ld == %ld\n", output_batch.size(), output_batch_naive.size());
57 |     assert(output_batch.size() == output_batch_naive.size());
58 |     for (size_t i = 0; i < output_batch.size(); i++)
59 |     {
60 |         printf("%ld == %ld\n", output_batch[i].as_ulong(), output_batch_naive[i].as_ulong());
61 |         assert(output_batch[i] == output_batch_naive[i]);
62 |     }
63 | }
64 | 
65 | int main()
66 | {
67 |     libff::mnt4_pp::init_public_params();
68 |     test_verifier<libff::Fr<libff::mnt4_pp> >();
69 |     return 0;
70 | }
71 | 


--------------------------------------------------------------------------------
/src/proof_system/domain.hpp:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  Declaration of interfaces for domain.
 4 |  
 5 |  *****************************************************************************
 6 |  * @author     This file is part of bace, developed by SCIPR Lab
 7 |  *             and contributors (see AUTHORS).
 8 |  * @copyright  MIT license (see LICENSE file)
 9 |  *****************************************************************************/
10 | 
11 | #ifndef DOMAIN_HPP_
12 | #define DOMAIN_HPP_
13 | 
14 | #include "evaluation_domain/evaluation_domain.hpp"
15 | 
16 | namespace bace {
17 | 
18 | template<typename FieldT>
19 | using domain_t = std::shared_ptr<libfqfft::evaluation_domain<FieldT> >;
20 | 
21 | /*
22 |  * Returns an evaluation domain given the domain_size.
23 |  *
24 |  * Our construction makes the assumption that the roots of unity always exist
25 |  * by choosing to use the basic radix-2 domain. This ensures the small domain
26 |  * used to construct the column_lde_t will always be embedded within the
27 |  * large domain. This structure makes it convenient to select the embedded
28 |  * indices of the output on the large domain, as the points will be a power
29 |  * of two apart.
30 |  */
31 | template<typename FieldT>
32 | domain_t<FieldT> get_evaluation_domain(const size_t &domain_size);
33 | 
34 | /*
35 |  * Returns the closest previous power of two, or itself if it's a power of two.
36 |  *
37 |  * Note: The technique will only work up to 32-bit values. For the purposes of
38 |  * this library, this issue should not arise, as it is used with respect to
39 |  * the circuit's degree size.
40 |  *
41 |  * https://stackoverflow.com/questions/2679815/previous-power-of-2
42 |  */
43 | unsigned int get_previous_power_of_two(const unsigned int &n);
44 | 
45 | /*
46 |  * Returns the corresponding, embedded index in the large_domain_size for a
47 |  * given index in the small_domain_size.
48 |  *
49 |  * The function assumes the small domain is embedded in the large domain,
50 |  * allowing it to find a corresponding relation in index between the the
51 |  * two domains. This implementation uses the basic radix-2 domain, where
52 |  * the large_domain_size is a factor of the small_domain_size. So the jump
53 |  * between points of interest in the large domain is some distance apart,
54 |  * namely the factor's previous power of two in a radix-2 domain.
55 |  */
56 | unsigned int get_embedded_index(const size_t &index,
57 |                                 const size_t &small_domain_size,
58 |                                 const size_t &large_domain_size);
59 | 
60 | /*
61 |  * Returns the column size given a batch_size.
62 |  *
63 |  * This function extends the batch size to the nearest power of two. This is
64 |  * necessary for constructing a column_lde_t on the radix-2 domain.
65 |  */
66 | size_t get_column_size(const size_t &batch_size);
67 | 
68 | /*
69 |  * Returns the large_degree domain size given a column_size and circuit degree.
70 |  *
71 |  * This function determines the large_degree domain size by extending the
72 |  * product of the column_size and degree to the nearest power of two. This
73 |  * ensures there exists an embedding of the small domain in the large domain.
74 |  */
75 | size_t get_large_degree(const size_t &column_size, const size_t &degree);
76 | 
77 | } // bace
78 | 
79 | #include "domain.tcc"
80 | 
81 | #endif // DOMAIN_HPP_
82 | 


--------------------------------------------------------------------------------
/src/test/test_circuit.cpp:
--------------------------------------------------------------------------------
 1 | /** @file
 2 |  *****************************************************************************
 3 |  * @author     This file is part of bace, developed by SCIPR Lab
 4 |  *             and contributors (see AUTHORS).
 5 |  * @copyright  MIT license (see LICENSE file)
 6 |  *****************************************************************************/
 7 |  
 8 | #include <cassert>
 9 | #include <stdio.h>
10 | #include <stdlib.h>
11 | #include <vector>
12 | 
13 | #include "algebra/curves/mnt/mnt4/mnt4_pp.hpp"
14 | 
15 | #include "src/arithmetic_circuit/arithmetic_circuit.hpp"
16 | 
17 | using namespace bace;
18 | 
19 | template<typename FieldT>
20 | void test_circuit_evaluate()
21 | {
22 |     /* Arithmetic circuit C over F_q with n variables 
23 |      * C = ((x_1 + x_2) + x_3 + x_3) * (x_1 + x_2) * x_4 */
24 |     const size_t n = 4;
25 |     arithmetic_circuit_t<FieldT> C = arithmetic_circuit_t<FieldT>(n);
26 | 
27 |     /* First gate */
28 |     const input_element_t<FieldT> e1 = { VARIABLE, 1 };
29 |     const input_element_t<FieldT> e2 = { VARIABLE, 2 };
30 |     const gate_t<FieldT> g1 = { SUM, std::vector<input_element_t<FieldT> > { e1, e2 } };
31 |     const int g1_number = C.add_gate(g1);
32 | 
33 |     /* Second gate */
34 |     const input_element_t<FieldT> e3 = { VARIABLE, g1_number };
35 |     const input_element_t<FieldT> e4 = { VARIABLE, 3 };
36 |     const gate_t<FieldT> g2 = { SUM, std::vector<input_element_t<FieldT> > { e3, e4, e4 } };
37 |     const int g2_number = C.add_gate(g2);
38 | 
39 |     /* Second gate */
40 |     const input_element_t<FieldT> e5 = { VARIABLE, g2_number };
41 |     const input_element_t<FieldT> e6 = { VARIABLE, 4 };
42 |     const gate_t<FieldT> g3 = { PRODUCT, std::vector<input_element_t<FieldT> > { e5, e6, e3 } };
43 |     C.add_gate(g3);
44 | 
45 |     /* Output y_1, ... , y_k in F_q, s.t. y_i = C(x_i) */
46 |     const FieldT res = C.evaluate(std::vector<FieldT> { 2, 7, 6, 2 });
47 |     printf("%ld == 378\n", res.as_ulong());
48 |     assert(res == 378);
49 | }
50 | 
51 | template<typename FieldT>
52 | void test_circuit_evaluate_inner_product()
53 | {
54 |     /* Arithmetic circuit C over F_q with input_size variables */
55 |     const size_t input_size = 4;
56 |     arithmetic_circuit_t<FieldT> circuit = arithmetic_circuit_t<FieldT>(input_size);
57 |     circuit.add_inner_product_gates();
58 | 
59 |     /* Output y_1, ... , y_k in F_q, s.t. y_i = C(x_i) */
60 |     const FieldT res = circuit.evaluate(std::vector<FieldT> { 2, 7, 6, 2 });
61 |     printf("%ld == 26\n", res.as_ulong());
62 |     assert(res == 26);
63 | }
64 | 
65 | template<typename FieldT>
66 | void test_circuit_evaluate_quadratic_inner_product()
67 | {
68 |     /* Arithmetic circuit C over F_q with input_size variables */
69 |     const size_t input_size = 4;
70 |     arithmetic_circuit_t<FieldT> circuit = arithmetic_circuit_t<FieldT>(input_size);
71 |     circuit.add_quadratic_inner_product_gates();
72 | 
73 |     /* Output y_1, ... , y_k in F_q, s.t. y_i = C(x_i) */
74 |     const FieldT res = circuit.evaluate(std::vector<FieldT> { 2, 7, 6, 2 });
75 |     printf("%ld == 424\n", res.as_ulong());
76 |     assert(res == 424);
77 | }
78 | 
79 | int main()
80 | {
81 |     libff::mnt4_pp::init_public_params();
82 |     test_circuit_evaluate<libff::Fr<libff::mnt4_pp> >();
83 |     test_circuit_evaluate_inner_product<libff::Fr<libff::mnt4_pp> >();
84 |     test_circuit_evaluate_quadratic_inner_product<libff::Fr<libff::mnt4_pp> >();
85 |     return 0;
86 | }
87 | 


--------------------------------------------------------------------------------
/src/arithmetic_circuit/arithmetic_circuit.hpp:
--------------------------------------------------------------------------------
  1 | /** @file
  2 |  *****************************************************************************
  3 |  Declaration of interfaces for arithmetic circuit.
  4 |  
  5 |  *****************************************************************************
  6 |  * @author     This file is part of bace, developed by SCIPR Lab
  7 |  *             and contributors (see AUTHORS).
  8 |  * @copyright  MIT license (see LICENSE file)
  9 |  *****************************************************************************/
 10 | 
 11 | #ifndef ARITHMETIC_CIRCUIT_HPP_
 12 | #define ARITHMETIC_CIRCUIT_HPP_
 13 | 
 14 | #include "src/proof_system/common.hpp"
 15 | 
 16 | namespace bace {
 17 | 
 18 | /************************ ARITHMETIC CIRCUIT GATE ****************************/
 19 | 
 20 | /* 
 21 |  * A circuit gate is composed of a type (ex. SUM, PRODUCT) and a vector of
 22 |  * input gates. Each input gate is defined by its input type, which is
 23 |  * either an index reference to the variable (gate number), or a field element
 24 |  * treated as a constant value.
 25 |  *
 26 |  * For a detailed explanation and example, see the evaluate() function below.
 27 |  */
 28 | 
 29 | enum input_type_t { CONSTANT, VARIABLE };
 30 | 
 31 | template<typename FieldT>
 32 | union input_value_t
 33 | {
 34 |     int variable;
 35 |     FieldT constant;
 36 | };
 37 | 
 38 | template<typename FieldT>
 39 | struct input_element_t
 40 | {
 41 |     input_type_t type;
 42 |     input_value_t<FieldT> value;
 43 | };
 44 | 
 45 | enum gate_type_t { SUM, PRODUCT };
 46 | 
 47 | template<typename FieldT>
 48 | struct gate_t
 49 | {
 50 |     gate_type_t type;
 51 |     std::vector<input_element_t<FieldT> > input_gates;
 52 | };
 53 | 
 54 | /*************************** ARITHMETIC CIRCUIT ******************************/
 55 | 
 56 | template<typename FieldT>
 57 | class arithmetic_circuit_t {
 58 | public:
 59 |     arithmetic_circuit_t(const size_t &input_size) : _input_size(input_size) {};
 60 | 
 61 |     /*
 62 |      * Returns the evaluation of the circuit for the given input. Note that
 63 |      * the size of input_t must match the circuit's input size. If the circuit
 64 |      * contains no gates, the evaluation will return 0.
 65 |      */
 66 |     FieldT evaluate(const input_t<FieldT> &input) const;
 67 | 
 68 |     /* 
 69 |      * Adds the provided gate to the circuit. Each gate is composed of
 70 |      * two parts, a gate type (ex. SUM, PRODUCT) and a vector of input gates.
 71 |      *
 72 |      * The input gates are composed of input_element_t's. Each input_element_t
 73 |      * is composed of a type (ex. CONSTANT, VARIABLE) and a value. For an
 74 |      * input type of CONSTANT, provide the constant field element. For an
 75 |      * input type of VARIABLE, provide the integer gate number.
 76 |      *
 77 |      * The following is an example construction:
 78 |      *
 79 |      * input_element_t<FieldT> e1 = { VARIABLE, gate_number_1 };
 80 |      * input_element_t<FieldT> e2 = { VARIABLE, gate_number_2 };
 81 |      * gate_t<FieldT> gate = { PRODUCT, std::vector<input_element_t<FieldT> > { e1, e2 } };
 82 |      */
 83 |     int add_gate(const gate_t<FieldT> &g);
 84 | 
 85 |     /* Clears all sum and product gates from the circuit */
 86 |     void clear_gates();
 87 | 
 88 |     /* Returns the sum of input gates, sum gates, and product gates. */
 89 |     size_t size() const;
 90 | 
 91 |     /* Returns the largest degree computed by any particular gate. */
 92 |     size_t degree() const;
 93 | 
 94 |     /* Returns the number of inputs for the circuit */
 95 |     size_t num_inputs() const;
 96 | 
 97 |     /* Prints circuit size, circuit degree, and number of inputs */
 98 |     void print_info() const;
 99 | 
100 |     /* 
101 |      * Adds a quadratic circuit of degree 3, by dividing the input length
102 |      * into two components, left and right, each of length middle = input / 2.
103 |      * The circuit takes an inner product of the left component with the
104 |      * right component.
105 |     */
106 |     void add_inner_product_gates();
107 | 
108 |     /* 
109 |      * Adds a quadratic circuit of degree 3, by dividing the input length
110 |      * into two components, left and right, each of length middle = input / 2.
111 |      * The circuit takes an inner product of the left component with itself
112 |      * length middle times. This constructs a new length middle component,
113 |      * call it square. The circuit then takes an inner product of the 
114 |      * square component with the right component.
115 |     */
116 |     void add_quadratic_inner_product_gates();
117 | 
118 | private:
119 |     const size_t _input_size;
120 |     std::vector<gate_t<FieldT> > _gates;
121 | };
122 | 
123 | } // bace
124 | 
125 | #include "arithmetic_circuit.tcc"
126 | 
127 | #endif // ARITHMETIC_CIRCUIT_HPP_
128 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
  1 | <h1 align="center">Batch Arithmetic Circuit Evaluation (BACE)</h1>
  2 | 
  3 | __BACE__ is a C++ library for evaluating arithmetic circuits on batches of inputs.
  4 | 
  5 | The protocol is an efficient implementation of the Merlin-Arthur proof system presented in the paper "_Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch Evaluation_" (Williams, CCC 2016). The paper can be found [here](https://arxiv.org/pdf/1601.04743v1) and slides can be found [here](http://computationalcomplexity.org/Archive/2016/slides/williams-ccc2016.pdf). The proof system consists of a single message from the (deterministic) prover to the (probabilistic) verifier; the statement being proved is about the correctness of evaluating an arithmetic circuit on a batch of inputs.
  6 | 
  7 | The library is developed by [SCIPR Lab] and contributors (see [AUTHORS] file) and is released under the MIT License (see [LICENSE] file). Check out the [__Performance__](#performance) section for runtime data.
  8 | 
  9 | ## Table of contents
 10 | 
 11 | - [Directory Structure](#directory-structure)
 12 | - [Build guide](#build-guide)
 13 | - [Testing](#testing)
 14 | - [Profiling](#profiling)
 15 | - [Performance](#performance)
 16 | 
 17 | ## Directory structure
 18 | 
 19 | The directory structure is as follows:
 20 | 
 21 | * [__src__](src): C++ source code, containing the following modules:
 22 |   * [__arithmetic\_circuit__](src/arithmetic_circuit): interface for arithmetic circuit
 23 |   * [__proof\_system__](src/proof_system): prover, verifier, and naive evaluation
 24 |   * [__profiling__](src/profiling): profile and plot runtimes
 25 |   * [__tests__](src/tests): collection of tests
 26 | 
 27 | ## Build guide
 28 | 
 29 | The library has the following dependencies:
 30 | 
 31 | * [CMake](http://cmake.org/)
 32 | * [GMP](http://gmplib.org/)
 33 | * [gnuplot](http://www.gnuplot.info/)
 34 | * [libprocps](http://packages.ubuntu.com/trusty/libprocps3-dev)
 35 | * [libff](https://github.com/scipr-lab/libff)
 36 | * [libfqfft](https://github.com/scipr-lab/libfqfft)
 37 | 
 38 | The library has been tested on Linux, but it is compatible with Windows and Mac OS X.
 39 | 
 40 | ### Installation
 41 | 
 42 | On Ubuntu 14.04 LTS:
 43 | 
 44 | ```
 45 | sudo apt-get install build-essential git cmake gnuplot-x11 libgmp3-dev libprocps3-dev
 46 | ```
 47 | 
 48 | Then follow the build guide for [libff](https://github.com/scipr-lab/libff) and [libfqfft](https://github.com/scipr-lab/libfqfft).
 49 | 
 50 | ### Compilation
 51 | 
 52 | To compile, starting at the project root directory and setup the `build` directory:
 53 | 
 54 | ```
 55 | mkdir build && cd build && cmake ..
 56 | ```
 57 | 
 58 | Then, to compile the library and profiler, run:
 59 | 
 60 | ```
 61 | make
 62 | ```
 63 | 
 64 | The above makes the `build` folder and compiles the profiler to the project root directory. To remove all executables, from the build folder, run `make clean`.
 65 | 
 66 | #### Options
 67 | 
 68 | The following flags change the behavior of the compiled code:
 69 | 
 70 | * `cmake .. -DMULTICORE=ON`
 71 | Enables parallelized execution using OpenMP. This will utilize all cores on the CPU for heavyweight parallelizable operations such as FFT.
 72 | 
 73 | * `cmake .. -DOPT_FLAGS={ FLAGS }`
 74 | Passes specified optimizations flags to compiler.
 75 | 
 76 | * `cmake .. -PROF_DOUBLE=ON`
 77 | Enables profiling with Double (default: ON). If the flag is turned off, profiling will use `Fr<alt_bn128_pp>`.
 78 | 
 79 | ## Testing
 80 | 
 81 | This library includes unit tests that cover arithmetic circuit, prover, and verifier evaluation. The test suite is easily extensible to support a wide range of fields and domain sizes. To run the tests for this library, after [Compilation](#compilation), run:
 82 | 
 83 | ```
 84 | make check
 85 | ```
 86 | 
 87 | ## Profiling
 88 | 
 89 | The library profiles runtimes with multi-threading support, and plots the resulting data using [gnuplot](http://www.gnuplot.info/). All profiling and plotting activity is logged under `src/profiling/logs`; logs are sorted into a directory hierarchy by timestamp.
 90 | 
 91 | After [Compilation](#compilation), start the profiler by running ```./profile``` from the project root directory. The profiler logs runtimes for the naive evaluation, prover, and verifier, across varying batch and input sizes. Then, it plots graphs comparing naive evaluation with the verifier, naive evaluation with the prover, and runtimes across threads for the naive evaluation, prover, and verifier. Profiling results and plots are saved under ```src/profiling/logs/{datetime}```.
 92 | 
 93 | ## Performance
 94 | 
 95 | __Machine Specification:__ The following benchmark data was obtained on a 64-bit Intel i7 Quad-Core machine with 16GB RAM (2x8GB) running Ubuntu 14.04 LTS. The code is compiled using g++ 4.8.4.
 96 | 
 97 | ```
 98 | Architecture:          x86_64
 99 | CPU op-mode(s):        32-bit, 64-bit
100 | Byte Order:            Little Endian
101 | CPU(s):                8
102 | On-line CPU(s) list:   0-7
103 | Thread(s) per core:    1
104 | Core(s) per socket:    2
105 | Socket(s):             4
106 | NUMA node(s):          1
107 | Vendor ID:             GenuineIntel
108 | CPU family:            6
109 | Model:                 94
110 | Stepping:              3
111 | CPU MHz:               4008.007
112 | BogoMIPS:              8016.01
113 | Virtualization:        VT-x
114 | L1d cache:             32K
115 | L1i cache:             32K
116 | L2 cache:              256K
117 | L3 cache:              8192K
118 | NUMA node0 CPU(s):     0-7
119 | ```
120 | 
121 | ### Runtime
122 | 
123 | These runtime benchmarks are determined by constructing an arithmetic circuit of degree 3 using quadratic inner product gates. For every batch size, the input size is varied by powers of two to determine the threshold values for which the verifier's evaluation becomes more cost effective than performing the naive evaluation.
124 | 
125 | <p align="center"><img src="https://cloud.githubusercontent.com/assets/9260812/17748214/24e61f30-646d-11e6-8c41-5dff1a858e04.png" width="50%"><img src="https://cloud.githubusercontent.com/assets/9260812/17748213/24c6bcbc-646d-11e6-8e52-3da658dda4ad.png" width="50%"></p>
126 | 
127 | The left graph compares the runtime cost of naive evaluation with the prover's cost of constructing a proof for the verifier. The right graph compares runtime cost of naive evaluation with the verifier's cost of performing a probabilistic check and evaluation from the proof.
128 | 
129 | [SCIPR Lab]: http://www.scipr-lab.org/ (Succinct Computational Integrity and Privacy Research Lab)
130 | 
131 | [LICENSE]: LICENSE (LICENSE file in top directory of bace distribution)
132 | 
133 | [AUTHORS]: AUTHORS (AUTHORS file in top directory of bace distribution)


--------------------------------------------------------------------------------
/src/profiling/profile.cpp:
--------------------------------------------------------------------------------
  1 | /** @file
  2 |  *****************************************************************************
  3 |  Implementation of functions for profiler.
  4 |  *****************************************************************************
  5 |  * @author     This file is part of bace, developed by SCIPR Lab
  6 |  *             and contributors (see AUTHORS).
  7 |  * @copyright  MIT license (see LICENSE file)
  8 |  *****************************************************************************/
  9 | 
 10 | #include <ctime>
 11 | #include <iostream>
 12 | #include <fstream>
 13 | #include <omp.h>
 14 | #include <sstream>
 15 | #include <stdio.h>
 16 | #include <string.h>
 17 | #include <stdint.h>
 18 | #include <stdlib.h>
 19 | #include <sys/resource.h>
 20 | #include <unistd.h>
 21 | #include <vector>
 22 | 
 23 | #include "algebra/curves/alt_bn128/alt_bn128_pp.hpp"
 24 | #include "common/double.hpp"
 25 | 
 26 | #include "src/proof_system/prover.hpp"
 27 | #include "src/proof_system/verifier.hpp"
 28 | #include "src/proof_system/naive_evaluation.hpp"
 29 | 
 30 | using namespace bace;
 31 | 
 32 | void plot(const std::string &path)
 33 | {
 34 |     /* System Call */
 35 |     std::string cmd = "gnuplot -e \"input_directory=\'" + path + "\'\" src/profiling/plot/runtime_plot.gp";
 36 |     if (system(cmd.c_str()) == 0) printf("Plotted profile to %s\n", path.c_str());
 37 | }
 38 | 
 39 | template <typename FieldT>
 40 | std::pair<std::pair<double, double>, std::pair<size_t, size_t> > profile(const std::vector<std::vector<FieldT> > &input_batch,
 41 |                                                                          const size_t &input_size,
 42 |                                                                          const std::string &type)
 43 | {
 44 |     double start;
 45 |     double end;
 46 | 
 47 |     double start_prover;
 48 |     double end_prover;
 49 | 
 50 |     proof_t<FieldT> proof;
 51 |     std::vector<FieldT> output_batch;
 52 | 
 53 |     arithmetic_circuit_t<FieldT> circuit = arithmetic_circuit_t<FieldT>(input_size);
 54 |     circuit.add_quadratic_inner_product_gates();
 55 | 
 56 |     /* Perform operation */
 57 |     if (type == "naive")
 58 |     {
 59 |         start = omp_get_wtime();
 60 |         naive_evaluate(circuit, input_batch, output_batch);
 61 |         end = omp_get_wtime() - start;
 62 |     }
 63 |     else
 64 |     {
 65 |         start_prover = omp_get_wtime();
 66 |         prover(circuit, input_batch, proof);
 67 |         end_prover = omp_get_wtime() - start_prover;
 68 | 
 69 |         start = omp_get_wtime();
 70 |         verifier(circuit, input_batch, output_batch, proof);
 71 |         end = omp_get_wtime() - start;
 72 |     }
 73 | 
 74 |     return std::make_pair(std::make_pair(end, end_prover), std::make_pair(circuit.degree(), circuit.size()));
 75 | }
 76 | 
 77 | template <typename FieldT>
 78 | void initialize(const std::string &path, const std::string &type, const int &num_threads)
 79 | {
 80 |     size_t batch_size;
 81 |     size_t input_size;
 82 | 
 83 |     double runtime;
 84 |     double runtime_prover;
 85 |     size_t degree;
 86 |     size_t circuit_size;
 87 | 
 88 |     std::pair<std::pair<double, double>, std::pair<size_t, size_t> > profile_stats;
 89 | 
 90 |     /* Runtime File */
 91 |     std::ofstream runtime_file;
 92 |     runtime_file.open(path + type + "-" + std::to_string(num_threads) + "-thread.csv");
 93 |     runtime_file << "batch_size, input_size, circuit_size, degree, time (in sec)\n";
 94 | 
 95 |     std::ofstream prover_runtime_file;
 96 |     if (type == "verifier")
 97 |     {
 98 |         prover_runtime_file.open(path + "prover-" + std::to_string(num_threads) + "-thread.csv");
 99 |         prover_runtime_file << "batch_size, input_size, circuit_size, degree, time (in sec)\n";
100 |     }
101 | 
102 |     printf("\n%s-%d-thread\n", type.c_str(), num_threads);
103 | 
104 |     /* Assess on varying domain sizes */
105 |     std::vector<std::vector<FieldT> > input_batch;
106 |     for (int i = 1; i < 8; i++) /* batch_size */
107 |     {
108 |         for (int j = 1; j < 13; j++) /* input_size */
109 |         {
110 |             /* Initialization */
111 |             batch_size = pow(2, i);
112 |             input_size = pow(2, j);
113 | 
114 |             input_batch.resize(batch_size);
115 |             for (int k = 0; k < batch_size; k++)
116 |             {
117 |                 input_batch[k] = std::vector<FieldT>(input_size);
118 |                 for (int l = 0; l < input_size; l++)
119 |                 {
120 |                     input_batch[k][l] = FieldT::random_element();
121 |                 }
122 |             }
123 |             
124 |             /* Profiling */
125 |             profile_stats = profile<FieldT>(input_batch, input_size, type);
126 |             runtime = profile_stats.first.first;
127 |             runtime_prover = profile_stats.first.second;
128 |             degree = profile_stats.second.first;
129 |             circuit_size = profile_stats.second.second;
130 | 
131 |             /* Logging */
132 |             runtime_file << batch_size << "," << input_size << "," << circuit_size << "," << degree << "," << runtime << "\n";
133 |             if (type == "verifier")
134 |             {
135 |                 prover_runtime_file << batch_size << "," << input_size << "," << circuit_size << "," << degree << "," << runtime_prover << "\n";
136 |                 prover_runtime_file.flush();
137 |             }
138 |             printf("batch_size %ld, input_size %ld, circuit_size %ld, degree %ld, %f seconds\n", batch_size, input_size, circuit_size, degree, runtime);
139 |             
140 |             runtime_file.flush();
141 |             input_batch.clear();
142 |         }
143 | 
144 |         runtime_file << ",,,,\n";
145 |         runtime_file.flush();
146 |         if (type == "verifier")
147 |         {
148 |             prover_runtime_file << ",,,,\n";
149 |             prover_runtime_file.flush(); 
150 |         }
151 |         printf("\n");
152 |     }
153 | 
154 |     /* Close file */
155 |     runtime_file.close();
156 |     if (type == "verifier") prover_runtime_file.close();
157 | }
158 | 
159 | int main()
160 | {
161 |   /* Get Current Timestamp */
162 |   time_t rawtime;
163 |   time(&rawtime);
164 |   struct tm* timeinfo = localtime(&rawtime);
165 |   char buffer[40];
166 |   strftime(buffer, 40, "%m-%d_%I:%M", timeinfo);
167 |   std::string datetime(buffer);
168 | 
169 |   /* Make log file directory */
170 |   std::string path = "src/profiling/logs/" + datetime + "/";
171 |   if (system( ("mkdir -p " + path).c_str() )) return 0;
172 | 
173 |   /* Profile on 1, 2, 4, or 8 threads */
174 |   const int max_threads = omp_get_max_threads();
175 |   for (int num_threads = 1; num_threads <= max_threads; num_threads *= 2)
176 |   {
177 |     /* Fix number of threads, no dynamic adjustment */
178 |     omp_set_dynamic(0);
179 |     omp_set_num_threads(num_threads);
180 | 
181 | #ifndef PROF_DOUBLE
182 |     printf("Profiling with alt_bn128_pp\n");
183 |     libff::alt_bn128_pp::init_public_params();
184 |     initialize<libff::Fr<libff::alt_bn128_pp> >(path, "naive", num_threads);
185 |     initialize<libff::Fr<libff::alt_bn128_pp> >(path, "verifier", num_threads);
186 | #else
187 |     printf("Profiling with Double\n");
188 |     initialize<libff::Double>(path, "naive", num_threads);
189 |     initialize<libff::Double>(path, "verifier", num_threads);
190 | #endif
191 |   }
192 | 
193 |   plot(path);
194 |   
195 |   return 0;
196 | }
197 | 


--------------------------------------------------------------------------------
/src/arithmetic_circuit/arithmetic_circuit.tcc:
--------------------------------------------------------------------------------
  1 | /** @file
  2 |  *****************************************************************************
  3 |  Implementation of interfaces for arithmetic circuit.
  4 |  
  5 |  See arithmetic_circuit.hpp .
  6 | 
  7 |  *****************************************************************************
  8 |  * @author     This file is part of bace, developed by SCIPR Lab
  9 |  *             and contributors (see AUTHORS).
 10 |  * @copyright  MIT license (see LICENSE file)
 11 |  *****************************************************************************/
 12 | 
 13 | #ifndef ARITHMETIC_CIRCUIT_TCC_
 14 | #define ARITHMETIC_CIRCUIT_TCC_
 15 | 
 16 | #include <algorithm>
 17 | #include <cassert>
 18 | #include <stdlib.h>
 19 | #include <vector>
 20 | 
 21 | namespace bace {
 22 | 
 23 | template<typename FieldT>
 24 | FieldT arithmetic_circuit_t<FieldT>::evaluate(const input_t<FieldT> &input) const
 25 | {
 26 |     assert(input.size() == this->_input_size);
 27 |     assert(this->_gates.size() > 0);
 28 | 
 29 |     std::vector<FieldT> gate_output(input);
 30 |     gate_output.resize(this->size(), FieldT::zero());
 31 | 
 32 |     FieldT output;
 33 |     size_t i = this->_input_size;
 34 |     for (auto gate: this->_gates)
 35 |     {
 36 |         if (gate.type == SUM)
 37 |         {
 38 |             output = FieldT::zero();
 39 |             for (auto input_gate: gate.input_gates)
 40 |             {
 41 |                 if (input_gate.type == CONSTANT) output += input_gate.value.constant;
 42 |                 else output += gate_output[input_gate.value.variable - 1];
 43 |             }
 44 |         }
 45 |         else if (gate.type == PRODUCT)
 46 |         {
 47 |             if (gate.input_gates[0].type == CONSTANT) output = gate.input_gates[0].value.constant;
 48 |             else output = gate_output[gate.input_gates[0].value.variable - 1];
 49 | 
 50 |             for (int j = 1; j < gate.input_gates.size(); j++)
 51 |             {
 52 |                 if (gate.input_gates[j].type == CONSTANT) output *= gate.input_gates[j].value.constant;
 53 |                 else output *= gate_output[gate.input_gates[j].value.variable - 1];
 54 |             }
 55 |         }
 56 |         gate_output[i++] = output;
 57 |     }
 58 | 
 59 |     return output;
 60 | }
 61 | 
 62 | template<typename FieldT>
 63 | int arithmetic_circuit_t<FieldT>::add_gate(const gate_t<FieldT> &g)
 64 | {
 65 |     assert(g.input_gates.size() > 0);
 66 |     assert(g.type == SUM || g.type == PRODUCT);
 67 | 
 68 |     this->_gates.emplace_back(g);
 69 |     return this->size();
 70 | }
 71 | 
 72 | template<typename FieldT>
 73 | void arithmetic_circuit_t<FieldT>::clear_gates()
 74 | {
 75 |     this->_gates.clear();
 76 | }
 77 | 
 78 | template<typename FieldT>
 79 | size_t arithmetic_circuit_t<FieldT>::size() const
 80 | {
 81 |     return this->_input_size + this->_gates.size();
 82 | }
 83 | 
 84 | template<typename FieldT>
 85 | size_t arithmetic_circuit_t<FieldT>::degree() const
 86 | {
 87 |     std::vector<size_t> degree(this->_input_size, 1);
 88 |     degree.resize(this->size(), 0);
 89 | 
 90 |     size_t max_degree = 0;
 91 |     size_t i = this->_input_size;
 92 |     for (auto gate: this->_gates)
 93 |     {
 94 |         size_t gate_degree = 0;
 95 |         if (gate.type == SUM)
 96 |         {
 97 |             for (auto input_gate: gate.input_gates)
 98 |             {
 99 |                 if (input_gate.type == VARIABLE)
100 |                 {
101 |                     gate_degree = std::max(gate_degree, degree[input_gate.value.variable - 1]);
102 |                 }
103 |             }
104 |         }
105 |         else if (gate.type == PRODUCT)
106 |         {
107 |             for (auto input_gate: gate.input_gates)
108 |             {
109 |                 if (input_gate.type == VARIABLE)
110 |                 {
111 |                     gate_degree += degree[input_gate.value.variable - 1];
112 |                 }
113 |             }
114 |         }
115 | 
116 |         degree[i++] = gate_degree;
117 |         max_degree = std::max(max_degree, gate_degree);
118 |     }
119 | 
120 |     return max_degree;
121 | }
122 | 
123 | template<typename FieldT>
124 | size_t arithmetic_circuit_t<FieldT>::num_inputs() const
125 | {
126 |     return this->_input_size;
127 | }
128 | 
129 | template<typename FieldT>
130 | void arithmetic_circuit_t<FieldT>::print_info() const
131 | {
132 |     printf("* Circuit size: %zu\n", this->size());
133 |     printf("* Circuit degree: %zu\n", this->degree());
134 |     printf("* Number of inputs: %zu\n", this->num_inputs());
135 | }
136 | 
137 | template<typename FieldT>
138 | void arithmetic_circuit_t<FieldT>::add_inner_product_gates()
139 | {
140 |     const bool odd = this->_input_size % 2 == 1;
141 |     const int mid = odd ? (this->_input_size / 2) + 1 : this->_input_size / 2;
142 | 
143 |     std::vector<input_element_t<FieldT> > input_gates;
144 |     for (int i = 1; i <= mid; i++)
145 |     {
146 |         if (i == mid - 1 && odd) continue;
147 | 
148 |         const input_element_t<FieldT> left = { VARIABLE, i };
149 |         const input_element_t<FieldT> right = { VARIABLE, mid + i };
150 |         const gate_t<FieldT> product_gate = { PRODUCT, std::vector<input_element_t<FieldT> > { left, right } };
151 |         const int gate_number = this->add_gate(product_gate);
152 | 
153 |         const input_element_t<FieldT> element = { VARIABLE, gate_number };
154 |         input_gates.emplace_back(element);
155 |     }
156 | 
157 |     const gate_t<FieldT> sum_gate = { SUM, input_gates };
158 |     this->add_gate(sum_gate);
159 | }
160 | 
161 | template<typename FieldT>
162 | void arithmetic_circuit_t<FieldT>::add_quadratic_inner_product_gates()
163 | {
164 |     const bool odd = this->_input_size % 2 == 1;
165 |     const int mid = odd ? (this->_input_size / 2) + 1 : this->_input_size / 2;
166 | 
167 |     std::vector<input_element_t<FieldT> > product_input_gates;
168 |     for (int i = 0; i < mid; i++)
169 |     {
170 |         std::vector<input_element_t<FieldT> > input_gates;
171 |         for (int j = 1; j <= mid; j++)
172 |         {
173 |             if (j == mid - 1 && odd) continue;
174 | 
175 |             const input_element_t<FieldT> left = { VARIABLE, j };
176 |             const input_element_t<FieldT> right = { VARIABLE, j };
177 |             const gate_t<FieldT> product_gate = { PRODUCT, std::vector<input_element_t<FieldT> > { left, right } };
178 |             const int gate_number = this->add_gate(product_gate);
179 | 
180 |             const input_element_t<FieldT> element = { VARIABLE, gate_number };
181 |             input_gates.emplace_back(element);
182 |         }
183 | 
184 |         const gate_t<FieldT> sum_gate = { SUM, input_gates };
185 |         const int gate_number = this->add_gate(sum_gate);
186 | 
187 |         const input_element_t<FieldT> element = { VARIABLE, gate_number };
188 |         product_input_gates.emplace_back(element);
189 |     }
190 |     
191 |     std::vector<input_element_t<FieldT> > input_gates;
192 |     for (int i = 1; i <= mid; i++)
193 |     {
194 |         if (i == mid - 1 && odd) continue;
195 | 
196 |         const input_element_t<FieldT> right = { VARIABLE, mid + i };
197 |         const gate_t<FieldT> product_gate = { PRODUCT, std::vector<input_element_t<FieldT> > { product_input_gates[i-1], right } };
198 |         const int gate_number = this->add_gate(product_gate);
199 | 
200 |         const input_element_t<FieldT> element = { VARIABLE, gate_number };
201 |         input_gates.emplace_back(element);
202 |     }
203 | 
204 |     const gate_t<FieldT> sum_gate = { SUM, input_gates };
205 |     this->add_gate(sum_gate);
206 | }
207 | 
208 | } // bace
209 | 
210 | #endif // ARITHMETIC_CIRCUIT_TCC_
211 | 


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/src/profiling/logs/08-17_01:43/naive-prover-1.ps:
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 299 |   currentrgbcolor
 300 |   /ColB exch def /ColG exch def /ColR exch def
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 302 |   /ColG ColG Fillden mul Fillden sub 1 add def
 303 |   /ColB ColB Fillden mul Fillden sub 1 add def
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 307 | /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def
 308 | %
 309 | % PostScript Level 1 Pattern Fill routine for rectangles
 310 | % Usage: x y w h s a XX PatternFill
 311 | %	x,y = lower left corner of box to be filled
 312 | %	w,h = width and height of box
 313 | %	  a = angle in degrees between lines and x-axis
 314 | %	 XX = 0/1 for no/yes cross-hatch
 315 | %
 316 | /PatternFill {gsave /PFa [ 9 2 roll ] def
 317 |   PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate
 318 |   PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec
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 323 |   0 0 M PFa 5 get rotate PFs -2 div dup translate
 324 |   0 1 PFs PFa 4 get div 1 add floor cvi
 325 | 	{PFa 4 get mul 0 M 0 PFs V} for
 326 |   0 PFa 6 get ne {
 327 | 	0 1 PFs PFa 4 get div 1 add floor cvi
 328 | 	{PFa 4 get mul 0 2 1 roll M PFs 0 V} for
 329 |  } if
 330 |   stroke grestore} def
 331 | %
 332 | /languagelevel where
 333 |  {pop languagelevel} {1} ifelse
 334 |  2 lt
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 336 | 	{/InterpretLevel1 Level1 def}
 337 |  ifelse
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 349 | << Tile8x8
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 363 | /Pat4 exch def
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 366 | 	0 -4 M 12 8 L stroke}
 367 | >> matrix makepattern
 368 | /Pat5 exch def
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 376 | 	0 -4 M 8 12 L 4 -4 M 10 8 L stroke}
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 380 |  /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L
 381 | 	12 0 M -4 8 L 12 4 M 0 10 L stroke}
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 386 | 	-4 0 M 12 8 L -4 4 M 8 10 L stroke}
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 400 | %
 401 | /PatternBgnd {
 402 |   TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse
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 404 | %
 405 | % Substitute for Level 2 pattern fill codes with
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 407 | %
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 411 | /Pattern3 {0.750 Density} bind def
 412 | /Pattern4 {0.125 Density} bind def
 413 | /Pattern5 {0.375 Density} bind def
 414 | /Pattern6 {0.625 Density} bind def
 415 | /Pattern7 {0.875 Density} bind def
 416 | } def
 417 | %
 418 | % Now test for support of Level 2 code
 419 | %
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 455 | /SDict 10 dict def
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 459 | SDict begin [
 460 |   /Title (naive-prover-1.ps)
 461 |   /Subject (gnuplot plot)
 462 |   /Creator (gnuplot 4.6 patchlevel 4)
 463 |   /Author (vagrant)
 464 | %  /Producer (gnuplot)
 465 | %  /Keywords ()
 466 |   /CreationDate (Wed Aug 17 09:40:33 2016)
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2011 | showpage
2012 | %%Trailer
2013 | %%DocumentFonts: Helvetica
2014 | %%Pages: 1
2015 | 


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 132 |   hpt neg vpt 1.62 mul V closepath stroke
 133 |   Pnt} def
 134 | /Star {2 copy Pls Crs} def
 135 | /BoxF {stroke [] 0 setdash exch hpt sub exch vpt add M
 136 |   0 vpt2 neg V hpt2 0 V 0 vpt2 V
 137 |   hpt2 neg 0 V closepath fill} def
 138 | /TriUF {stroke [] 0 setdash vpt 1.12 mul add M
 139 |   hpt neg vpt -1.62 mul V
 140 |   hpt 2 mul 0 V
 141 |   hpt neg vpt 1.62 mul V closepath fill} def
 142 | /TriD {stroke [] 0 setdash 2 copy vpt 1.12 mul sub M
 143 |   hpt neg vpt 1.62 mul V
 144 |   hpt 2 mul 0 V
 145 |   hpt neg vpt -1.62 mul V closepath stroke
 146 |   Pnt} def
 147 | /TriDF {stroke [] 0 setdash vpt 1.12 mul sub M
 148 |   hpt neg vpt 1.62 mul V
 149 |   hpt 2 mul 0 V
 150 |   hpt neg vpt -1.62 mul V closepath fill} def
 151 | /DiaF {stroke [] 0 setdash vpt add M
 152 |   hpt neg vpt neg V hpt vpt neg V
 153 |   hpt vpt V hpt neg vpt V closepath fill} def
 154 | /Pent {stroke [] 0 setdash 2 copy gsave
 155 |   translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
 156 |   closepath stroke grestore Pnt} def
 157 | /PentF {stroke [] 0 setdash gsave
 158 |   translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
 159 |   closepath fill grestore} def
 160 | /Circle {stroke [] 0 setdash 2 copy
 161 |   hpt 0 360 arc stroke Pnt} def
 162 | /CircleF {stroke [] 0 setdash hpt 0 360 arc fill} def
 163 | /C0 {BL [] 0 setdash 2 copy moveto vpt 90 450 arc} bind def
 164 | /C1 {BL [] 0 setdash 2 copy moveto
 165 | 	2 copy vpt 0 90 arc closepath fill
 166 | 	vpt 0 360 arc closepath} bind def
 167 | /C2 {BL [] 0 setdash 2 copy moveto
 168 | 	2 copy vpt 90 180 arc closepath fill
 169 | 	vpt 0 360 arc closepath} bind def
 170 | /C3 {BL [] 0 setdash 2 copy moveto
 171 | 	2 copy vpt 0 180 arc closepath fill
 172 | 	vpt 0 360 arc closepath} bind def
 173 | /C4 {BL [] 0 setdash 2 copy moveto
 174 | 	2 copy vpt 180 270 arc closepath fill
 175 | 	vpt 0 360 arc closepath} bind def
 176 | /C5 {BL [] 0 setdash 2 copy moveto
 177 | 	2 copy vpt 0 90 arc
 178 | 	2 copy moveto
 179 | 	2 copy vpt 180 270 arc closepath fill
 180 | 	vpt 0 360 arc} bind def
 181 | /C6 {BL [] 0 setdash 2 copy moveto
 182 | 	2 copy vpt 90 270 arc closepath fill
 183 | 	vpt 0 360 arc closepath} bind def
 184 | /C7 {BL [] 0 setdash 2 copy moveto
 185 | 	2 copy vpt 0 270 arc closepath fill
 186 | 	vpt 0 360 arc closepath} bind def
 187 | /C8 {BL [] 0 setdash 2 copy moveto
 188 | 	2 copy vpt 270 360 arc closepath fill
 189 | 	vpt 0 360 arc closepath} bind def
 190 | /C9 {BL [] 0 setdash 2 copy moveto
 191 | 	2 copy vpt 270 450 arc closepath fill
 192 | 	vpt 0 360 arc closepath} bind def
 193 | /C10 {BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill
 194 | 	2 copy moveto
 195 | 	2 copy vpt 90 180 arc closepath fill
 196 | 	vpt 0 360 arc closepath} bind def
 197 | /C11 {BL [] 0 setdash 2 copy moveto
 198 | 	2 copy vpt 0 180 arc closepath fill
 199 | 	2 copy moveto
 200 | 	2 copy vpt 270 360 arc closepath fill
 201 | 	vpt 0 360 arc closepath} bind def
 202 | /C12 {BL [] 0 setdash 2 copy moveto
 203 | 	2 copy vpt 180 360 arc closepath fill
 204 | 	vpt 0 360 arc closepath} bind def
 205 | /C13 {BL [] 0 setdash 2 copy moveto
 206 | 	2 copy vpt 0 90 arc closepath fill
 207 | 	2 copy moveto
 208 | 	2 copy vpt 180 360 arc closepath fill
 209 | 	vpt 0 360 arc closepath} bind def
 210 | /C14 {BL [] 0 setdash 2 copy moveto
 211 | 	2 copy vpt 90 360 arc closepath fill
 212 | 	vpt 0 360 arc} bind def
 213 | /C15 {BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill
 214 | 	vpt 0 360 arc closepath} bind def
 215 | /Rec {newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
 216 | 	neg 0 rlineto closepath} bind def
 217 | /Square {dup Rec} bind def
 218 | /Bsquare {vpt sub exch vpt sub exch vpt2 Square} bind def
 219 | /S0 {BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare} bind def
 220 | /S1 {BL [] 0 setdash 2 copy vpt Square fill Bsquare} bind def
 221 | /S2 {BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare} bind def
 222 | /S3 {BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare} bind def
 223 | /S4 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def
 224 | /S5 {BL [] 0 setdash 2 copy 2 copy vpt Square fill
 225 | 	exch vpt sub exch vpt sub vpt Square fill Bsquare} bind def
 226 | /S6 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare} bind def
 227 | /S7 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill
 228 | 	2 copy vpt Square fill Bsquare} bind def
 229 | /S8 {BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare} bind def
 230 | /S9 {BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare} bind def
 231 | /S10 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill
 232 | 	Bsquare} bind def
 233 | /S11 {BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill
 234 | 	Bsquare} bind def
 235 | /S12 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare} bind def
 236 | /S13 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
 237 | 	2 copy vpt Square fill Bsquare} bind def
 238 | /S14 {BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill
 239 | 	2 copy exch vpt sub exch vpt Square fill Bsquare} bind def
 240 | /S15 {BL [] 0 setdash 2 copy Bsquare fill Bsquare} bind def
 241 | /D0 {gsave translate 45 rotate 0 0 S0 stroke grestore} bind def
 242 | /D1 {gsave translate 45 rotate 0 0 S1 stroke grestore} bind def
 243 | /D2 {gsave translate 45 rotate 0 0 S2 stroke grestore} bind def
 244 | /D3 {gsave translate 45 rotate 0 0 S3 stroke grestore} bind def
 245 | /D4 {gsave translate 45 rotate 0 0 S4 stroke grestore} bind def
 246 | /D5 {gsave translate 45 rotate 0 0 S5 stroke grestore} bind def
 247 | /D6 {gsave translate 45 rotate 0 0 S6 stroke grestore} bind def
 248 | /D7 {gsave translate 45 rotate 0 0 S7 stroke grestore} bind def
 249 | /D8 {gsave translate 45 rotate 0 0 S8 stroke grestore} bind def
 250 | /D9 {gsave translate 45 rotate 0 0 S9 stroke grestore} bind def
 251 | /D10 {gsave translate 45 rotate 0 0 S10 stroke grestore} bind def
 252 | /D11 {gsave translate 45 rotate 0 0 S11 stroke grestore} bind def
 253 | /D12 {gsave translate 45 rotate 0 0 S12 stroke grestore} bind def
 254 | /D13 {gsave translate 45 rotate 0 0 S13 stroke grestore} bind def
 255 | /D14 {gsave translate 45 rotate 0 0 S14 stroke grestore} bind def
 256 | /D15 {gsave translate 45 rotate 0 0 S15 stroke grestore} bind def
 257 | /DiaE {stroke [] 0 setdash vpt add M
 258 |   hpt neg vpt neg V hpt vpt neg V
 259 |   hpt vpt V hpt neg vpt V closepath stroke} def
 260 | /BoxE {stroke [] 0 setdash exch hpt sub exch vpt add M
 261 |   0 vpt2 neg V hpt2 0 V 0 vpt2 V
 262 |   hpt2 neg 0 V closepath stroke} def
 263 | /TriUE {stroke [] 0 setdash vpt 1.12 mul add M
 264 |   hpt neg vpt -1.62 mul V
 265 |   hpt 2 mul 0 V
 266 |   hpt neg vpt 1.62 mul V closepath stroke} def
 267 | /TriDE {stroke [] 0 setdash vpt 1.12 mul sub M
 268 |   hpt neg vpt 1.62 mul V
 269 |   hpt 2 mul 0 V
 270 |   hpt neg vpt -1.62 mul V closepath stroke} def
 271 | /PentE {stroke [] 0 setdash gsave
 272 |   translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
 273 |   closepath stroke grestore} def
 274 | /CircE {stroke [] 0 setdash 
 275 |   hpt 0 360 arc stroke} def
 276 | /Opaque {gsave closepath 1 setgray fill grestore 0 setgray closepath} def
 277 | /DiaW {stroke [] 0 setdash vpt add M
 278 |   hpt neg vpt neg V hpt vpt neg V
 279 |   hpt vpt V hpt neg vpt V Opaque stroke} def
 280 | /BoxW {stroke [] 0 setdash exch hpt sub exch vpt add M
 281 |   0 vpt2 neg V hpt2 0 V 0 vpt2 V
 282 |   hpt2 neg 0 V Opaque stroke} def
 283 | /TriUW {stroke [] 0 setdash vpt 1.12 mul add M
 284 |   hpt neg vpt -1.62 mul V
 285 |   hpt 2 mul 0 V
 286 |   hpt neg vpt 1.62 mul V Opaque stroke} def
 287 | /TriDW {stroke [] 0 setdash vpt 1.12 mul sub M
 288 |   hpt neg vpt 1.62 mul V
 289 |   hpt 2 mul 0 V
 290 |   hpt neg vpt -1.62 mul V Opaque stroke} def
 291 | /PentW {stroke [] 0 setdash gsave
 292 |   translate 0 hpt M 4 {72 rotate 0 hpt L} repeat
 293 |   Opaque stroke grestore} def
 294 | /CircW {stroke [] 0 setdash 
 295 |   hpt 0 360 arc Opaque stroke} def
 296 | /BoxFill {gsave Rec 1 setgray fill grestore} def
 297 | /Density {
 298 |   /Fillden exch def
 299 |   currentrgbcolor
 300 |   /ColB exch def /ColG exch def /ColR exch def
 301 |   /ColR ColR Fillden mul Fillden sub 1 add def
 302 |   /ColG ColG Fillden mul Fillden sub 1 add def
 303 |   /ColB ColB Fillden mul Fillden sub 1 add def
 304 |   ColR ColG ColB setrgbcolor} def
 305 | /BoxColFill {gsave Rec PolyFill} def
 306 | /PolyFill {gsave Density fill grestore grestore} def
 307 | /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def
 308 | %
 309 | % PostScript Level 1 Pattern Fill routine for rectangles
 310 | % Usage: x y w h s a XX PatternFill
 311 | %	x,y = lower left corner of box to be filled
 312 | %	w,h = width and height of box
 313 | %	  a = angle in degrees between lines and x-axis
 314 | %	 XX = 0/1 for no/yes cross-hatch
 315 | %
 316 | /PatternFill {gsave /PFa [ 9 2 roll ] def
 317 |   PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate
 318 |   PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec
 319 |   TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse
 320 |   clip
 321 |   currentlinewidth 0.5 mul setlinewidth
 322 |   /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def
 323 |   0 0 M PFa 5 get rotate PFs -2 div dup translate
 324 |   0 1 PFs PFa 4 get div 1 add floor cvi
 325 | 	{PFa 4 get mul 0 M 0 PFs V} for
 326 |   0 PFa 6 get ne {
 327 | 	0 1 PFs PFa 4 get div 1 add floor cvi
 328 | 	{PFa 4 get mul 0 2 1 roll M PFs 0 V} for
 329 |  } if
 330 |   stroke grestore} def
 331 | %
 332 | /languagelevel where
 333 |  {pop languagelevel} {1} ifelse
 334 |  2 lt
 335 | 	{/InterpretLevel1 true def}
 336 | 	{/InterpretLevel1 Level1 def}
 337 |  ifelse
 338 | %
 339 | % PostScript level 2 pattern fill definitions
 340 | %
 341 | /Level2PatternFill {
 342 | /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8}
 343 | 	bind def
 344 | /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def
 345 | << Tile8x8
 346 |  /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} 
 347 | >> matrix makepattern
 348 | /Pat1 exch def
 349 | << Tile8x8
 350 |  /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke
 351 | 	0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke}
 352 | >> matrix makepattern
 353 | /Pat2 exch def
 354 | << Tile8x8
 355 |  /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L
 356 | 	8 8 L 8 0 L 0 0 L fill}
 357 | >> matrix makepattern
 358 | /Pat3 exch def
 359 | << Tile8x8
 360 |  /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L
 361 | 	0 12 M 12 0 L stroke}
 362 | >> matrix makepattern
 363 | /Pat4 exch def
 364 | << Tile8x8
 365 |  /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L
 366 | 	0 -4 M 12 8 L stroke}
 367 | >> matrix makepattern
 368 | /Pat5 exch def
 369 | << Tile8x8
 370 |  /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L
 371 | 	0 12 M 8 -4 L 4 12 M 10 0 L stroke}
 372 | >> matrix makepattern
 373 | /Pat6 exch def
 374 | << Tile8x8
 375 |  /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L
 376 | 	0 -4 M 8 12 L 4 -4 M 10 8 L stroke}
 377 | >> matrix makepattern
 378 | /Pat7 exch def
 379 | << Tile8x8
 380 |  /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L
 381 | 	12 0 M -4 8 L 12 4 M 0 10 L stroke}
 382 | >> matrix makepattern
 383 | /Pat8 exch def
 384 | << Tile8x8
 385 |  /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L
 386 | 	-4 0 M 12 8 L -4 4 M 8 10 L stroke}
 387 | >> matrix makepattern
 388 | /Pat9 exch def
 389 | /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def
 390 | /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def
 391 | /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def
 392 | /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def
 393 | /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def
 394 | /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def
 395 | /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def
 396 | } def
 397 | %
 398 | %
 399 | %End of PostScript Level 2 code
 400 | %
 401 | /PatternBgnd {
 402 |   TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse
 403 | } def
 404 | %
 405 | % Substitute for Level 2 pattern fill codes with
 406 | % grayscale if Level 2 support is not selected.
 407 | %
 408 | /Level1PatternFill {
 409 | /Pattern1 {0.250 Density} bind def
 410 | /Pattern2 {0.500 Density} bind def
 411 | /Pattern3 {0.750 Density} bind def
 412 | /Pattern4 {0.125 Density} bind def
 413 | /Pattern5 {0.375 Density} bind def
 414 | /Pattern6 {0.625 Density} bind def
 415 | /Pattern7 {0.875 Density} bind def
 416 | } def
 417 | %
 418 | % Now test for support of Level 2 code
 419 | %
 420 | Level1 {Level1PatternFill} {Level2PatternFill} ifelse
 421 | %
 422 | /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont
 423 | dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall
 424 | currentdict end definefont pop
 425 | /MFshow {
 426 |    { dup 5 get 3 ge
 427 |      { 5 get 3 eq {gsave} {grestore} ifelse }
 428 |      {dup dup 0 get findfont exch 1 get scalefont setfont
 429 |      [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6
 430 |      get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq
 431 |      {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5
 432 |      get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div
 433 |      dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get
 434 |      show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop
 435 |      pop aload pop M} ifelse }ifelse }ifelse }
 436 |      ifelse }
 437 |    forall} def
 438 | /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def
 439 | /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse }
 440 |  {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont
 441 |      6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def
 442 | /MLshow { currentpoint stroke M
 443 |   0 exch R
 444 |   Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def
 445 | /MRshow { currentpoint stroke M
 446 |   exch dup MFwidth neg 3 -1 roll R
 447 |   Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def
 448 | /MCshow { currentpoint stroke M
 449 |   exch dup MFwidth -2 div 3 -1 roll R
 450 |   Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def
 451 | /XYsave    { [( ) 1 2 true false 3 ()] } bind def
 452 | /XYrestore { [( ) 1 2 true false 4 ()] } bind def
 453 | Level1 SuppressPDFMark or 
 454 | {} {
 455 | /SDict 10 dict def
 456 | systemdict /pdfmark known not {
 457 |   userdict /pdfmark systemdict /cleartomark get put
 458 | } if
 459 | SDict begin [
 460 |   /Title (naive-prover-8.ps)
 461 |   /Subject (gnuplot plot)
 462 |   /Creator (gnuplot 4.6 patchlevel 4)
 463 |   /Author (vagrant)
 464 | %  /Producer (gnuplot)
 465 | %  /Keywords ()
 466 |   /CreationDate (Wed Aug 17 09:40:33 2016)
 467 |   /DOCINFO pdfmark
 468 | end
 469 | } ifelse
 470 | end
 471 | %%EndProlog
 472 | %%Page: 1 1
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 775 | LC2 setrgbcolor
 776 | 4797 3439 M
 777 | 160 185 V
 778 | stroke
 779 | LT2
 780 | LC2 setrgbcolor
 781 | 3045 2859 M
 782 | 160 202 V
 783 | stroke
 784 | LT2
 785 | LC2 setrgbcolor
 786 | 2168 2693 M
 787 | 161 78 V
 788 | stroke
 789 | LT0
 790 | LC0 setrgbcolor
 791 | 2008 2264 M
 792 | 160 163 V
 793 | stroke
 794 | LT0
 795 | LC0 setrgbcolor
 796 | 2884 2547 M
 797 | 161 183 V
 798 | stroke
 799 | LT0
 800 | LC0 setrgbcolor
 801 | 3760 2861 M
 802 | 160 187 V
 803 | stroke
 804 | LT0
 805 | LC0 setrgbcolor
 806 | 4636 3176 M
 807 | 161 185 V
 808 | stroke
 809 | LT0
 810 | LC0 setrgbcolor
 811 | 5513 3488 M
 812 | 160 188 V
 813 | stroke
 814 | LT2
 815 | LC2 setrgbcolor
 816 | 1292 2429 M
 817 | 160 101 V
 818 | stroke
 819 | LT0
 820 | LC0 setrgbcolor
 821 | 1131 2070 M
 822 | 161 103 V
 823 | stroke
 824 | LT2
 825 | LC2 setrgbcolor
 826 | 3760 2983 M
 827 | 160 150 V
 828 | stroke
 829 | LT2
 830 | LC2 setrgbcolor
 831 | 4636 3255 M
 832 | 161 184 V
 833 | stroke
 834 | LT2
 835 | LC2 setrgbcolor
 836 | 5513 3566 M
 837 | 160 186 V
 838 | stroke
 839 | LT2
 840 | LC2 setrgbcolor
 841 | 2884 2710 M
 842 | 161 149 V
 843 | stroke
 844 | LT0
 845 | LC0 setrgbcolor
 846 | 2724 2379 M
 847 | 160 168 V
 848 | stroke
 849 | LT0
 850 | LC0 setrgbcolor
 851 | 3600 2679 M
 852 | 160 182 V
 853 | stroke
 854 | LT0
 855 | LC0 setrgbcolor
 856 | 1847 2109 M
 857 | 161 155 V
 858 | stroke
 859 | LT0
 860 | LC0 setrgbcolor
 861 | 4476 2992 M
 862 | 160 184 V
 863 | stroke
 864 | LT0
 865 | LC0 setrgbcolor
 866 | 5353 3303 M
 867 | 160 185 V
 868 | stroke
 869 | LT2
 870 | LC2 setrgbcolor
 871 | 2008 2494 M
 872 | 160 199 V
 873 | stroke
 874 | LT2
 875 | LC2 setrgbcolor
 876 | 4476 3073 M
 877 | 160 182 V
 878 | stroke
 879 | LT2
 880 | LC2 setrgbcolor
 881 | 5353 3380 M
 882 | 160 186 V
 883 | stroke
 884 | LT2
 885 | LC2 setrgbcolor
 886 | 1131 2319 M
 887 | 161 110 V
 888 | stroke
 889 | LT2
 890 | LC2 setrgbcolor
 891 | 3600 2877 M
 892 | 160 106 V
 893 | stroke
 894 | LT2
 895 | LC2 setrgbcolor
 896 | 2724 2555 M
 897 | 160 155 V
 898 | stroke
 899 | LT0
 900 | LC0 setrgbcolor
 901 | 3440 2496 M
 902 | 160 183 V
 903 | stroke
 904 | LT0
 905 | LC0 setrgbcolor
 906 | 2564 2205 M
 907 | 160 174 V
 908 | stroke
 909 | LT0
 910 | LC0 setrgbcolor
 911 | 4316 2805 M
 912 | 160 187 V
 913 | stroke
 914 | LT0
 915 | LC0 setrgbcolor
 916 | 5192 3118 M
 917 | 161 185 V
 918 | stroke
 919 | LT0
 920 | LC0 setrgbcolor
 921 | 1687 2003 M
 922 | 160 106 V
 923 | stroke
 924 | LT0
 925 | LC0 setrgbcolor
 926 | 6069 3434 M
 927 | 160 186 V
 928 | stroke
 929 | LT2
 930 | LC2 setrgbcolor
 931 | 1847 2355 M
 932 | 161 139 V
 933 | stroke
 934 | LT2
 935 | LC2 setrgbcolor
 936 | 4316 2906 M
 937 | 160 167 V
 938 | stroke
 939 | LT2
 940 | LC2 setrgbcolor
 941 | 5192 3199 M
 942 | 161 181 V
 943 | stroke
 944 | LT2
 945 | LC2 setrgbcolor
 946 | 6069 3511 M
 947 | 160 186 V
 948 | stroke
 949 | LT0
 950 | LC0 setrgbcolor
 951 | 3280 2328 M
 952 | 160 168 V
 953 | stroke
 954 | LT2
 955 | LC2 setrgbcolor
 956 | 2564 2417 M
 957 | 160 138 V
 958 | stroke
 959 | LT0
 960 | LC0 setrgbcolor
 961 | 4155 2620 M
 962 | 161 185 V
 963 | stroke
 964 | LT0
 965 | LC0 setrgbcolor
 966 | 2403 2044 M
 967 | 161 161 V
 968 | stroke
 969 | LT0
 970 | LC0 setrgbcolor
 971 | 5032 2934 M
 972 | 160 184 V
 973 | stroke
 974 | LT2
 975 | LC2 setrgbcolor
 976 | 3440 2681 M
 977 | 160 196 V
 978 | stroke
 979 | LT0
 980 | LC0 setrgbcolor
 981 | 5908 3250 M
 982 | 161 184 V
 983 | stroke
 984 | LT2
 985 | LC2 setrgbcolor
 986 | 5032 3018 M
 987 | 160 181 V
 988 | stroke
 989 | LT2
 990 | LC2 setrgbcolor
 991 | 1687 2545 M
 992 | 160 -190 V
 993 | stroke
 994 | LT2
 995 | LC2 setrgbcolor
 996 | 4155 2725 M
 997 | 161 181 V
 998 | stroke
 999 | LT2
1000 | LC2 setrgbcolor
1001 | 5908 3324 M
1002 | 161 187 V
1003 | stroke
1004 | LT0
1005 | LC0 setrgbcolor
1006 | 3995 2437 M
1007 | 160 183 V
1008 | stroke
1009 | LT2
1010 | LC2 setrgbcolor
1011 | 3280 2486 M
1012 | 160 195 V
1013 | stroke
1014 | LT0
1015 | LC0 setrgbcolor
1016 | 3119 2160 M
1017 | 161 168 V
1018 | stroke
1019 | LT0
1020 | LC0 setrgbcolor
1021 | 4871 2748 M
1022 | 161 186 V
1023 | stroke
1024 | LT0
1025 | LC0 setrgbcolor
1026 | 5748 3064 M
1027 | 160 186 V
1028 | stroke
1029 | LT0
1030 | LC0 setrgbcolor
1031 | 2243 1927 M
1032 | 160 117 V
1033 | stroke
1034 | LT2
1035 | LC2 setrgbcolor
1036 | 2403 2550 M
1037 | 161 -133 V
1038 | stroke
1039 | LT2
1040 | LC2 setrgbcolor
1041 | 4871 2839 M
1042 | 161 179 V
1043 | stroke
1044 | LT2
1045 | LC2 setrgbcolor
1046 | 5748 3143 M
1047 | 160 181 V
1048 | stroke
1049 | LT2
1050 | LC2 setrgbcolor
1051 | 3995 2662 M
1052 | 160 63 V
1053 | stroke
1054 | LT2
1055 | LC2 setrgbcolor
1056 | 3119 2343 M
1057 | 161 143 V
1058 | stroke
1059 | LT0
1060 | LC0 setrgbcolor
1061 | 3834 2262 M
1062 | 161 175 V
1063 | stroke
1064 | LT0
1065 | LC0 setrgbcolor
1066 | 4711 2565 M
1067 | 160 183 V
1068 | stroke
1069 | LT0
1070 | LC0 setrgbcolor
1071 | 5587 2877 M
1072 | 161 187 V
1073 | stroke
1074 | LT0
1075 | LC0 setrgbcolor
1076 | 2959 1988 M
1077 | 160 172 V
1078 | stroke
1079 | LT2
1080 | LC2 setrgbcolor
1081 | 4711 2700 M
1082 | 160 139 V
1083 | stroke
1084 | LT2
1085 | LC2 setrgbcolor
1086 | 5587 2962 M
1087 | 161 181 V
1088 | stroke
1089 | LT0
1090 | LC0 setrgbcolor
1091 | 3674 2091 M
1092 | 160 171 V
1093 | stroke
1094 | LT0
1095 | LC0 setrgbcolor
1096 | 4550 2383 M
1097 | 161 182 V
1098 | stroke
1099 | LT0
1100 | LC0 setrgbcolor
1101 | 5427 2693 M
1102 | 160 184 V
1103 | stroke
1104 | LT2
1105 | LC2 setrgbcolor
1106 | 2959 2269 M
1107 | 160 74 V
1108 | stroke
1109 | LT0
1110 | LC0 setrgbcolor
1111 | 2798 1860 M
1112 | 161 128 V
1113 | stroke
1114 | LT2
1115 | LC2 setrgbcolor
1116 | 3834 2422 M
1117 | 161 240 V
1118 | stroke
1119 | LT2
1120 | LC2 setrgbcolor
1121 | 5427 2788 M
1122 | 160 174 V
1123 | stroke
1124 | LT2
1125 | LC2 setrgbcolor
1126 | 4550 2573 M
1127 | 161 127 V
1128 | stroke
1129 | LT2
1130 | LC2 setrgbcolor
1131 | 3674 2274 M
1132 | 160 148 V
1133 | stroke
1134 | LT0
1135 | LC0 setrgbcolor
1136 | 4390 2210 M
1137 | 160 173 V
1138 | stroke
1139 | LT2
1140 | LC2 setrgbcolor
1141 | 2243 2520 M
1142 | 160 30 V
1143 | stroke
1144 | LT0
1145 | LC0 setrgbcolor
1146 | 5267 2510 M
1147 | 160 183 V
1148 | stroke
1149 | LT0
1150 | LC0 setrgbcolor
1151 | 3515 1929 M
1152 | 159 162 V
1153 | stroke
1154 | LT2
1155 | LC2 setrgbcolor
1156 | 5267 2609 M
1157 | 160 179 V
1158 | stroke
1159 | LT2
1160 | LC2 setrgbcolor
1161 | 2798 2370 M
1162 | 161 -101 V
1163 | stroke
1164 | LT0
1165 | LC0 setrgbcolor
1166 | 5106 2327 M
1167 | 161 183 V
1168 | stroke
1169 | LT0
1170 | LC0 setrgbcolor
1171 | 4230 2040 M
1172 | 160 170 V
1173 | stroke
1174 | LT2
1175 | LC2 setrgbcolor
1176 | 4390 2378 M
1177 | 160 195 V
1178 | stroke
1179 | LT2
1180 | LC2 setrgbcolor
1181 | 3515 2136 M
1182 | 159 138 V
1183 | stroke
1184 | LT0
1185 | LC0 setrgbcolor
1186 | 3354 1797 M
1187 | 161 132 V
1188 | stroke
1189 | LT2
1190 | LC2 setrgbcolor
1191 | 5106 2486 M
1192 | 161 123 V
1193 | stroke
1194 | LT2
1195 | LC2 setrgbcolor
1196 | 4230 2211 M
1197 | 160 167 V
1198 | stroke
1199 | LT0
1200 | LC0 setrgbcolor
1201 | 4946 2151 M
1202 | 160 176 V
1203 | stroke
1204 | LT0
1205 | LC0 setrgbcolor
1206 | 4069 1887 M
1207 | 161 153 V
1208 | stroke
1209 | LT2
1210 | LC2 setrgbcolor
1211 | 3354 2264 M
1212 | 161 -128 V
1213 | stroke
1214 | LT2
1215 | LC2 setrgbcolor
1216 | 4946 2292 M
1217 | 160 194 V
1218 | stroke
1219 | LT0
1220 | LC0 setrgbcolor
1221 | 4785 1986 M
1222 | 161 165 V
1223 | stroke
1224 | LT2
1225 | LC2 setrgbcolor
1226 | 4069 2072 M
1227 | 161 139 V
1228 | stroke
1229 | LT0
1230 | LC0 setrgbcolor
1231 | 3909 1735 M
1232 | 160 152 V
1233 | stroke
1234 | LT2
1235 | LC2 setrgbcolor
1236 | 4785 2263 M
1237 | 161 29 V
1238 | stroke
1239 | LT0
1240 | LC0 setrgbcolor
1241 | 4625 1824 M
1242 | 160 162 V
1243 | stroke
1244 | LT2
1245 | LC2 setrgbcolor
1246 | 3909 2164 M
1247 | 160 -92 V
1248 | stroke
1249 | LT0
1250 | LC0 setrgbcolor
1251 | 4465 1698 M
1252 | 160 126 V
1253 | stroke
1254 | LT2
1255 | LC2 setrgbcolor
1256 | 4625 2009 M
1257 | 160 254 V
1258 | stroke
1259 | LT2
1260 | LC2 setrgbcolor
1261 | 4465 2077 M
1262 | 160 -68 V
1263 | % End plot #1
1264 | % Begin plot #2
1265 | stroke
1266 | LCb setrgbcolor
1267 | 5662 4416 M
1268 | [ [(Helvetica) 140.0 0.0 true true 0 (naive \(8-thread\))]
1269 | ] -46.7 MRshow
1270 | 1.000 UL
1271 | LT0
1272 | LC0 setrgbcolor
1273 | 5746 4416 M
1274 | 399 0 V
1275 | % End plot #2
1276 | % Begin plot #3
1277 | stroke
1278 | LCb setrgbcolor
1279 | 5662 4276 M
1280 | [ [(Helvetica) 140.0 0.0 true true 0 (prover \(8-thread\))]
1281 | ] -46.7 MRshow
1282 | 1.000 UL
1283 | LT2
1284 | LC2 setrgbcolor
1285 | 5746 4276 M
1286 | 399 0 V
1287 | % End plot #3
1288 | stroke
1289 | LTb
1290 | LCb setrgbcolor
1291 | 6229 1674 M
1292 | 4304 601 L
1293 | stroke
1294 | LTb
1295 | LCb setrgbcolor
1296 | 971 1221 M
1297 | 4304 601 L
1298 | stroke
1299 | LTb
1300 | LCb setrgbcolor
1301 | 971 1221 M
1302 | 2896 2294 L
1303 | stroke
1304 | LTb
1305 | LCb setrgbcolor
1306 | 6229 1674 M
1307 | 2896 2294 L
1308 | stroke
1309 | LTb
1310 | LCb setrgbcolor
1311 | 971 1221 M
1312 | 0 2145 V
1313 | stroke
1314 | LTa
1315 | LCa setrgbcolor
1316 | 971 1221 M
1317 | 2896 2294 L
1318 | stroke
1319 | LTb
1320 | LCb setrgbcolor
1321 | 971 1221 M
1322 | 49 27 V
1323 | stroke
1324 | LTb
1325 | LCb setrgbcolor
1326 | 906 1105 M
1327 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1328 | [(Helvetica) 112.0 70.0 true true 0 (1)]
1329 | ] -60.7 MCshow
1330 | 1.000 UL
1331 | LTb
1332 | LCb setrgbcolor
1333 | 1.000 UL
1334 | LTb
1335 | LCb setrgbcolor
1336 | 2896 2294 M
1337 | -49 -28 V
1338 | stroke
1339 | LTa
1340 | LCa setrgbcolor
1341 | 1527 1117 M
1342 | 3452 2190 L
1343 | stroke
1344 | LTb
1345 | LCb setrgbcolor
1346 | 1527 1117 M
1347 | 49 28 V
1348 | stroke
1349 | LTb
1350 | LCb setrgbcolor
1351 | 1461 1002 M
1352 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1353 | [(Helvetica) 112.0 70.0 true true 0 (2)]
1354 | ] -60.7 MCshow
1355 | 1.000 UL
1356 | LTb
1357 | LCb setrgbcolor
1358 | 1.000 UL
1359 | LTb
1360 | LCb setrgbcolor
1361 | 3452 2190 M
1362 | -49 -27 V
1363 | stroke
1364 | LTa
1365 | LCa setrgbcolor
1366 | 2082 1014 M
1367 | 4006 2087 L
1368 | stroke
1369 | LTb
1370 | LCb setrgbcolor
1371 | 2082 1014 M
1372 | 49 28 V
1373 | stroke
1374 | LTb
1375 | LCb setrgbcolor
1376 | 2017 899 M
1377 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1378 | [(Helvetica) 112.0 70.0 true true 0 (3)]
1379 | ] -60.7 MCshow
1380 | 1.000 UL
1381 | LTb
1382 | LCb setrgbcolor
1383 | 1.000 UL
1384 | LTb
1385 | LCb setrgbcolor
1386 | 4006 2087 M
1387 | -49 -27 V
1388 | stroke
1389 | LTa
1390 | LCa setrgbcolor
1391 | 2638 911 M
1392 | 4562 1984 L
1393 | stroke
1394 | LTb
1395 | LCb setrgbcolor
1396 | 2638 911 M
1397 | 49 27 V
1398 | stroke
1399 | LTb
1400 | LCb setrgbcolor
1401 | 2573 795 M
1402 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1403 | [(Helvetica) 112.0 70.0 true true 0 (4)]
1404 | ] -60.7 MCshow
1405 | 1.000 UL
1406 | LTb
1407 | LCb setrgbcolor
1408 | 1.000 UL
1409 | LTb
1410 | LCb setrgbcolor
1411 | 4562 1984 M
1412 | -49 -27 V
1413 | stroke
1414 | LTa
1415 | LCa setrgbcolor
1416 | 3194 808 M
1417 | 5118 1881 L
1418 | stroke
1419 | LTb
1420 | LCb setrgbcolor
1421 | 3194 808 M
1422 | 49 27 V
1423 | stroke
1424 | LTb
1425 | LCb setrgbcolor
1426 | 3128 692 M
1427 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1428 | [(Helvetica) 112.0 70.0 true true 0 (5)]
1429 | ] -60.7 MCshow
1430 | 1.000 UL
1431 | LTb
1432 | LCb setrgbcolor
1433 | 1.000 UL
1434 | LTb
1435 | LCb setrgbcolor
1436 | 5118 1881 M
1437 | -49 -28 V
1438 | stroke
1439 | LTa
1440 | LCa setrgbcolor
1441 | 3748 704 M
1442 | 5673 1777 L
1443 | stroke
1444 | LTb
1445 | LCb setrgbcolor
1446 | 3748 704 M
1447 | 49 28 V
1448 | stroke
1449 | LTb
1450 | LCb setrgbcolor
1451 | 3683 589 M
1452 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1453 | [(Helvetica) 112.0 70.0 true true 0 (6)]
1454 | ] -60.7 MCshow
1455 | 1.000 UL
1456 | LTb
1457 | LCb setrgbcolor
1458 | 1.000 UL
1459 | LTb
1460 | LCb setrgbcolor
1461 | 5673 1777 M
1462 | -49 -27 V
1463 | stroke
1464 | LTa
1465 | LCa setrgbcolor
1466 | 4304 601 M
1467 | 6229 1674 L
1468 | stroke
1469 | LTb
1470 | LCb setrgbcolor
1471 | 4304 601 M
1472 | 49 28 V
1473 | stroke
1474 | LTb
1475 | LCb setrgbcolor
1476 | 4239 486 M
1477 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1478 | [(Helvetica) 112.0 70.0 true true 0 (7)]
1479 | ] -60.7 MCshow
1480 | 1.000 UL
1481 | LTb
1482 | LCb setrgbcolor
1483 | 1.000 UL
1484 | LTb
1485 | LCb setrgbcolor
1486 | 6229 1674 M
1487 | -49 -27 V
1488 | stroke
1489 | LCb setrgbcolor
1490 | 2157 643 M
1491 | [ [(Helvetica) 140.0 0.0 true true 0 (Batch Size)]
1492 | ] -46.7 MCshow
1493 | LTb
1494 | 1.000 UL
1495 | LTa
1496 | LCa setrgbcolor
1497 | 4304 601 M
1498 | 971 1221 L
1499 | stroke
1500 | LTb
1501 | LCb setrgbcolor
1502 | 4304 601 M
1503 | -54 10 V
1504 | stroke
1505 | 4377 524 M
1506 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1507 | [(Helvetica) 112.0 70.0 true true 0 (0)]
1508 | ] -60.7 MCshow
1509 | 1.000 UL
1510 | LTb
1511 | LCb setrgbcolor
1512 | 1.000 UL
1513 | LTb
1514 | LCb setrgbcolor
1515 | 971 1221 M
1516 | 54 -10 V
1517 | stroke
1518 | LTb
1519 | LCb setrgbcolor
1520 | 4465 691 M
1521 | -28 5 V
1522 | stroke
1523 | LTb
1524 | LCb setrgbcolor
1525 | 1131 1310 M
1526 | 28 -5 V
1527 | stroke
1528 | LTa
1529 | LCa setrgbcolor
1530 | 4625 780 M
1531 | 1292 1400 L
1532 | stroke
1533 | LTb
1534 | LCb setrgbcolor
1535 | 4625 780 M
1536 | -55 10 V
1537 | stroke
1538 | 4698 703 M
1539 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1540 | [(Helvetica) 112.0 70.0 true true 0 (2)]
1541 | ] -60.7 MCshow
1542 | 1.000 UL
1543 | LTb
1544 | LCb setrgbcolor
1545 | 1.000 UL
1546 | LTb
1547 | LCb setrgbcolor
1548 | 1292 1400 M
1549 | 54 -11 V
1550 | stroke
1551 | LTb
1552 | LCb setrgbcolor
1553 | 4785 869 M
1554 | -27 6 V
1555 | stroke
1556 | LTb
1557 | LCb setrgbcolor
1558 | 1452 1489 M
1559 | 27 -5 V
1560 | stroke
1561 | LTa
1562 | LCa setrgbcolor
1563 | 4946 959 M
1564 | 1613 1578 L
1565 | stroke
1566 | LTb
1567 | LCb setrgbcolor
1568 | 4946 959 M
1569 | -55 10 V
1570 | stroke
1571 | 5019 881 M
1572 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1573 | [(Helvetica) 112.0 70.0 true true 0 (4)]
1574 | ] -60.7 MCshow
1575 | 1.000 UL
1576 | LTb
1577 | LCb setrgbcolor
1578 | 1.000 UL
1579 | LTb
1580 | LCb setrgbcolor
1581 | 1613 1578 M
1582 | 54 -10 V
1583 | stroke
1584 | LTb
1585 | LCb setrgbcolor
1586 | 5106 1048 M
1587 | -27 5 V
1588 | stroke
1589 | LTb
1590 | LCb setrgbcolor
1591 | 1773 1668 M
1592 | 27 -5 V
1593 | stroke
1594 | LTa
1595 | LCa setrgbcolor
1596 | 5267 1138 M
1597 | 1933 1757 L
1598 | stroke
1599 | LTb
1600 | LCb setrgbcolor
1601 | 5267 1138 M
1602 | -55 10 V
1603 | stroke
1604 | 5339 1060 M
1605 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1606 | [(Helvetica) 112.0 70.0 true true 0 (6)]
1607 | ] -60.7 MCshow
1608 | 1.000 UL
1609 | LTb
1610 | LCb setrgbcolor
1611 | 1.000 UL
1612 | LTb
1613 | LCb setrgbcolor
1614 | 1933 1757 M
1615 | 55 -10 V
1616 | stroke
1617 | LTb
1618 | LCb setrgbcolor
1619 | 5427 1227 M
1620 | -27 5 V
1621 | stroke
1622 | LTb
1623 | LCb setrgbcolor
1624 | 2094 1847 M
1625 | 27 -5 V
1626 | stroke
1627 | LTa
1628 | LCa setrgbcolor
1629 | 5587 1317 M
1630 | 2254 1936 L
1631 | stroke
1632 | LTb
1633 | LCb setrgbcolor
1634 | 5587 1317 M
1635 | -54 10 V
1636 | stroke
1637 | 5660 1239 M
1638 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1639 | [(Helvetica) 112.0 70.0 true true 0 (8)]
1640 | ] -60.7 MCshow
1641 | 1.000 UL
1642 | LTb
1643 | LCb setrgbcolor
1644 | 1.000 UL
1645 | LTb
1646 | LCb setrgbcolor
1647 | 2254 1936 M
1648 | 55 -10 V
1649 | stroke
1650 | LTb
1651 | LCb setrgbcolor
1652 | 5748 1406 M
1653 | -27 5 V
1654 | stroke
1655 | LTb
1656 | LCb setrgbcolor
1657 | 2415 2025 M
1658 | 27 -5 V
1659 | stroke
1660 | LTa
1661 | LCa setrgbcolor
1662 | 5908 1495 M
1663 | 2575 2115 L
1664 | stroke
1665 | LTb
1666 | LCb setrgbcolor
1667 | 5908 1495 M
1668 | -54 11 V
1669 | stroke
1670 | 5981 1418 M
1671 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1672 | [(Helvetica) 112.0 70.0 true true 0 (10)]
1673 | ] -60.7 MCshow
1674 | 1.000 UL
1675 | LTb
1676 | LCb setrgbcolor
1677 | 1.000 UL
1678 | LTb
1679 | LCb setrgbcolor
1680 | 2575 2115 M
1681 | 55 -10 V
1682 | stroke
1683 | LTb
1684 | LCb setrgbcolor
1685 | 6069 1585 M
1686 | -28 5 V
1687 | stroke
1688 | LTb
1689 | LCb setrgbcolor
1690 | 2735 2204 M
1691 | 28 -5 V
1692 | stroke
1693 | LTa
1694 | LCa setrgbcolor
1695 | 6229 1674 M
1696 | 2896 2294 L
1697 | stroke
1698 | LTb
1699 | LCb setrgbcolor
1700 | 6229 1674 M
1701 | -54 10 V
1702 | stroke
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2013 | %%DocumentFonts: Helvetica
2014 | %%Pages: 1
2015 | 


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 303 |   /ColB ColB Fillden mul Fillden sub 1 add def
 304 |   ColR ColG ColB setrgbcolor} def
 305 | /BoxColFill {gsave Rec PolyFill} def
 306 | /PolyFill {gsave Density fill grestore grestore} def
 307 | /h {rlineto rlineto rlineto gsave closepath fill grestore} bind def
 308 | %
 309 | % PostScript Level 1 Pattern Fill routine for rectangles
 310 | % Usage: x y w h s a XX PatternFill
 311 | %	x,y = lower left corner of box to be filled
 312 | %	w,h = width and height of box
 313 | %	  a = angle in degrees between lines and x-axis
 314 | %	 XX = 0/1 for no/yes cross-hatch
 315 | %
 316 | /PatternFill {gsave /PFa [ 9 2 roll ] def
 317 |   PFa 0 get PFa 2 get 2 div add PFa 1 get PFa 3 get 2 div add translate
 318 |   PFa 2 get -2 div PFa 3 get -2 div PFa 2 get PFa 3 get Rec
 319 |   TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse
 320 |   clip
 321 |   currentlinewidth 0.5 mul setlinewidth
 322 |   /PFs PFa 2 get dup mul PFa 3 get dup mul add sqrt def
 323 |   0 0 M PFa 5 get rotate PFs -2 div dup translate
 324 |   0 1 PFs PFa 4 get div 1 add floor cvi
 325 | 	{PFa 4 get mul 0 M 0 PFs V} for
 326 |   0 PFa 6 get ne {
 327 | 	0 1 PFs PFa 4 get div 1 add floor cvi
 328 | 	{PFa 4 get mul 0 2 1 roll M PFs 0 V} for
 329 |  } if
 330 |   stroke grestore} def
 331 | %
 332 | /languagelevel where
 333 |  {pop languagelevel} {1} ifelse
 334 |  2 lt
 335 | 	{/InterpretLevel1 true def}
 336 | 	{/InterpretLevel1 Level1 def}
 337 |  ifelse
 338 | %
 339 | % PostScript level 2 pattern fill definitions
 340 | %
 341 | /Level2PatternFill {
 342 | /Tile8x8 {/PaintType 2 /PatternType 1 /TilingType 1 /BBox [0 0 8 8] /XStep 8 /YStep 8}
 343 | 	bind def
 344 | /KeepColor {currentrgbcolor [/Pattern /DeviceRGB] setcolorspace} bind def
 345 | << Tile8x8
 346 |  /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke} 
 347 | >> matrix makepattern
 348 | /Pat1 exch def
 349 | << Tile8x8
 350 |  /PaintProc {0.5 setlinewidth pop 0 0 M 8 8 L 0 8 M 8 0 L stroke
 351 | 	0 4 M 4 8 L 8 4 L 4 0 L 0 4 L stroke}
 352 | >> matrix makepattern
 353 | /Pat2 exch def
 354 | << Tile8x8
 355 |  /PaintProc {0.5 setlinewidth pop 0 0 M 0 8 L
 356 | 	8 8 L 8 0 L 0 0 L fill}
 357 | >> matrix makepattern
 358 | /Pat3 exch def
 359 | << Tile8x8
 360 |  /PaintProc {0.5 setlinewidth pop -4 8 M 8 -4 L
 361 | 	0 12 M 12 0 L stroke}
 362 | >> matrix makepattern
 363 | /Pat4 exch def
 364 | << Tile8x8
 365 |  /PaintProc {0.5 setlinewidth pop -4 0 M 8 12 L
 366 | 	0 -4 M 12 8 L stroke}
 367 | >> matrix makepattern
 368 | /Pat5 exch def
 369 | << Tile8x8
 370 |  /PaintProc {0.5 setlinewidth pop -2 8 M 4 -4 L
 371 | 	0 12 M 8 -4 L 4 12 M 10 0 L stroke}
 372 | >> matrix makepattern
 373 | /Pat6 exch def
 374 | << Tile8x8
 375 |  /PaintProc {0.5 setlinewidth pop -2 0 M 4 12 L
 376 | 	0 -4 M 8 12 L 4 -4 M 10 8 L stroke}
 377 | >> matrix makepattern
 378 | /Pat7 exch def
 379 | << Tile8x8
 380 |  /PaintProc {0.5 setlinewidth pop 8 -2 M -4 4 L
 381 | 	12 0 M -4 8 L 12 4 M 0 10 L stroke}
 382 | >> matrix makepattern
 383 | /Pat8 exch def
 384 | << Tile8x8
 385 |  /PaintProc {0.5 setlinewidth pop 0 -2 M 12 4 L
 386 | 	-4 0 M 12 8 L -4 4 M 8 10 L stroke}
 387 | >> matrix makepattern
 388 | /Pat9 exch def
 389 | /Pattern1 {PatternBgnd KeepColor Pat1 setpattern} bind def
 390 | /Pattern2 {PatternBgnd KeepColor Pat2 setpattern} bind def
 391 | /Pattern3 {PatternBgnd KeepColor Pat3 setpattern} bind def
 392 | /Pattern4 {PatternBgnd KeepColor Landscape {Pat5} {Pat4} ifelse setpattern} bind def
 393 | /Pattern5 {PatternBgnd KeepColor Landscape {Pat4} {Pat5} ifelse setpattern} bind def
 394 | /Pattern6 {PatternBgnd KeepColor Landscape {Pat9} {Pat6} ifelse setpattern} bind def
 395 | /Pattern7 {PatternBgnd KeepColor Landscape {Pat8} {Pat7} ifelse setpattern} bind def
 396 | } def
 397 | %
 398 | %
 399 | %End of PostScript Level 2 code
 400 | %
 401 | /PatternBgnd {
 402 |   TransparentPatterns {} {gsave 1 setgray fill grestore} ifelse
 403 | } def
 404 | %
 405 | % Substitute for Level 2 pattern fill codes with
 406 | % grayscale if Level 2 support is not selected.
 407 | %
 408 | /Level1PatternFill {
 409 | /Pattern1 {0.250 Density} bind def
 410 | /Pattern2 {0.500 Density} bind def
 411 | /Pattern3 {0.750 Density} bind def
 412 | /Pattern4 {0.125 Density} bind def
 413 | /Pattern5 {0.375 Density} bind def
 414 | /Pattern6 {0.625 Density} bind def
 415 | /Pattern7 {0.875 Density} bind def
 416 | } def
 417 | %
 418 | % Now test for support of Level 2 code
 419 | %
 420 | Level1 {Level1PatternFill} {Level2PatternFill} ifelse
 421 | %
 422 | /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont
 423 | dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall
 424 | currentdict end definefont pop
 425 | /MFshow {
 426 |    { dup 5 get 3 ge
 427 |      { 5 get 3 eq {gsave} {grestore} ifelse }
 428 |      {dup dup 0 get findfont exch 1 get scalefont setfont
 429 |      [ currentpoint ] exch dup 2 get 0 exch R dup 5 get 2 ne {dup dup 6
 430 |      get exch 4 get {Gshow} {stringwidth pop 0 R} ifelse }if dup 5 get 0 eq
 431 |      {dup 3 get {2 get neg 0 exch R pop} {pop aload pop M} ifelse} {dup 5
 432 |      get 1 eq {dup 2 get exch dup 3 get exch 6 get stringwidth pop -2 div
 433 |      dup 0 R} {dup 6 get stringwidth pop -2 div 0 R 6 get
 434 |      show 2 index {aload pop M neg 3 -1 roll neg R pop pop} {pop pop pop
 435 |      pop aload pop M} ifelse }ifelse }ifelse }
 436 |      ifelse }
 437 |    forall} def
 438 | /Gswidth {dup type /stringtype eq {stringwidth} {pop (n) stringwidth} ifelse} def
 439 | /MFwidth {0 exch { dup 5 get 3 ge { 5 get 3 eq { 0 } { pop } ifelse }
 440 |  {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont
 441 |      6 get Gswidth pop add} {pop} ifelse} ifelse} forall} def
 442 | /MLshow { currentpoint stroke M
 443 |   0 exch R
 444 |   Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def
 445 | /MRshow { currentpoint stroke M
 446 |   exch dup MFwidth neg 3 -1 roll R
 447 |   Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def
 448 | /MCshow { currentpoint stroke M
 449 |   exch dup MFwidth -2 div 3 -1 roll R
 450 |   Blacktext {gsave 0 setgray MFshow grestore} {MFshow} ifelse } bind def
 451 | /XYsave    { [( ) 1 2 true false 3 ()] } bind def
 452 | /XYrestore { [( ) 1 2 true false 4 ()] } bind def
 453 | Level1 SuppressPDFMark or 
 454 | {} {
 455 | /SDict 10 dict def
 456 | systemdict /pdfmark known not {
 457 |   userdict /pdfmark systemdict /cleartomark get put
 458 | } if
 459 | SDict begin [
 460 |   /Title (naive-prover-2.ps)
 461 |   /Subject (gnuplot plot)
 462 |   /Creator (gnuplot 4.6 patchlevel 4)
 463 |   /Author (vagrant)
 464 | %  /Producer (gnuplot)
 465 | %  /Keywords ()
 466 |   /CreationDate (Wed Aug 17 09:40:33 2016)
 467 |   /DOCINFO pdfmark
 468 | end
 469 | } ifelse
 470 | end
 471 | %%EndProlog
 472 | %%Page: 1 1
 473 | gnudict begin
 474 | gsave
 475 | doclip
 476 | 50 50 translate
 477 | 0.100 0.100 scale
 478 | 90 rotate
 479 | 0 -5040 translate
 480 | 0 setgray
 481 | newpath
 482 | (Helvetica) findfont 140 scalefont setfont
 483 | BackgroundColor 0 lt 3 1 roll 0 lt exch 0 lt or or not {gsave BackgroundColor C clippath fill grestore} if
 484 | 1.000 UL
 485 | LTb
 486 | LCb setrgbcolor
 487 | LTb
 488 | 3600 4773 M
 489 | [ [(Helvetica) 140.0 0.0 true true 0 (Runtime)]
 490 | ] -46.7 MCshow
 491 | 1.000 UP
 492 | % Begin plot #1
 493 | 1.000 UL
 494 | LT0
 495 | LC0 setrgbcolor
 496 | 2735 3755 M
 497 | 161 184 V
 498 | stroke
 499 | LT2
 500 | LC2 setrgbcolor
 501 | 2735 3853 M
 502 | 161 183 V
 503 | stroke
 504 | LT0
 505 | LC0 setrgbcolor
 506 | 2575 3569 M
 507 | 160 186 V
 508 | stroke
 509 | LT2
 510 | LC2 setrgbcolor
 511 | 2575 3669 M
 512 | 160 184 V
 513 | stroke
 514 | LT0
 515 | LC0 setrgbcolor
 516 | 2415 3386 M
 517 | 160 183 V
 518 | stroke
 519 | LT0
 520 | LC0 setrgbcolor
 521 | 3291 3697 M
 522 | 161 184 V
 523 | stroke
 524 | LT2
 525 | LC2 setrgbcolor
 526 | 2415 3490 M
 527 | 160 179 V
 528 | stroke
 529 | LT2
 530 | LC2 setrgbcolor
 531 | 3291 3791 M
 532 | 161 184 V
 533 | stroke
 534 | LT0
 535 | LC0 setrgbcolor
 536 | 2254 3198 M
 537 | 161 188 V
 538 | stroke
 539 | LT0
 540 | LC0 setrgbcolor
 541 | 3131 3513 M
 542 | 160 184 V
 543 | stroke
 544 | LT2
 545 | LC2 setrgbcolor
 546 | 3131 3607 M
 547 | 160 184 V
 548 | stroke
 549 | LT2
 550 | LC2 setrgbcolor
 551 | 2254 3312 M
 552 | 161 178 V
 553 | stroke
 554 | LT0
 555 | LC0 setrgbcolor
 556 | 2094 3012 M
 557 | 160 186 V
 558 | stroke
 559 | LT0
 560 | LC0 setrgbcolor
 561 | 2970 3333 M
 562 | 161 180 V
 563 | stroke
 564 | LT0
 565 | LC0 setrgbcolor
 566 | 3846 3641 M
 567 | 160 187 V
 568 | stroke
 569 | LT2
 570 | LC2 setrgbcolor
 571 | 2970 3426 M
 572 | 161 181 V
 573 | stroke
 574 | LT2
 575 | LC2 setrgbcolor
 576 | 2094 3138 M
 577 | 160 174 V
 578 | stroke
 579 | LT2
 580 | LC2 setrgbcolor
 581 | 3846 3734 M
 582 | 160 184 V
 583 | stroke
 584 | LT0
 585 | LC0 setrgbcolor
 586 | 1933 2824 M
 587 | 161 188 V
 588 | stroke
 589 | LT0
 590 | LC0 setrgbcolor
 591 | 2810 3142 M
 592 | 160 191 V
 593 | stroke
 594 | LT0
 595 | LC0 setrgbcolor
 596 | 3685 3455 M
 597 | 161 186 V
 598 | stroke
 599 | LT2
 600 | LC2 setrgbcolor
 601 | 2810 3249 M
 602 | 160 177 V
 603 | stroke
 604 | LT2
 605 | LC2 setrgbcolor
 606 | 3685 3548 M
 607 | 161 186 V
 608 | stroke
 609 | LT2
 610 | LC2 setrgbcolor
 611 | 1933 2978 M
 612 | 161 160 V
 613 | stroke
 614 | LT0
 615 | LC0 setrgbcolor
 616 | 1773 2641 M
 617 | 160 183 V
 618 | stroke
 619 | LT0
 620 | LC0 setrgbcolor
 621 | 2650 2956 M
 622 | 160 186 V
 623 | stroke
 624 | LT0
 625 | LC0 setrgbcolor
 626 | 3526 3274 M
 627 | 159 181 V
 628 | stroke
 629 | LT0
 630 | LC0 setrgbcolor
 631 | 4402 3588 M
 632 | 160 182 V
 633 | stroke
 634 | LT2
 635 | LC2 setrgbcolor
 636 | 3526 3365 M
 637 | 159 183 V
 638 | stroke
 639 | LT2
 640 | LC2 setrgbcolor
 641 | 2650 3071 M
 642 | 160 178 V
 643 | stroke
 644 | LT2
 645 | LC2 setrgbcolor
 646 | 4402 3678 M
 647 | 160 184 V
 648 | stroke
 649 | LT2
 650 | LC2 setrgbcolor
 651 | 1773 2822 M
 652 | 160 156 V
 653 | stroke
 654 | LT0
 655 | LC0 setrgbcolor
 656 | 1613 2470 M
 657 | 160 171 V
 658 | stroke
 659 | LT0
 660 | LC0 setrgbcolor
 661 | 2489 2769 M
 662 | 161 187 V
 663 | stroke
 664 | LT0
 665 | LC0 setrgbcolor
 666 | 3366 3086 M
 667 | 160 188 V
 668 | stroke
 669 | LT0
 670 | LC0 setrgbcolor
 671 | 4241 3401 M
 672 | 161 187 V
 673 | stroke
 674 | LT2
 675 | LC2 setrgbcolor
 676 | 3366 3187 M
 677 | 160 178 V
 678 | stroke
 679 | LT2
 680 | LC2 setrgbcolor
 681 | 2489 2904 M
 682 | 161 167 V
 683 | stroke
 684 | LT2
 685 | LC2 setrgbcolor
 686 | 4241 3492 M
 687 | 161 186 V
 688 | stroke
 689 | LT2
 690 | LC2 setrgbcolor
 691 | 1613 2679 M
 692 | 160 143 V
 693 | stroke
 694 | LT0
 695 | LC0 setrgbcolor
 696 | 2329 2598 M
 697 | 160 171 V
 698 | stroke
 699 | LT0
 700 | LC0 setrgbcolor
 701 | 1452 2314 M
 702 | 161 156 V
 703 | stroke
 704 | LT0
 705 | LC0 setrgbcolor
 706 | 3205 2898 M
 707 | 161 188 V
 708 | stroke
 709 | LT0
 710 | LC0 setrgbcolor
 711 | 4081 3217 M
 712 | 160 184 V
 713 | stroke
 714 | LT0
 715 | LC0 setrgbcolor
 716 | 4957 3530 M
 717 | 161 186 V
 718 | stroke
 719 | LT2
 720 | LC2 setrgbcolor
 721 | 3205 3009 M
 722 | 161 178 V
 723 | stroke
 724 | LT2
 725 | LC2 setrgbcolor
 726 | 4081 3308 M
 727 | 160 184 V
 728 | stroke
 729 | LT2
 730 | LC2 setrgbcolor
 731 | 4957 3623 M
 732 | 161 184 V
 733 | stroke
 734 | LT2
 735 | LC2 setrgbcolor
 736 | 2329 2744 M
 737 | 160 160 V
 738 | stroke
 739 | LT0
 740 | LC0 setrgbcolor
 741 | 3045 2715 M
 742 | 160 183 V
 743 | stroke
 744 | LT0
 745 | LC0 setrgbcolor
 746 | 2168 2412 M
 747 | 161 186 V
 748 | stroke
 749 | LT0
 750 | LC0 setrgbcolor
 751 | 3920 3031 M
 752 | 161 186 V
 753 | stroke
 754 | LT0
 755 | LC0 setrgbcolor
 756 | 1292 2173 M
 757 | 160 141 V
 758 | stroke
 759 | LT0
 760 | LC0 setrgbcolor
 761 | 4797 3343 M
 762 | 160 187 V
 763 | stroke
 764 | LT2
 765 | LC2 setrgbcolor
 766 | 1452 2545 M
 767 | 161 134 V
 768 | stroke
 769 | LT2
 770 | LC2 setrgbcolor
 771 | 3920 3127 M
 772 | 161 181 V
 773 | stroke
 774 | LT2
 775 | LC2 setrgbcolor
 776 | 3045 2858 M
 777 | 160 151 V
 778 | stroke
 779 | LT2
 780 | LC2 setrgbcolor
 781 | 4797 3436 M
 782 | 160 187 V
 783 | stroke
 784 | LT2
 785 | LC2 setrgbcolor
 786 | 2168 2598 M
 787 | 161 146 V
 788 | stroke
 789 | LT0
 790 | LC0 setrgbcolor
 791 | 2008 2251 M
 792 | 160 161 V
 793 | stroke
 794 | LT0
 795 | LC0 setrgbcolor
 796 | 2884 2531 M
 797 | 161 184 V
 798 | stroke
 799 | LT0
 800 | LC0 setrgbcolor
 801 | 3760 2844 M
 802 | 160 187 V
 803 | stroke
 804 | LT0
 805 | LC0 setrgbcolor
 806 | 4636 3157 M
 807 | 161 186 V
 808 | stroke
 809 | LT0
 810 | LC0 setrgbcolor
 811 | 5513 3477 M
 812 | 160 183 V
 813 | stroke
 814 | LT0
 815 | LC0 setrgbcolor
 816 | 1131 2072 M
 817 | 161 101 V
 818 | stroke
 819 | LT2
 820 | LC2 setrgbcolor
 821 | 1292 2431 M
 822 | 160 114 V
 823 | stroke
 824 | LT2
 825 | LC2 setrgbcolor
 826 | 3760 2950 M
 827 | 160 177 V
 828 | stroke
 829 | LT2
 830 | LC2 setrgbcolor
 831 | 4636 3252 M
 832 | 161 184 V
 833 | stroke
 834 | LT2
 835 | LC2 setrgbcolor
 836 | 5513 3566 M
 837 | 160 186 V
 838 | stroke
 839 | LT2
 840 | LC2 setrgbcolor
 841 | 2884 2707 M
 842 | 161 151 V
 843 | stroke
 844 | LT0
 845 | LC0 setrgbcolor
 846 | 2724 2367 M
 847 | 160 164 V
 848 | stroke
 849 | LT0
 850 | LC0 setrgbcolor
 851 | 3600 2664 M
 852 | 160 180 V
 853 | stroke
 854 | LT2
 855 | LC2 setrgbcolor
 856 | 2008 2461 M
 857 | 160 137 V
 858 | stroke
 859 | LT0
 860 | LC0 setrgbcolor
 861 | 1847 2110 M
 862 | 161 141 V
 863 | stroke
 864 | LT0
 865 | LC0 setrgbcolor
 866 | 4476 2975 M
 867 | 160 182 V
 868 | stroke
 869 | LT0
 870 | LC0 setrgbcolor
 871 | 5353 3289 M
 872 | 160 188 V
 873 | stroke
 874 | LT2
 875 | LC2 setrgbcolor
 876 | 4476 3069 M
 877 | 160 183 V
 878 | stroke
 879 | LT2
 880 | LC2 setrgbcolor
 881 | 3600 2777 M
 882 | 160 173 V
 883 | stroke
 884 | LT2
 885 | LC2 setrgbcolor
 886 | 5353 3380 M
 887 | 160 186 V
 888 | stroke
 889 | LT2
 890 | LC2 setrgbcolor
 891 | 1131 2387 M
 892 | 161 44 V
 893 | stroke
 894 | LT2
 895 | LC2 setrgbcolor
 896 | 2724 2555 M
 897 | 160 152 V
 898 | stroke
 899 | LT0
 900 | LC0 setrgbcolor
 901 | 3440 2482 M
 902 | 160 182 V
 903 | stroke
 904 | LT0
 905 | LC0 setrgbcolor
 906 | 2564 2194 M
 907 | 160 173 V
 908 | stroke
 909 | LT0
 910 | LC0 setrgbcolor
 911 | 4316 2786 M
 912 | 160 189 V
 913 | stroke
 914 | LT0
 915 | LC0 setrgbcolor
 916 | 5192 3104 M
 917 | 161 185 V
 918 | stroke
 919 | LT0
 920 | LC0 setrgbcolor
 921 | 6069 3418 M
 922 | 160 186 V
 923 | stroke
 924 | LT2
 925 | LC2 setrgbcolor
 926 | 1847 2337 M
 927 | 161 124 V
 928 | stroke
 929 | LT0
 930 | LC0 setrgbcolor
 931 | 1687 2023 M
 932 | 160 87 V
 933 | stroke
 934 | LT2
 935 | LC2 setrgbcolor
 936 | 4316 2891 M
 937 | 160 178 V
 938 | stroke
 939 | LT2
 940 | LC2 setrgbcolor
 941 | 5192 3195 M
 942 | 161 185 V
 943 | stroke
 944 | LT2
 945 | LC2 setrgbcolor
 946 | 3440 2612 M
 947 | 160 165 V
 948 | stroke
 949 | LT2
 950 | LC2 setrgbcolor
 951 | 6069 3510 M
 952 | 160 185 V
 953 | stroke
 954 | LT0
 955 | LC0 setrgbcolor
 956 | 3280 2331 M
 957 | 160 151 V
 958 | stroke
 959 | LT0
 960 | LC0 setrgbcolor
 961 | 4155 2601 M
 962 | 161 185 V
 963 | stroke
 964 | LT0
 965 | LC0 setrgbcolor
 966 | 2403 2043 M
 967 | 161 151 V
 968 | stroke
 969 | LT0
 970 | LC0 setrgbcolor
 971 | 5032 2917 M
 972 | 160 187 V
 973 | stroke
 974 | LT2
 975 | LC2 setrgbcolor
 976 | 2564 2420 M
 977 | 160 135 V
 978 | stroke
 979 | LT0
 980 | LC0 setrgbcolor
 981 | 5908 3231 M
 982 | 161 187 V
 983 | stroke
 984 | LT2
 985 | LC2 setrgbcolor
 986 | 1687 2282 M
 987 | 160 55 V
 988 | stroke
 989 | LT2
 990 | LC2 setrgbcolor
 991 | 4155 2718 M
 992 | 161 173 V
 993 | stroke
 994 | LT2
 995 | LC2 setrgbcolor
 996 | 5032 3012 M
 997 | 160 183 V
 998 | stroke
 999 | LT2
1000 | LC2 setrgbcolor
1001 | 5908 3326 M
1002 | 161 184 V
1003 | stroke
1004 | LT2
1005 | LC2 setrgbcolor
1006 | 3280 2457 M
1007 | 160 155 V
1008 | stroke
1009 | LT0
1010 | LC0 setrgbcolor
1011 | 3995 2425 M
1012 | 160 176 V
1013 | stroke
1014 | LT0
1015 | LC0 setrgbcolor
1016 | 4871 2732 M
1017 | 161 185 V
1018 | stroke
1019 | LT0
1020 | LC0 setrgbcolor
1021 | 5748 3046 M
1022 | 160 185 V
1023 | stroke
1024 | LT0
1025 | LC0 setrgbcolor
1026 | 3119 2134 M
1027 | 161 197 V
1028 | stroke
1029 | LT0
1030 | LC0 setrgbcolor
1031 | 2243 1938 M
1032 | 160 105 V
1033 | stroke
1034 | LT2
1035 | LC2 setrgbcolor
1036 | 2403 2282 M
1037 | 161 138 V
1038 | stroke
1039 | LT2
1040 | LC2 setrgbcolor
1041 | 4871 2834 M
1042 | 161 178 V
1043 | stroke
1044 | LT2
1045 | LC2 setrgbcolor
1046 | 3995 2551 M
1047 | 160 167 V
1048 | stroke
1049 | LT2
1050 | LC2 setrgbcolor
1051 | 5748 3142 M
1052 | 160 184 V
1053 | stroke
1054 | LT2
1055 | LC2 setrgbcolor
1056 | 3119 2314 M
1057 | 161 143 V
1058 | stroke
1059 | LT0
1060 | LC0 setrgbcolor
1061 | 3834 2246 M
1062 | 161 179 V
1063 | stroke
1064 | LT0
1065 | LC0 setrgbcolor
1066 | 4711 2550 M
1067 | 160 182 V
1068 | stroke
1069 | LT0
1070 | LC0 setrgbcolor
1071 | 2959 1977 M
1072 | 160 157 V
1073 | stroke
1074 | LT0
1075 | LC0 setrgbcolor
1076 | 5587 2859 M
1077 | 161 187 V
1078 | stroke
1079 | LT2
1080 | LC2 setrgbcolor
1081 | 2243 2470 M
1082 | 160 -188 V
1083 | stroke
1084 | LT2
1085 | LC2 setrgbcolor
1086 | 4711 2661 M
1087 | 160 173 V
1088 | stroke
1089 | LT2
1090 | LC2 setrgbcolor
1091 | 5587 2959 M
1092 | 161 183 V
1093 | stroke
1094 | LT2
1095 | LC2 setrgbcolor
1096 | 3834 2394 M
1097 | 161 157 V
1098 | stroke
1099 | LT0
1100 | LC0 setrgbcolor
1101 | 3674 2098 M
1102 | 160 148 V
1103 | stroke
1104 | LT0
1105 | LC0 setrgbcolor
1106 | 4550 2367 M
1107 | 161 183 V
1108 | stroke
1109 | LT0
1110 | LC0 setrgbcolor
1111 | 5427 2676 M
1112 | 160 183 V
1113 | stroke
1114 | LT2
1115 | LC2 setrgbcolor
1116 | 2959 2180 M
1117 | 160 134 V
1118 | stroke
1119 | LT0
1120 | LC0 setrgbcolor
1121 | 2798 1862 M
1122 | 161 115 V
1123 | stroke
1124 | LT2
1125 | LC2 setrgbcolor
1126 | 5427 2779 M
1127 | 160 180 V
1128 | stroke
1129 | LT2
1130 | LC2 setrgbcolor
1131 | 4550 2495 M
1132 | 161 166 V
1133 | stroke
1134 | LT2
1135 | LC2 setrgbcolor
1136 | 3674 2249 M
1137 | 160 145 V
1138 | stroke
1139 | LT0
1140 | LC0 setrgbcolor
1141 | 4390 2192 M
1142 | 160 175 V
1143 | stroke
1144 | LT0
1145 | LC0 setrgbcolor
1146 | 5267 2493 M
1147 | 160 183 V
1148 | stroke
1149 | LT0
1150 | LC0 setrgbcolor
1151 | 3515 1918 M
1152 | 159 180 V
1153 | stroke
1154 | LT2
1155 | LC2 setrgbcolor
1156 | 2798 2367 M
1157 | 161 -187 V
1158 | stroke
1159 | LT2
1160 | LC2 setrgbcolor
1161 | 5267 2606 M
1162 | 160 173 V
1163 | stroke
1164 | LT2
1165 | LC2 setrgbcolor
1166 | 4390 2338 M
1167 | 160 157 V
1168 | stroke
1169 | LT0
1170 | LC0 setrgbcolor
1171 | 5106 2308 M
1172 | 161 185 V
1173 | stroke
1174 | LT0
1175 | LC0 setrgbcolor
1176 | 4230 2026 M
1177 | 160 166 V
1178 | stroke
1179 | LT2
1180 | LC2 setrgbcolor
1181 | 3515 2112 M
1182 | 159 137 V
1183 | stroke
1184 | LT0
1185 | LC0 setrgbcolor
1186 | 3354 1792 M
1187 | 161 126 V
1188 | stroke
1189 | LT2
1190 | LC2 setrgbcolor
1191 | 5106 2459 M
1192 | 161 147 V
1193 | stroke
1194 | LT2
1195 | LC2 setrgbcolor
1196 | 4230 2190 M
1197 | 160 148 V
1198 | stroke
1199 | LT0
1200 | LC0 setrgbcolor
1201 | 4946 2133 M
1202 | 160 175 V
1203 | stroke
1204 | LT0
1205 | LC0 setrgbcolor
1206 | 4069 1860 M
1207 | 161 166 V
1208 | stroke
1209 | LT2
1210 | LC2 setrgbcolor
1211 | 3354 2265 M
1212 | 161 -153 V
1213 | stroke
1214 | LT2
1215 | LC2 setrgbcolor
1216 | 4946 2281 M
1217 | 160 178 V
1218 | stroke
1219 | LT0
1220 | LC0 setrgbcolor
1221 | 4785 1969 M
1222 | 161 164 V
1223 | stroke
1224 | LT2
1225 | LC2 setrgbcolor
1226 | 4069 2052 M
1227 | 161 138 V
1228 | stroke
1229 | LT0
1230 | LC0 setrgbcolor
1231 | 3909 1734 M
1232 | 160 126 V
1233 | stroke
1234 | LT2
1235 | LC2 setrgbcolor
1236 | 4785 2134 M
1237 | 161 147 V
1238 | stroke
1239 | LT0
1240 | LC0 setrgbcolor
1241 | 4625 1805 M
1242 | 160 164 V
1243 | stroke
1244 | LT2
1245 | LC2 setrgbcolor
1246 | 3909 2165 M
1247 | 160 -113 V
1248 | stroke
1249 | LT2
1250 | LC2 setrgbcolor
1251 | 4625 1996 M
1252 | 160 138 V
1253 | stroke
1254 | LT0
1255 | LC0 setrgbcolor
1256 | 4465 1672 M
1257 | 160 133 V
1258 | stroke
1259 | LT2
1260 | LC2 setrgbcolor
1261 | 4465 2065 M
1262 | 160 -69 V
1263 | % End plot #1
1264 | % Begin plot #2
1265 | stroke
1266 | LCb setrgbcolor
1267 | 5662 4416 M
1268 | [ [(Helvetica) 140.0 0.0 true true 0 (naive \(2-thread\))]
1269 | ] -46.7 MRshow
1270 | 1.000 UL
1271 | LT0
1272 | LC0 setrgbcolor
1273 | 5746 4416 M
1274 | 399 0 V
1275 | % End plot #2
1276 | % Begin plot #3
1277 | stroke
1278 | LCb setrgbcolor
1279 | 5662 4276 M
1280 | [ [(Helvetica) 140.0 0.0 true true 0 (prover \(2-thread\))]
1281 | ] -46.7 MRshow
1282 | 1.000 UL
1283 | LT2
1284 | LC2 setrgbcolor
1285 | 5746 4276 M
1286 | 399 0 V
1287 | % End plot #3
1288 | stroke
1289 | LTb
1290 | LCb setrgbcolor
1291 | 6229 1674 M
1292 | 4304 601 L
1293 | stroke
1294 | LTb
1295 | LCb setrgbcolor
1296 | 971 1221 M
1297 | 4304 601 L
1298 | stroke
1299 | LTb
1300 | LCb setrgbcolor
1301 | 971 1221 M
1302 | 2896 2294 L
1303 | stroke
1304 | LTb
1305 | LCb setrgbcolor
1306 | 6229 1674 M
1307 | 2896 2294 L
1308 | stroke
1309 | LTb
1310 | LCb setrgbcolor
1311 | 971 1221 M
1312 | 0 2145 V
1313 | stroke
1314 | LTa
1315 | LCa setrgbcolor
1316 | 971 1221 M
1317 | 2896 2294 L
1318 | stroke
1319 | LTb
1320 | LCb setrgbcolor
1321 | 971 1221 M
1322 | 49 27 V
1323 | stroke
1324 | LTb
1325 | LCb setrgbcolor
1326 | 906 1105 M
1327 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1328 | [(Helvetica) 112.0 70.0 true true 0 (1)]
1329 | ] -60.7 MCshow
1330 | 1.000 UL
1331 | LTb
1332 | LCb setrgbcolor
1333 | 1.000 UL
1334 | LTb
1335 | LCb setrgbcolor
1336 | 2896 2294 M
1337 | -49 -28 V
1338 | stroke
1339 | LTa
1340 | LCa setrgbcolor
1341 | 1527 1117 M
1342 | 3452 2190 L
1343 | stroke
1344 | LTb
1345 | LCb setrgbcolor
1346 | 1527 1117 M
1347 | 49 28 V
1348 | stroke
1349 | LTb
1350 | LCb setrgbcolor
1351 | 1461 1002 M
1352 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1353 | [(Helvetica) 112.0 70.0 true true 0 (2)]
1354 | ] -60.7 MCshow
1355 | 1.000 UL
1356 | LTb
1357 | LCb setrgbcolor
1358 | 1.000 UL
1359 | LTb
1360 | LCb setrgbcolor
1361 | 3452 2190 M
1362 | -49 -27 V
1363 | stroke
1364 | LTa
1365 | LCa setrgbcolor
1366 | 2082 1014 M
1367 | 4006 2087 L
1368 | stroke
1369 | LTb
1370 | LCb setrgbcolor
1371 | 2082 1014 M
1372 | 49 28 V
1373 | stroke
1374 | LTb
1375 | LCb setrgbcolor
1376 | 2017 899 M
1377 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1378 | [(Helvetica) 112.0 70.0 true true 0 (3)]
1379 | ] -60.7 MCshow
1380 | 1.000 UL
1381 | LTb
1382 | LCb setrgbcolor
1383 | 1.000 UL
1384 | LTb
1385 | LCb setrgbcolor
1386 | 4006 2087 M
1387 | -49 -27 V
1388 | stroke
1389 | LTa
1390 | LCa setrgbcolor
1391 | 2638 911 M
1392 | 4562 1984 L
1393 | stroke
1394 | LTb
1395 | LCb setrgbcolor
1396 | 2638 911 M
1397 | 49 27 V
1398 | stroke
1399 | LTb
1400 | LCb setrgbcolor
1401 | 2573 795 M
1402 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1403 | [(Helvetica) 112.0 70.0 true true 0 (4)]
1404 | ] -60.7 MCshow
1405 | 1.000 UL
1406 | LTb
1407 | LCb setrgbcolor
1408 | 1.000 UL
1409 | LTb
1410 | LCb setrgbcolor
1411 | 4562 1984 M
1412 | -49 -27 V
1413 | stroke
1414 | LTa
1415 | LCa setrgbcolor
1416 | 3194 808 M
1417 | 5118 1881 L
1418 | stroke
1419 | LTb
1420 | LCb setrgbcolor
1421 | 3194 808 M
1422 | 49 27 V
1423 | stroke
1424 | LTb
1425 | LCb setrgbcolor
1426 | 3128 692 M
1427 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1428 | [(Helvetica) 112.0 70.0 true true 0 (5)]
1429 | ] -60.7 MCshow
1430 | 1.000 UL
1431 | LTb
1432 | LCb setrgbcolor
1433 | 1.000 UL
1434 | LTb
1435 | LCb setrgbcolor
1436 | 5118 1881 M
1437 | -49 -28 V
1438 | stroke
1439 | LTa
1440 | LCa setrgbcolor
1441 | 3748 704 M
1442 | 5673 1777 L
1443 | stroke
1444 | LTb
1445 | LCb setrgbcolor
1446 | 3748 704 M
1447 | 49 28 V
1448 | stroke
1449 | LTb
1450 | LCb setrgbcolor
1451 | 3683 589 M
1452 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1453 | [(Helvetica) 112.0 70.0 true true 0 (6)]
1454 | ] -60.7 MCshow
1455 | 1.000 UL
1456 | LTb
1457 | LCb setrgbcolor
1458 | 1.000 UL
1459 | LTb
1460 | LCb setrgbcolor
1461 | 5673 1777 M
1462 | -49 -27 V
1463 | stroke
1464 | LTa
1465 | LCa setrgbcolor
1466 | 4304 601 M
1467 | 6229 1674 L
1468 | stroke
1469 | LTb
1470 | LCb setrgbcolor
1471 | 4304 601 M
1472 | 49 28 V
1473 | stroke
1474 | LTb
1475 | LCb setrgbcolor
1476 | 4239 486 M
1477 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1478 | [(Helvetica) 112.0 70.0 true true 0 (7)]
1479 | ] -60.7 MCshow
1480 | 1.000 UL
1481 | LTb
1482 | LCb setrgbcolor
1483 | 1.000 UL
1484 | LTb
1485 | LCb setrgbcolor
1486 | 6229 1674 M
1487 | -49 -27 V
1488 | stroke
1489 | LCb setrgbcolor
1490 | 2157 643 M
1491 | [ [(Helvetica) 140.0 0.0 true true 0 (Batch Size)]
1492 | ] -46.7 MCshow
1493 | LTb
1494 | 1.000 UL
1495 | LTa
1496 | LCa setrgbcolor
1497 | 4304 601 M
1498 | 971 1221 L
1499 | stroke
1500 | LTb
1501 | LCb setrgbcolor
1502 | 4304 601 M
1503 | -54 10 V
1504 | stroke
1505 | 4377 524 M
1506 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1507 | [(Helvetica) 112.0 70.0 true true 0 (0)]
1508 | ] -60.7 MCshow
1509 | 1.000 UL
1510 | LTb
1511 | LCb setrgbcolor
1512 | 1.000 UL
1513 | LTb
1514 | LCb setrgbcolor
1515 | 971 1221 M
1516 | 54 -10 V
1517 | stroke
1518 | LTb
1519 | LCb setrgbcolor
1520 | 4465 691 M
1521 | -28 5 V
1522 | stroke
1523 | LTb
1524 | LCb setrgbcolor
1525 | 1131 1310 M
1526 | 28 -5 V
1527 | stroke
1528 | LTa
1529 | LCa setrgbcolor
1530 | 4625 780 M
1531 | 1292 1400 L
1532 | stroke
1533 | LTb
1534 | LCb setrgbcolor
1535 | 4625 780 M
1536 | -55 10 V
1537 | stroke
1538 | 4698 703 M
1539 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1540 | [(Helvetica) 112.0 70.0 true true 0 (2)]
1541 | ] -60.7 MCshow
1542 | 1.000 UL
1543 | LTb
1544 | LCb setrgbcolor
1545 | 1.000 UL
1546 | LTb
1547 | LCb setrgbcolor
1548 | 1292 1400 M
1549 | 54 -11 V
1550 | stroke
1551 | LTb
1552 | LCb setrgbcolor
1553 | 4785 869 M
1554 | -27 6 V
1555 | stroke
1556 | LTb
1557 | LCb setrgbcolor
1558 | 1452 1489 M
1559 | 27 -5 V
1560 | stroke
1561 | LTa
1562 | LCa setrgbcolor
1563 | 4946 959 M
1564 | 1613 1578 L
1565 | stroke
1566 | LTb
1567 | LCb setrgbcolor
1568 | 4946 959 M
1569 | -55 10 V
1570 | stroke
1571 | 5019 881 M
1572 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1573 | [(Helvetica) 112.0 70.0 true true 0 (4)]
1574 | ] -60.7 MCshow
1575 | 1.000 UL
1576 | LTb
1577 | LCb setrgbcolor
1578 | 1.000 UL
1579 | LTb
1580 | LCb setrgbcolor
1581 | 1613 1578 M
1582 | 54 -10 V
1583 | stroke
1584 | LTb
1585 | LCb setrgbcolor
1586 | 5106 1048 M
1587 | -27 5 V
1588 | stroke
1589 | LTb
1590 | LCb setrgbcolor
1591 | 1773 1668 M
1592 | 27 -5 V
1593 | stroke
1594 | LTa
1595 | LCa setrgbcolor
1596 | 5267 1138 M
1597 | 1933 1757 L
1598 | stroke
1599 | LTb
1600 | LCb setrgbcolor
1601 | 5267 1138 M
1602 | -55 10 V
1603 | stroke
1604 | 5339 1060 M
1605 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1606 | [(Helvetica) 112.0 70.0 true true 0 (6)]
1607 | ] -60.7 MCshow
1608 | 1.000 UL
1609 | LTb
1610 | LCb setrgbcolor
1611 | 1.000 UL
1612 | LTb
1613 | LCb setrgbcolor
1614 | 1933 1757 M
1615 | 55 -10 V
1616 | stroke
1617 | LTb
1618 | LCb setrgbcolor
1619 | 5427 1227 M
1620 | -27 5 V
1621 | stroke
1622 | LTb
1623 | LCb setrgbcolor
1624 | 2094 1847 M
1625 | 27 -5 V
1626 | stroke
1627 | LTa
1628 | LCa setrgbcolor
1629 | 5587 1317 M
1630 | 2254 1936 L
1631 | stroke
1632 | LTb
1633 | LCb setrgbcolor
1634 | 5587 1317 M
1635 | -54 10 V
1636 | stroke
1637 | 5660 1239 M
1638 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1639 | [(Helvetica) 112.0 70.0 true true 0 (8)]
1640 | ] -60.7 MCshow
1641 | 1.000 UL
1642 | LTb
1643 | LCb setrgbcolor
1644 | 1.000 UL
1645 | LTb
1646 | LCb setrgbcolor
1647 | 2254 1936 M
1648 | 55 -10 V
1649 | stroke
1650 | LTb
1651 | LCb setrgbcolor
1652 | 5748 1406 M
1653 | -27 5 V
1654 | stroke
1655 | LTb
1656 | LCb setrgbcolor
1657 | 2415 2025 M
1658 | 27 -5 V
1659 | stroke
1660 | LTa
1661 | LCa setrgbcolor
1662 | 5908 1495 M
1663 | 2575 2115 L
1664 | stroke
1665 | LTb
1666 | LCb setrgbcolor
1667 | 5908 1495 M
1668 | -54 11 V
1669 | stroke
1670 | 5981 1418 M
1671 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1672 | [(Helvetica) 112.0 70.0 true true 0 (10)]
1673 | ] -60.7 MCshow
1674 | 1.000 UL
1675 | LTb
1676 | LCb setrgbcolor
1677 | 1.000 UL
1678 | LTb
1679 | LCb setrgbcolor
1680 | 2575 2115 M
1681 | 55 -10 V
1682 | stroke
1683 | LTb
1684 | LCb setrgbcolor
1685 | 6069 1585 M
1686 | -28 5 V
1687 | stroke
1688 | LTb
1689 | LCb setrgbcolor
1690 | 2735 2204 M
1691 | 28 -5 V
1692 | stroke
1693 | LTa
1694 | LCa setrgbcolor
1695 | 6229 1674 M
1696 | 2896 2294 L
1697 | stroke
1698 | LTb
1699 | LCb setrgbcolor
1700 | 6229 1674 M
1701 | -54 10 V
1702 | stroke
1703 | 6302 1597 M
1704 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1705 | [(Helvetica) 112.0 70.0 true true 0 (12)]
1706 | ] -60.7 MCshow
1707 | 1.000 UL
1708 | LTb
1709 | LCb setrgbcolor
1710 | 1.000 UL
1711 | LTb
1712 | LCb setrgbcolor
1713 | 2896 2294 M
1714 | 54 -10 V
1715 | stroke
1716 | LCb setrgbcolor
1717 | 6100 983 M
1718 | [ [(Helvetica) 140.0 0.0 true true 0 (Input Size)]
1719 | ] -46.7 MCshow
1720 | LTb
1721 | 1.000 UL
1722 | LTa
1723 | LCa setrgbcolor
1724 | 971 1936 M
1725 | 2896 3008 L
1726 | stroke
1727 | LTa
1728 | LCa setrgbcolor
1729 | 2896 3008 M
1730 | 6229 2390 L
1731 | stroke
1732 | LTb
1733 | LCb setrgbcolor
1734 | 971 1936 M
1735 | 63 0 V
1736 | stroke
1737 | 845 1936 M
1738 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1739 | [(Helvetica) 112.0 70.0 true true 0 (-20)]
1740 | ] -60.7 MRshow
1741 | 1.000 UL
1742 | LTb
1743 | LCb setrgbcolor
1744 | 1.000 UL
1745 | LTb
1746 | LCb setrgbcolor
1747 | 971 1984 M
1748 | 31 0 V
1749 | stroke
1750 | LTb
1751 | LCb setrgbcolor
1752 | 971 2031 M
1753 | 31 0 V
1754 | stroke
1755 | LTb
1756 | LCb setrgbcolor
1757 | 971 2079 M
1758 | 31 0 V
1759 | stroke
1760 | LTb
1761 | LCb setrgbcolor
1762 | 971 2127 M
1763 | 31 0 V
1764 | stroke
1765 | LTa
1766 | LCa setrgbcolor
1767 | 971 2175 M
1768 | 2896 3247 L
1769 | stroke
1770 | LTa
1771 | LCa setrgbcolor
1772 | 2896 3247 M
1773 | 6229 2627 L
1774 | stroke
1775 | LTb
1776 | LCb setrgbcolor
1777 | 971 2175 M
1778 | 63 0 V
1779 | stroke
1780 | 845 2175 M
1781 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1782 | [(Helvetica) 112.0 70.0 true true 0 (-15)]
1783 | ] -60.7 MRshow
1784 | 1.000 UL
1785 | LTb
1786 | LCb setrgbcolor
1787 | 1.000 UL
1788 | LTb
1789 | LCb setrgbcolor
1790 | 971 2222 M
1791 | 31 0 V
1792 | stroke
1793 | LTb
1794 | LCb setrgbcolor
1795 | 971 2270 M
1796 | 31 0 V
1797 | stroke
1798 | LTb
1799 | LCb setrgbcolor
1800 | 971 2318 M
1801 | 31 0 V
1802 | stroke
1803 | LTb
1804 | LCb setrgbcolor
1805 | 971 2365 M
1806 | 31 0 V
1807 | stroke
1808 | LTa
1809 | LCa setrgbcolor
1810 | 971 2413 M
1811 | 2896 3485 L
1812 | stroke
1813 | LTa
1814 | LCa setrgbcolor
1815 | 2896 3485 M
1816 | 6229 2865 L
1817 | stroke
1818 | LTb
1819 | LCb setrgbcolor
1820 | 971 2413 M
1821 | 63 0 V
1822 | stroke
1823 | 845 2413 M
1824 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1825 | [(Helvetica) 112.0 70.0 true true 0 (-10)]
1826 | ] -60.7 MRshow
1827 | 1.000 UL
1828 | LTb
1829 | LCb setrgbcolor
1830 | 1.000 UL
1831 | LTb
1832 | LCb setrgbcolor
1833 | 971 2461 M
1834 | 31 0 V
1835 | stroke
1836 | LTb
1837 | LCb setrgbcolor
1838 | 971 2508 M
1839 | 31 0 V
1840 | stroke
1841 | LTb
1842 | LCb setrgbcolor
1843 | 971 2555 M
1844 | 31 0 V
1845 | stroke
1846 | LTb
1847 | LCb setrgbcolor
1848 | 971 2603 M
1849 | 31 0 V
1850 | stroke
1851 | LTa
1852 | LCa setrgbcolor
1853 | 971 2650 M
1854 | 2896 3723 L
1855 | stroke
1856 | LTa
1857 | LCa setrgbcolor
1858 | 2896 3723 M
1859 | 6229 3104 L
1860 | stroke
1861 | LTb
1862 | LCb setrgbcolor
1863 | 971 2650 M
1864 | 63 0 V
1865 | stroke
1866 | 845 2650 M
1867 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1868 | [(Helvetica) 112.0 70.0 true true 0 (-5)]
1869 | ] -60.7 MRshow
1870 | 1.000 UL
1871 | LTb
1872 | LCb setrgbcolor
1873 | 1.000 UL
1874 | LTb
1875 | LCb setrgbcolor
1876 | 971 2698 M
1877 | 31 0 V
1878 | stroke
1879 | LTb
1880 | LCb setrgbcolor
1881 | 971 2746 M
1882 | 31 0 V
1883 | stroke
1884 | LTb
1885 | LCb setrgbcolor
1886 | 971 2793 M
1887 | 31 0 V
1888 | stroke
1889 | LTb
1890 | LCb setrgbcolor
1891 | 971 2841 M
1892 | 31 0 V
1893 | stroke
1894 | LTa
1895 | LCa setrgbcolor
1896 | 971 2889 M
1897 | 2896 3962 L
1898 | stroke
1899 | LTa
1900 | LCa setrgbcolor
1901 | 2896 3962 M
1902 | 6229 3342 L
1903 | stroke
1904 | LTb
1905 | LCb setrgbcolor
1906 | 971 2889 M
1907 | 63 0 V
1908 | stroke
1909 | 845 2889 M
1910 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1911 | [(Helvetica) 112.0 70.0 true true 0 (0)]
1912 | ] -60.7 MRshow
1913 | 1.000 UL
1914 | LTb
1915 | LCb setrgbcolor
1916 | 1.000 UL
1917 | LTb
1918 | LCb setrgbcolor
1919 | 971 2937 M
1920 | 31 0 V
1921 | stroke
1922 | LTb
1923 | LCb setrgbcolor
1924 | 971 2984 M
1925 | 31 0 V
1926 | stroke
1927 | LTb
1928 | LCb setrgbcolor
1929 | 971 3032 M
1930 | 31 0 V
1931 | stroke
1932 | LTb
1933 | LCb setrgbcolor
1934 | 971 3080 M
1935 | 31 0 V
1936 | stroke
1937 | LTa
1938 | LCa setrgbcolor
1939 | 971 3127 M
1940 | 2896 4200 L
1941 | stroke
1942 | LTa
1943 | LCa setrgbcolor
1944 | 2896 4200 M
1945 | 6229 3581 L
1946 | stroke
1947 | LTb
1948 | LCb setrgbcolor
1949 | 971 3127 M
1950 | 63 0 V
1951 | stroke
1952 | 845 3127 M
1953 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1954 | [(Helvetica) 112.0 70.0 true true 0 (5)]
1955 | ] -60.7 MRshow
1956 | 1.000 UL
1957 | LTb
1958 | LCb setrgbcolor
1959 | 1.000 UL
1960 | LTb
1961 | LCb setrgbcolor
1962 | 971 3175 M
1963 | 31 0 V
1964 | stroke
1965 | LTb
1966 | LCb setrgbcolor
1967 | 971 3223 M
1968 | 31 0 V
1969 | stroke
1970 | LTb
1971 | LCb setrgbcolor
1972 | 971 3270 M
1973 | 31 0 V
1974 | stroke
1975 | LTb
1976 | LCb setrgbcolor
1977 | 971 3318 M
1978 | 31 0 V
1979 | stroke
1980 | LTa
1981 | LCa setrgbcolor
1982 | 971 3366 M
1983 | 2896 4439 L
1984 | stroke
1985 | LTa
1986 | LCa setrgbcolor
1987 | 2896 4439 M
1988 | 6229 3819 L
1989 | stroke
1990 | LTb
1991 | LCb setrgbcolor
1992 | 971 3366 M
1993 | 63 0 V
1994 | stroke
1995 | 845 3366 M
1996 | [ [(Helvetica) 140.0 0.0 true true 0 (2)]
1997 | [(Helvetica) 112.0 70.0 true true 0 (10)]
1998 | ] -60.7 MRshow
1999 | 1.000 UL
2000 | LTb
2001 | LCb setrgbcolor
2002 | LCb setrgbcolor
2003 | 383 1531 M
2004 | [ [(Helvetica) 140.0 0.0 true true 0 (Time \(in seconds\))]
2005 | ] -46.7 MCshow
2006 | LTb
2007 | 1.000 UP
2008 | stroke
2009 | grestore
2010 | end
2011 | showpage
2012 | %%Trailer
2013 | %%DocumentFonts: Helvetica
2014 | %%Pages: 1
2015 | 


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