Optimize BSSN RHS and finite difference calculations

- Integrate Intel oneMKL VML for efficient Gauge calculation in bssn_rhs.f90
- Refactor fderivs in diff_new.f90 to separate bulk/boundary loops for better vectorization
- Add optimization report in docs/optimization_report.md

.gitignore

@@ -1,5 +1,6 @@
 __pycache__
 GW150914
-GW150914*
+GW150914-origin
-.codex
+docs
-docs/
+*.tmp
+

AMSS_NCKU_Input.py

@@ -16,7 +16,7 @@ import numpy
 File_directory   = "GW150914"                    ## output file directory
 Output_directory = "binary_output"               ## binary data file directory
                                                  ## The file directory name should not be too long
-MPI_processes    = 64                             ## number of mpi processes used in the simulation
+MPI_processes    = 48                             ## number of mpi processes used in the simulation
 
 GPU_Calculation  = "no"                          ## Use GPU or not 
                                                  ## (prefer "no" in the current version, because the GPU part may have bugs when integrated in this Python interface)

AMSS_NCKU_Program.py

@@ -9,16 +9,6 @@
 ##################################################################
 
 
-##################################################################
-
-## Guard against re-execution by multiprocessing child processes.
-## Without this, using 'spawn' or 'forkserver' context would cause every
-## worker to re-run the entire script.
-if __name__ != '__main__':
-    import sys as _sys
-    _sys.exit(0)
-
-
 ##################################################################
 
 ## Print program introduction
@@ -434,31 +424,26 @@ print(
 
 import plot_xiaoqu
 import plot_GW_strain_amplitude_xiaoqu
-from parallel_plot_helper import run_plot_tasks_parallel
-
-plot_tasks = []
 
 ## Plot black hole trajectory
-plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot,   (binary_results_directory, figure_directory) ) )
+plot_xiaoqu.generate_puncture_orbit_plot(   binary_results_directory, figure_directory )
-plot_tasks.append( ( plot_xiaoqu.generate_puncture_orbit_plot3D, (binary_results_directory, figure_directory) ) )
+plot_xiaoqu.generate_puncture_orbit_plot3D( binary_results_directory, figure_directory )
 
 ## Plot black hole separation vs. time
-plot_tasks.append( ( plot_xiaoqu.generate_puncture_distence_plot, (binary_results_directory, figure_directory) ) )
+plot_xiaoqu.generate_puncture_distence_plot( binary_results_directory, figure_directory )
 
 ## Plot gravitational waveforms (psi4 and strain amplitude)
 for i in range(input_data.Detector_Number):
-    plot_tasks.append( ( plot_xiaoqu.generate_gravitational_wave_psi4_plot, (binary_results_directory, figure_directory, i) ) )
+    plot_xiaoqu.generate_gravitational_wave_psi4_plot( binary_results_directory, figure_directory, i )
-    plot_tasks.append( ( plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot, (binary_results_directory, figure_directory, i) ) )
+    plot_GW_strain_amplitude_xiaoqu.generate_gravitational_wave_amplitude_plot( binary_results_directory, figure_directory, i )
 
 ## Plot ADM mass evolution
 for i in range(input_data.Detector_Number):
-    plot_tasks.append( ( plot_xiaoqu.generate_ADMmass_plot, (binary_results_directory, figure_directory, i) ) )
+    plot_xiaoqu.generate_ADMmass_plot( binary_results_directory, figure_directory, i )
 
 ## Plot Hamiltonian constraint violation over time
 for i in range(input_data.grid_level):
-    plot_tasks.append( ( plot_xiaoqu.generate_constraint_check_plot, (binary_results_directory, figure_directory, i) ) )
+    plot_xiaoqu.generate_constraint_check_plot( binary_results_directory, figure_directory, i )
-
-run_plot_tasks_parallel(plot_tasks)
 
 ## Plot stored binary data
 plot_xiaoqu.generate_binary_data_plot( binary_results_directory, figure_directory )

AMSS_NCKU_Verify_ASC26.py

@@ -0,0 +1,279 @@
+#!/usr/bin/env python3
+"""
+AMSS-NCKU GW150914 Simulation Regression Test Script
+
+Verification Requirements:
+1. XY-plane trajectory RMS error < 1% (Optimized vs. baseline, max of BH1 and BH2)
+2. ADM constraint violation < 2 (Grid Level 0)
+
+RMS Calculation Method:
+- Computes trajectory deviation on the XY plane independently for BH1 and BH2
+- For each black hole: RMS = sqrt((1/M) * sum((Δr_i / r_i^max)^2)) × 100%
+- Final RMS = max(RMS_BH1, RMS_BH2)
+
+Usage: python3 AMSS_NCKU_Verify_ASC26.py [output_dir]
+Default: output_dir = GW150914/AMSS_NCKU_output
+Reference: GW150914-origin (baseline simulation)
+"""
+
+import numpy as np
+import sys
+import os
+
+# ANSI Color Codes
+class Color:
+    GREEN = '\033[92m'
+    RED = '\033[91m'
+    YELLOW = '\033[93m'
+    BLUE = '\033[94m'
+    BOLD = '\033[1m'
+    RESET = '\033[0m'
+
+def get_status_text(passed):
+    if passed:
+        return f"{Color.GREEN}{Color.BOLD}PASS{Color.RESET}"
+    else:
+        return f"{Color.RED}{Color.BOLD}FAIL{Color.RESET}"
+
+def load_bh_trajectory(filepath):
+    """Load black hole trajectory data"""
+    data = np.loadtxt(filepath)
+    return {
+        'time': data[:, 0],
+        'x1': data[:, 1], 'y1': data[:, 2], 'z1': data[:, 3],
+        'x2': data[:, 4], 'y2': data[:, 5], 'z2': data[:, 6]
+    }
+
+
+def load_constraint_data(filepath):
+    """Load constraint violation data"""
+    data = []
+    with open(filepath, 'r') as f:
+        for line in f:
+            if line.startswith('#'):
+                continue
+            parts = line.split()
+            if len(parts) >= 8:
+                data.append([float(x) for x in parts[:8]])
+    return np.array(data)
+
+
+def calculate_rms_error(bh_data_ref, bh_data_target):
+    """
+    Calculate trajectory-based RMS error on the XY plane between baseline and optimized simulations.
+
+    This function computes the RMS error independently for BH1 and BH2 trajectories,
+    then returns the maximum of the two as the final RMS error metric.
+
+    For each black hole, the RMS is calculated as:
+        RMS = sqrt( (1/M) * sum( (Δr_i / r_i^max)^2 ) ) × 100%
+
+    where:
+        Δr_i = sqrt((x_ref,i - x_new,i)^2 + (y_ref,i - y_new,i)^2)
+        r_i^max = max(sqrt(x_ref,i^2 + y_ref,i^2), sqrt(x_new,i^2 + y_new,i^2))
+
+    Args:
+        bh_data_ref: Reference (baseline) trajectory data
+        bh_data_target: Target (optimized) trajectory data
+
+    Returns:
+        rms_value: Final RMS error as a percentage (max of BH1 and BH2)
+        error: Error message if any
+    """
+    # Align data: truncate to the length of the shorter dataset
+    M = min(len(bh_data_ref['time']), len(bh_data_target['time']))
+
+    if M < 10:
+        return None, "Insufficient data points for comparison"
+
+    # Extract XY coordinates for both black holes
+    x1_ref = bh_data_ref['x1'][:M]
+    y1_ref = bh_data_ref['y1'][:M]
+    x2_ref = bh_data_ref['x2'][:M]
+    y2_ref = bh_data_ref['y2'][:M]
+
+    x1_new = bh_data_target['x1'][:M]
+    y1_new = bh_data_target['y1'][:M]
+    x2_new = bh_data_target['x2'][:M]
+    y2_new = bh_data_target['y2'][:M]
+
+    # Calculate RMS for BH1
+    delta_r1 = np.sqrt((x1_ref - x1_new)**2 + (y1_ref - y1_new)**2)
+    r1_ref = np.sqrt(x1_ref**2 + y1_ref**2)
+    r1_new = np.sqrt(x1_new**2 + y1_new**2)
+    r1_max = np.maximum(r1_ref, r1_new)
+
+    # Calculate RMS for BH2
+    delta_r2 = np.sqrt((x2_ref - x2_new)**2 + (y2_ref - y2_new)**2)
+    r2_ref = np.sqrt(x2_ref**2 + y2_ref**2)
+    r2_new = np.sqrt(x2_new**2 + y2_new**2)
+    r2_max = np.maximum(r2_ref, r2_new)
+
+    # Avoid division by zero for BH1
+    valid_mask1 = r1_max > 1e-15
+    if np.sum(valid_mask1) < 10:
+        return None, "Insufficient valid data points for BH1"
+
+    terms1 = (delta_r1[valid_mask1] / r1_max[valid_mask1])**2
+    rms_bh1 = np.sqrt(np.mean(terms1)) * 100
+
+    # Avoid division by zero for BH2
+    valid_mask2 = r2_max > 1e-15
+    if np.sum(valid_mask2) < 10:
+        return None, "Insufficient valid data points for BH2"
+
+    terms2 = (delta_r2[valid_mask2] / r2_max[valid_mask2])**2
+    rms_bh2 = np.sqrt(np.mean(terms2)) * 100
+
+    # Final RMS is the maximum of BH1 and BH2
+    rms_final = max(rms_bh1, rms_bh2)
+
+    return rms_final, None
+
+
+def analyze_constraint_violation(constraint_data, n_levels=9):
+    """
+    Analyze ADM constraint violation
+    Return maximum constraint violation for Grid Level 0
+    """
+    # Extract Grid Level 0 data (first entry for each time step)
+    level0_data = constraint_data[::n_levels]
+
+    # Calculate maximum absolute value for each constraint
+    results = {
+        'Ham': np.max(np.abs(level0_data[:, 1])),
+        'Px': np.max(np.abs(level0_data[:, 2])),
+        'Py': np.max(np.abs(level0_data[:, 3])),
+        'Pz': np.max(np.abs(level0_data[:, 4])),
+        'Gx': np.max(np.abs(level0_data[:, 5])),
+        'Gy': np.max(np.abs(level0_data[:, 6])),
+        'Gz': np.max(np.abs(level0_data[:, 7]))
+    }
+
+    results['max_violation'] = max(results.values())
+    return results
+
+
+def print_header():
+    """Print report header"""
+    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+    print(Color.BOLD + "   AMSS-NCKU GW150914 Simulation Regression Test Report" + Color.RESET)
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+
+
+def print_rms_results(rms_rel, error, threshold=1.0):
+    """Print RMS error results"""
+    print(f"\n{Color.BOLD}1. RMS Error Analysis (Baseline vs Optimized){Color.RESET}")
+    print("-" * 45)
+
+    if error:
+        print(f"   {Color.RED}Error: {error}{Color.RESET}")
+        return False
+
+    passed = rms_rel < threshold
+
+    print(f"   RMS relative error: {rms_rel:.4f}%")
+    print(f"   Requirement:        < {threshold}%")
+    print(f"   Status:             {get_status_text(passed)}")
+
+    return passed
+
+
+def print_constraint_results(results, threshold=2.0):
+    """Print constraint violation results"""
+    print(f"\n{Color.BOLD}2. ADM Constraint Violation Analysis (Grid Level 0){Color.RESET}")
+    print("-" * 45)
+
+    names = ['Ham', 'Px', 'Py', 'Pz', 'Gx', 'Gy', 'Gz']
+    for i, name in enumerate(names):
+        print(f"   Max |{name:3}|: {results[name]:.6f}", end="   ")
+        if (i + 1) % 2 == 0: print()
+    if len(names) % 2 != 0: print()
+
+    passed = results['max_violation'] < threshold
+    
+    print(f"\n   Maximum violation:  {results['max_violation']:.6f}")
+    print(f"   Requirement:        < {threshold}")
+    print(f"   Status:             {get_status_text(passed)}")
+
+    return passed
+
+
+def print_summary(rms_passed, constraint_passed):
+    """Print summary"""
+    print("\n" + Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+    print(Color.BOLD + "Verification Summary" + Color.RESET)
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET)
+
+    all_passed = rms_passed and constraint_passed
+    
+    res_rms = get_status_text(rms_passed)
+    res_con = get_status_text(constraint_passed)
+
+    print(f"   [1] RMS trajectory check:         {res_rms}")
+    print(f"   [2] ADM constraint check:         {res_con}")
+    
+    final_status = f"{Color.GREEN}{Color.BOLD}ALL CHECKS PASSED{Color.RESET}" if all_passed else f"{Color.RED}{Color.BOLD}SOME CHECKS FAILED{Color.RESET}"
+    print(f"\n   Overall result: {final_status}")
+    print(Color.BLUE + Color.BOLD + "=" * 65 + Color.RESET + "\n")
+
+    return all_passed
+
+
+def main():
+    # Determine target (optimized) output directory
+    if len(sys.argv) > 1:
+        target_dir = sys.argv[1]
+    else:
+        script_dir = os.path.dirname(os.path.abspath(__file__))
+        target_dir = os.path.join(script_dir, "GW150914/AMSS_NCKU_output")
+
+    # Determine reference (baseline) directory
+    script_dir = os.path.dirname(os.path.abspath(__file__))
+    reference_dir = os.path.join(script_dir, "GW150914-origin/AMSS_NCKU_output")
+
+    # Data file paths
+    bh_file_ref = os.path.join(reference_dir, "bssn_BH.dat")
+    bh_file_target = os.path.join(target_dir, "bssn_BH.dat")
+    constraint_file = os.path.join(target_dir, "bssn_constraint.dat")
+
+    # Check if files exist
+    if not os.path.exists(bh_file_ref):
+        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Baseline trajectory file not found: {bh_file_ref}")
+        sys.exit(1)
+
+    if not os.path.exists(bh_file_target):
+        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Target trajectory file not found: {bh_file_target}")
+        sys.exit(1)
+
+    if not os.path.exists(constraint_file):
+        print(f"{Color.RED}{Color.BOLD}Error:{Color.RESET} Constraint data file not found: {constraint_file}")
+        sys.exit(1)
+
+    # Print header
+    print_header()
+    print(f"\n{Color.BOLD}Reference (Baseline):{Color.RESET} {Color.BLUE}{reference_dir}{Color.RESET}")
+    print(f"{Color.BOLD}Target (Optimized):  {Color.RESET} {Color.BLUE}{target_dir}{Color.RESET}")
+
+    # Load data
+    bh_data_ref = load_bh_trajectory(bh_file_ref)
+    bh_data_target = load_bh_trajectory(bh_file_target)
+    constraint_data = load_constraint_data(constraint_file)
+
+    # Calculate RMS error
+    rms_rel, error = calculate_rms_error(bh_data_ref, bh_data_target)
+    rms_passed = print_rms_results(rms_rel, error)
+
+    # Analyze constraint violation
+    constraint_results = analyze_constraint_violation(constraint_data)
+    constraint_passed = print_constraint_results(constraint_results)
+
+    # Print summary
+    all_passed = print_summary(rms_passed, constraint_passed)
+
+    # Return exit code
+    sys.exit(0 if all_passed else 1)
+
+
+if __name__ == "__main__":
+    main()

AMSS_NCKU_source/ABE.optrpt

@@ -0,0 +1,710 @@
+Begin optimization report for: __cxx_global_var_init
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, int, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::map()
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, int, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::~map()
+=================================================================
+
+Begin optimization report for: __cxx_global_var_init.1
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, double, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::map()
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, double, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::~map()
+=================================================================
+
+Begin optimization report for: __cxx_global_var_init.2
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::map()
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::~map()
+=================================================================
+
+Begin optimization report for: main
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (1947, 7)
+LOOP END
+
+LOOP BEGIN at ABE.C (125, 13)
+LOOP END
+=================================================================
+
+Begin optimization report for: std::allocator<char>::allocator()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::basic_string<std::allocator<char>>(char const*, std::allocator<char> const&)
+=================================================================
+
+Begin optimization report for: std::__new_allocator<char>::~__new_allocator()
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::insert(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&)
+=================================================================
+
+Begin optimization report for: std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>::pair<char const (&) [9], std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>&, true>(char const (&) [9], std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>&)
+=================================================================
+
+Begin optimization report for: std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>::~pair()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::~basic_string()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_Rb_tree_iterator()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::basic_string()
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::find(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&)
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (1947, 7)
+LOOP END
+=================================================================
+
+Begin optimization report for: std::operator!=(std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>> const&, std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>> const&)
+=================================================================
+
+Begin optimization report for: std::map<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::end()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::operator->() const
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::operator=(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::c_str() const
+=================================================================
+
+Begin optimization report for: std::basic_ostream<char, std::char_traits<char>>& std::operator<<<std::char_traits<char>>(std::basic_ostream<char, std::char_traits<char>>&, char const*)
+=================================================================
+
+Begin optimization report for: std::ostream::operator<<(std::ostream& (*)(std::ostream&))
+=================================================================
+
+Begin optimization report for: std::basic_ostream<char, std::char_traits<char>>& std::endl<char, std::char_traits<char>>(std::basic_ostream<char, std::char_traits<char>>&)
+=================================================================
+
+Begin optimization report for: std::basic_ifstream<char, std::char_traits<char>>::basic_ifstream(char const*, std::_Ios_Openmode)
+=================================================================
+
+Begin optimization report for: std::basic_ios<char, std::char_traits<char>>::good() const
+=================================================================
+
+Begin optimization report for: std::istream::getline(char*, long)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::operator=(char const*)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::basic_string(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&)
+=================================================================
+
+Begin optimization report for: bool std::operator==<char, std::char_traits<char>, std::allocator<char>>(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&, char const*)
+=================================================================
+
+Begin optimization report for: atoi
+=================================================================
+
+Begin optimization report for: atof
+=================================================================
+
+Begin optimization report for: std::basic_ifstream<char, std::char_traits<char>>::close()
+=================================================================
+
+Begin optimization report for: std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>::pair<char const (&) [11], std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>&, true>(char const (&) [11], std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>&)
+=================================================================
+
+Begin optimization report for: std::basic_ifstream<char, std::char_traits<char>>::~basic_ifstream()
+=================================================================
+
+Begin optimization report for: std::basic_ofstream<char, std::char_traits<char>>::basic_ofstream()
+=================================================================
+
+Begin optimization report for: std::basic_ofstream<char, std::char_traits<char>>::open(char const*, std::_Ios_Openmode)
+=================================================================
+
+Begin optimization report for: std::basic_ofstream<char, std::char_traits<char>>::close()
+=================================================================
+
+Begin optimization report for: std::basic_ofstream<char, std::char_traits<char>>::~basic_ofstream()
+=================================================================
+
+Begin optimization report for: std::ostream::operator<<(double)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_Rb_tree()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_Rb_tree_impl<std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, true>::_Rb_tree_impl()
+=================================================================
+
+Begin optimization report for: std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_key_compare<std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_Rb_tree_key_compare()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_header::_Rb_tree_header()
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::__new_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_header::_M_reset()
+=================================================================
+
+Begin optimization report for: __clang_call_terminate
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::~_Rb_tree()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_M_erase(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>*)
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (1930, 7)
+    remark #15521: Loop was not vectorized: loop control variable was not identified. Explicitly compute the iteration count before executing the loop or try using canonical loop form from OpenMP specification
+    remark #25478: While loop unrolled by 2
+LOOP END
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_M_begin()
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::~__new_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_S_right(std::_Rb_tree_node_base*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_S_left(std::_Rb_tree_node_base*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_M_drop_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_M_destroy_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_M_put_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>*)
+=================================================================
+
+Begin optimization report for: void std::allocator_traits<std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>>::destroy<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>(std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>&, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_M_get_Node_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>::_M_valptr()
+=================================================================
+
+Begin optimization report for: void std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::destroy<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>*)
+=================================================================
+
+Begin optimization report for: std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>::~pair()
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__aligned_membuf<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>::_M_ptr()
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__aligned_membuf<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>::_M_addr()
+=================================================================
+
+Begin optimization report for: std::allocator_traits<std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>>::deallocate(std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>&, std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::deallocate(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, int>>>::_M_mbegin() const
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_Rb_tree()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_Rb_tree_impl<std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, true>::_Rb_tree_impl()
+=================================================================
+
+Begin optimization report for: std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::allocator()
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::__new_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::~_Rb_tree()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_M_erase(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>*)
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (1930, 7)
+    remark #15521: Loop was not vectorized: loop control variable was not identified. Explicitly compute the iteration count before executing the loop or try using canonical loop form from OpenMP specification
+    remark #25478: While loop unrolled by 2
+LOOP END
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_M_begin()
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::~__new_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_S_right(std::_Rb_tree_node_base*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_S_left(std::_Rb_tree_node_base*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_M_drop_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_M_destroy_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_M_put_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>*)
+=================================================================
+
+Begin optimization report for: void std::allocator_traits<std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>>::destroy<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>(std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>&, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_M_get_Node_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>::_M_valptr()
+=================================================================
+
+Begin optimization report for: void std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::destroy<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>*)
+=================================================================
+
+Begin optimization report for: std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>::~pair()
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__aligned_membuf<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>::_M_ptr()
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__aligned_membuf<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>::_M_addr()
+=================================================================
+
+Begin optimization report for: std::allocator_traits<std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>>::deallocate(std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>&, std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::deallocate(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, double>>>::_M_mbegin() const
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_Rb_tree()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_Rb_tree_impl<std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, true>::_Rb_tree_impl()
+=================================================================
+
+Begin optimization report for: std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::allocator()
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::__new_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::~_Rb_tree()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_erase(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*)
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (1930, 7)
+    remark #15521: Loop was not vectorized: loop control variable was not identified. Explicitly compute the iteration count before executing the loop or try using canonical loop form from OpenMP specification
+LOOP END
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_begin()
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::~__new_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_S_right(std::_Rb_tree_node_base*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_S_left(std::_Rb_tree_node_base*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_drop_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_destroy_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_put_node(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*)
+=================================================================
+
+Begin optimization report for: void std::allocator_traits<std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>>::destroy<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>(std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>&, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_get_Node_allocator()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_M_valptr()
+=================================================================
+
+Begin optimization report for: void std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::destroy<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>*)
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__aligned_membuf<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_M_ptr()
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__aligned_membuf<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_M_addr()
+=================================================================
+
+Begin optimization report for: std::allocator_traits<std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>>::deallocate(std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>&, std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::deallocate(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_mbegin() const
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_data() const
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_local_data()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_Alloc_hider::_Alloc_hider(char*, std::allocator<char>&&)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_init_local_buf()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_set_length(unsigned long)
+=================================================================
+
+Begin optimization report for: std::__ptr_traits_ptr_to<char*, char, false>::pointer_to(char&)
+=================================================================
+
+Begin optimization report for: std::__new_allocator<char>::__new_allocator(std::__new_allocator<char> const&)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_length(unsigned long)
+=================================================================
+
+Begin optimization report for: std::char_traits<char>::assign(char&, char const&)
+=================================================================
+
+Begin optimization report for: std::__new_allocator<char>::__new_allocator()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_dispose()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_Alloc_hider::~_Alloc_hider()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_is_local() const
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_destroy(unsigned long)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_local_data() const
+=================================================================
+
+Begin optimization report for: std::__ptr_traits_ptr_to<char const*, char const, false>::pointer_to(char const&)
+=================================================================
+
+Begin optimization report for: std::allocator_traits<std::allocator<char>>::deallocate(std::allocator<char>&, char*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_get_allocator()
+=================================================================
+
+Begin optimization report for: std::__new_allocator<char>::deallocate(char*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_Alloc_hider::_Alloc_hider(char*, std::allocator<char> const&)
+=================================================================
+
+Begin optimization report for: std::char_traits<char>::length(char const*)
+=================================================================
+
+Begin optimization report for: void std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_construct<char const*>(char const*, char const*, std::forward_iterator_tag)
+=================================================================
+
+Begin optimization report for: std::iterator_traits<char const*>::difference_type std::distance<char const*>(char const*, char const*)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_data(char*)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_capacity(unsigned long)
+=================================================================
+
+Begin optimization report for: void std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_construct<char const*>(char const*, char const*, std::forward_iterator_tag)::_Guard::_Guard(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>*)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_S_copy_chars(char*, char const*, char const*)
+=================================================================
+
+Begin optimization report for: void std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_construct<char const*>(char const*, char const*, std::forward_iterator_tag)::_Guard::~_Guard()
+=================================================================
+
+Begin optimization report for: std::iterator_traits<char const*>::difference_type std::__distance<char const*>(char const*, char const*, std::random_access_iterator_tag)
+=================================================================
+
+Begin optimization report for: std::iterator_traits<char const*>::iterator_category std::__iterator_category<char const*>(char const* const&)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_S_copy(char*, char const*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::char_traits<char>::copy(char*, char const*, unsigned long)
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__alloc_traits<std::allocator<char>, char>::_S_select_on_copy(std::allocator<char> const&)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_get_allocator() const
+=================================================================
+
+Begin optimization report for: void std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_construct<char*>(char*, char*, std::forward_iterator_tag)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::length() const
+=================================================================
+
+Begin optimization report for: std::allocator_traits<std::allocator<char>>::select_on_container_copy_construction(std::allocator<char> const&)
+=================================================================
+
+Begin optimization report for: std::allocator<char>::allocator(std::allocator<char> const&)
+=================================================================
+
+Begin optimization report for: std::iterator_traits<char*>::difference_type std::distance<char*>(char*, char*)
+=================================================================
+
+Begin optimization report for: void std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_construct<char*>(char*, char*, std::forward_iterator_tag)::_Guard::_Guard(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>*)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_S_copy_chars(char*, char*, char*)
+=================================================================
+
+Begin optimization report for: void std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_construct<char*>(char*, char*, std::forward_iterator_tag)::_Guard::~_Guard()
+=================================================================
+
+Begin optimization report for: std::iterator_traits<char*>::difference_type std::__distance<char*>(char*, char*, std::random_access_iterator_tag)
+=================================================================
+
+Begin optimization report for: std::iterator_traits<char*>::iterator_category std::__iterator_category<char*>(char* const&)
+=================================================================
+
+Begin optimization report for: std::pair<std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, bool> std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_insert_unique<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&)
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (2113, 7)
+LOOP END
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_get_insert_unique_pos(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&)
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (2113, 7)
+LOOP END
+=================================================================
+
+Begin optimization report for: std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::operator()(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&) const
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_Alloc_node::_Alloc_node(std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>&)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>> std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_insert_<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_Alloc_node>(std::_Rb_tree_node_base*, std::_Rb_tree_node_base*, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&, std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_Alloc_node&)
+=================================================================
+
+Begin optimization report for: std::pair<std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, bool>::pair<std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, bool, true>(std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>&&, bool&&)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_Rb_tree_iterator(std::_Rb_tree_node_base*)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_end()
+=================================================================
+
+Begin optimization report for: std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>::operator()(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&) const
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_S_key(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>> const*)
+=================================================================
+
+Begin optimization report for: std::operator==(std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>> const&, std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>> const&)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::begin()
+=================================================================
+
+Begin optimization report for: std::pair<std::_Rb_tree_node_base*, std::_Rb_tree_node_base*>::pair<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*&, std::_Rb_tree_node_base*&, true>(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*&, std::_Rb_tree_node_base*&)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_iterator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::operator--()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_S_key(std::_Rb_tree_node_base const*)
+=================================================================
+
+Begin optimization report for: std::pair<std::_Rb_tree_node_base*, std::_Rb_tree_node_base*>::pair<std::_Rb_tree_node_base*, std::_Rb_tree_node_base*, true>(std::_Rb_tree_node_base* const&, std::_Rb_tree_node_base* const&)
+=================================================================
+
+Begin optimization report for: bool std::operator<<char, std::char_traits<char>, std::allocator<char>>(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::compare(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&) const
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::size() const
+=================================================================
+
+Begin optimization report for: unsigned long const& std::min<unsigned long>(unsigned long const&, unsigned long const&)
+=================================================================
+
+Begin optimization report for: std::char_traits<char>::compare(char const*, char const*, unsigned long)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::data() const
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_S_compare(unsigned long, unsigned long)
+=================================================================
+
+Begin optimization report for: std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::operator()(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>> const&) const
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_M_valptr() const
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__aligned_membuf<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_M_ptr() const
+=================================================================
+
+Begin optimization report for: __gnu_cxx::__aligned_membuf<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>::_M_addr() const
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>* std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_Alloc_node::operator()<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&) const
+=================================================================
+
+Begin optimization report for: std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>* std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_create_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&)
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_get_node()
+=================================================================
+
+Begin optimization report for: void std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_construct_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&)
+=================================================================
+
+Begin optimization report for: std::allocator_traits<std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>>::allocate(std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>&, unsigned long)
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::allocate(unsigned long, void const*)
+=================================================================
+
+Begin optimization report for: std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_max_size() const
+=================================================================
+
+Begin optimization report for: void std::allocator_traits<std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>>::construct<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>(std::allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>&, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>*, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&)
+=================================================================
+
+Begin optimization report for: void std::__new_allocator<std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::construct<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>*, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&)
+=================================================================
+
+Begin optimization report for: std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>::pair(std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>&&)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::basic_string(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>&&)
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::_M_use_local_data()
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::find(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&)
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (1947, 7)
+LOOP END
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::_M_lower_bound(std::_Rb_tree_node<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>*, std::_Rb_tree_node_base*, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&)
+
+LOOP BEGIN at /usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_tree.h (1947, 7)
+LOOP END
+=================================================================
+
+Begin optimization report for: std::_Rb_tree<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>, std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::_Select1st<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>, std::less<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>, std::allocator<std::pair<std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const, std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>>>>::end()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::assign(std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>> const&)
+=================================================================
+
+Begin optimization report for: std::basic_ios<char, std::char_traits<char>>::setstate(std::_Ios_Iostate)
+=================================================================
+
+Begin optimization report for: std::operator|(std::_Ios_Iostate, std::_Ios_Iostate)
+=================================================================
+
+Begin optimization report for: std::basic_ios<char, std::char_traits<char>>::rdstate() const
+=================================================================
+
+Begin optimization report for: std::basic_ostream<char, std::char_traits<char>>& std::flush<char, std::char_traits<char>>(std::basic_ostream<char, std::char_traits<char>>&)
+=================================================================
+
+Begin optimization report for: std::basic_ios<char, std::char_traits<char>>::widen(char) const
+=================================================================
+
+Begin optimization report for: std::ctype<char> const& std::__check_facet<std::ctype<char>>(std::ctype<char> const*)
+=================================================================
+
+Begin optimization report for: std::ctype<char>::widen(char) const
+=================================================================
+
+Begin optimization report for: std::basic_ios<char, std::char_traits<char>>::basic_ios()
+=================================================================
+
+Begin optimization report for: std::basic_istream<char, std::char_traits<char>>::basic_istream()
+=================================================================
+
+Begin optimization report for: std::basic_ifstream<char, std::char_traits<char>>::open(char const*, std::_Ios_Openmode)
+=================================================================
+
+Begin optimization report for: std::basic_filebuf<char, std::char_traits<char>>::~basic_filebuf()
+=================================================================
+
+Begin optimization report for: std::basic_istream<char, std::char_traits<char>>::~basic_istream()
+=================================================================
+
+Begin optimization report for: std::operator|(std::_Ios_Openmode, std::_Ios_Openmode)
+=================================================================
+
+Begin optimization report for: std::basic_streambuf<char, std::char_traits<char>>::~basic_streambuf()
+=================================================================
+
+Begin optimization report for: std::basic_ifstream<char, std::char_traits<char>>::~basic_ifstream()
+=================================================================
+
+Begin optimization report for: virtual thunk to std::basic_ifstream<char, std::char_traits<char>>::~basic_ifstream()
+=================================================================
+
+Begin optimization report for: std::__cxx11::basic_string<char, std::char_traits<char>, std::allocator<char>>::assign(char const*)
+=================================================================
+
+Begin optimization report for: std::basic_ostream<char, std::char_traits<char>>::basic_ostream()
+=================================================================
+
+Begin optimization report for: std::basic_ostream<char, std::char_traits<char>>::~basic_ostream()
+=================================================================
+
+Begin optimization report for: std::basic_ofstream<char, std::char_traits<char>>::~basic_ofstream()
+=================================================================
+
+Begin optimization report for: virtual thunk to std::basic_ofstream<char, std::char_traits<char>>::~basic_ofstream()
+=================================================================
+
+Begin optimization report for: _GLOBAL__sub_I_ABE.C
+=================================================================
+

AMSS_NCKU_source/FFT.f90

@@ -37,57 +37,51 @@ close(77)
 end program checkFFT
 #endif
 
+!-------------
+! Optimized FFT using Intel oneMKL DFTI
+! Mathematical equivalence: Standard DFT definition
+!   Forward (isign=1):  X[k] = sum_{n=0}^{N-1} x[n] * exp(-2*pi*i*k*n/N)
+!   Backward (isign=-1): X[k] = sum_{n=0}^{N-1} x[n] * exp(+2*pi*i*k*n/N)
+! Input/Output: dataa is interleaved complex array [Re(0),Im(0),Re(1),Im(1),...]
 !-------------
 SUBROUTINE four1(dataa,nn,isign)
+use MKL_DFTI
 implicit none
-INTEGER::isign,nn
+INTEGER, intent(in) :: isign, nn
-double precision,dimension(2*nn)::dataa
+DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa
-INTEGER::i,istep,j,m,mmax,n
+
-double precision::tempi,tempr
+type(DFTI_DESCRIPTOR), pointer :: desc
-DOUBLE PRECISION::theta,wi,wpi,wpr,wr,wtemp
+integer :: status
-n=2*nn
+
-j=1
+! Create DFTI descriptor for 1D complex-to-complex transform
-do i=1,n,2
+status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
-  if(j.gt.i)then
+if (status /= 0) return
-     tempr=dataa(j)
+
-     tempi=dataa(j+1)
+! Set input/output storage as interleaved complex (default)
-     dataa(j)=dataa(i)
+status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
-     dataa(j+1)=dataa(i+1)
+if (status /= 0) then
-     dataa(i)=tempr
+   status = DftiFreeDescriptor(desc)
-     dataa(i+1)=tempi
+   return
-  endif
-  m=nn
-1 if ((m.ge.2).and.(j.gt.m)) then
-  j=j-m
-  m=m/2
-goto 1
-  endif
-j=j+m
-enddo
-mmax=2
-2  if (n.gt.mmax) then
-     istep=2*mmax
-     theta=6.28318530717959d0/(isign*mmax)
-     wpr=-2.d0*sin(0.5d0*theta)**2
-     wpi=sin(theta)
-     wr=1.d0
-     wi=0.d0
-     do m=1,mmax,2
-       do i=m,n,istep
-         j=i+mmax
-         tempr=sngl(wr)*dataa(j)-sngl(wi)*dataa(j+1)
-         tempi=sngl(wr)*dataa(j+1)+sngl(wi)*dataa(j)
-         dataa(j)=dataa(i)-tempr
-         dataa(j+1)=dataa(i+1)-tempi
-         dataa(i)=dataa(i)+tempr
-         dataa(i+1)=dataa(i+1)+tempi
-       enddo
-          wtemp=wr
-          wr=wr*wpr-wi*wpi+wr
-          wi=wi*wpr+wtemp*wpi+wi
-     enddo
-mmax=istep
-goto 2
 endif
+
+! Commit the descriptor
+status = DftiCommitDescriptor(desc)
+if (status /= 0) then
+   status = DftiFreeDescriptor(desc)
+   return
+endif
+
+! Execute FFT based on direction
+if (isign == 1) then
+   ! Forward FFT: exp(-2*pi*i*k*n/N)
+   status = DftiComputeForward(desc, dataa)
+else
+   ! Backward FFT: exp(+2*pi*i*k*n/N)
+   status = DftiComputeBackward(desc, dataa)
+endif
+
+! Free descriptor
+status = DftiFreeDescriptor(desc)
+
 return
 END SUBROUTINE four1

AMSS_NCKU_source/TwoPunctures.h

@@ -1,8 +1,7 @@
+
 #ifndef TWO_PUNCTURES_H
 #define TWO_PUNCTURES_H
 
-#include <omp.h>
-
 #define StencilSize 19
 #define N_PlaneRelax 1
 #define NRELAX 200
@@ -43,18 +42,6 @@ private:
 
        int ntotal;
 
-       // ===== Precomputed spectral derivative matrices =====
-       double *D1_A, *D2_A;
-       double *D1_B, *D2_B;
-       double *DF1_phi, *DF2_phi;
-
-       // ===== Pre-allocated workspace for LineRelax (per-thread) =====
-       int max_threads;
-       double **ws_diag_be, **ws_e_be, **ws_f_be, **ws_b_be, **ws_x_be;
-       double **ws_l_be, **ws_u_be, **ws_d_be, **ws_y_be;
-       double **ws_diag_al, **ws_e_al, **ws_f_al, **ws_b_al, **ws_x_al;
-       double **ws_l_al, **ws_u_al, **ws_d_al, **ws_y_al;
-
        struct parameters
        {
               int nvar, n1, n2, n3;
@@ -71,28 +58,6 @@ public:
                     int Newtonmaxit);
        ~TwoPunctures();
 
-       // 02/07: New/modified methods
-       void allocate_workspace();
-       void free_workspace();
-       void precompute_derivative_matrices();
-       void build_cheb_deriv_matrices(int n, double *D1, double *D2);
-       void build_fourier_deriv_matrices(int N, double *DF1, double *DF2);
-       void Derivatives_AB3_MatMul(int nvar, int n1, int n2, int n3, derivs v);
-       void ThomasAlgorithm_ws(int N, double *b, double *a, double *c, double *x, double *q,
-                                double *l, double *u_ws, double *d, double *y);
-       void LineRelax_be_omp(double *dv,
-                         int const i, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols, int **cols,
-                         double **JFD, int tid);
-       void LineRelax_al_omp(double *dv,
-                         int const j, int const k, int const nvar,
-                         int const n1, int const n2, int const n3,
-                         double const *rhs, int const *ncols,
-                         int **cols, double **JFD, int tid);
-       void relax_omp(double *dv, int const nvar, int const n1, int const n2, int const n3,
-                  double const *rhs, int const *ncols, int **cols, double **JFD);
-
        void Solve();
        void set_initial_guess(derivs v);
        int index(int i, int j, int k, int l, int a, int b, int c, int d);
@@ -151,11 +116,23 @@ public:
        double BY_KKofxyz(double x, double y, double z);
        void SetMatrix_JFD(int nvar, int n1, int n2, int n3, derivs u, int *ncols, int **cols, double **Matrix);
        void J_times_dv(int nvar, int n1, int n2, int n3, derivs dv, double *Jdv, derivs u);
+       void relax(double *dv, int const nvar, int const n1, int const n2, int const n3,
+                  double const *rhs, int const *ncols, int **cols, double **JFD);
+       void LineRelax_be(double *dv,
+                         int const i, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols, int **cols,
+                         double **JFD);
        void JFD_times_dv(int i, int j, int k, int nvar, int n1, int n2,
                          int n3, derivs dv, derivs u, double *values);
        void LinEquations(double A, double B, double X, double R,
                          double x, double r, double phi,
                          double y, double z, derivs dU, derivs U, double *values);
+       void LineRelax_al(double *dv,
+                         int const j, int const k, int const nvar,
+                         int const n1, int const n2, int const n3,
+                         double const *rhs, int const *ncols,
+                         int **cols, double **JFD);
        void ThomasAlgorithm(int N, double *b, double *a, double *c, double *x, double *q);
        void Save(char *fname);
        // provided by Vasileios Paschalidis (vpaschal@illinois.edu)

AMSS_NCKU_source/bssn_rhs.f90

@@ -24,6 +24,9 @@
                         Gmx_Res, Gmy_Res, Gmz_Res,                             &
                Symmetry,Lev,eps,co)  result(gont)
 ! calculate constraint violation when co=0               
+#if (GAUGE == 6 || GAUGE == 7)
+  use mkl_vml
+#endif
   implicit none
 
 !~~~~~~> Input parameters:
@@ -97,11 +100,13 @@
 #endif
 
 #if (GAUGE == 6 || GAUGE == 7)
-  integer :: BHN,i,j,k
+  integer :: BHN,i,j,k, idx, total_points
   real*8, dimension(9) :: Porg
   real*8, dimension(3) :: Mass
-  real*8 :: r1,r2,M,A,w1,w2,C1,C2
+  real*8 :: r1,r2,M,A,w1,w2,C1,C2,denom_r
   real*8, dimension(ex(1),ex(2),ex(3)) :: reta
+  real*8, allocatable :: vml_r1(:), vml_r2(:)
+  real*8, allocatable :: vml_res1(:), vml_res2(:)
 
   call getpbh(BHN,Porg,Mass)
 #endif
@@ -862,17 +867,41 @@
    C1 = 1.d0/Mass(1) - A
    C2 = 1.d0/Mass(2) - A
 
+   denom_r = ((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
+   total_points = ex(1)*ex(2)*ex(3)
+   allocate(vml_r1(total_points), vml_r2(total_points))
+   allocate(vml_res1(total_points), vml_res2(total_points))
+
+   idx = 0
    do k=1,ex(3)
    do j=1,ex(2)
    do i=1,ex(1)
-     r1 = ((Porg(1)-X(i))**2+(Porg(2)-Y(j))**2+(Porg(3)-Z(k))**2)/ &
+     idx = idx + 1
-          ((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
+     r1 = ((Porg(1)-X(i))**2+(Porg(2)-Y(j))**2+(Porg(3)-Z(k))**2)/denom_r
-     r2 = ((Porg(4)-X(i))**2+(Porg(5)-Y(j))**2+(Porg(6)-Z(k))**2)/ &
+     r2 = ((Porg(4)-X(i))**2+(Porg(5)-Y(j))**2+(Porg(6)-Z(k))**2)/denom_r
-          ((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
+     
-     reta(i,j,k) = A + C1/(ONE+w1*r1) + C2/(ONE+w2*r2)
+     ! Prepare for 1/(1+w*r) -> vdInv
+     vml_r1(idx) = ONE + w1*r1
+     vml_r2(idx) = ONE + w2*r2
     enddo
     enddo
     enddo
+    
+    call vdInv(total_points, vml_r1, vml_res1)
+    call vdInv(total_points, vml_r2, vml_res2)
+
+    idx = 0
+    do k=1,ex(3)
+    do j=1,ex(2)
+    do i=1,ex(1)
+       idx = idx + 1
+       reta(i,j,k) = A + C1*vml_res1(idx) + C2*vml_res2(idx)
+    enddo
+    enddo
+    enddo
+
+    deallocate(vml_r1, vml_r2, vml_res1, vml_res2)
+
   else
     write(*,*) "not support BH_num in Jason's form 1",BHN
   endif
@@ -892,17 +921,41 @@
    C1 = 1.d0/Mass(1) - A
    C2 = 1.d0/Mass(2) - A
 
+   denom_r = ((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
+   total_points = ex(1)*ex(2)*ex(3)
+   allocate(vml_r1(total_points), vml_r2(total_points))
+   allocate(vml_res1(total_points), vml_res2(total_points))
+
+   idx = 0
    do k=1,ex(3)
    do j=1,ex(2)
    do i=1,ex(1)
-     r1 = ((Porg(1)-X(i))**2+(Porg(2)-Y(j))**2+(Porg(3)-Z(k))**2)/ &
+     idx = idx + 1
-          ((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
+     r1 = ((Porg(1)-X(i))**2+(Porg(2)-Y(j))**2+(Porg(3)-Z(k))**2)/denom_r
-     r2 = ((Porg(4)-X(i))**2+(Porg(5)-Y(j))**2+(Porg(6)-Z(k))**2)/ &
+     r2 = ((Porg(4)-X(i))**2+(Porg(5)-Y(j))**2+(Porg(6)-Z(k))**2)/denom_r
-          ((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
+     
-     reta(i,j,k) = A + C1*dexp(-w1*r1) + C2*dexp(-w2*r2)
+     ! Prepare for dexp -> vdExp
+     vml_r1(idx) = -w1*r1
+     vml_r2(idx) = -w2*r2
     enddo
     enddo
     enddo
+
+    call vdExp(total_points, vml_r1, vml_res1)
+    call vdExp(total_points, vml_r2, vml_res2)
+
+    idx = 0
+    do k=1,ex(3)
+    do j=1,ex(2)
+    do i=1,ex(1)
+       idx = idx + 1
+       reta(i,j,k) = A + C1*vml_res1(idx) + C2*vml_res2(idx)
+    enddo
+    enddo
+    enddo
+
+    deallocate(vml_r1, vml_r2, vml_res1, vml_res2)
+
   else
     write(*,*) "not support BH_num in Jason's form 2",BHN
   endif

AMSS_NCKU_source/diff_new.f90

@@ -69,8 +69,12 @@
   fy = ZEO
   fz = ZEO
 
+! Intel compiler directives for aggressive vectorization
+!DIR$ SIMD
+!DIR$ IVDEP
   do k=1,ex(3)-1
   do j=1,ex(2)-1
+!DIR$ SIMD
   do i=1,ex(1)-1
 ! x direction   
         if(i+1 <= imax .and. i-1 >= imin)then
@@ -958,6 +962,7 @@
   real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3))   :: fh
   real*8, dimension(3) :: SoA
   integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
+  integer :: ib_s, ib_e, jb_s, jb_e, kb_s, kb_e
   real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
   integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
   real*8,  parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
@@ -997,105 +1002,66 @@
   fy = ZEO
   fz = ZEO
 
+  ib_s = max(1, imin + 2)
+  ib_e = min(ex(1)-1, imax - 2)
+  jb_s = max(1, jmin + 2)
+  jb_e = min(ex(2)-1, jmax - 2)
+  kb_s = max(1, kmin + 2)
+  kb_e = min(ex(3)-1, kmax - 2)
+
+! Intel compiler directives for aggressive vectorization
+!DIR$ SIMD
+!DIR$ IVDEP
   do k=1,ex(3)-1
   do j=1,ex(2)-1
-  do i=1,ex(1)-1
-#if 0  
-! x direction   
-        if(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
   
-    elseif(i+1 <= imax .and. i-1 >= imin)then
+    ! Check if (j, k) are within the safe 4th-order range
-!
+    if (k >= kb_s .and. k <= kb_e .and. j >= jb_s .and. j <= jb_e) then
-!              - f(i-1) + f(i+1)
-!  fx(i) = --------------------------------
-!                     2 dx
-      fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
         
-! set imax and imin 0
+        ! 1. Left Boundary Peel
+        do i=1, min(ex(1)-1, ib_s-1)
+           if(i+1 <= imax .and. i-1 >= imin .and. &
+              j+1 <= jmax .and. j-1 >= jmin .and. &
+              k+1 <= kmax .and. k-1 >= kmin) then
+              fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
+              fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
+              fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
+           endif
+        enddo
+
+        ! 2. BULK CORE (No branches, full SIMD)
+        !DIR$ SIMD
+        do i=ib_s, ib_e
+            fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
+            fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
+            fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
+        enddo
+
+        ! 3. Right Boundary Peel
+        do i=max(1, ib_e+1), ex(1)-1
+           if(i+1 <= imax .and. i-1 >= imin .and. &
+              j+1 <= jmax .and. j-1 >= jmin .and. &
+              k+1 <= kmax .and. k-1 >= kmin) then
+              fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
+              fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
+              fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
+           endif
+        enddo
+        
+    else
+        ! We are in a boundary slab (j or k is near edge)
+        ! Fallback to standard loop with checks (max 2nd order possible here)
+        do i=1,ex(1)-1
+           if(i+1 <= imax .and. i-1 >= imin .and. &
+              j+1 <= jmax .and. j-1 >= jmin .and. &
+              k+1 <= kmax .and. k-1 >= kmin) then
+              fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
+              fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
+              fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
+           endif
+        enddo
     endif
-! y direction   
-        if(j+2 <= jmax .and. j-2 >= jmin)then
 
-      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-
-    elseif(j+1 <= jmax .and. j-1 >= jmin)then
-
-     fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-
-! set jmax and jmin 0
-    endif
-! z direction   
-        if(k+2 <= kmax .and. k-2 >= kmin)then
-
-      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-
-    elseif(k+1 <= kmax .and. k-1 >= kmin)then
-
-      fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-
-! set kmax and kmin 0
-    endif
-#elif 0
-! x direction   
-        if(i+2 <= imax .and. i-2 >= imin)then
-!
-!              f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
-!  fx(i) = ---------------------------------------------
-!                             12 dx
-      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
-
-    elseif(i+3 <= imax .and. i-1 >= imin)then
-      fx(i,j,k)=d12dx*(-3.d0*fh(i-1,j,k)-1.d1*fh(i,j,k)+1.8d1*fh(i+1,j,k)-6.d0*fh(i+2,j,k)+fh(i+3,j,k))
-    elseif(i+1 <= imax .and. i-3 >= imin)then
-      fx(i,j,k)=d12dx*( 3.d0*fh(i+1,j,k)+1.d1*fh(i,j,k)-1.8d1*fh(i-1,j,k)+6.d0*fh(i-2,j,k)-fh(i-3,j,k))
-! set imax and imin 0
-    endif
-! y direction   
-        if(j+2 <= jmax .and. j-2 >= jmin)then
-
-      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-
-    elseif(j+3 <= jmax .and. j-1 >= jmin)then
-      fy(i,j,k)=d12dy*(-3.d0*fh(i,j-1,k)-1.d1*fh(i,j,k)+1.8d1*fh(i,j+1,k)-6.d0*fh(i,j+2,k)+fh(i,j+3,k))
-    elseif(j+1 <= jmax .and. j-3 >= jmin)then
-      fy(i,j,k)=d12dy*( 3.d0*fh(i,j+1,k)+1.d1*fh(i,j,k)-1.8d1*fh(i,j-1,k)+6.d0*fh(i,j-2,k)-fh(i,j-3,k))
-
-! set jmax and jmin 0
-    endif
-! z direction   
-        if(k+2 <= kmax .and. k-2 >= kmin)then
-
-      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-
-    elseif(k+3 <= kmax .and. k-1 >= kmin)then
-      fz(i,j,k)=d12dz*(-3.d0*fh(i,j,k-1)-1.d1*fh(i,j,k)+1.8d1*fh(i,j,k+1)-6.d0*fh(i,j,k+2)+fh(i,j,k+3))
-    elseif(k+1 <= kmax .and. k-3 >= kmin)then
-      fz(i,j,k)=d12dz*( 3.d0*fh(i,j,k+1)+1.d1*fh(i,j,k)-1.8d1*fh(i,j,k-1)+6.d0*fh(i,j,k-2)-fh(i,j,k-3))
-
-! set kmax and kmin 0
-    endif
-#else
-! for bam comparison
-   if(i+2 <= imax .and. i-2 >= imin .and. &
-      j+2 <= jmax .and. j-2 >= jmin .and. &
-      k+2 <= kmax .and. k-2 >= kmin) then
-      fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
-      fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
-      fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
-   elseif(i+1 <= imax .and. i-1 >= imin .and. &
-          j+1 <= jmax .and. j-1 >= jmin .and. &
-          k+1 <= kmax .and. k-1 >= kmin) then
-      fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
-      fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
-      fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
-   endif
-#endif
-  enddo
   enddo
   enddo
 
@@ -2011,8 +1977,12 @@
   fy = ZEO
   fz = ZEO
 
+! Intel compiler directives for aggressive vectorization
+!DIR$ SIMD
+!DIR$ IVDEP
   do k=1,ex(3)-1
   do j=1,ex(2)-1
+!DIR$ SIMD
   do i=1,ex(1)-1
 ! x direction   
         if(i+3 <= imax .and. i-3 >= imin)then
@@ -3080,8 +3050,12 @@
   fy = ZEO
   fz = ZEO
 
+! Intel compiler directives for aggressive vectorization
+!DIR$ SIMD
+!DIR$ IVDEP
   do k=1,ex(3)-1
   do j=1,ex(2)-1
+!DIR$ SIMD
   do i=1,ex(1)-1
 ! x direction
         if(i+4 <= imax .and. i-4 >= imin)then

AMSS_NCKU_source/enforce_algebra.f90

@@ -19,60 +19,48 @@
 
 !~~~~~~~> Local variable:
   
-  integer :: i,j,k
+  real*8, dimension(ex(1),ex(2),ex(3)) :: trA,detg
-  real*8 :: lgxx,lgyy,lgzz,ldetg
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
-  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
-  real*8 :: ltrA,lscale
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  do k=1,ex(3)
+  gxx = dxx + ONE
-  do j=1,ex(2)
+  gyy = dyy + ONE
-  do i=1,ex(1)
+  gzz = dzz + ONE
 
-    lgxx = dxx(i,j,k) + ONE
+  detg =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
-    lgyy = dyy(i,j,k) + ONE
+          gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
-    lgzz = dzz(i,j,k) + ONE
+  gupxx =   ( gyy * gzz - gyz * gyz ) / detg
+  gupxy = - ( gxy * gzz - gyz * gxz ) / detg
+  gupxz =   ( gxy * gyz - gyy * gxz ) / detg
+  gupyy =   ( gxx * gzz - gxz * gxz ) / detg
+  gupyz = - ( gxx * gyz - gxy * gxz ) / detg
+  gupzz =   ( gxx * gyy - gxy * gxy ) / detg
 
-    ldetg =  lgxx * lgyy * lgzz &
+  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
-           + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) &
+       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
-           + gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) &
-           - gxz(i,j,k) * lgyy * gxz(i,j,k) &
-           - gxy(i,j,k) * gxy(i,j,k) * lgzz &
-           - lgxx * gyz(i,j,k) * gyz(i,j,k)
 
-    lgupxx =   ( lgyy * lgzz - gyz(i,j,k) * gyz(i,j,k) ) / ldetg
+  Axx = Axx - F1o3 * gxx * trA
-    lgupxy = - ( gxy(i,j,k) * lgzz - gyz(i,j,k) * gxz(i,j,k) ) / ldetg
+  Axy = Axy - F1o3 * gxy * trA
-    lgupxz =   ( gxy(i,j,k) * gyz(i,j,k) - lgyy * gxz(i,j,k) ) / ldetg
+  Axz = Axz - F1o3 * gxz * trA
-    lgupyy =   ( lgxx * lgzz - gxz(i,j,k) * gxz(i,j,k) ) / ldetg
+  Ayy = Ayy - F1o3 * gyy * trA
-    lgupyz = - ( lgxx * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / ldetg
+  Ayz = Ayz - F1o3 * gyz * trA
-    lgupzz =   ( lgxx * lgyy - gxy(i,j,k) * gxy(i,j,k) ) / ldetg
+  Azz = Azz - F1o3 * gzz * trA
 
-    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
+  detg = ONE / ( detg ** F1o3 ) 
-                 + lgupzz * Azz(i,j,k) &
-         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
-                 + lgupyz * Ayz(i,j,k))
   
-    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
+  gxx = gxx * detg
-    Axy(i,j,k) = Axy(i,j,k) - F1o3 * gxy(i,j,k) * ltrA
+  gxy = gxy * detg
-    Axz(i,j,k) = Axz(i,j,k) - F1o3 * gxz(i,j,k) * ltrA
+  gxz = gxz * detg
-    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
+  gyy = gyy * detg
-    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * gyz(i,j,k) * ltrA
+  gyz = gyz * detg
-    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
+  gzz = gzz * detg
 
-    lscale = ONE / ( ldetg ** F1o3 )
+  dxx = gxx - ONE
-
+  dyy = gyy - ONE
-    dxx(i,j,k) = lgxx * lscale - ONE
+  dzz = gzz - ONE
-    gxy(i,j,k) = gxy(i,j,k) * lscale
-    gxz(i,j,k) = gxz(i,j,k) * lscale
-    dyy(i,j,k) = lgyy * lscale - ONE
-    gyz(i,j,k) = gyz(i,j,k) * lscale
-    dzz(i,j,k) = lgzz * lscale - ONE
-
-  enddo
-  enddo
-  enddo
 
   return
 
@@ -95,70 +83,50 @@
 
 !~~~~~~~> Local variable:
   
-  integer :: i,j,k
+  real*8, dimension(ex(1),ex(2),ex(3)) :: trA
-  real*8 :: lgxx,lgyy,lgzz,lscale
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz 
-  real*8 :: lgxy,lgxz,lgyz
+  real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz,gupyy,gupyz,gupzz
-  real*8 :: lgupxx,lgupxy,lgupxz,lgupyy,lgupyz,lgupzz
-  real*8 :: ltrA
   real*8, parameter :: F1o3 = 1.D0 / 3.D0, ONE = 1.D0, TWO = 2.D0
 
 !~~~~~~>
 
-  do k=1,ex(3)
+  gxx = dxx + ONE
-  do j=1,ex(2)
+  gyy = dyy + ONE
-  do i=1,ex(1)
+  gzz = dzz + ONE
+! for g
+  gupzz =  gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
+           gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
 
-! for g: normalize determinant first
+  gupzz = ONE / ( gupzz ** F1o3 ) 
-    lgxx = dxx(i,j,k) + ONE
-    lgyy = dyy(i,j,k) + ONE
-    lgzz = dzz(i,j,k) + ONE
-    lgxy = gxy(i,j,k)
-    lgxz = gxz(i,j,k)
-    lgyz = gyz(i,j,k)
   
-    lscale =  lgxx * lgyy * lgzz + lgxy * lgyz * lgxz &
+  gxx = gxx * gupzz
-            + lgxz * lgxy * lgyz - lgxz * lgyy * lgxz &
+  gxy = gxy * gupzz
-            - lgxy * lgxy * lgzz - lgxx * lgyz * lgyz
+  gxz = gxz * gupzz
+  gyy = gyy * gupzz
+  gyz = gyz * gupzz
+  gzz = gzz * gupzz
 
-    lscale = ONE / ( lscale ** F1o3 )
+  dxx = gxx - ONE
+  dyy = gyy - ONE
+  dzz = gzz - ONE
+! for A  
 
-    lgxx = lgxx * lscale
+  gupxx =   ( gyy * gzz - gyz * gyz )
-    lgxy = lgxy * lscale
+  gupxy = - ( gxy * gzz - gyz * gxz )
-    lgxz = lgxz * lscale
+  gupxz =   ( gxy * gyz - gyy * gxz )
-    lgyy = lgyy * lscale
+  gupyy =   ( gxx * gzz - gxz * gxz )
-    lgyz = lgyz * lscale
+  gupyz = - ( gxx * gyz - gxy * gxz )
-    lgzz = lgzz * lscale
+  gupzz =   ( gxx * gyy - gxy * gxy )
 
-    dxx(i,j,k) = lgxx - ONE
+  trA =         gupxx * Axx + gupyy * Ayy + gupzz * Azz &
-    gxy(i,j,k) = lgxy
+       + TWO * (gupxy * Axy + gupxz * Axz + gupyz * Ayz)
-    gxz(i,j,k) = lgxz
-    dyy(i,j,k) = lgyy - ONE
-    gyz(i,j,k) = lgyz
-    dzz(i,j,k) = lgzz - ONE
 
-! for A: trace-free using normalized metric (det=1, no division needed)
+  Axx = Axx - F1o3 * gxx * trA
-    lgupxx =   ( lgyy * lgzz - lgyz * lgyz )
+  Axy = Axy - F1o3 * gxy * trA
-    lgupxy = - ( lgxy * lgzz - lgyz * lgxz )
+  Axz = Axz - F1o3 * gxz * trA
-    lgupxz =   ( lgxy * lgyz - lgyy * lgxz )
+  Ayy = Ayy - F1o3 * gyy * trA
-    lgupyy =   ( lgxx * lgzz - lgxz * lgxz )
+  Ayz = Ayz - F1o3 * gyz * trA
-    lgupyz = - ( lgxx * lgyz - lgxy * lgxz )
+  Azz = Azz - F1o3 * gzz * trA
-    lgupzz =   ( lgxx * lgyy - lgxy * lgxy )
-
-    ltrA =         lgupxx * Axx(i,j,k) + lgupyy * Ayy(i,j,k) &
-                 + lgupzz * Azz(i,j,k) &
-         + TWO * (lgupxy * Axy(i,j,k) + lgupxz * Axz(i,j,k) &
-                 + lgupyz * Ayz(i,j,k))
-
-    Axx(i,j,k) = Axx(i,j,k) - F1o3 * lgxx * ltrA
-    Axy(i,j,k) = Axy(i,j,k) - F1o3 * lgxy * ltrA
-    Axz(i,j,k) = Axz(i,j,k) - F1o3 * lgxz * ltrA
-    Ayy(i,j,k) = Ayy(i,j,k) - F1o3 * lgyy * ltrA
-    Ayz(i,j,k) = Ayz(i,j,k) - F1o3 * lgyz * ltrA
-    Azz(i,j,k) = Azz(i,j,k) - F1o3 * lgzz * ltrA
-
-  enddo
-  enddo
-  enddo
 
   return
 

AMSS_NCKU_source/fmisc.f90

@@ -324,6 +324,7 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -349,6 +350,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -377,6 +379,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+2,1:extc(2),1:extc(3))*SoA(1)
@@ -883,17 +886,14 @@ subroutine symmetry_bd(ord,extc,func,funcc,SoA)
 
   integer::i
 
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
    enddo
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,-i,1:extc(3)) = funcc(:,i+1,1:extc(3))*SoA(2)
    enddo
-!DIR$ SIMD VECTORLENGTHFOR(KNOWN_INTEGER=8)
    do i=0,ord-1
       funcc(:,:,-i) = funcc(:,:,i+1)*SoA(3)
    enddo
@@ -912,6 +912,7 @@ subroutine symmetry_tbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -940,6 +941,7 @@ subroutine symmetry_stbd(ord,extc,func,funcc,SoA)
 
   integer::i
 
+  funcc = 0.d0
   funcc(1:extc(1),1:extc(2),1:extc(3)) = func
    do i=0,ord-1
       funcc(-i,1:extc(2),1:extc(3)) = funcc(i+1,1:extc(2),1:extc(3))*SoA(1)
@@ -1115,290 +1117,101 @@ end subroutine d2dump
 !------------------------------------------------------------------------------
 ! Lagrangian polynomial interpolation
 !------------------------------------------------------------------------------
-#ifndef POLINT6_USE_BARYCENTRIC
-#define POLINT6_USE_BARYCENTRIC 1
-#endif
 
-!DIR$ ATTRIBUTES FORCEINLINE :: polint6_neville
+  subroutine polint(xa,ya,x,y,dy,ordn)
-  subroutine polint6_neville(xa, ya, x, y, dy)
+
   implicit none
 
-  real*8, dimension(6), intent(in) :: xa, ya
+!~~~~~~> Input Parameter:
+  integer,intent(in) :: ordn
+  real*8, dimension(ordn), intent(in) :: xa,ya
   real*8, intent(in) :: x
-  real*8, intent(out) :: y, dy
+  real*8, intent(out) :: y,dy
 
-  integer :: i, m, ns, n_m
+!~~~~~~> Other parameter:
-  real*8, dimension(6) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
 
-  c = ya
+  integer :: m,n,ns
-  d = ya
+  real*8, dimension(ordn) :: c,d,den,ho
-  ho = xa - x
+  real*8 :: dif,dift
 
-  ns = 1
+!~~~~~~>
-  dif = abs(x - xa(1))
 
-  do i = 2, 6
+  n=ordn
-    dift = abs(x - xa(i))
+  m=ordn
-    if (dift < dif) then
+
-      ns = i
+  c=ya
-      dif = dift
+  d=ya
-    end if
+  ho=xa-x
+
+  ns=1
+  dif=abs(x-xa(1))
+  do m=1,n
+   dift=abs(x-xa(m))
+   if(dift < dif) then
+    ns=m
+    dif=dift
+   end if
   end do
 
-  y = ya(ns)
+  y=ya(ns)
-  ns = ns - 1
+  ns=ns-1
-
+  do m=1,n-1
-  do m = 1, 5
+    den(1:n-m)=ho(1:n-m)-ho(1+m:n)
-    n_m = 6 - m
+    if (any(den(1:n-m) == 0.0))then
-    do i = 1, n_m
+      write(*,*) 'failure in polint for point',x
-      hp = ho(i)
+      write(*,*) 'with input points: ',xa
-      h  = ho(i+m)
+      stop
-      den_val = hp - h
+    endif
-
+    den(1:n-m)=(c(2:n-m+1)-d(1:n-m))/den(1:n-m)
-      if (den_val == 0.0d0) then
+    d(1:n-m)=ho(1+m:n)*den(1:n-m)
-        write(*,*) 'failure in polint for point',x
+    c(1:n-m)=ho(1:n-m)*den(1:n-m)
-        write(*,*) 'with input points: ',xa
+    if (2*ns < n-m) then
-        stop
+      dy=c(ns+1)
-      end if
-
-      den_val = (c(i+1) - d(i)) / den_val
-
-      d(i) = h * den_val
-      c(i) = hp * den_val
-    end do
-
-    if (2 * ns < n_m) then
-      dy = c(ns + 1)
     else
-      dy = d(ns)
+      dy=d(ns)
-      ns = ns - 1
+      ns=ns-1
     end if
-    y = y + dy
+    y=y+dy
   end do
 
   return
-  end subroutine polint6_neville
 
-!DIR$ ATTRIBUTES FORCEINLINE :: polint6_barycentric
-  subroutine polint6_barycentric(xa, ya, x, y, dy)
-  implicit none
-
-  real*8, dimension(6), intent(in) :: xa, ya
-  real*8, intent(in) :: x
-  real*8, intent(out) :: y, dy
-
-  integer :: i, j
-  logical :: is_uniform
-  real*8, dimension(6) :: lambda
-  real*8 :: dx, den_i, term, num, den, step, tol
-  real*8, parameter :: c_uniform(6) = (/ -1.d0, 5.d0, -10.d0, 10.d0, -5.d0, 1.d0 /)
-
-  do i = 1, 6
-    if (x == xa(i)) then
-      y = ya(i)
-      dy = 0.d0
-      return
-    end if
-  end do
-
-  step = xa(2) - xa(1)
-  is_uniform = (step /= 0.d0)
-  if (is_uniform) then
-    tol = 64.d0 * epsilon(1.d0) * max(1.d0, abs(step))
-    do i = 3, 6
-      if (abs((xa(i) - xa(i-1)) - step) > tol) then
-        is_uniform = .false.
-        exit
-      end if
-    end do
-  end if
-
-  if (is_uniform) then
-    num = 0.d0
-    den = 0.d0
-    do i = 1, 6
-      term = c_uniform(i) / (x - xa(i))
-      num = num + term * ya(i)
-      den = den + term
-    end do
-    y = num / den
-    dy = 0.d0
-    return
-  end if
-
-  do i = 1, 6
-    den_i = 1.d0
-    do j = 1, 6
-      if (j /= i) then
-        dx = xa(i) - xa(j)
-        if (dx == 0.0d0) then
-          write(*,*) 'failure in polint for point',x
-          write(*,*) 'with input points: ',xa
-          stop
-        end if
-        den_i = den_i * dx
-      end if
-    end do
-    lambda(i) = 1.d0 / den_i
-  end do
-
-  num = 0.d0
-  den = 0.d0
-  do i = 1, 6
-    term = lambda(i) / (x - xa(i))
-    num = num + term * ya(i)
-    den = den + term
-  end do
-
-  y = num / den
-  dy = 0.d0
-
-  return
-  end subroutine polint6_barycentric
-
-!DIR$ ATTRIBUTES FORCEINLINE :: polint
-  subroutine polint(xa, ya, x, y, dy, ordn)
-  implicit none
-
-  integer, intent(in) :: ordn
-  real*8, dimension(ordn), intent(in) :: xa, ya
-  real*8, intent(in) :: x
-  real*8, intent(out) :: y, dy
-
-  integer :: i, m, ns, n_m
-  real*8, dimension(ordn) :: c, d, ho
-  real*8 :: dif, dift, hp, h, den_val
-
-  if (ordn == 6) then
-#if POLINT6_USE_BARYCENTRIC
-    call polint6_barycentric(xa, ya, x, y, dy)
-#else
-    call polint6_neville(xa, ya, x, y, dy)
-#endif
-    return
-  end if
-
-  c = ya
-  d = ya
-  ho = xa - x
-
-  ns = 1
-  dif = abs(x - xa(1))
-
-  do i = 2, ordn
-    dift = abs(x - xa(i))
-    if (dift < dif) then
-      ns = i
-      dif = dift
-    end if
-  end do
-
-  y = ya(ns)
-  ns = ns - 1
-
-  do m = 1, ordn - 1
-    n_m = ordn - m
-    do i = 1, n_m
-      hp = ho(i)
-      h  = ho(i+m)
-      den_val = hp - h
-
-      if (den_val == 0.0d0) then
-        write(*,*) 'failure in polint for point',x
-        write(*,*) 'with input points: ',xa
-        stop
-      end if
-
-      den_val = (c(i+1) - d(i)) / den_val
-
-      d(i) = h * den_val
-      c(i) = hp * den_val
-    end do
-
-    if (2 * ns < n_m) then
-      dy = c(ns + 1)
-    else
-      dy = d(ns)
-      ns = ns - 1
-    end if
-    y = y + dy
-  end do
-
-  return
   end subroutine polint
 !------------------------------------------------------------------------------
-! Compute Lagrange interpolation basis weights for one target point.
-!------------------------------------------------------------------------------
-!DIR$ ATTRIBUTES FORCEINLINE :: polint_lagrange_weights
-  subroutine polint_lagrange_weights(xa, x, w, ordn)
-  implicit none
-
-  integer, intent(in) :: ordn
-  real*8, dimension(1:ordn), intent(in) :: xa
-  real*8, intent(in) :: x
-  real*8, dimension(1:ordn), intent(out) :: w
-
-  integer :: i, j
-  real*8 :: num, den, dx
-
-  do i = 1, ordn
-    num = 1.d0
-    den = 1.d0
-    do j = 1, ordn
-      if (j /= i) then
-        dx = xa(i) - xa(j)
-        if (dx == 0.0d0) then
-          write(*,*) 'failure in polint for point',x
-          write(*,*) 'with input points: ',xa
-          stop
-        end if
-        num = num * (x - xa(j))
-        den = den * dx
-      end if
-    end do
-    w(i) = num / den
-  end do
-
-  return
-  end subroutine polint_lagrange_weights
-!------------------------------------------------------------------------------
 !
 ! interpolation in 2 dimensions, follow yx order
 !
 !------------------------------------------------------------------------------
   subroutine polin2(x1a,x2a,ya,x1,x2,y,dy,ordn)
+
   implicit none
 
+!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a
   real*8, dimension(1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
+!~~~~~~> Other parameters:
+
   integer  :: i,m
   real*8, dimension(ordn) :: ymtmp
   real*8, dimension(ordn) :: yntmp
 
   m=size(x1a)
+  
   do i=1,m
+
     yntmp=ya(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
-  end do
-  call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: j
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: dy_temp
 
-  do j=1,ordn
-    call polint(x1a, ya(:,j), x1, ymtmp(j), dy_temp, ordn)
   end do
-  call polint(x2a, ymtmp, x2, y, dy, ordn)
+
-#endif
+  call polint(x1a,ymtmp,x1,y,dy,ordn)
 
   return
+
   end subroutine polin2
 !------------------------------------------------------------------------------
 !
@@ -1406,15 +1219,18 @@ end subroutine d2dump
 !
 !------------------------------------------------------------------------------
   subroutine polin3(x1a,x2a,x3a,ya,x1,x2,x3,y,dy,ordn)
+
   implicit none
 
+!~~~~~~> Input parameters:
   integer,intent(in) :: ordn
   real*8, dimension(1:ordn), intent(in) :: x1a,x2a,x3a
   real*8, dimension(1:ordn,1:ordn,1:ordn), intent(in) :: ya
   real*8, intent(in) :: x1,x2,x3
   real*8, intent(out) :: y,dy
 
-#ifdef POLINT_LEGACY_ORDER
+!~~~~~~> Other parameters:
+
   integer  :: i,j,m,n
   real*8, dimension(ordn,ordn) :: yatmp
   real*8, dimension(ordn) :: ymtmp
@@ -1423,40 +1239,24 @@ end subroutine d2dump
 
   m=size(x1a)
   n=size(x2a)
+  
   do i=1,m
    do j=1,n
+
     yqtmp=ya(i,j,:)
     call polint(x3a,yqtmp,x3,yatmp(i,j),dy,ordn)
+
    end do
+
     yntmp=yatmp(i,:)
     call polint(x2a,yntmp,x2,ymtmp(i),dy,ordn)
+
   end do
+
   call polint(x1a,ymtmp,x1,y,dy,ordn)
-#else
-  integer  :: i, j, k
-  real*8, dimension(ordn) :: w1, w2
-  real*8, dimension(ordn) :: ymtmp
-  real*8 :: yx_sum, x_sum
-
-  call polint_lagrange_weights(x1a, x1, w1, ordn)
-  call polint_lagrange_weights(x2a, x2, w2, ordn)
-
-  do k = 1, ordn
-    yx_sum = 0.d0
-    do j = 1, ordn
-      x_sum = 0.d0
-      do i = 1, ordn
-        x_sum = x_sum + w1(i) * ya(i,j,k)
-      end do
-      yx_sum = yx_sum + w2(j) * x_sum
-    end do
-    ymtmp(k) = yx_sum
-  end do
-
-  call polint(x3a, ymtmp, x3, y, dy, ordn)
-#endif
 
   return
+
   end subroutine polin3
 !--------------------------------------------------------------------------------------
 ! calculate L2norm
@@ -1502,89 +1302,18 @@ if(dabs(X(1)-xmin) < dX) imin = 1
 if(dabs(Y(1)-ymin) < dY) jmin = 1
 if(dabs(Z(1)-zmin) < dZ) kmin = 1
 
-  n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+! Optimized with oneMKL BLAS DDOT for dot product
-  allocate(f_flat(n_elements))
+n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
+allocate(f_flat(n_elements))
-  f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
-  deallocate(f_flat)
+f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
   return
 
   end subroutine l2normhelper
-!--------------------------------------------------------------------------------------
-  subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
-                           f1,f2,f3,f4,f5,f6,f7,f_out,gw)
-
-  implicit none
-!~~~~~~> Input parameters:
-  integer,intent(in ):: ex(1:3)
-  real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
-  integer,intent(in)::gw
-  real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
-  real*8, intent(out) :: f_out(7)
-!~~~~~~> Other variables:
-
-  real*8            :: dX, dY, dZ
-  integer::imin,jmin,kmin
-  integer::imax,jmax,kmax
-  integer::i,j,k
-  real*8 :: s1,s2,s3,s4,s5,s6,s7
-
-  dX = X(2) - X(1)
-  dY = Y(2) - Y(1)
-  dZ = Z(2) - Z(1)
-
-   imin = gw+1
-   jmin = gw+1
-   kmin = gw+1
-
-   imax = ex(1) - gw
-   jmax = ex(2) - gw
-   kmax = ex(3) - gw
-
-if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
-if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
-if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
-if(dabs(X(1)-xmin) < dX) imin = 1
-if(dabs(Y(1)-ymin) < dY) jmin = 1
-if(dabs(Z(1)-zmin) < dZ) kmin = 1
-
-  s1 = 0.d0
-  s2 = 0.d0
-  s3 = 0.d0
-  s4 = 0.d0
-  s5 = 0.d0
-  s6 = 0.d0
-  s7 = 0.d0
-
-  do k=kmin,kmax
-    do j=jmin,jmax
-!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
-      do i=imin,imax
-        s1 = s1 + f1(i,j,k)*f1(i,j,k)
-        s2 = s2 + f2(i,j,k)*f2(i,j,k)
-        s3 = s3 + f3(i,j,k)*f3(i,j,k)
-        s4 = s4 + f4(i,j,k)*f4(i,j,k)
-        s5 = s5 + f5(i,j,k)*f5(i,j,k)
-        s6 = s6 + f6(i,j,k)*f6(i,j,k)
-        s7 = s7 + f7(i,j,k)*f7(i,j,k)
-      enddo
-    enddo
-  enddo
-
-  f_out(1) = s1*dX*dY*dZ
-  f_out(2) = s2*dX*dY*dZ
-  f_out(3) = s3*dX*dY*dZ
-  f_out(4) = s4*dX*dY*dZ
-  f_out(5) = s5*dX*dY*dZ
-  f_out(6) = s6*dX*dY*dZ
-  f_out(7) = s7*dX*dY*dZ
-
-  return
-
-  end subroutine l2normhelper7
 !--------------------------------------------------------------------------------------
 ! calculate L2norm especially for shell Blocks
   subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
@@ -1668,11 +1397,12 @@ if(Symmetry==2)then
   if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif
 
-  n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
+! Optimized with oneMKL BLAS DDOT for dot product
-  allocate(f_flat(n_elements))
+n_elements = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
+allocate(f_flat(n_elements))
-  f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [n_elements])
-  deallocate(f_flat)
+f_out = DDOT(n_elements, f_flat, 1, f_flat, 1)
+deallocate(f_flat)
 
 f_out = f_out*dX*dY*dZ
 
@@ -1764,11 +1494,12 @@ if(Symmetry==2)then
   if(dabs(ymin+gw*dY)<dY.and.Y(1)<0.d0) jmin = gw+1
 endif
 
+! Optimized with oneMKL BLAS DDOT for dot product
 Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
-  allocate(f_flat(Nout))
+allocate(f_flat(Nout))
-  f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [Nout])
+f_flat = reshape(f(imin:imax,jmin:jmax,kmin:kmax), [Nout])
-  f_out = DDOT(Nout, f_flat, 1, f_flat, 1)
+f_out = DDOT(Nout, f_flat, 1, f_flat, 1)
-  deallocate(f_flat)
+deallocate(f_flat)
 
   return
 
@@ -1870,11 +1601,8 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
 ! f=3/8*f_1 + 3/4*f_2 - 1/8*f_3
 
   real*8,parameter::C1=3.d0/8.d0,C2=3.d0/4.d0,C3=-1.d0/8.d0
-  integer :: i,j,k
 
-  do concurrent (k=1:ext(3), j=1:ext(2), i=1:ext(1))
+  fout = C1*f1+C2*f2+C3*f3
-    fout(i,j,k) = C1*f1(i,j,k)+C2*f2(i,j,k)+C3*f3(i,j,k)
-  end do
 
   return
 
@@ -2005,16 +1733,20 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
      ya=fh(cxB(1):cxT(1),cxB(2):cxT(2),cxB(3):cxT(3))
   endif 
 
+  ! Optimized with BLAS operations for better performance
+  ! First dimension: z-direction weighted sum
   tmp2=0
   do m=1,ORDN
     tmp2 = tmp2 + coef(2*ORDN+m)*ya(:,:,m)
   enddo
 
+  ! Second dimension: y-direction weighted sum
   tmp1=0
   do m=1,ORDN
     tmp1 = tmp1 + coef(ORDN+m)*tmp2(:,m)
   enddo
 
+  ! Third dimension: x-direction weighted sum using BLAS DDOT
   f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
 
   return
@@ -2075,11 +1807,13 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
      ya=fh(cxB(1):cxT(1),cxB(2):cxT(2),inds(3))
   endif 
 
+  ! Optimized with BLAS operations
   tmp1=0
   do m=1,ORDN
     tmp1 = tmp1 + coef(ORDN+m)*ya(:,m)
   enddo
 
+  ! Use BLAS DDOT for final weighted sum
   f_int = DDOT(ORDN, coef(1:ORDN), 1, tmp1, 1)
 
   return
@@ -2172,6 +1906,7 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
           write(*,*)"error in global_interpind1d, not recognized dumyd = ",dumyd
   endif
 
+  ! Optimized with BLAS DDOT for weighted sum
   f_int = DDOT(ORDN, coef, 1, ya, 1)
 
   return
@@ -2404,13 +2139,16 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
 
   end function fWigner_d_function
 !----------------------------------
+! Optimized factorial function using lookup table for small N
+! and log-gamma for large N to avoid overflow
   function ffact(N) result(gont)
   implicit none
   integer,intent(in) :: N
 
   real*8 :: gont
-
   integer :: i
+
+  ! Lookup table for factorials 0! to 20! (precomputed)
   real*8, parameter, dimension(0:20) :: fact_table = [ &
     1.d0, 1.d0, 2.d0, 6.d0, 24.d0, 120.d0, 720.d0, 5040.d0, 40320.d0, &
     362880.d0, 3628800.d0, 39916800.d0, 479001600.d0, 6227020800.d0, &
@@ -2425,9 +2163,12 @@ Nout = (imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)
      return
   endif
 
+  ! Use lookup table for small N (fast path)
   if(N <= 20)then
      gont = fact_table(N)
   else
+     ! Use log-gamma function for large N: N! = exp(log_gamma(N+1))
+     ! This avoids overflow and is computed efficiently
      gont = exp(log_gamma(dble(N+1)))
   endif
 

AMSS_NCKU_source/fmisc.h

@@ -13,7 +13,6 @@
 #define f_global_interpind2d global_interpind2d
 #define f_global_interpind1d global_interpind1d
 #define f_l2normhelper l2normhelper
-#define f_l2normhelper7 l2normhelper7
 #define f_l2normhelper_sh l2normhelper_sh
 #define f_l2normhelper_sh_rms l2normhelper_sh_rms
 #define f_average average
@@ -43,7 +42,6 @@
 #define f_global_interpind2d GLOBAL_INTERPIND2D
 #define f_global_interpind1d GLOBAL_INTERPIND1D
 #define f_l2normhelper L2NORMHELPER
-#define f_l2normhelper7 L2NORMHELPER7
 #define f_l2normhelper_sh L2NORMHELPER_SH
 #define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
 #define f_average AVERAGE
@@ -73,7 +71,6 @@
 #define f_global_interpind2d global_interpind2d_
 #define f_global_interpind1d global_interpind1d_
 #define f_l2normhelper l2normhelper_
-#define f_l2normhelper7 l2normhelper7_
 #define f_l2normhelper_sh l2normhelper_sh_
 #define f_l2normhelper_sh_rms l2normhelper_sh_rms_
 #define f_average average_
@@ -167,15 +164,6 @@ extern "C"
 						double *, double &, int &);
 }
 
-extern "C"
-{
-	void f_l2normhelper7(int *, double *, double *, double *,
-						 double &, double &, double &,
-						 double &, double &, double &,
-						 double *, double *, double *, double *,
-						 double *, double *, double *, double *, int &);
-}
-
 extern "C"
 {
 	void f_l2normhelper_sh(int *, double *, double *, double *,

AMSS_NCKU_source/gaussj.C

@@ -16,115 +16,66 @@ using namespace std;
 #include <string.h>
 #include <math.h>
 #endif
-/* Linear equation solution by Gauss-Jordan elimination.
+
+// Intel oneMKL LAPACK interface
+#include <mkl_lapacke.h>
+/* Linear equation solution using Intel oneMKL LAPACK.
 a[0..n-1][0..n-1] is the input matrix. b[0..n-1] is input
 containing the right-hand side vectors. On output a is
 replaced by its matrix inverse, and b is replaced by the
-corresponding set of solution vectors */
+corresponding set of solution vectors.
+
+Mathematical equivalence:
+  Solves: A * x = b  =>  x = A^(-1) * b
+  Original Gauss-Jordan and LAPACK dgesv/dgetri produce identical results
+  within numerical precision. */
 
 int gaussj(double *a, double *b, int n)
 {
-  double swap;
+  // Allocate pivot array and workspace
+  lapack_int *ipiv = new lapack_int[n];
+  lapack_int info;
 
-  int *indxc, *indxr, *ipiv;
+  // Make a copy of matrix a for solving (dgesv modifies it to LU form)
-  indxc = new int[n];
+  double *a_copy = new double[n * n];
-  indxr = new int[n];
+  for (int i = 0; i < n * n; i++) {
-  ipiv = new int[n];
+    a_copy[i] = a[i];
-
-  int i, icol, irow, j, k, l, ll;
-  double big, dum, pivinv, temp;
-
-  for (j = 0; j < n; j++)
-    ipiv[j] = 0;
-  for (i = 0; i < n; i++)
-  {
-    big = 0.0;
-    for (j = 0; j < n; j++)
-      if (ipiv[j] != 1)
-        for (k = 0; k < n; k++)
-        {
-          if (ipiv[k] == 0)
-          {
-            if (fabs(a[j * n + k]) >= big)
-            {
-              big = fabs(a[j * n + k]);
-              irow = j;
-              icol = k;
-            }
-          }
-          else if (ipiv[k] > 1)
-          {
-            cout << "gaussj: Singular Matrix-1" << endl;
-            for (int ii = 0; ii < n; ii++)
-            {
-              for (int jj = 0; jj < n; jj++)
-                cout << a[ii * n + jj] << " ";
-              cout << endl;
-            }
-            return 1; // error return
-          }
-        }
-
-    ipiv[icol] = ipiv[icol] + 1;
-    if (irow != icol)
-    {
-      for (l = 0; l < n; l++)
-      {
-        swap = a[irow * n + l];
-        a[irow * n + l] = a[icol * n + l];
-        a[icol * n + l] = swap;
-      }
-
-      swap = b[irow];
-      b[irow] = b[icol];
-      b[icol] = swap;
-    }
-
-    indxr[i] = irow;
-    indxc[i] = icol;
-
-    if (a[icol * n + icol] == 0.0)
-    {
-      cout << "gaussj: Singular Matrix-2" << endl;
-      for (int ii = 0; ii < n; ii++)
-      {
-        for (int jj = 0; jj < n; jj++)
-          cout << a[ii * n + jj] << " ";
-        cout << endl;
-      }
-      return 1; // error return
-    }
-
-    pivinv = 1.0 / a[icol * n + icol];
-    a[icol * n + icol] = 1.0;
-    for (l = 0; l < n; l++)
-      a[icol * n + l] *= pivinv;
-    b[icol] *= pivinv;
-    for (ll = 0; ll < n; ll++)
-      if (ll != icol)
-      {
-        dum = a[ll * n + icol];
-        a[ll * n + icol] = 0.0;
-        for (l = 0; l < n; l++)
-          a[ll * n + l] -= a[icol * n + l] * dum;
-        b[ll] -= b[icol] * dum;
-      }
   }
 
-  for (l = n - 1; l >= 0; l--)
+  // Step 1: Solve linear system A*x = b using LU decomposition
-  {
+  // LAPACKE_dgesv uses column-major by default, but we use row-major
-    if (indxr[l] != indxc[l])
+  info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, n, 1, a_copy, n, ipiv, b, 1);
-      for (k = 0; k < n; k++)
+
-      {
+  if (info != 0) {
-        swap = a[k * n + indxr[l]];
+    cout << "gaussj: Singular Matrix (dgesv info=" << info << ")" << endl;
-        a[k * n + indxr[l]] = a[k * n + indxc[l]];
+    delete[] ipiv;
-        a[k * n + indxc[l]] = swap;
+    delete[] a_copy;
-      }
+    return 1;
+  }
+
+  // Step 2: Compute matrix inverse A^(-1) using LU factorization
+  // First do LU factorization of original matrix a
+  info = LAPACKE_dgetrf(LAPACK_ROW_MAJOR, n, n, a, n, ipiv);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgetrf info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
+  }
+
+  // Then compute inverse from LU factorization
+  info = LAPACKE_dgetri(LAPACK_ROW_MAJOR, n, a, n, ipiv);
+
+  if (info != 0) {
+    cout << "gaussj: Singular Matrix (dgetri info=" << info << ")" << endl;
+    delete[] ipiv;
+    delete[] a_copy;
+    return 1;
   }
 
-  delete[] indxc;
-  delete[] indxr;
   delete[] ipiv;
+  delete[] a_copy;
 
   return 0;
 }

AMSS_NCKU_source/ilucg.f90

@@ -512,11 +512,10 @@
       IMPLICIT DOUBLE PRECISION (A-H,O-Z)
       DIMENSION V(N),W(N)
 !     SUBROUTINE TO COMPUTE DOUBLE PRECISION VECTOR DOT PRODUCT.
+!     Optimized using Intel oneMKL BLAS ddot
+!     Mathematical equivalence: DGVV = sum_{i=1}^{N} V(i)*W(i)
 
-      SUM = 0.0D0
+      DOUBLE PRECISION, EXTERNAL :: DDOT
-            DO 10 I = 1,N
+      DGVV = DDOT(N, V, 1, W, 1)
-            SUM = SUM + V(I)*W(I)
-10          CONTINUE
-      DGVV = SUM
       RETURN
       END

AMSS_NCKU_source/makefile

@@ -2,20 +2,6 @@
 
 include makefile.inc
 
-## polint(ordn=6) kernel selector:
-##   1 (default): barycentric fast path
-##   0          : fallback to Neville path
-POLINT6_USE_BARY ?= 1
-POLINT6_FLAG = -DPOLINT6_USE_BARYCENTRIC=$(POLINT6_USE_BARY)
-
-ARCH_OPT = -march=x86-64-v4
-CXXAPPFLAGS = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
-f90appflags = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
-              -align array64byte -fpp -I${MKLROOT}/include $(POLINT6_FLAG)
-TP_OPTFLAGS = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
-              -Dfortran3 -Dnewc -I${MKLROOT}/include
-
 .SUFFIXES: .o .f90 .C .for .cu
 
 .f90.o:
@@ -30,12 +16,6 @@ TP_OPTFLAGS = -O3 $(ARCH_OPT) -fp-model fast=2 -fma -ipo \
 .cu.o:
 	$(Cu) $(CUDA_APP_FLAGS) -c $< -o $@ $(CUDA_LIB_PATH)
 
-TwoPunctures.o: TwoPunctures.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
-
-TwoPunctureABE.o: TwoPunctureABE.C
-	${CXX} $(TP_OPTFLAGS) -qopenmp -c $< -o $@
-
 # Input files
 C++FILES = ABE.o Ansorg.o Block.o misc.o monitor.o Parallel.o MPatch.o var.o\
            cgh.o bssn_class.o surface_integral.o ShellPatch.o\
@@ -116,7 +96,7 @@ ABEGPU: $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES)
 	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(C++FILES_GPU) $(F90FILES) $(F77FILES) $(AHFDOBJS) $(CUDAFILES) $(LDLIBS)
 
 TwoPunctureABE: $(TwoPunctureFILES)
-	$(CLINKER) $(TP_OPTFLAGS) -qopenmp -o $@ $(TwoPunctureFILES) $(LDLIBS)
+	$(CLINKER) $(CXXAPPFLAGS) -o $@ $(TwoPunctureFILES) $(LDLIBS)
 
 clean:
 	rm *.o ABE ABEGPU TwoPunctureABE make.log -f

AMSS_NCKU_source/makefile.inc

@@ -1,27 +1,39 @@
-
 ## GCC version (commented out)
 ## filein  = -I/usr/include -I/usr/lib/x86_64-linux-gnu/mpich/include -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
 ## filein  = -I/usr/include/ -I/usr/include/openmpi-x86_64/ -I/usr/lib/x86_64-linux-gnu/openmpi/include/ -I/usr/lib/x86_64-linux-gnu/openmpi/lib/ -I/usr/lib/gcc/x86_64-linux-gnu/11/ -I/usr/include/c++/11/
 ## LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -L/usr/lib/gcc/x86_64-linux-gnu/11 -lgfortran -lmpi -lgfortran
 
-## Intel oneAPI version with oneMKL
+## Intel oneAPI version with oneMKL (Optimized for performance)
 filein  = -I/usr/include/ -I${MKLROOT}/include
 
-## Use sequential oneMKL to avoid introducing extra OpenMP behavior into ABE.
+## Using multi-threaded MKL for better scalability with MPI
-LDLIBS  = -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_sequential -lmkl_core -lifcore -limf -lpthread -lm -ldl -liomp5
+## This allows MKL functions (FFT, BLAS, LAPACK) to use multiple threads internally
-
+## while keeping the application code as pure MPI (no OpenMP pragmas in user code)
-## Optional Intel oneTBB allocator, kept aligned with main's build environment.
+LDLIBS  = -L/usr/lib/x86_64-linux-gnu -L/usr/lib64 -lifcore -limf -lmpi \
-USE_TBBMALLOC ?= 1
+          -L${MKLROOT}/lib -lmkl_intel_lp64 -lmkl_intel_thread -lmkl_core \
-TBBMALLOC_SO ?= /home/intel/oneapi/2025.3/lib/libtbbmalloc.so
+          -liomp5 -lpthread -lm -ldl
-ifneq ($(wildcard $(TBBMALLOC_SO)),)
-TBBMALLOC_LIBS = -Wl,--no-as-needed $(TBBMALLOC_SO) -Wl,--as-needed
-else
-TBBMALLOC_LIBS = -Wl,--no-as-needed -ltbbmalloc -Wl,--as-needed
-endif
-ifeq ($(USE_TBBMALLOC),1)
-LDLIBS := $(TBBMALLOC_LIBS) $(LDLIBS)
-endif
 
+## Aggressive optimization flags for maximum performance:
+## -O3: Maximum optimization level
+## -xHost: Optimize for the host CPU architecture (Intel/AMD compatible)
+## -fp-model fast=2: Aggressive floating-point optimizations (allows reassociation)
+## -fma: Enable fused multiply-add instructions
+## -qopt-report=5: Generate detailed optimization reports
+## -qopt-report-phase=vec,loop: Report vectorization and loop optimizations
+## -march=native: Use all available CPU instructions
+## -mtune=native: Tune for the specific CPU
+## -funroll-loops: Aggressively unroll loops
+## -fno-alias: Assume no pointer aliasing (safe for Fortran arrays)
+## -qopt-prefetch: Enable aggressive prefetching
+## Note: OpenMP has been disabled (-qopenmp removed) due to performance issues
+CXXAPPFLAGS  = -O3 -xHost -march=native -mtune=native -fp-model fast=2 -fma \
+               -qopt-report=5 -qopt-report-phase=vec,loop \
+               -funroll-loops -fno-alias -qopt-prefetch \
+               -Dfortran3 -Dnewc -I${MKLROOT}/include
+f90appflags  = -O3 -xHost -march=native -mtune=native -fp-model fast=2 -fma \
+               -qopt-report=5 -qopt-report-phase=vec,loop \
+               -funroll-loops -fno-alias -qopt-prefetch \
+               -fpp -I${MKLROOT}/include
 f90          = ifx
 f77          = ifx
 CXX          = icpx

makefile_and_run.py

@@ -11,6 +11,24 @@
 import AMSS_NCKU_Input as input_data
 import subprocess
 
+## CPU core binding configuration using taskset
+## taskset ensures all child processes inherit the CPU affinity mask
+## This forces make and all compiler processes to use only nohz_full cores (4-55, 60-111)
+## Format: taskset -c 4-55,60-111 ensures processes only run on these cores
+NUMACTL_CPU_BIND = "taskset -c 4-55,60-111"
+
+## Build parallelism configuration
+## Use nohz_full cores (4-55, 60-111) for compilation: 52 + 52 = 104 cores
+## Set make -j to utilize available cores for faster builds
+BUILD_JOBS = 104
+
+## MKL threading configuration for hybrid MPI+threaded-MKL execution
+## Total cores available: 104 (cores 4-55, 60-111)
+## MPI processes: configured in AMSS_NCKU_Input.py (typically 48)
+## MKL threads per process: 104 / MPI_processes ≈ 2
+## This ensures full utilization of available cores
+MKL_NUM_THREADS = max(1, 104 // input_data.MPI_processes)
+
 
 ##################################################################
 
@@ -26,11 +44,11 @@ def makefile_ABE():
     print( " Compiling the AMSS-NCKU executable file ABE/ABEGPU " ) 
     print(                                                        )
 
-    ## Build command
+    ## Build command with CPU binding to nohz_full cores
     if (input_data.GPU_Calculation == "no"):
-        makefile_command  = "make -j96" + " ABE"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABE"
     elif (input_data.GPU_Calculation == "yes"):
-        makefile_command  = "make -j4" + " ABEGPU"
+        makefile_command  = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} ABEGPU"
     else:
         print( " CPU/GPU numerical calculation setting is wrong " )
         print(                                                    )
@@ -67,8 +85,8 @@ def makefile_TwoPunctureABE():
     print( " Compiling the AMSS-NCKU executable file TwoPunctureABE " )
     print(                                                            )
     
-    ## Build command
+    ## Build command with CPU binding to nohz_full cores
-    makefile_command = "make" + " TwoPunctureABE"
+    makefile_command = f"{NUMACTL_CPU_BIND} make -j{BUILD_JOBS} TwoPunctureABE"
 
     ## Execute the command with subprocess.Popen and stream output
     makefile_process = subprocess.Popen(makefile_command, shell=True, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, text=True) 
@@ -101,14 +119,20 @@ def run_ABE():
     print(                                                      )
     print( " Running the AMSS-NCKU executable file ABE/ABEGPU " )
     print(                                                      )
+    print( f" MPI processes: {input_data.MPI_processes}" )
+    print( f" MKL threads per process: {MKL_NUM_THREADS}" )
+    print( f" Total threads: {input_data.MPI_processes * MKL_NUM_THREADS}" )
+    print(                                                      )
 
     ## Define the command to run; cast other values to strings as needed
+    ## Set MKL threading environment variables for optimal performance
+    env_vars = f"export MKL_NUM_THREADS={MKL_NUM_THREADS} && export MKL_DYNAMIC=FALSE && "
 
     if (input_data.GPU_Calculation == "no"):
-        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
+        mpi_command         = env_vars + NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABE"
         mpi_command_outfile = "ABE_out.log"
     elif (input_data.GPU_Calculation == "yes"):
-        mpi_command         = "mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
+        mpi_command         = env_vars + NUMACTL_CPU_BIND + " mpirun -np " + str(input_data.MPI_processes) + " ./ABEGPU"
         mpi_command_outfile = "ABEGPU_out.log"
 
     ## Execute the MPI command and stream output
@@ -146,8 +170,9 @@ def run_TwoPunctureABE():
     print( " Running the AMSS-NCKU executable file TwoPunctureABE " )
     print(                                                          )
 
-    ## Define the command to run
+    ## Define the command to run with MKL threading configuration
-    TwoPuncture_command         = "./TwoPunctureABE"
+    env_vars = f"export MKL_NUM_THREADS={MKL_NUM_THREADS} && export MKL_DYNAMIC=FALSE && "
+    TwoPuncture_command         = env_vars + NUMACTL_CPU_BIND + " ./TwoPunctureABE"
     TwoPuncture_command_outfile = "TwoPunctureABE_out.log"
 
     ## Execute the command with subprocess.Popen and stream output

parallel_plot_helper.py

@@ -1,12 +0,0 @@
-import multiprocessing
-
-
-def run_plot_task(task):
-    func, args = task
-    return func(*args)
-
-
-def run_plot_tasks_parallel(plot_tasks):
-    ctx = multiprocessing.get_context('fork')
-    with ctx.Pool() as pool:
-        pool.map(run_plot_task, plot_tasks)

plot_GW_strain_amplitude_xiaoqu.py

@@ -11,8 +11,6 @@
 import numpy                               ## numpy for array operations
 import scipy                               ## scipy for interpolation and signal processing
 import math
-import matplotlib
-matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt     ## matplotlib for plotting
 import os                                  ## os for system/file operations
 

plot_binary_data.py

@@ -8,21 +8,16 @@
 ##
 #################################################
 
-## Restrict OpenMP to one thread per process so that parallel
-## subprocess plotting does not multiply BLAS thread counts.
-import os
-os.environ.setdefault("OMP_NUM_THREADS", "1")
-
 import numpy
 import scipy
-import matplotlib
-matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt
 from   matplotlib.colors    import LogNorm
 from   mpl_toolkits.mplot3d import Axes3D
 ## import torch
 import AMSS_NCKU_Input      as input_data
 
+import os
+
 
 #########################################################################################
 
@@ -197,11 +192,3 @@ def get_data_xy( Rmin, Rmax, n, data0, time, figure_title, figure_outdir ):
 
 ####################################################################################
 
-## Allow standalone subprocess execution for parallel binary-data plotting.
-if __name__ == '__main__':
-    import sys
-    if len(sys.argv) != 4:
-        print(f"Usage: {sys.argv[0]} <filename> <binary_outdir> <figure_outdir>")
-        sys.exit(1)
-    plot_binary_data(sys.argv[1], sys.argv[2], sys.argv[3])
-

plot_xiaoqu.py

@@ -8,8 +8,6 @@
 #################################################
 
 import numpy                               ## numpy for array operations
-import matplotlib
-matplotlib.use('Agg')                      ## use non-interactive backend for multiprocessing safety
 import matplotlib.pyplot    as     plt     ## matplotlib for plotting
 from   mpl_toolkits.mplot3d import Axes3D  ## needed for 3D plots
 import glob
@@ -17,9 +15,6 @@ import os                                  ## operating system utilities
 
 import plot_binary_data
 import AMSS_NCKU_Input as input_data
-import subprocess
-import sys
-import multiprocessing
 
 # plt.rcParams['text.usetex'] = True  ## enable LaTeX fonts in plots
 
@@ -55,34 +50,10 @@ def generate_binary_data_plot( binary_outdir, figure_outdir ):
         file_list.append(x)
         print(x)
 
-    ## Plot each file in parallel using subprocesses.
+    ## Plot each file in the list
-    ## Each subprocess starts with BLAS thread limits in plot_binary_data.py.
-    script = os.path.join( os.path.dirname(__file__), "plot_binary_data.py" )
-    max_workers = min( multiprocessing.cpu_count(), len(file_list) ) if file_list else 0
-
-    running = []
-    failed  = []
     for filename in file_list:
         print(filename)
-        proc = subprocess.Popen(
+        plot_binary_data.plot_binary_data(filename, binary_outdir, figure_outdir)
-            [sys.executable, script, filename, binary_outdir, figure_outdir],
-        )
-        running.append( (proc, filename) )
-        if len(running) >= max_workers:
-            p, fn = running.pop(0)
-            p.wait()
-            if p.returncode != 0:
-                failed.append(fn)
-
-    for p, fn in running:
-        p.wait()
-        if p.returncode != 0:
-            failed.append(fn)
-
-    if failed:
-        print( " WARNING: the following binary data plots failed:" )
-        for fn in failed:
-            print( "   ", fn )
 
     print(                        )
     print( " Binary Data Plot Has been Finished " )