function_internal.cpp

/*
 *    This file is part of CasADi.
 *
 *    CasADi -- A symbolic framework for dynamic optimization.
 *    Copyright (C) 2010-2014 Joel Andersson, Joris Gillis, Moritz Diehl, Kobe Bergmans
 *                            KU Leuven. All rights reserved.
 *    Copyright (C) 2011-2014 Greg Horn
 *
 *    CasADi is free software; you can redistribute it and/or
 *    modify it under the terms of the GNU Lesser General Public
 *    License as published by the Free Software Foundation; either
 *    version 3 of the License, or (at your option) any later version.
 *
 *    CasADi is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *    Lesser General Public License for more details.
 *
 *    You should have received a copy of the GNU Lesser General Public
 *    License along with CasADi; if not, write to the Free Software
 *    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 */
 
 
#include "function_internal.hpp"
#include "casadi_call.hpp"
#include "call_sx.hpp"
#include "casadi_misc.hpp"
#include "global_options.hpp"
#include "external.hpp"
#include "finite_differences.hpp"
#include "serializing_stream.hpp"
#include "mx_function.hpp"
#include "sx_function.hpp"
#include "rootfinder_impl.hpp"
#include "map.hpp"
#include "mapsum.hpp"
#include "switch.hpp"
#include "interpolant_impl.hpp"
#include "nlpsol_impl.hpp"
#include "conic_impl.hpp"
#include "integrator_impl.hpp"
#include "external_impl.hpp"
#include "fmu_function.hpp"
#include "blazing_spline_impl.hpp"
#include "onnx_function_impl.hpp"
#include "filesystem_impl.hpp"
 
#include <cctype>
#include <typeinfo>
#ifdef WITH_DL
#include <cstdlib>
#include <ctime>
#endif // WITH_DL
#include <iomanip>
 
namespace casadi {
 
  ProtoFunction::ProtoFunction(const std::string& name) : name_(name) {
    // Default options (can be overridden in derived classes)
    verbose_ = false;
    print_time_ = false;
    record_time_ = false;
    regularity_check_ = false;
    error_on_fail_ = true;
  }
 
  FunctionInternal::FunctionInternal(const std::string& name) : ProtoFunction(name) {
    // Make sure valid function name
    if (!Function::check_name(name_)) {
      casadi_error("Function name is not valid. A valid function name is a std::string "
                   "starting with a letter followed by letters, numbers or "
                   "non-consecutive underscores. It may also not match the keywords "
                   "'null', 'jac' or 'hess'. Got '" + name_ + "'");
    }
 
    // By default, reverse mode is about twice as expensive as forward mode
    ad_weight_ = 0.33; // i.e. nf <= 2*na <=> 1/3*nf <= (1-1/3)*na, forward when tie
    // Both modes equally expensive by default (no "taping" needed)
    ad_weight_sp_ = 0.49; // Forward when tie
    always_inline_ = false;
    never_inline_ = false;
    jac_penalty_ = 2;
    max_num_dir_ = GlobalOptions::getMaxNumDir();
    user_data_ = nullptr;
    inputs_check_ = true;
    jit_ = false;
    jit_cleanup_ = true;
    jit_serialize_ = "source";
    jit_base_name_ = "jit_tmp";
    jit_temp_suffix_ = true;
    compiler_plugin_ = CASADI_STR(CASADI_DEFAULT_COMPILER_PLUGIN);
 
    eval_ = nullptr;
    checkout_ = nullptr;
    release_ = nullptr;
    incref_ = nullptr;
    decref_ = nullptr;
    has_refcount_ = false;
    enable_forward_op_ = true;
    enable_reverse_op_ = true;
    enable_jacobian_op_ = true;
    enable_fd_op_ = false;
    print_in_ = false;
    print_out_ = false;
    print_canonical_ = false;
    max_io_ = 10000;
    dump_in_ = false;
    dump_out_ = false;
    dump_dir_ = ".";
    dump_format_ = "mtx";
    dump_ = false;
    sz_arg_tmp_ = 0;
    sz_res_tmp_ = 0;
    sz_iw_tmp_ = 0;
    sz_w_tmp_ = 0;
    sz_arg_per_ = 0;
    sz_res_per_ = 0;
    sz_iw_per_ = 0;
    sz_w_per_ = 0;
 
    dump_count_ = 0;
  }
 
  ProtoFunction::~ProtoFunction() {
    for (void* m : mem_) {
      if (m!=nullptr) casadi_warning("Memory object has not been properly freed");
    }
    mem_.clear();
  }
 
  FunctionInternal::~FunctionInternal() {
    if (decref_) decref_();
    if (jit_cleanup_ && jit_) {
      std::string jit_name = jit_directory_ + jit_name_ + ".c";
      if (remove(jit_name.c_str())) casadi_warning("Failed to remove " + jit_name);
    }
  }
 
  void ProtoFunction::construct(const Dict& opts) {
    // Sanitize dictionary is needed
    if (!Options::is_sane(opts)) {
      // Call recursively
      construct(Options::sanitize(opts));
      return;
    }
 
    // Make sure all options exist
    get_options().check(opts);
 
    // Initialize the class hierarchy
    try {
      init(opts);
    } catch(std::exception& e) {
      casadi_error("Error calling " + class_name() + "::init for '" + name_ + "':\n"
        + std::string(e.what()));
    }
 
    // Revisit class hierarchy in reverse order
    try {
      finalize();
    } catch(std::exception& e) {
      casadi_error("Error calling " + class_name() + "::finalize for '" + name_ + "':\n"
        + std::string(e.what()));
    }
  }
 
  const Options ProtoFunction::options_
  = {{},
     {{"verbose",
       {OT_BOOL,
        "Verbose evaluation -- for debugging"}},
      {"print_time",
       {OT_BOOL,
        "print information about execution time. Implies record_time."}},
      {"record_time",
       {OT_BOOL,
        "record information about execution time, for retrieval with stats()."}},
      {"regularity_check",
       {OT_BOOL,
        "Throw exceptions when NaN or Inf appears during evaluation"}},
      {"error_on_fail",
       {OT_BOOL,
        "Throw exceptions when function evaluation fails (default true)."}}
      }
  };
 
  const Options FunctionInternal::options_
  = {{&ProtoFunction::options_},
      {{"ad_weight",
       {OT_DOUBLE,
        "Weighting factor for derivative calculation."
        "When there is an option of either using forward or reverse mode "
        "directional derivatives, the condition ad_weight*nf<=(1-ad_weight)*na "
        "is used where nf and na are estimates of the number of forward/reverse "
        "mode directional derivatives needed. By default, ad_weight is calculated "
        "automatically, but this can be overridden by setting this option. "
        "In particular, 0 means forcing forward mode and 1 forcing reverse mode. "
        "Leave unset for (class specific) heuristics."}},
      {"ad_weight_sp",
       {OT_DOUBLE,
        "Weighting factor for sparsity pattern calculation calculation."
        "Overrides default behavior. Set to 0 and 1 to force forward and "
        "reverse mode respectively. Cf. option \"ad_weight\". "
        "When set to -1, sparsity is completely ignored and dense matrices are used."}},
      {"always_inline",
       {OT_BOOL,
        "Force inlining."}},
      {"never_inline",
       {OT_BOOL,
        "Forbid inlining."}},
      {"jac_penalty",
       {OT_DOUBLE,
        "When requested for a number of forward/reverse directions,   "
        "it may be cheaper to compute first the full jacobian and then "
        "multiply with seeds, rather than obtain the requested directions "
        "in a straightforward manner. "
        "Casadi uses a heuristic to decide which is cheaper. "
        "A high value of 'jac_penalty' makes it less likely for the heurstic "
        "to chose the full Jacobian strategy. "
        "The special value -1 indicates never to use the full Jacobian strategy"}},
      {"user_data",
       {OT_VOIDPTR,
        "A user-defined field that can be used to identify "
        "the function or pass additional information"}},
      {"inputs_check",
       {OT_BOOL,
        "Throw exceptions when the numerical values of the inputs don't make sense"}},
      {"gather_stats",
       {OT_BOOL,
        "Deprecated option (ignored): Statistics are now always collected."}},
      {"jit",
       {OT_BOOL,
        "Use just-in-time compiler to speed up the evaluation"}},
      {"jit_cleanup",
       {OT_BOOL,
        "Cleanup up the temporary source file that jit creates. Default: true"}},
      {"jit_serialize",
       {OT_STRING,
        "Specify behaviour when serializing a jitted function: SOURCE|link|embed."}},
      {"jit_name",
       {OT_STRING,
        "The file name used to write out code. "
        "The actual file names used depend on 'jit_temp_suffix' and include extensions. "
        "Default: 'jit_tmp'"}},
      {"jit_temp_suffix",
       {OT_BOOL,
        "Use a temporary (seemingly random) filename suffix for generated code and libraries. "
        "This is desired for thread-safety. "
        "This behaviour may defeat caching compiler wrappers. "
        "Default: true"}},
      {"compiler",
       {OT_STRING,
        "Just-in-time compiler plugin to be used."}},
      {"jit_options",
       {OT_DICT,
        "Options to be passed to the jit compiler."}},
      {"codegen_options",
       {OT_DICT,
        "Options to be passed to the code generator of jit, e.g. {\"stats\": true} to "
        "record statistics inside the compiled code. Default: none"}},
      {"derivative_of",
       {OT_FUNCTION,
        "The function is a derivative of another function. "
        "The type of derivative (directional derivative, Jacobian) "
        "is inferred from the function name."}},
      {"max_num_dir",
       {OT_INT,
        "Specify the maximum number of directions for derivative functions."
        " Overrules the builtin optimized_num_dir."}},
      {"enable_forward",
       {OT_BOOL,
        "Enable derivative calculation using generated functions for"
        " Jacobian-times-vector products - typically using forward mode AD"
        " - if available. [default: true]"}},
      {"enable_reverse",
        {OT_BOOL,
        "Enable derivative calculation using generated functions for"
        " transposed Jacobian-times-vector products - typically using reverse mode AD"
        " - if available. [default: true]"}},
      {"enable_jacobian",
        {OT_BOOL,
        "Enable derivative calculation using generated functions for"
        " Jacobians of all differentiable outputs with respect to all differentiable inputs"
        " - if available. [default: true]"}},
      {"enable_fd",
       {OT_BOOL,
        "Enable derivative calculation by finite differencing. [default: false]]"}},
      {"fd_options",
       {OT_DICT,
        "Options to be passed to the finite difference instance"}},
      {"fd_method",
       {OT_STRING,
        "Method for finite differencing [default 'central']"}},
      {"print_in",
       {OT_BOOL,
        "Print numerical values of inputs [default: false]"}},
      {"print_out",
       {OT_BOOL,
        "Print numerical values of outputs [default: false]"}},
      {"print_canonical",
        {OT_BOOL,
        "When printing numerical matrices, use a format that is "
        "exact and reproducible in generated C code."}},
      {"max_io",
       {OT_INT,
        "Acceptable number of inputs and outputs. Warn if exceeded."}},
      {"dump_in",
       {OT_BOOL,
        "Dump numerical values of inputs to file (readable with DM.from_file) [default: false] "
        "A counter is used to generate unique names. "
        "The counter may be reset using reset_dump_count."}},
      {"dump_out",
       {OT_BOOL,
        "Dump numerical values of outputs to file (readable with DM.from_file) [default: false] "
        "A counter is used to generate unique names. "
        "The counter may be reset using reset_dump_count."}},
      {"dump",
       {OT_BOOL,
        "Dump function to file upon first evaluation. [false]"}},
      {"dump_dir",
       {OT_STRING,
        "Directory to dump inputs/outputs and traces to. Make sure the directory exists [.]"}},
      {"dump_format",
       {OT_STRING,
        "Choose file format to dump matrices. See DM.from_file [mtx]"}},
      {"forward_options",
       {OT_DICT,
        "Options to be passed to a forward mode constructor"}},
      {"reverse_options",
       {OT_DICT,
        "Options to be passed to a reverse mode constructor"}},
      {"jacobian_options",
       {OT_DICT,
        "Options to be passed to a Jacobian constructor"}},
      {"der_options",
       {OT_DICT,
        "Default options to be used to populate forward_options, reverse_options, and "
        "jacobian_options before those options are merged in."}},
      {"custom_jacobian",
       {OT_FUNCTION,
        "Override CasADi's AD. Use together with 'jac_penalty': 0. "
        "Note: Highly experimental. Syntax may break often."}},
      {"is_diff_in",
       {OT_BOOLVECTOR,
        "Indicate for each input if it should be differentiable."}},
      {"is_diff_out",
       {OT_BOOLVECTOR,
        "Indicate for each output if it should be differentiable."}},
      {"post_expand",
       {OT_BOOL,
        "After construction, expand this Function. Default: False"}},
      {"post_expand_options",
       {OT_DICT,
        "Options to be passed to post-construction expansion. Default: empty"}},
      {"cache",
       {OT_DICT,
        "Prepopulate the function cache. Default: empty"}},
      {"external_transform",
       {OT_VECTORVECTOR,
        "List of external_transform instruction arguments. Default: empty"}}
     }
  };
 
  void ProtoFunction::init(const Dict& opts) {
    // Read options
    for (auto&& op : opts) {
      if (op.first=="verbose") {
        verbose_ = op.second;
      } else if (op.first=="print_time") {
        print_time_ = op.second;
      } else if (op.first=="record_time") {
        record_time_ = op.second;
      } else if (op.first=="regularity_check") {
        regularity_check_ = op.second;
      } else if (op.first=="error_on_fail") {
        error_on_fail_ = op.second;
      }
    }
  }
 
  Dict ProtoFunction::generate_options(const std::string& target) const {
    Dict opts;
    opts["verbose"] = verbose_;
    opts["print_time"] = print_time_;
    opts["record_time"] = record_time_;
    opts["regularity_check"] = regularity_check_;
    opts["error_on_fail"] = error_on_fail_;
    return opts;
  }
 
  Dict FunctionInternal::generate_options(const std::string& target) const {
    Dict opts = ProtoFunction::generate_options(target);
    opts["jac_penalty"] = jac_penalty_;
    opts["user_data"] = user_data_;
    opts["inputs_check"] = inputs_check_;
    if (target!="tmp") opts["jit"] = jit_;
    opts["jit_cleanup"] = jit_cleanup_;
    opts["jit_serialize"] = jit_serialize_;
    opts["compiler"] = compiler_plugin_;
    opts["jit_options"] = jit_options_;
    opts["codegen_options"] = codegen_options_;
    opts["jit_name"] = jit_base_name_;
    opts["jit_temp_suffix"] = jit_temp_suffix_;
    opts["ad_weight"] = ad_weight_;
    opts["ad_weight_sp"] = ad_weight_sp_;
    opts["always_inline"] = always_inline_;
    opts["never_inline"] = never_inline_;
    opts["max_num_dir"] = max_num_dir_;
    if (target=="clone" || target=="tmp") {
      opts["enable_forward"] = enable_forward_op_;
      opts["enable_reverse"] = enable_reverse_op_;
      opts["enable_jacobian"] = enable_jacobian_op_;
      opts["enable_fd"] = enable_fd_op_;
      opts["reverse_options"] = reverse_options_;
      opts["forward_options"] = forward_options_;
      opts["jacobian_options"] = jacobian_options_;
      opts["der_options"] = der_options_;
      opts["derivative_of"] = derivative_of_;
    }
    opts["fd_options"] = fd_options_;
    opts["fd_method"] = fd_method_;
    opts["print_in"] = print_in_;
    opts["print_out"] = print_out_;
    opts["print_canonical"] = print_canonical_;
    opts["max_io"] = max_io_;
    opts["dump_in"] = dump_in_;
    opts["dump_out"] = dump_out_;
    opts["dump_dir"] = dump_dir_;
    opts["dump_format"] = dump_format_;
    opts["dump"] = dump_;
    if (target=="clone") {
      opts["is_diff_in"] = is_diff_in_;
      opts["is_diff_out"] = is_diff_out_;
    }
    if (target=="forward") {
      opts["is_diff_in"] = join(is_diff_in_, is_diff_out_, is_diff_in_);
      opts["is_diff_out"] = is_diff_out_;
    }
    if (target=="reverse") {
      opts["is_diff_in"] = join(is_diff_in_, is_diff_out_, is_diff_out_);
      opts["is_diff_out"] = is_diff_in_;
    }
    return opts;
  }
 
  void FunctionInternal::change_option(const std::string& option_name,
      const GenericType& option_value) {
    if (option_name == "print_in") {
      print_in_ = option_value;
    } else if (option_name == "print_out") {
      print_out_ = option_value;
    } else if (option_name == "print_canonical") {
      print_canonical_ = option_value;
    } else if (option_name=="ad_weight") {
      ad_weight_ = option_value;
    } else if (option_name=="ad_weight_sp") {
      ad_weight_sp_ = option_value;
    } else if (option_name=="dump") {
      dump_ = option_value;
    } else if (option_name=="dump_in") {
      dump_in_ = option_value;
    } else if (option_name=="dump_out") {
      dump_out_ = option_value;
    } else if (option_name=="dump_dir") {
      dump_dir_ = option_value.to_string();
    } else if (option_name=="dump_format") {
      dump_format_ = option_value.to_string();
    } else {
      // Option not found - continue to base classes
      ProtoFunction::change_option(option_name, option_value);
    }
  }
 
  void FunctionInternal::reset_dump_count() {
    dump_count_ = 0;
  }
 
  void FunctionInternal::init(const Dict& opts) {
    // Call the initialization method of the base class
    ProtoFunction::init(opts);
 
    // Default options
    fd_step_ = 1e-8;
 
    // Read options
    for (auto&& op : opts) {
      if (op.first=="jac_penalty") {
        jac_penalty_ = op.second;
      } else if (op.first=="user_data") {
        user_data_ = op.second.to_void_pointer();
      } else if (op.first=="inputs_check") {
        inputs_check_ = op.second;
      } else if (op.first=="gather_stats") {
        casadi_warning("Deprecated option \"gather_stats\": Always enabled");
      } else if (op.first=="jit") {
        jit_ = op.second;
      } else if (op.first=="jit_cleanup") {
        jit_cleanup_ = op.second;
      } else if (op.first=="jit_serialize") {
        jit_serialize_ = op.second.to_string();
        casadi_assert(jit_serialize_=="source" || jit_serialize_=="link" || jit_serialize_=="embed",
          "jit_serialize option not understood. Pick one of source, link, embed.");
      } else if (op.first=="compiler") {
        compiler_plugin_ = op.second.to_string();
      } else if (op.first=="jit_options") {
        jit_options_ = op.second;
      } else if (op.first=="codegen_options") {
        codegen_options_ = op.second;
      } else if (op.first=="jit_name") {
        jit_base_name_ = op.second.to_string();
      } else if (op.first=="jit_temp_suffix") {
        jit_temp_suffix_ = op.second;
      } else if (op.first=="derivative_of") {
        derivative_of_ = op.second;
      } else if (op.first=="ad_weight") {
        ad_weight_ = op.second;
      } else if (op.first=="ad_weight_sp") {
        ad_weight_sp_ = op.second;
      } else if (op.first=="max_num_dir") {
        max_num_dir_ = op.second;
      } else if (op.first=="enable_forward") {
        enable_forward_op_ = op.second;
      } else if (op.first=="enable_reverse") {
        enable_reverse_op_ = op.second;
      } else if (op.first=="enable_jacobian") {
        enable_jacobian_op_ = op.second;
      } else if (op.first=="enable_fd") {
        enable_fd_op_ = op.second;
      } else if (op.first=="fd_options") {
        fd_options_ = op.second;
      } else if (op.first=="fd_method") {
        fd_method_ = op.second.to_string();
      } else if (op.first=="print_in") {
        print_in_ = op.second;
      } else if (op.first=="print_out") {
        print_out_ = op.second;
      } else if (op.first=="print_canonical") {
        print_canonical_ = op.second;
      } else if (op.first=="max_io") {
        max_io_ = op.second;
      } else if (op.first=="dump_in") {
        dump_in_ = op.second;
      } else if (op.first=="dump_out") {
        dump_out_ = op.second;
      } else if (op.first=="dump") {
        dump_ = op.second;
      } else if (op.first=="dump_dir") {
        dump_dir_ = op.second.to_string();
      } else if (op.first=="dump_format") {
        dump_format_ = op.second.to_string();
      } else if (op.first=="forward_options") {
        forward_options_ = op.second;
      } else if (op.first=="reverse_options") {
        reverse_options_ = op.second;
      } else if (op.first=="jacobian_options") {
        jacobian_options_ = op.second;
      } else if (op.first=="der_options") {
        der_options_ = op.second;
      } else if (op.first=="custom_jacobian") {
        custom_jacobian_ = op.second.to_function();
        casadi_assert(custom_jacobian_.name() == "jac_" + name_,
          "Inconsistent naming of custom Jacobian, expected: jac_" + name_);
        tocache(custom_jacobian_);
      } else if (op.first=="always_inline") {
        always_inline_ = op.second;
      } else if (op.first=="never_inline") {
        never_inline_ = op.second;
      } else if (op.first=="is_diff_in") {
        is_diff_in_ = op.second;
      } else if (op.first=="is_diff_out") {
        is_diff_out_ = op.second;
      } else if (op.first=="cache") {
        cache_init_ = op.second;
      }
    }
 
    // print_time implies record_time
    if (print_time_) record_time_ = true;
 
    // Verbose?
    if (verbose_) casadi_message(name_ + "::init");
 
    // Get the number of inputs
    n_in_ = get_n_in();
    if (max_io_ > 0 && n_in_ > max_io_) {
      casadi_warning("Function " + name_ + " has many inputs (" + str(n_in_) + " > "
        + "max_io (=" + str(max_io_) + ")). "
        + "Changing the problem formulation is strongly encouraged.");
    }
 
    // Get the number of outputs
    n_out_ = get_n_out();
    if (max_io_ > 0 && n_out_ > max_io_) {
      casadi_warning("Function " + name_ + " has many outputs (" + str(n_out_) + " > "
        + "max_io (=" + str(max_io_) + ")). "
        + "Changing the problem formulation is strongly encouraged.");
    }
 
    // Query which inputs are differentiable if not already provided
    if (is_diff_in_.empty()) {
      is_diff_in_.resize(n_in_);
      for (casadi_int i = 0; i < n_in_; ++i) is_diff_in_[i] = get_diff_in(i);
    } else {
      casadi_assert(n_in_ == is_diff_in_.size(), "Function " + name_ + " has " + str(n_in_)
        + " inputs, but is_diff_in has length " + str(is_diff_in_.size()) + ".");
    }
 
    // Query which outputs are differentiable if not already provided
    if (is_diff_out_.empty()) {
      is_diff_out_.resize(n_out_);
      for (casadi_int i = 0; i < n_out_; ++i) is_diff_out_[i] = get_diff_out(i);
    } else {
      casadi_assert(n_out_ == is_diff_out_.size(), "Function " + name_ + " has " + str(n_out_)
        + " outputs, but is_diff_out has length " + str(is_diff_out_.size()) + ".");
    }
 
    // Query input sparsities if not already provided
    if (sparsity_in_.empty()) {
      sparsity_in_.resize(n_in_);
      for (casadi_int i=0; i<n_in_; ++i) sparsity_in_[i] = get_sparsity_in(i);
    } else {
      casadi_assert(sparsity_in_.size() == n_in_, "Function " + name_ + " has " + str(n_in_)
        + " inputs, but sparsity_in has length " + str(sparsity_in_.size()) + ".");
    }
 
    // Query output sparsities if not already provided
    if (sparsity_out_.empty()) {
      sparsity_out_.resize(n_out_);
      for (casadi_int i=0; i<n_out_; ++i) sparsity_out_[i] = get_sparsity_out(i);
    } else {
      casadi_assert(sparsity_out_.size() == n_out_, "Function " + name_ + " has " + str(n_out_)
        + " outputs, but sparsity_out has length " + str(sparsity_out_.size()) + ".");
    }
 
    // Query input names if not already provided
    if (name_in_.empty()) {
      name_in_.resize(n_in_);
      for (casadi_int i=0; i<n_in_; ++i) name_in_[i] = get_name_in(i);
    } else {
      casadi_assert(name_in_.size()==n_in_, "Function " + name_ + " has " + str(n_in_)
        + " inputs, but name_in has length " + str(name_in_.size()) + ".");
    }
 
    // Query output names if not already provided
    if (name_out_.empty()) {
      name_out_.resize(n_out_);
      for (casadi_int i=0; i<n_out_; ++i) name_out_[i] = get_name_out(i);
    } else {
      casadi_assert(name_out_.size()==n_out_, "Function " + name_ + " has " + str(n_out_)
        + " outputs, but name_out has length " + str(name_out_.size()) + ".");
    }
 
    // Prepopulate function cache
    for (auto&& c : cache_init_) {
      const Function& f = c.second;
      if (c.first != f.name()) {
        casadi_warning("Cannot add '" + c.first + "' a.k.a. '" + f.name()
          + "' to cache. Mismatching names not implemented.");
      } else {
        tocache(f);
      }
    }
 
    // Allocate memory for function inputs and outputs
    sz_arg_per_ += n_in_;
    sz_res_per_ += n_out_;
 
    // Type of derivative calculations enabled
    enable_forward_ = enable_forward_op_ && has_forward(1);
    enable_reverse_ = enable_reverse_op_ && has_reverse(1);
    enable_jacobian_ = enable_jacobian_op_ && has_jacobian();
    enable_fd_ = enable_fd_op_ && !enable_forward_;
 
    alloc_arg(0);
    alloc_res(0);
  }
 
  std::string FunctionInternal::get_name_in(casadi_int i) {
    if (!derivative_of_.is_null()) {
      std::string n = derivative_of_.name();
      if (name_ == "jac_" + n || name_ == "adj1_" + n) {
        if (i < derivative_of_.n_in()) {
          // Same as nondifferentiated function
          return derivative_of_.name_in(i);
        } else if (i < derivative_of_.n_in() + derivative_of_.n_out()) {
          // Nondifferentiated output
          return "out_" + derivative_of_.name_out(i - derivative_of_.n_in());
        } else {
          // Adjoint seed
          return "adj_" + derivative_of_.name_out(i - derivative_of_.n_in()
            - derivative_of_.n_out());
        }
      }
    }
    // Default name
    return "i" + str(i);
  }
 
  std::string FunctionInternal::get_name_out(casadi_int i) {
    if (!derivative_of_.is_null()) {
      std::string n = derivative_of_.name();
      if (name_ == "jac_" + n) {
        // Jacobian block
        casadi_int oind = i / derivative_of_.n_in(), iind = i % derivative_of_.n_in();
        return "jac_" + derivative_of_.name_out(oind) + "_" + derivative_of_.name_in(iind);
      } else if (name_ == "adj1_" + n) {
        // Adjoint sensitivity
        return "adj_" + derivative_of_.name_in(i);
      }
    }
    // Default name
    return "o" + str(i);
  }
 
  std::string FunctionInternal::get_jit_directory(const Dict& jit_options) {
    // Start with default temp work dir
    std::string jit_directory = GlobalOptions::getTempWorkDir();
 
    // Get user-specified directory
    std::string directory;
    directory = get_from_dict(jit_options, "directory", std::string(""));
 
    // What if directory itself is absolute?
    if (Filesystem::is_absolute(directory)) {
      // Override
      jit_directory = directory;
    } else {
      jit_directory = jit_directory + directory;
      if (Filesystem::is_enabled()) {
        jit_directory = Filesystem::absolute(jit_directory);
      }
    }
 
    return Filesystem::ensure_trailing_slash(jit_directory);
  }
 
  void FunctionInternal::finalize() {
    if (codegen_needs_mem()) has_refcount_ = true;
    if (dump_in_ || dump_out_) has_refcount_ = true;
 
    has_refcount_in_deps_ = has_refcount_;
 
    // Does any embedded function have reference counting for codegen?
    for (const Function& f : shared_from_this<Function>().find_functions(0)) {
      if (f->has_refcount_in_deps_) {
        has_refcount_in_deps_ = true;
        break;
      }
    }
 
    if (jit_) {
      jit_name_ = jit_base_name_;
      jit_directory_ = get_jit_directory(jit_options_);
      if (jit_temp_suffix_) {
        jit_name_ = temporary_file(jit_name_, ".c", jit_directory_);
        jit_name_ = std::string(jit_name_.begin()+jit_directory_.size(),
                                jit_name_.begin()+jit_name_.size()-2);
      }
      if (has_codegen()) {
        if (compiler_.is_null()) {
          if (verbose_) casadi_message("Codegenerating function '" + name_ + "'.");
          // JIT everything
          Dict opts = codegen_options_;
          // Override the default to avoid random strings in the generated code
          if (opts.find("prefix")==opts.end()) opts["prefix"] = "jit";
          CodeGenerator gen(jit_name_, opts);
          gen.add(self());
          if (verbose_) casadi_message("Compiling function '" + name_ + "'..");
          compiler_ = Importer(gen.generate(jit_directory_), compiler_plugin_, jit_options_);
          if (verbose_) casadi_message("Compiling function '" + name_ + "' done.");
        }
        // Try to load
        eval_ = (eval_t) compiler_.get_function(name_);
        checkout_ = (casadi_checkout_t) compiler_.get_function(name_ + "_checkout");
        release_ = (casadi_release_t) compiler_.get_function(name_ + "_release");
        incref_ = (signal_t) compiler_.get_function(name_ + "_incref");
        decref_ = (signal_t) compiler_.get_function(name_ + "_decref");
        casadi_assert(eval_!=nullptr, "Cannot load JIT'ed function.");
        if (incref_) incref_();
      } else {
        // Just jit dependencies
        jit_dependencies(jit_name_);
      }
    }
 
    // Finalize base classes
    ProtoFunction::finalize();
 
    // Dump if requested
    if (dump_) dump();
  }
 
  void ProtoFunction::finalize() {
    // Create memory object
    int mem = checkout();
    casadi_assert_dev(mem==0);
  }
 
  void FunctionInternal::generate_in(const std::string& fname, const double** arg) const {
    // Set up output stream
    auto of_ptr = Filesystem::ofstream_ptr(fname);
    std::ostream& of = *of_ptr;
    normalized_setup(of);
 
    // Encode each input
    for (casadi_int i=0; i<n_in_; ++i) {
      const double* v = arg[i];
      for (casadi_int k=0;k<nnz_in(i);++k) {
        normalized_out(of, v ? v[k] : 0);
        of << std::endl;
      }
    }
  }
 
  void FunctionInternal::generate_out(const std::string& fname, double** res) const {
    // Set up output stream
    auto of_ptr = Filesystem::ofstream_ptr(fname);
    std::ostream& of = *of_ptr;
    normalized_setup(of);
 
    // Encode each input
    for (casadi_int i=0; i<n_out_; ++i) {
      const double* v = res[i];
      for (casadi_int k=0;k<nnz_out(i);++k) {
        normalized_out(of, v ? v[k] : std::numeric_limits<double>::quiet_NaN());
        of << std::endl;
      }
    }
  }
 
  void FunctionInternal::
  trace_values(std::ostream& trace, const double* values, casadi_int nnz) {
    if (!values) {
      trace << "null";
      return;
    }
    trace << "[";
    for (casadi_int i = 0; i < nnz; ++i) {
      if (i) trace << ",";
      double v = values[i];
      if (isnan(v)) {
        trace << "\"nan\"";
      } else if (isinf(v)) {
        trace << (v < 0 ? "\"-inf\"" : "\"inf\"");
      } else {
        normalized_out(trace, v);
      }
    }
    trace << "]";
  }
 
  std::unique_ptr<std::ostream> FunctionInternal::
  open_trace(const double** arg, casadi_int dump_id) const {
    if (dump_id < 0) dump_id = get_dump_id();
    std::stringstream filename;
    filename << dump_dir_ << filesep() << name_ << "." << std::setfill('0')
             << std::setw(6) << dump_id << ".trace.jsonl";
    auto output = Filesystem::ofstream_ptr(filename.str());
    std::ostream& trace = *output;
    normalized_setup(trace);
    trace << "{\"event\":\"header\",\"format\":\"casadi_trace\",\"version\":1,"
          << "\"function\":\"" << name_ << "\",\"type\":\"" << class_name()
          << "\",\"dump_id\":" << dump_id << "}\n";
    trace << "{\"event\":\"inputs\",\"values\":[";
    for (casadi_int i = 0; i < n_in_; ++i) {
      if (i) trace << ",";
      trace_values(trace, arg[i], nnz_in(i));
    }
    trace << "]}\n";
    return output;
  }
 
  void FunctionInternal::
  finish_trace(std::ostream& trace, double** res, int ret) const {
    if (ret == 0) {
      trace << "{\"event\":\"outputs\",\"values\":[";
      for (casadi_int i = 0; i < n_out_; ++i) {
        if (i) trace << ",";
        trace_values(trace, res[i], nnz_out(i));
      }
      trace << "]}\n";
    }
    trace << "{\"event\":\"end\",\"status\":" << ret << "}\n";
    trace.flush();
    casadi_assert(trace.good(), "Failed to write dump_trace for '" + name_ + "'");
  }
 
  void FunctionInternal::dump_in(casadi_int id, const double** arg) const {
    std::stringstream ss;
    ss << std::setfill('0') << std::setw(6) << id;
    std::string count = ss.str();
    for (casadi_int i=0;i<n_in_;++i) {
      DM::to_file(dump_dir_+ filesep() + name_ + "." + count + ".in." + name_in_[i] + "." +
        dump_format_, sparsity_in_[i], arg[i]);
    }
    std::string name = dump_dir_+ filesep() + name_ + "." + count + ".in.txt";
    if (verbose_) {
      casadi_message("dump_in for " + name_ + " -> " + name);
    }
    generate_in(name, arg);
  }
 
  void FunctionInternal::dump_out(casadi_int id, double** res) const {
    std::stringstream ss;
    ss << std::setfill('0') << std::setw(6) << id;
    std::string count = ss.str();
    for (casadi_int i=0;i<n_out_;++i) {
      DM::to_file(dump_dir_+ filesep() + name_ + "." + count + ".out." + name_out_[i] + "." +
        dump_format_, sparsity_out_[i], res[i]);
    }
    std::string name = dump_dir_+ filesep() + name_ + "." + count + ".out.txt";
    if (verbose_) {
      casadi_message("dump_out for " + name_ + " -> " + name);
    }
    generate_out(name, res);
  }
 
  void FunctionInternal::dump() const {
    shared_from_this<Function>().save(dump_dir_+ filesep() + name_ + ".casadi");
  }
 
  casadi_int FunctionInternal::get_dump_id() const {
    return dump_count_++;
  }
 
  int ProtoFunction::init_mem(void* mem) const {
    auto *m = static_cast<ProtoFunctionMemory*>(mem);
    if (record_time_) {
      m->add_stat("total");
      m->t_total = &m->fstats.at("total");
    } else {
      m->t_total = nullptr;
    }
    return 0;
  }
 
  void FunctionInternal::print_in(std::ostream &stream, const double** arg, bool truncate) const {
    stream << "Function " << name_ << " (" << this << ")" << std::endl;
    for (casadi_int i=0; i<n_in_; ++i) {
      stream << "Input " << i << " (" << name_in_[i] << "): ";
      if (arg[i]) {
        if (print_canonical_) {
          print_canonical(stream, sparsity_in_[i], arg[i]);
        } else {
          DM::print_default(stream, sparsity_in_[i], arg[i], truncate);
        }
        stream << std::endl;
      } else {
        stream << "NULL" << std::endl;
      }
    }
  }
 
  void FunctionInternal::print_out(std::ostream &stream, double** res, bool truncate) const {
    stream << "Function " << name_ << " (" << this << ")" << std::endl;
    for (casadi_int i=0; i<n_out_; ++i) {
      stream << "Output " << i << " (" << name_out_[i] << "): ";
      if (res[i]) {
        if (print_canonical_) {
          print_canonical(stream, sparsity_out_[i], res[i]);
        } else {
          DM::print_default(stream, sparsity_out_[i], res[i], truncate);
        }
        stream << std::endl;
      } else {
        stream << "NULL" << std::endl;
      }
    }
  }
 
  void FunctionInternal::print_canonical(std::ostream &stream, casadi_int sz, const double* nz) {
    StreamStateGuard backup(stream);
    normalized_setup(stream);
    if (nz) {
      stream << "[";
      for (casadi_int i=0; i<sz; ++i) {
        if (i>0) stream << ", ";
        normalized_out(stream, nz[i]);
      }
      stream << "]";
    } else {
      stream << "NULL";
    }
  }
 
  void FunctionInternal::print_canonical(std::ostream &stream,
      const Sparsity& sp, const double* nz) {
    StreamStateGuard backup(stream);
    normalized_setup(stream);
    if (nz) {
      if (!sp.is_scalar(true)) {
        stream << sp.dim(false) << ": ";
        stream << "[";
      }
      for (casadi_int i=0; i<sp.nnz(); ++i) {
        if (i>0) stream << ", ";
        normalized_out(stream, nz[i]);
      }
      if (!sp.is_scalar(true)) {
        stream << "]";
        if (!sp.is_dense()) {
          stream << ", colind: [";
          for (casadi_int i=0; i<sp.size2()+1; ++i) {
            if (i>0) stream << ", ";
            stream << sp.colind()[i];
          }
          stream << "]";
          stream << ", row: [";
          for (casadi_int i=0; i<sp.nnz(); ++i) {
            if (i>0) stream << ", ";
            stream << sp.row()[i];
          }
          stream << "]";
        }
      }
    } else {
      stream << "NULL";
    }
  }
 
  void FunctionInternal::print_canonical(std::ostream &stream, double a) {
    StreamStateGuard backup(stream);
    normalized_setup(stream);
    normalized_out(stream, a);
  }
 
  int FunctionInternal::
  eval_gen(const double** arg, double** res, casadi_int* iw, double* w, void* mem,
      bool always_inline, bool never_inline) const {
    casadi_int dump_id = (dump_in_ || dump_out_ || dump_) ? get_dump_id() : -1;
    if (dump_in_) dump_in(dump_id, arg);
    if (dump_ && dump_id==0) dump();
    if (print_in_) print_in(uout(), arg, false);
    auto *m = static_cast<FunctionMemory*>(mem);
 
    // Avoid memory corruption
    for (casadi_int i=0;i<n_in_;++i) {
      casadi_assert(arg[i]==nullptr || arg[i]+nnz_in(i)<=w || arg[i]>=w+sz_w(),
        "Memory corruption detected for input " + name_in_[i] + ".\n"+
        "arg[" + str(i) + "] " + str(arg[i]) + "-" + str(arg[i]+nnz_in(i)) +
        " intersects with w " + str(w)+"-"+str(w+sz_w())+".");
    }
    for (casadi_int i=0;i<n_out_;++i) {
      casadi_assert(res[i]==nullptr || res[i]+nnz_out(i)<=w || res[i]>=w+sz_w(),
        "Memory corruption detected for output " + name_out_[i]);
    }
    // Reset statistics
    for (auto&& s : m->fstats) s.second.reset();
    if (m->t_total) m->t_total->tic();
    m->dump_id = dump_id;
    int ret;
    if (eval_) {
      auto *m = static_cast<FunctionMemory*>(mem);
      m->stats_available = true;
      int mem_ = 0;
      if (checkout_) {
#ifdef CASADI_WITH_THREAD
    std::lock_guard<std::mutex> lock(mtx_);
#endif //CASADI_WITH_THREAD
        mem_ = checkout_();
      }
      ret = eval_(arg, res, iw, w, mem_);
      if (release_) {
#ifdef CASADI_WITH_THREAD
    std::lock_guard<std::mutex> lock(mtx_);
#endif //CASADI_WITH_THREAD
        release_(mem_);
      }
    } else {
      ret = eval(arg, res, iw, w, mem);
    }
    if (m->t_total) m->t_total->toc();
    // Show statistics
    print_time(m->fstats);
 
    if (dump_out_) dump_out(dump_id, res);
    if (print_out_) print_out(uout(), res, false);
    // Check all outputs for NaNs
    if (regularity_check_) {
      for (casadi_int i = 0; i < n_out_; ++i) {
        // Skip of not calculated
        if (!res[i]) continue;
        // Loop over nonzeros
        casadi_int nnz = this->nnz_out(i);
        for (casadi_int nz = 0; nz < nnz; ++nz) {
          if (isnan(res[i][nz]) || isinf(res[i][nz])) {
            // Throw readable error message
            casadi_error(str(res[i][nz]) + " detected for output " + name_out_[i] + " at "
              + sparsity_out(i).repr_el(nz));
          }
        }
      }
    }
    return ret;
  }
 
  void FunctionInternal::print_dimensions(std::ostream &stream) const {
    stream << " Number of inputs: " << n_in_ << std::endl;
    for (casadi_int i=0; i<n_in_; ++i) {
      stream << "  Input " << i  << " (\"" << name_in_[i] << "\"): "
             << sparsity_in_[i].dim() << std::endl;
    }
    stream << " Number of outputs: " << n_out_ << std::endl;
    for (casadi_int i=0; i<n_out_; ++i) {
      stream << "  Output " << i  << " (\"" << name_out_[i] << "\"): "
             << sparsity_out_[i].dim() << std::endl;
    }
  }
 
  void ProtoFunction::print_options(std::ostream &stream) const {
    get_options().print_all(stream);
  }
 
  void ProtoFunction::print_option(const std::string &name, std::ostream &stream) const {
    get_options().print_one(name, stream);
  }
 
  bool ProtoFunction::has_option(const std::string &option_name) const {
    return get_options().find(option_name) != nullptr;
  }
 
  void ProtoFunction::change_option(const std::string& option_name,
      const GenericType& option_value) {
    if (option_name == "verbose") {
      verbose_ = option_value;
    } else if (option_name == "regularity_check") {
      regularity_check_ = option_value;
    } else {
      // Failure
      casadi_error("Option '" + option_name + "' cannot be changed");
    }
  }
 
  std::vector<std::string> FunctionInternal::get_free() const {
    casadi_assert_dev(!has_free());
    return std::vector<std::string>();
  }
 
  std::string FunctionInternal::definition() const {
    std::stringstream s;
 
    // Print name
    s << name_ << ":(";
    // Print input arguments
    for (casadi_int i=0; i<n_in_; ++i) {
      if (!is_diff_in_.empty() && !is_diff_in_[i]) s << "#";
      s << name_in_[i] << sparsity_in_[i].postfix_dim() << (i==n_in_-1 ? "" : ",");
    }
    s << ")->(";
    // Print output arguments
    for (casadi_int i=0; i<n_out_; ++i) {
      if (!is_diff_out_.empty() && !is_diff_out_[i]) s << "#";
      s << name_out_[i] << sparsity_out_[i].postfix_dim() << (i==n_out_-1 ? "" : ",");
    }
    s << ")";
 
    return s.str();
  }
 
  void FunctionInternal::disp(std::ostream &stream, bool more) const {
    stream << definition() << " " << class_name();
    if (more) {
      stream << std::endl;
      disp_more(stream);
    }
  }
 
  Dict FunctionInternal::cache() const {
    // Return value
    Dict ret;
 
    // Retrieve all Function instances that haven't been deleted
    std::vector<std::string> keys;
    std::vector<Function> entries;
    cache_.cache(keys, entries);
 
    for (size_t i=0; i<keys.size(); ++i) {
      // Get the name of the key
      std::string s = keys[i];
      casadi_assert_dev(s.size() > 0);
      // Replace ':' with '_'
      std::replace(s.begin(), s.end(), ':', '_');
      // Remove trailing underscore, if any
      if (s.back() == '_') s.resize(s.size() - 1);
      // Add entry to function return
      ret[s] = entries[i];
    }
 
    return ret;
  }
 
  bool FunctionInternal::incache(const std::string& fname, Function& f,
      const std::string& suffix) const {
    return cache_.incache(fname + ":" + suffix, f);
  }
 
  void FunctionInternal::tocache(const Function& f, const std::string& suffix) const {
    cache_.tocache(f.name() + ":" + suffix, f);
  }
 
  void FunctionInternal::tocache_if_missing(Function& f, const std::string& suffix) const {
    cache_.tocache_if_missing(f.name() + ":" + suffix, f);
  }
 
  Function FunctionInternal::map(casadi_int n, const std::string& parallelization) const {
    Function f;
    if (parallelization=="serial") {
      // Serial maps are cached
      std::string fname = "map" + str(n) + "_" + name_;
      if (!incache(fname, f)) {
        // Create new serial map
        f = Map::create(parallelization, self(), n);
        casadi_assert_dev(f.name()==fname);
        // Save in cache
        tocache_if_missing(f);
      }
    } else {
      // Non-serial maps are not cached
      f = Map::create(parallelization, self(), n);
    }
    return f;
  }
 
  Function FunctionInternal::wrap_as_needed(const Dict& opts) const {
    return wrap_as_needed("wrap_" + name_, opts);
  }
 
  Function FunctionInternal::wrap_as_needed(const std::string& name, const Dict& opts) const {
    if (opts.empty() && name==name_) return shared_from_this<Function>();
    // Options
    Dict my_opts = opts;
    my_opts["derivative_of"] = derivative_of_;
    if (my_opts.find("ad_weight")==my_opts.end())
      my_opts["ad_weight"] = ad_weight();
    if (my_opts.find("ad_weight_sp")==my_opts.end())
      my_opts["ad_weight_sp"] = sp_weight();
    if (my_opts.find("max_num_dir")==my_opts.end())
      my_opts["max_num_dir"] = max_num_dir_;
    // Wrap the function
    std::vector<MX> arg = mx_in();
    std::vector<MX> res = self()(arg);
    return Function(name, arg, res, name_in_, name_out_, my_opts);
  }
 
  Function FunctionInternal::wrap() const {
    return wrap("wrap_" + name_);
  }
 
  Function FunctionInternal::wrap(const std::string& name) const {
    Function f;
    if (!incache(name, f)) {
      // Options
      Dict opts;
      opts["derivative_of"] = derivative_of_;
      opts["ad_weight"] = ad_weight();
      opts["ad_weight_sp"] = sp_weight();
      opts["max_num_dir"] = max_num_dir_;
      opts["is_diff_in"] = is_diff_in_;
      opts["is_diff_out"] = is_diff_out_;
      // Wrap the function
      std::vector<MX> arg = mx_in();
      std::vector<MX> res = self()(arg);
      f = Function(name, arg, res, name_in_, name_out_, opts);
      // Save in cache
      tocache_if_missing(f);
    }
    return f;
  }
 
  std::vector<MX> FunctionInternal::symbolic_output(const std::vector<MX>& arg) const {
    return self()(arg);
  }
 
 
  void bvec_toggle(bvec_t* s, casadi_int begin, casadi_int end, casadi_int j) {
    for (casadi_int i=begin; i<end; ++i) {
      s[i] ^= (bvec_t(1) << j);
    }
  }
 
  void bvec_clear(bvec_t* s, casadi_int begin, casadi_int end) {
    for (casadi_int i=begin; i<end; ++i) {
      s[i] = 0;
    }
  }
 
 
  void bvec_or(const bvec_t* s, bvec_t & r, casadi_int begin, casadi_int end) {
    r = 0;
    for (casadi_int i=begin; i<end; ++i) r |= s[i];
  }
 
  // Traits
  template<bool fwd> struct JacSparsityTraits {};
  template<> struct JacSparsityTraits<true> {
    typedef const bvec_t* arg_t;
    static inline void sp(const FunctionInternal *f,
                          const bvec_t** arg, bvec_t** res,
                          casadi_int* iw, bvec_t* w, void* mem) {
      std::vector<const bvec_t*> argm(f->sz_arg(), nullptr);
      std::vector<bvec_t> wm(f->nnz_in(), bvec_t(0));
      bvec_t* wp = get_ptr(wm);
 
      for (casadi_int i=0;i<f->n_in_;++i) {
        if (f->is_diff_in_[i]) {
          argm[i] = arg[i];
        } else  {
          argm[i] = arg[i] ? wp : nullptr;
          wp += f->nnz_in(i);
        }
      }
      f->sp_forward(get_ptr(argm), res, iw, w, mem);
      for (casadi_int i=0;i<f->n_out_;++i) {
        if (!f->is_diff_out_[i] && res[i]) casadi_clear(res[i], f->nnz_out(i));
      }
    }
  };
  template<> struct JacSparsityTraits<false> {
    typedef bvec_t* arg_t;
    static inline void sp(const FunctionInternal *f,
                          bvec_t** arg, bvec_t** res,
                          casadi_int* iw, bvec_t* w, void* mem) {
      for (casadi_int i=0;i<f->n_out_;++i) {
        if (!f->is_diff_out_[i] && res[i]) casadi_clear(res[i], f->nnz_out(i));
      }
      f->sp_reverse(arg, res, iw, w, mem);
      for (casadi_int i=0;i<f->n_in_;++i) {
        if (!f->is_diff_in_[i] && arg[i]) casadi_clear(arg[i], f->nnz_in(i));
      }
    }
  };
 
  template<bool fwd>
  Sparsity FunctionInternal::get_jac_sparsity_gen(casadi_int oind, casadi_int iind) const {
    // Number of nonzero inputs and outputs
    casadi_int nz_in = nnz_in(iind);
    casadi_int nz_out = nnz_out(oind);
 
    // Evaluation buffers
    std::vector<typename JacSparsityTraits<fwd>::arg_t> arg(sz_arg(), nullptr);
    std::vector<bvec_t*> res(sz_res(), nullptr);
    std::vector<casadi_int> iw(sz_iw());
    std::vector<bvec_t> w(sz_w(), 0);
 
    // Seeds and sensitivities
    std::vector<bvec_t> seed(nz_in, 0);
    arg[iind] = get_ptr(seed);
    std::vector<bvec_t> sens(nz_out, 0);
    res[oind] = get_ptr(sens);
    if (!fwd) std::swap(seed, sens);
 
    // Number of forward sweeps we must make
    casadi_int nsweep = seed.size() / bvec_size;
    if (seed.size() % bvec_size) nsweep++;
 
    // Print
    if (verbose_) {
      casadi_message(str(nsweep) + std::string(fwd ? " forward" : " reverse") + " sweeps "
                     "needed for " + str(seed.size()) + " directions");
    }
 
    // Progress
    casadi_int progress = -10;
 
    // Temporary vectors
    std::vector<casadi_int> jcol, jrow;
 
    // Loop over the variables, bvec_size variables at a time
    for (casadi_int s=0; s<nsweep; ++s) {
 
      // Print progress
      if (verbose_) {
        casadi_int progress_new = (s*100)/nsweep;
        // Print when entering a new decade
        if (progress_new / 10 > progress / 10) {
          progress = progress_new;
          casadi_message(str(progress) + " %");
        }
      }
 
      // Nonzero offset
      casadi_int offset = s*bvec_size;
 
      // Number of local seed directions
      casadi_int ndir_local = seed.size()-offset;
      ndir_local = std::min(static_cast<casadi_int>(bvec_size), ndir_local);
 
      for (casadi_int i=0; i<ndir_local; ++i) {
        seed[offset+i] |= bvec_t(1)<<i;
      }
 
      // Propagate the dependencies
      JacSparsityTraits<fwd>::sp(this, get_ptr(arg), get_ptr(res),
                                  get_ptr(iw), get_ptr(w), memory(0));
 
      // Loop over the nonzeros of the output
      for (casadi_int el=0; el<sens.size(); ++el) {
 
        // Get the sparsity sensitivity
        bvec_t spsens = sens[el];
 
        if (!fwd) {
          // Clear the sensitivities for the next sweep
          sens[el] = 0;
        }
 
        // If there is a dependency in any of the directions
        if (spsens!=0) {
 
          // Loop over seed directions
          for (casadi_int i=0; i<ndir_local; ++i) {
 
            // If dependents on the variable
            if ((bvec_t(1) << i) & spsens) {
              // Add to pattern
              jcol.push_back(el);
              jrow.push_back(i+offset);
            }
          }
        }
      }
 
      // Remove the seeds
      for (casadi_int i=0; i<ndir_local; ++i) {
        seed[offset+i] = 0;
      }
    }
 
    // Construct sparsity pattern and return
    if (!fwd) swap(jrow, jcol);
    Sparsity ret = Sparsity::triplet(nz_out, nz_in, jcol, jrow);
    if (verbose_) {
      casadi_message("Formed Jacobian sparsity pattern (dimension " + str(ret.size()) + ", "
          + str(ret.nnz()) + " (" + str(ret.density()) + " %) nonzeros.");
    }
    return ret;
  }
 
  Sparsity FunctionInternal::get_jac_sparsity_hierarchical_symm(casadi_int oind,
      casadi_int iind) const {
    casadi_assert_dev(has_spfwd());
 
    // Number of nonzero inputs
    casadi_int nz = nnz_in(iind);
    casadi_assert_dev(nz==nnz_out(oind));
 
    // Evaluation buffers
    std::vector<const bvec_t*> arg(sz_arg(), nullptr);
    std::vector<bvec_t*> res(sz_res(), nullptr);
    std::vector<casadi_int> iw(sz_iw());
    std::vector<bvec_t> w(sz_w());
 
    // Seeds
    std::vector<bvec_t> seed(nz, 0);
    arg[iind] = get_ptr(seed);
 
    // Sensitivities
    std::vector<bvec_t> sens(nz, 0);
    res[oind] = get_ptr(sens);
 
    // Sparsity triplet accumulator
    std::vector<casadi_int> jcol, jrow;
 
    // Cols/rows of the coarse blocks
    std::vector<casadi_int> coarse(2, 0); coarse[1] = nz;
 
    // Cols/rows of the fine blocks
    std::vector<casadi_int> fine;
 
    // In each iteration, subdivide each coarse block in this many fine blocks
    casadi_int subdivision = bvec_size;
 
    Sparsity r = Sparsity::dense(1, 1);
 
    // The size of a block
    casadi_int granularity = nz;
 
    casadi_int nsweeps = 0;
 
    bool hasrun = false;
 
    while (!hasrun || coarse.size()!=nz+1) {
      if (verbose_) casadi_message("Block size: " + str(granularity));
 
      // Clear the sparsity triplet acccumulator
      jcol.clear();
      jrow.clear();
 
      // Clear the fine block structure
      fine.clear();
 
      Sparsity D = r.star_coloring();
 
      if (verbose_) {
        casadi_message("Star coloring on " + str(r.dim()) + ": "
          + str(D.size2()) + " <-> " + str(D.size1()));
      }
 
      // Clear the seeds
      std::fill(seed.begin(), seed.end(), 0);
 
      // Subdivide the coarse block
      for (casadi_int k=0; k<coarse.size()-1; ++k) {
        casadi_int diff = coarse[k+1]-coarse[k];
        casadi_int new_diff = diff/subdivision;
        if (diff%subdivision>0) new_diff++;
        std::vector<casadi_int> temp = range(coarse[k], coarse[k+1], new_diff);
        fine.insert(fine.end(), temp.begin(), temp.end());
      }
      if (fine.back()!=coarse.back()) fine.push_back(coarse.back());
 
      granularity = fine[1] - fine[0];
 
      // The index into the bvec bit vector
      casadi_int bvec_i = 0;
 
      // Create lookup tables for the fine blocks
      std::vector<casadi_int> fine_lookup = lookupvector(fine, nz+1);
 
      // Triplet data used as a lookup table
      std::vector<casadi_int> lookup_col;
      std::vector<casadi_int> lookup_row;
      std::vector<casadi_int> lookup_value;
 
      // The maximum number of fine blocks contained in one coarse block
      casadi_int n_fine_blocks_max = 0;
      for (casadi_int i=0;i<coarse.size()-1;++i) {
        casadi_int del = fine_lookup[coarse[i+1]]-fine_lookup[coarse[i]];
        n_fine_blocks_max = std::max(n_fine_blocks_max, del);
      }
 
      // Loop over all coarse seed directions from the coloring
      for (casadi_int csd=0; csd<D.size2(); ++csd) {
 
 
        casadi_int fci_offset = 0;
        casadi_int fci_cap = bvec_size-bvec_i;
 
        // Flag to indicate if all fine blocks have been handled
        bool f_finished = false;
 
        // Loop while not finished
        while (!f_finished) {
 
          // Loop over all coarse rows that are found in the coloring for this coarse seed direction
          for (casadi_int k=D.colind(csd); k<D.colind(csd+1); ++k) {
            casadi_int cci = D.row(k);
 
            // The first and last rows of the fine block
            casadi_int fci_start = fine_lookup[coarse[cci]];
            casadi_int fci_end   = fine_lookup[coarse[cci+1]];
 
            // Local counter that modifies index into bvec
            casadi_int bvec_i_mod = 0;
 
            casadi_int value = -bvec_i + fci_offset + fci_start;
 
            //casadi_assert_dev(value>=0);
 
            // Loop over the rows of the fine block
            for (casadi_int fci = fci_offset; fci<std::min(fci_end-fci_start, fci_cap); ++fci) {
 
              // Loop over the coarse block cols that appear in the
              // coloring for the current coarse seed direction
              for (casadi_int cri=r.colind(cci);cri<r.colind(cci+1);++cri) {
                lookup_col.push_back(r.row(cri));
                lookup_row.push_back(bvec_i+bvec_i_mod);
                lookup_value.push_back(value);
              }
 
              // Toggle on seeds
              bvec_toggle(get_ptr(seed), fine[fci+fci_start], fine[fci+fci_start+1],
                          bvec_i+bvec_i_mod);
              bvec_i_mod++;
            }
          }
 
          // Bump bvec_i for next major coarse direction
          bvec_i += std::min(n_fine_blocks_max, fci_cap);
 
          // Check if bvec buffer is full
          if (bvec_i==bvec_size || csd==D.size2()-1) {
            // Calculate sparsity for bvec_size directions at once
 
            // Statistics
            nsweeps+=1;
 
            // Construct lookup table
            IM lookup = IM::triplet(lookup_row, lookup_col, lookup_value,
                                    bvec_size, coarse.size());
 
            std::reverse(lookup_col.begin(), lookup_col.end());
            std::reverse(lookup_row.begin(), lookup_row.end());
            std::reverse(lookup_value.begin(), lookup_value.end());
            IM duplicates =
              IM::triplet(lookup_row, lookup_col, lookup_value, bvec_size, coarse.size())
              - lookup;
            duplicates = sparsify(duplicates);
            lookup(duplicates.sparsity()) = -bvec_size;
 
            // Propagate the dependencies
            JacSparsityTraits<true>::sp(this, get_ptr(arg), get_ptr(res),
              get_ptr(iw), get_ptr(w), nullptr);
 
            // Temporary bit work vector
            bvec_t spsens;
 
            // Loop over the cols of coarse blocks
            for (casadi_int cri=0; cri<coarse.size()-1; ++cri) {
 
              // Loop over the cols of fine blocks within the current coarse block
              for (casadi_int fri=fine_lookup[coarse[cri]];fri<fine_lookup[coarse[cri+1]];++fri) {
                // Lump individual sensitivities together into fine block
                bvec_or(get_ptr(sens), spsens, fine[fri], fine[fri+1]);
 
                // Loop over all bvec_bits
                for (casadi_int bvec_i=0;bvec_i<bvec_size;++bvec_i) {
                  if (spsens & (bvec_t(1) << bvec_i)) {
                    // if dependency is found, add it to the new sparsity pattern
                    casadi_int ind = lookup.sparsity().get_nz(bvec_i, cri);
                    if (ind==-1) continue;
                    casadi_int lk = lookup->at(ind);
                    if (lk>-bvec_size) {
                      jrow.push_back(bvec_i+lk);
                      jcol.push_back(fri);
                      jrow.push_back(fri);
                      jcol.push_back(bvec_i+lk);
                    }
                  }
                }
              }
            }
 
            // Clear the forward seeds/adjoint sensitivities, ready for next bvec sweep
            std::fill(seed.begin(), seed.end(), 0);
 
            // Clean lookup table
            lookup_col.clear();
            lookup_row.clear();
            lookup_value.clear();
          }
 
          if (n_fine_blocks_max>fci_cap) {
            fci_offset += std::min(n_fine_blocks_max, fci_cap);
            bvec_i = 0;
            fci_cap = bvec_size;
          } else {
            f_finished = true;
          }
        }
      }
 
      // Construct fine sparsity pattern
      r = Sparsity::triplet(fine.size()-1, fine.size()-1, jrow, jcol);
 
      // There may be false positives here that are not present
      // in the reverse mode that precedes it.
      // This can lead to an assymetrical result
      //  cf. #1522
      r=r*r.T();
 
      coarse = fine;
      hasrun = true;
    }
    if (verbose_) {
      casadi_message("Number of sweeps: " + str(nsweeps));
      casadi_message("Formed Jacobian sparsity pattern (dimension " + str(r.size()) +
          ", " + str(r.nnz()) + " (" + str(r.density()) + " %) nonzeros.");
    }
 
    return r.T();
  }
 
  Sparsity FunctionInternal::get_jac_sparsity_hierarchical(casadi_int oind, casadi_int iind) const {
    // Number of nonzero inputs
    casadi_int nz_in = nnz_in(iind);
 
    // Number of nonzero outputs
    casadi_int nz_out = nnz_out(oind);
 
    // Seeds and sensitivities
    std::vector<bvec_t> s_in(nz_in, 0);
    std::vector<bvec_t> s_out(nz_out, 0);
 
    // Evaluation buffers
    std::vector<const bvec_t*> arg_fwd(sz_arg(), nullptr);
    std::vector<bvec_t*> arg_adj(sz_arg(), nullptr);
    arg_fwd[iind] = arg_adj[iind] = get_ptr(s_in);
    std::vector<bvec_t*> res(sz_res(), nullptr);
    res[oind] = get_ptr(s_out);
    std::vector<casadi_int> iw(sz_iw());
    std::vector<bvec_t> w(sz_w());
 
    // Sparsity triplet accumulator
    std::vector<casadi_int> jcol, jrow;
 
    // Cols of the coarse blocks
    std::vector<casadi_int> coarse_col(2, 0); coarse_col[1] = nz_out;
    // Rows of the coarse blocks
    std::vector<casadi_int> coarse_row(2, 0); coarse_row[1] = nz_in;
 
    // Cols of the fine blocks
    std::vector<casadi_int> fine_col;
 
    // Rows of the fine blocks
    std::vector<casadi_int> fine_row;
 
    // In each iteration, subdivide each coarse block in this many fine blocks
    casadi_int subdivision = bvec_size;
 
    Sparsity r = Sparsity::dense(1, 1);
 
    // The size of a block
    casadi_int granularity_row = nz_in;
    casadi_int granularity_col = nz_out;
 
    bool use_fwd = true;
 
    casadi_int nsweeps = 0;
 
    bool hasrun = false;
 
    // Get weighting factor
    double sp_w = sp_weight();
 
    // Lookup table for bvec_t
    std::vector<bvec_t> bvec_lookup;
    bvec_lookup.reserve(bvec_size);
    for (casadi_int i=0;i<bvec_size;++i) {
      bvec_lookup.push_back(bvec_t(1) << i);
    }
 
    while (!hasrun || coarse_col.size()!=nz_out+1 || coarse_row.size()!=nz_in+1) {
      if (verbose_) {
        casadi_message("Block size: " + str(granularity_col) + " x " + str(granularity_row));
      }
 
      // Clear the sparsity triplet acccumulator
      jcol.clear();
      jrow.clear();
 
      // Clear the fine block structure
      fine_row.clear();
      fine_col.clear();
 
      // r transpose will be needed in the algorithm
      Sparsity rT = r.T();
 
      // Forward mode
      Sparsity D1 = rT.uni_coloring(r);
      // Adjoint mode
      Sparsity D2 = r.uni_coloring(rT);
      if (verbose_) {
        casadi_message("Coloring on " + str(r.dim()) + " (fwd seeps: " + str(D1.size2()) +
                 " , adj sweeps: " + str(D2.size1()) + ")");
      }
 
      // Use whatever required less colors if we tried both (with preference to forward mode)
      double fwd_cost = static_cast<double>(use_fwd ? granularity_row : granularity_col) *
        sp_w*static_cast<double>(D1.size2());
      double adj_cost = static_cast<double>(use_fwd ? granularity_col : granularity_row) *
        (1-sp_w)*static_cast<double>(D2.size2());
      use_fwd = fwd_cost <= adj_cost;
      if (verbose_) {
        casadi_message(std::string(use_fwd ? "Forward" : "Reverse") + " mode chosen "
            "(fwd cost: " + str(fwd_cost) + ", adj cost: " + str(adj_cost) + ")");
      }
 
      // Get seeds and sensitivities
      bvec_t* seed_v = use_fwd ? get_ptr(s_in) : get_ptr(s_out);
      bvec_t* sens_v = use_fwd ? get_ptr(s_out) : get_ptr(s_in);
 
      // The number of zeros in the seed and sensitivity directions
      casadi_int nz_seed = use_fwd ? nz_in  : nz_out;
      casadi_int nz_sens = use_fwd ? nz_out : nz_in;
 
      // Clear the seeds
      for (casadi_int i=0; i<nz_seed; ++i) seed_v[i]=0;
 
      // Choose the active jacobian coloring scheme
      Sparsity D = use_fwd ? D1 : D2;
 
      // Adjoint mode amounts to swapping
      if (!use_fwd) {
        std::swap(coarse_col, coarse_row);
        std::swap(granularity_col, granularity_row);
        std::swap(r, rT);
      }
 
      // Subdivide the coarse block cols
      for (casadi_int k=0;k<coarse_col.size()-1;++k) {
        casadi_int diff = coarse_col[k+1]-coarse_col[k];
        casadi_int new_diff = diff/subdivision;
        if (diff%subdivision>0) new_diff++;
        std::vector<casadi_int> temp = range(coarse_col[k], coarse_col[k+1], new_diff);
        fine_col.insert(fine_col.end(), temp.begin(), temp.end());
      }
      // Subdivide the coarse block rows
      for (casadi_int k=0;k<coarse_row.size()-1;++k) {
        casadi_int diff = coarse_row[k+1]-coarse_row[k];
        casadi_int new_diff = diff/subdivision;
        if (diff%subdivision>0) new_diff++;
        std::vector<casadi_int> temp = range(coarse_row[k], coarse_row[k+1], new_diff);
        fine_row.insert(fine_row.end(), temp.begin(), temp.end());
      }
      if (fine_row.back()!=coarse_row.back()) fine_row.push_back(coarse_row.back());
      if (fine_col.back()!=coarse_col.back()) fine_col.push_back(coarse_col.back());
 
      granularity_col = fine_col[1] - fine_col[0];
      granularity_row = fine_row[1] - fine_row[0];
 
      // The index into the bvec bit vector
      casadi_int bvec_i = 0;
 
      // Create lookup tables for the fine blocks
      std::vector<casadi_int> fine_col_lookup = lookupvector(fine_col, nz_sens+1);
      std::vector<casadi_int> fine_row_lookup = lookupvector(fine_row, nz_seed+1);
 
      // Triplet data used as a lookup table
      std::vector<casadi_int> lookup_col;
      std::vector<casadi_int> lookup_row;
      std::vector<casadi_int> lookup_value;
 
 
      // The maximum number of fine blocks contained in one coarse block
      casadi_int n_fine_blocks_max = 0;
      for (casadi_int i=0;i<coarse_row.size()-1;++i) {
        casadi_int del = fine_row_lookup[coarse_row[i+1]]-fine_row_lookup[coarse_row[i]];
        n_fine_blocks_max = std::max(n_fine_blocks_max, del);
      }
 
      // Loop over all coarse seed directions from the coloring
      for (casadi_int csd=0; csd<D.size2(); ++csd) {
 
        casadi_int fci_offset = 0;
        casadi_int fci_cap = bvec_size-bvec_i;
 
        // Flag to indicate if all fine blocks have been handled
        bool f_finished = false;
 
        // Loop while not finished
        while (!f_finished) {
 
          // Loop over all coarse rows that are found in the coloring for this coarse seed direction
          for (casadi_int k=D.colind(csd); k<D.colind(csd+1); ++k) {
            casadi_int cci = D.row(k);
 
            // The first and last rows of the fine block
            casadi_int fci_start = fine_row_lookup[coarse_row[cci]];
            casadi_int fci_end   = fine_row_lookup[coarse_row[cci+1]];
 
            // Local counter that modifies index into bvec
            casadi_int bvec_i_mod = 0;
 
            casadi_int value = -bvec_i + fci_offset + fci_start;
 
            // Loop over the rows of the fine block
            for (casadi_int fci = fci_offset; fci < std::min(fci_end-fci_start, fci_cap); ++fci) {
 
              // Loop over the coarse block cols that appear in the coloring
              // for the current coarse seed direction
              for (casadi_int cri=rT.colind(cci);cri<rT.colind(cci+1);++cri) {
                lookup_col.push_back(rT.row(cri));
                lookup_row.push_back(bvec_i+bvec_i_mod);
                lookup_value.push_back(value);
              }
 
              // Toggle on seeds
              bvec_toggle(seed_v, fine_row[fci+fci_start], fine_row[fci+fci_start+1],
                          bvec_i+bvec_i_mod);
              bvec_i_mod++;
            }
          }
 
          // Bump bvec_i for next major coarse direction
          bvec_i+= std::min(n_fine_blocks_max, fci_cap);
 
          // Check if bvec buffer is full
          if (bvec_i==bvec_size || csd==D.size2()-1) {
            // Calculate sparsity for bvec_size directions at once
 
            // Statistics
            nsweeps+=1;
 
            // Construct lookup table
            IM lookup = IM::triplet(lookup_row, lookup_col, lookup_value, bvec_size,
                                    coarse_col.size());
 
            // Propagate the dependencies
            if (use_fwd) {
              JacSparsityTraits<true>::sp(this, get_ptr(arg_fwd), get_ptr(res),
                get_ptr(iw), get_ptr(w), memory(0));
            } else {
              std::fill(w.begin(), w.end(), 0);
              JacSparsityTraits<false>::sp(this, get_ptr(arg_adj), get_ptr(res),
                get_ptr(iw), get_ptr(w), memory(0));
            }
 
            // Temporary bit work vector
            bvec_t spsens;
 
            // Loop over the cols of coarse blocks
            for (casadi_int cri=0;cri<coarse_col.size()-1;++cri) {
 
              // Loop over the cols of fine blocks within the current coarse block
              for (casadi_int fri=fine_col_lookup[coarse_col[cri]];
                   fri<fine_col_lookup[coarse_col[cri+1]];++fri) {
                // Lump individual sensitivities together into fine block
                bvec_or(sens_v, spsens, fine_col[fri], fine_col[fri+1]);
 
                // Next iteration if no sparsity
                if (!spsens) continue;
 
                // Loop over all bvec_bits
                for (casadi_int bvec_i=0;bvec_i<bvec_size;++bvec_i) {
                  if (spsens & bvec_lookup[bvec_i]) {
                    // if dependency is found, add it to the new sparsity pattern
                    casadi_int ind = lookup.sparsity().get_nz(bvec_i, cri);
                    if (ind==-1) continue;
                    jrow.push_back(bvec_i+lookup->at(ind));
                    jcol.push_back(fri);
                  }
                }
              }
            }
 
            // Clear the forward seeds/adjoint sensitivities, ready for next bvec sweep
            std::fill(s_in.begin(), s_in.end(), 0);
 
            // Clear the adjoint seeds/forward sensitivities, ready for next bvec sweep
            std::fill(s_out.begin(), s_out.end(), 0);
 
            // Clean lookup table
            lookup_col.clear();
            lookup_row.clear();
            lookup_value.clear();
          }
 
          if (n_fine_blocks_max>fci_cap) {
            fci_offset += std::min(n_fine_blocks_max, fci_cap);
            bvec_i = 0;
            fci_cap = bvec_size;
          } else {
            f_finished = true;
          }
 
        }
 
      }
 
      // Swap results if adjoint mode was used
      if (use_fwd) {
        // Construct fine sparsity pattern
        r = Sparsity::triplet(fine_row.size()-1, fine_col.size()-1, jrow, jcol);
        coarse_col = fine_col;
        coarse_row = fine_row;
      } else {
        // Construct fine sparsity pattern
        r = Sparsity::triplet(fine_col.size()-1, fine_row.size()-1, jcol, jrow);
        coarse_col = fine_row;
        coarse_row = fine_col;
      }
      hasrun = true;
    }
    if (verbose_) {
      casadi_message("Number of sweeps: " + str(nsweeps));
      casadi_message("Formed Jacobian sparsity pattern (dimension " + str(r.size()) + ", " +
          str(r.nnz()) + " (" + str(r.density()) + " %) nonzeros.");
    }
 
    return r.T();
  }
 
  bool FunctionInternal::jac_is_symm(casadi_int oind, casadi_int iind) const {
    // If derivative expression
    if (!derivative_of_.is_null()) {
      std::string n = derivative_of_.name();
      // Reverse move
      if (name_ == "adj1_" + n) {
        if (iind == oind) return true;
      }
    }
    // Not symmetric by default
    return false;
  }
 
  Sparsity FunctionInternal::get_jac_sparsity(casadi_int oind, casadi_int iind,
      bool symmetric) const {
    if (symmetric) {
      casadi_assert(sparsity_out_[oind].is_dense(),
        "Symmetry exploitation in Jacobian assumes dense expression. "
        "A potential workaround is to apply densify().");
    }
    // Check if we are able to propagate dependencies through the function
    if (has_spfwd() || has_sprev()) {
      // Get weighting factor
      double w = sp_weight();
 
      // Skip generation, assume dense
      if (w == -1) return Sparsity();
 
      Sparsity sp;
      if (nnz_in(iind) > 3*bvec_size && nnz_out(oind) > 3*bvec_size &&
            GlobalOptions::hierarchical_sparsity) {
        if (symmetric) {
          sp = get_jac_sparsity_hierarchical_symm(oind, iind);
        } else {
          sp = get_jac_sparsity_hierarchical(oind, iind);
        }
      } else {
        // Number of nonzero inputs and outputs
        casadi_int nz_in = nnz_in(iind);
        casadi_int nz_out = nnz_out(oind);
 
        // Number of forward sweeps we must make
        casadi_int nsweep_fwd = nz_in/bvec_size;
        if (nz_in%bvec_size) nsweep_fwd++;
 
        // Number of adjoint sweeps we must make
        casadi_int nsweep_adj = nz_out/bvec_size;
        if (nz_out%bvec_size) nsweep_adj++;
 
        // Use forward mode?
        if (w*static_cast<double>(nsweep_fwd) <= (1-w)*static_cast<double>(nsweep_adj)) {
          sp = get_jac_sparsity_gen<true>(oind, iind);
        } else {
          sp = get_jac_sparsity_gen<false>(oind, iind);
        }
      }
      return sp;
    } else {
      // Not calculated
      return Sparsity();
    }
  }
 
  Sparsity FunctionInternal::to_compact(casadi_int oind, casadi_int iind,
      const Sparsity& sp) const {
    // Strip rows and columns
    std::vector<casadi_int> mapping;
    return sp.sub(sparsity_out(oind).find(), sparsity_in(iind).find(), mapping);
  }
 
  Sparsity FunctionInternal::from_compact(casadi_int oind, casadi_int iind,
      const Sparsity& sp) const {
    // Return value
    Sparsity r = sp;
    // Insert rows if sparse output
    if (numel_out(oind) != r.size1()) {
      casadi_assert_dev(r.size1() == nnz_out(oind));
      r.enlargeRows(numel_out(oind), sparsity_out(oind).find());
    }
    // Insert columns if sparse input
    if (numel_in(iind) != r.size2()) {
      casadi_assert_dev(r.size2() == nnz_in(iind));
      r.enlargeColumns(numel_in(iind), sparsity_in(iind).find());
    }
    // Return non-compact pattern
    return r;
  }
 
  Sparsity& FunctionInternal::jac_sparsity(casadi_int oind, casadi_int iind, bool compact,
      bool symmetric) const {
#ifdef CASADI_WITH_THREADSAFE_SYMBOLICS
    // Safe access to jac_sparsity_
    std::lock_guard<std::mutex> lock(jac_sparsity_mtx_);
#endif // CASADI_WITH_THREADSAFE_SYMBOLICS
    // If first call, allocate cache
    for (bool c : {false, true}) {
      if (jac_sparsity_[c].empty()) jac_sparsity_[c].resize(n_in_ * n_out_);
    }
    // Flat index
    casadi_int ind = iind + oind * n_in_;
    // Reference to the block
    Sparsity& jsp = jac_sparsity_[compact].at(ind);
    // If null, generate
    if (jsp.is_null()) {
      // Use (non)-compact pattern, if given
      Sparsity& jsp_other = jac_sparsity_[!compact].at(ind);
      if (!jsp_other.is_null()) {
        jsp = compact ? to_compact(oind, iind, jsp_other) : from_compact(oind, iind, jsp_other);
      } else {
        // Generate pattern
        Sparsity sp;
        bool sp_is_compact;
        if (!is_diff_out_.at(oind) || !is_diff_in_.at(iind)) {
          // All-zero sparse
          sp = Sparsity(nnz_out(oind), nnz_in(iind));
          sp_is_compact = true;
        } else {
          // Use internal routine to determine sparsity
          if (has_spfwd() || has_sprev() || has_jac_sparsity(oind, iind)) {
            sp = get_jac_sparsity(oind, iind, symmetric);
          }
          // If null, dense
          if (sp.is_null()) sp = Sparsity::dense(nnz_out(oind), nnz_in(iind));
          // Is the return the compact pattern?
          sp_is_compact = sp.size1() == nnz_out(oind) && sp.size2() == nnz_in(iind);
        }
        // Save to cache and convert if needed
        if (sp_is_compact == compact) {
          jsp = sp;
        } else {
          jsp_other = sp;
          jsp = compact ? to_compact(oind, iind, sp) : from_compact(oind, iind, sp);
        }
      }
    }
 
    // Make sure the Jacobian is symmetric if requested, cf. #1522, #3074, #3134
    if (symmetric) {
      if (compact) {
        Sparsity sp = from_compact(oind, iind, jsp);
        if (!sp.is_symmetric()) {
          sp = sp * sp.T();
          jsp = to_compact(oind, iind, sp);
        }
      } else {
        if (!jsp.is_symmetric()) jsp = jsp * jsp.T();
      }
    }
 
    // Return a reference to the block
    return jsp;
  }
 
  void FunctionInternal::get_partition(casadi_int iind, casadi_int oind, Sparsity& D1, Sparsity& D2,
                                       bool compact, bool symmetric,
                                       bool allow_forward, bool allow_reverse) const {
    if (verbose_) casadi_message(name_ + "::get_partition");
    casadi_assert(allow_forward || allow_reverse, "Inconsistent options");
 
    // Sparsity pattern with transpose
    Sparsity &AT = jac_sparsity(oind, iind, compact, symmetric);
    Sparsity A = symmetric ? AT : AT.T();
 
    // Get seed matrices by graph coloring
    if (symmetric) {
      casadi_assert_dev(enable_forward_ || enable_fd_);
      casadi_assert_dev(allow_forward);
 
      // Star coloring if symmetric
      if (verbose_) casadi_message("FunctionInternal::getPartition star_coloring");
      D1 = A.star_coloring();
      if (verbose_) {
        casadi_message("Star coloring completed: " + str(D1.size2())
          + " directional derivatives needed ("
                 + str(A.size1()) + " without coloring).");
      }
 
    } else {
      casadi_assert_dev(enable_forward_ || enable_fd_ || enable_reverse_);
      // Get weighting factor
      double w = ad_weight();
 
      // Which AD mode?
      if (w==1) allow_forward = false;
      if (w==0) allow_reverse = false;
      casadi_assert(allow_forward || allow_reverse, "Conflicting ad weights");
 
      // Best coloring encountered so far (relatively tight upper bound)
      double best_coloring = std::numeric_limits<double>::infinity();
 
      // Test forward mode first?
      bool test_fwd_first = allow_forward && w*static_cast<double>(A.size1()) <=
        (1-w)*static_cast<double>(A.size2());
      casadi_int mode_fwd = test_fwd_first ? 0 : 1;
 
      // Test both coloring modes
      for (casadi_int mode=0; mode<2; ++mode) {
        // Is this the forward mode?
        bool fwd = mode==mode_fwd;
 
        // Skip?
        if (!allow_forward && fwd) continue;
        if (!allow_reverse && !fwd) continue;
 
        // Perform the coloring
        if (fwd) {
          if (verbose_) casadi_message("Unidirectional coloring (forward mode)");
          bool d = best_coloring>=w*static_cast<double>(A.size1());
          casadi_int max_colorings_to_test =
            d ? A.size1() : static_cast<casadi_int>(floor(best_coloring/w));
          D1 = AT.uni_coloring(A, max_colorings_to_test);
          if (D1.is_null()) {
            if (verbose_) {
              casadi_message("Forward mode coloring interrupted (more than "
                             + str(max_colorings_to_test) + " needed).");
            }
          } else {
            if (verbose_) {
              casadi_message("Forward mode coloring completed: "
                             + str(D1.size2()) + " directional derivatives needed ("
                             + str(A.size1()) + " without coloring).");
            }
            D2 = Sparsity();
            best_coloring = w*static_cast<double>(D1.size2());
          }
        } else {
          if (verbose_) casadi_message("Unidirectional coloring (adjoint mode)");
          bool d = best_coloring>=(1-w)*static_cast<double>(A.size2());
          casadi_int max_colorings_to_test =
            d ? A.size2() : static_cast<casadi_int>(floor(best_coloring/(1-w)));
 
          D2 = A.uni_coloring(AT, max_colorings_to_test);
          if (D2.is_null()) {
            if (verbose_) {
              casadi_message("Adjoint mode coloring interrupted (more than "
                            + str(max_colorings_to_test) + " needed).");
            }
          } else {
            if (verbose_) {
              casadi_message("Adjoint mode coloring completed: "
                             + str(D2.size2()) + " directional derivatives needed ("
                             + str(A.size2()) + " without coloring).");
            }
            D1 = Sparsity();
            best_coloring = (1-w)*static_cast<double>(D2.size2());
          }
        }
      }
 
    }
  }
 
  std::vector<DM> FunctionInternal::eval_dm(const std::vector<DM>& arg) const {
    casadi_error("'eval_dm' not defined for " + class_name());
  }
 
  int FunctionInternal::
  eval_sx(const SXElem** arg, SXElem** res, casadi_int* iw, SXElem* w, void* mem,
    bool always_inline, bool never_inline) const {
 
    always_inline = always_inline || always_inline_;
    never_inline = never_inline || never_inline_;
 
    casadi_assert(!always_inline, "'eval_sx' not defined for " + class_name() +
    " in combination with always_inline true");
 
    return CallSX::eval_sx(self(), arg, res);
  }
 
  std::string FunctionInternal::diff_prefix(const std::string& prefix) const {
    // Highest index found in current inputs and outputs
    casadi_int highest_index = 0;
    // Loop over both input names and output names
    for (const std::vector<std::string>& name_io : {name_in_, name_out_}) {
      for (const std::string& n : name_io) {
        // Find end of prefix, skip if no prefix
        size_t end = n.find('_');
        if (end >= n.size()) continue;
        // Skip if too short
        if (end < prefix.size()) continue;
        // Skip if wrong prefix
        if (n.compare(0, prefix.size(), prefix) != 0) continue;
        // Beginning of index
        size_t begin = prefix.size();
        // Check if any index
        casadi_int this_index;
        if (begin == end) {
          // No prefix, implicitly 1
          this_index = 1;
        } else {
          // Read index from string
          this_index = std::stoi(n.substr(begin, end - begin));
        }
        // Find the highest index
        if (this_index > highest_index) highest_index = this_index;
      }
    }
    // Return one higher index
    if (highest_index == 0) {
      return prefix + "_";
    } else {
      return prefix + std::to_string(highest_index + 1) + "_";
    }
  }
 
  Function FunctionInternal::forward(casadi_int nfwd) const {
    casadi_assert_dev(nfwd>=0);
    // Used wrapped function if forward not available
    if (!enable_forward_ && !enable_fd_) {
      // Derivative information must be available
      casadi_assert(has_derivative(), "Derivatives cannot be calculated for " + name_);
      return wrap().forward(nfwd);
    }
    // Retrieve/generate cached
    Function f;
    std::string fname = forward_name(name_, nfwd);
    if (!incache(fname, f)) {
      casadi_int i;
      // Prefix to be used for forward seeds, sensitivities
      std::string pref = diff_prefix("fwd");
      // Names of inputs
      std::vector<std::string> inames;
      for (i=0; i<n_in_; ++i) inames.push_back(name_in_[i]);
      for (i=0; i<n_out_; ++i) inames.push_back("out_" + name_out_[i]);
      for (i=0; i<n_in_; ++i) inames.push_back(pref + name_in_[i]);
      // Names of outputs
      std::vector<std::string> onames;
      for (i=0; i<n_out_; ++i) onames.push_back(pref + name_out_[i]);
      // Options
      Dict opts = combine(forward_options_, der_options_);
      if (enable_forward_) {
        opts = combine(opts, generate_options("forward"));
      } else {
        opts = combine(opts, FunctionInternal::generate_options("forward"));
      }
      opts["derivative_of"] = self();
      // Generate derivative function
      casadi_assert_dev(enable_forward_ || enable_fd_);
      if (enable_forward_) {
        f = get_forward(nfwd, fname, inames, onames, opts);
      } else {
        opts = combine(opts, fd_options_);
        // Get FD method
        if (fd_method_.empty() || fd_method_=="central") {
          f = Function::create(new CentralDiff(fname, nfwd), opts);
        } else if (fd_method_=="forward") {
          f = Function::create(new ForwardDiff(fname, nfwd), opts);
        } else if (fd_method_=="backward") {
          f = Function::create(new BackwardDiff(fname, nfwd), opts);
        } else if (fd_method_=="smoothing") {
          f = Function::create(new Smoothing(fname, nfwd), opts);
        } else {
          casadi_error("Unknown 'fd_method': " + fd_method_);
        }
      }
      // Consistency check for inputs
      casadi_assert_dev(f.n_in()==n_in_ + n_out_ + n_in_);
      casadi_int ind=0;
      for (i=0; i<n_in_; ++i) f.assert_size_in(ind++, size1_in(i), size2_in(i));
      for (i=0; i<n_out_; ++i) f.assert_size_in(ind++, size1_out(i), size2_out(i));
      for (i=0; i<n_in_; ++i) f.assert_size_in(ind++, size1_in(i), nfwd*size2_in(i));
      // Consistency check for outputs
      casadi_assert_dev(f.n_out()==n_out_);
      for (i=0; i<n_out_; ++i) f.assert_sparsity_out(i, sparsity_out(i), nfwd);
      // Save to cache
      tocache_if_missing(f);
    }
    return f;
  }
 
  Function FunctionInternal::reverse(casadi_int nadj) const {
    casadi_assert_dev(nadj>=0);
    // Used wrapped function if reverse not available
    if (!enable_reverse_) {
      // Derivative information must be available
      casadi_assert(has_derivative(), "Derivatives cannot be calculated for " + name_);
      return wrap().reverse(nadj);
    }
    // Retrieve/generate cached
    Function f;
    std::string fname = reverse_name(name_, nadj);
    if (!incache(fname, f)) {
      casadi_int i;
      // Prefix to be used for adjoint seeds, sensitivities
      std::string pref = diff_prefix("adj");
      // Names of inputs
      std::vector<std::string> inames;
      for (i=0; i<n_in_; ++i) inames.push_back(name_in_[i]);
      for (i=0; i<n_out_; ++i) inames.push_back("out_" + name_out_[i]);
      for (i=0; i<n_out_; ++i) inames.push_back(pref + name_out_[i]);
      // Names of outputs
      std::vector<std::string> onames;
      for (casadi_int i=0; i<n_in_; ++i) onames.push_back(pref + name_in_[i]);
      // Options
      Dict opts = combine(reverse_options_, der_options_);
      opts = combine(opts, generate_options("reverse"));
      opts["derivative_of"] = self();
      // Generate derivative function
      casadi_assert_dev(enable_reverse_);
      f = get_reverse(nadj, fname, inames, onames, opts);
      // Consistency check for inputs
      casadi_assert_dev(f.n_in()==n_in_ + n_out_ + n_out_);
      casadi_int ind=0;
      for (i=0; i<n_in_; ++i) f.assert_size_in(ind++, size1_in(i), size2_in(i));
      for (i=0; i<n_out_; ++i) f.assert_size_in(ind++, size1_out(i), size2_out(i));
      for (i=0; i<n_out_; ++i) f.assert_size_in(ind++, size1_out(i), nadj*size2_out(i));
      // Consistency check for outputs
      casadi_assert_dev(f.n_out()==n_in_);
      for (i=0; i<n_in_; ++i) f.assert_sparsity_out(i, sparsity_in(i), nadj);
      // Save to cache
      tocache_if_missing(f);
    }
    return f;
  }
 
  Function FunctionInternal::
  get_forward(casadi_int nfwd, const std::string& name,
              const std::vector<std::string>& inames,
              const std::vector<std::string>& onames,
              const Dict& opts) const {
    casadi_error("'get_forward' not defined for " + class_name());
  }
 
  Function FunctionInternal::
  get_reverse(casadi_int nadj, const std::string& name,
              const std::vector<std::string>& inames,
              const std::vector<std::string>& onames,
              const Dict& opts) const {
    casadi_error("'get_reverse' not defined for " + class_name());
  }
 
  void FunctionInternal::export_code(const std::string& lang, std::ostream &stream,
      const Dict& options) const {
    casadi_error("'export_code' not defined for " + class_name());
  }
 
  void assert_read(std::istream &stream, const std::string& s) {
    casadi_int n = s.size();
    char c;
    std::stringstream ss;
    for (casadi_int i=0;i<n;++i) {
      stream >> c;
      ss << c;
    }
    casadi_assert_dev(s==ss.str());
  }
 
  casadi_int FunctionInternal::nnz_in() const {
    casadi_int ret=0;
    for (casadi_int iind=0; iind<n_in_; ++iind) ret += nnz_in(iind);
    return ret;
  }
 
  casadi_int FunctionInternal::nnz_out() const {
    casadi_int ret=0;
    for (casadi_int oind=0; oind<n_out_; ++oind) ret += nnz_out(oind);
    return ret;
  }
 
  casadi_int FunctionInternal::numel_in() const {
    casadi_int ret=0;
    for (casadi_int iind=0; iind<n_in_; ++iind) ret += numel_in(iind);
    return ret;
  }
 
  casadi_int FunctionInternal::numel_out() const {
    casadi_int ret=0;
    for (casadi_int oind=0; oind<n_out_; ++oind) ret += numel_out(oind);
    return ret;
  }
 
  void FunctionInternal::eval_mx(const MXVector& arg, MXVector& res,
                                 bool always_inline, bool never_inline) const {
 
    always_inline = always_inline || always_inline_;
    never_inline = never_inline || never_inline_;
 
    // The code below creates a call node, to inline, wrap in an MXFunction
    if (always_inline) {
      casadi_assert(!never_inline, "Inconsistent options for " + str(name_));
      wrap().call(arg, res, true);
      return;
    }
 
    // Create a call-node
    res = Call::create(self(), arg);
  }
 
  Function FunctionInternal::jacobian() const {
    // Used wrapped function if jacobian not available
    if (!has_jacobian()) {
      // Derivative information must be available
      casadi_assert(has_derivative(),
                            "Derivatives cannot be calculated for " + name_);
      return wrap().jacobian();
    }
    // Retrieve/generate cached
    Function f;
    std::string fname = "jac_" + name_;
    if (!incache(fname, f)) {
      // Names of inputs
      std::vector<std::string> inames;
      for (casadi_int i=0; i<n_in_; ++i) inames.push_back(name_in_[i]);
      for (casadi_int i=0; i<n_out_; ++i) inames.push_back("out_" + name_out_[i]);
      // Names of outputs
      std::vector<std::string> onames;
      onames.reserve(n_in_ * n_out_);
      for (size_t oind = 0; oind < n_out_; ++oind) {
        for (size_t iind = 0; iind < n_in_; ++iind) {
          onames.push_back("jac_" + name_out_[oind] + "_" + name_in_[iind]);
        }
      }
      // Options
      Dict opts = combine(jacobian_options_, der_options_);
      opts["derivative_of"] = self();
      // Generate derivative function
      casadi_assert_dev(enable_jacobian_);
      f = get_jacobian(fname, inames, onames, opts);
      // Consistency checks
      casadi_assert(f.n_in() == inames.size(),
        "Mismatching input signature, expected " + str(inames));
      casadi_assert(f.n_out() == onames.size(),
        "Mismatching output signature, expected " + str(onames));
      // Save to cache
      tocache_if_missing(f);
    }
    return f;
  }
 
  Function FunctionInternal::
  get_jacobian(const std::string& name,
               const std::vector<std::string>& inames,
               const std::vector<std::string>& onames,
               const Dict& opts) const {
    casadi_error("'get_jacobian' not defined for " + class_name());
  }
 
  void FunctionInternal::codegen(CodeGenerator& g, const std::string& fname) const {
    // Define function
    g << "/* " << definition() << " */\n";
    g << "static " << signature(fname) << " {\n";
 
    // Reset local variables, flush buffer
    g.flush(g.body);
 
    g.scope_enter();
 
    if (dump_in_ || dump_out_) {
      Function F = shared_from_this<Function>();
      std::string cg_name = codegen_name(g, false);
      std::string dump_counter = g.shorthand(cg_name + "_dump_counter");
      g.auxiliaries << "static int " << dump_counter << " = 0;\n";
      if (g.thread_safe()) {
        g.define_local_mutex(F, cg_name + "_dump_mutex");
        std::string dump_mutex = g.local_mutex(F, cg_name + "_dump_mutex");
        g << "CASADI_MUTEX_LOCK(&" << dump_mutex << ");\n";
        g << "int dump_id_local = " << dump_counter << "++;\n";
        g << "CASADI_MUTEX_UNLOCK(&" << dump_mutex << ");\n";
      } else {
        g << "int dump_id_local = " << dump_counter << "++;\n";
      }
    }
 
    if (dump_in_) g.generate_dump(shared_from_this<Function>(), "arg", true);
    if (print_in_) g.generate_print(shared_from_this<Function>(), "arg", true);
 
    // Generate function body (to buffer)
    codegen_body(g);
 
    if (dump_out_) g.generate_dump(shared_from_this<Function>(), "res", false);
    if (print_out_) g.generate_print(shared_from_this<Function>(), "res", false);
 
    g.scope_exit();
 
    // Finalize the function
    g << "return 0;\n";
    g << "}\n\n";
 
    // Flush to function body
    g.flush(g.body);
  }
 
  std::string FunctionInternal::signature(const std::string& fname) const {
    return "int " + fname + "(const casadi_real** arg, casadi_real** res, "
                            "casadi_int* iw, casadi_real* w, int mem)";
  }
 
  std::string FunctionInternal::signature_unrolled(const std::string& fname) const {
    std::vector<std::string> args;
    for (auto e : name_in_) {
      args.push_back("const casadi_real* " + str(e));
    }
    for (auto e : name_out_) {
      args.push_back("casadi_real* " + str(e));
    }
    args.push_back("const casadi_real** arg");
    args.push_back("casadi_real** res");
    args.push_back("casadi_int* iw");
    args.push_back("casadi_real* w");
    args.push_back("int mem");
    return "int " + fname + "_unrolled(" + join(args, ", ") + ")";
  }
 
  void FunctionInternal::codegen_incref(CodeGenerator& g) const {
    if (has_refcount_) {
      std::string name = codegen_name(g, false);
      std::string ref_counter = g.shorthand(name + "_ref_counter");
      g.auxiliaries << "static int " << ref_counter  << " = 0;\n";
 
      Function F = shared_from_this<Function>();
      if (g.thread_safe()) {
        for (const auto& m : g.local_mutexes(F)) {
          std::string mtx = g.local_mutex(F, m);
          g << "#if CASADI_MUTEX_USE_STATIC_INIT == 0\n";
          g << "if (" << ref_counter << "==0) CASADI_MUTEX_INIT(&" << mtx << ");\n";
          g << "#endif\n";
        }
      }
      g << ref_counter << "++;\n";
    }
 
    // Treat dependent functions
    std::set<void*> added;
    Function F = shared_from_this<Function>();
    for (const Function& f : F.find_functions(0)) {
      if (f->has_refcount_in_deps_) {
        std::string cg_name = f->codegen_name(g, false);
        auto i = added.insert(f.get());
        if (i.second) { // prevent duplicate calls
          std::string incref = g.shorthand(cg_name + "_incref");
          g << incref << "();\n";
        }
      }
    }
  }
 
  void FunctionInternal::codegen_decref(CodeGenerator& g) const {
 
    // Treat dependent functions
    std::set<void*> added;
    Function F = shared_from_this<Function>();
    for (const Function& f : F.find_functions(0)) {
      if (f->has_refcount_in_deps_) {
        std::string cg_name = f->codegen_name(g, false);
        auto i = added.insert(f.get());
        if (i.second) { // prevent duplicate calls
          std::string decref = g.shorthand(cg_name + "_decref");
          g << decref << "();\n";
        }
      }
    }
 
    if (has_refcount_) {
      std::string name = codegen_name(g, false);
      std::string ref_counter = g.shorthand(name + "_ref_counter");
      std::string mem_counter = g.shorthand(name + "_mem_counter");
      std::string free_mem = g.shorthand(name + "_free_mem");
      g << ref_counter << "--;\n";
      g << "if (" << ref_counter << "==0) {\n";
      if (codegen_needs_mem())  {
        g << "while (" << mem_counter << ">0) {\n";
        g << free_mem << "(--" << mem_counter << ");\n";
        g << "}\n";
      }
      if (g.thread_safe()) {
        Function F = shared_from_this<Function>();
        for (const auto& m : g.local_mutexes(F)) {
          std::string mtx = g.local_mutex(F, m);
          g << "#if CASADI_MUTEX_USE_STATIC_INIT == 0\n";
          g << "CASADI_MUTEX_DESTROY(&" << mtx << ");\n";
          g << "#endif\n";
        }
      }
      g << "}\n";
    }
  }
 
  void FunctionInternal::codegen_init_mem(CodeGenerator& g) const {
    g << "return 0;\n";
  }
 
  void FunctionInternal::codegen_alloc_mem(CodeGenerator& g) const {
    bool needs_mem = codegen_needs_mem();
    if (needs_mem) {
      std::string name = codegen_name(g, false);
      std::string mem_counter = g.shorthand(name + "_mem_counter");
      g << "return " + mem_counter + "++;\n";
    }
  }
 
  void FunctionInternal::codegen_checkout(CodeGenerator& g) const {
    std::string name = codegen_name(g, false);
    std::string stack_counter = g.shorthand(name + "_unused_stack_counter");
    std::string stack = g.shorthand(name + "_unused_stack");
    std::string mem_counter = g.shorthand(name + "_mem_counter");
    std::string mem_array = g.shorthand(name + "_mem");
    std::string alloc_mem = g.shorthand(name + "_alloc_mem");
    std::string init_mem = g.shorthand(name + "_init_mem");
 
 
    g.auxiliaries << "static int " << mem_counter  << " = 0;\n";
    g.auxiliaries << "static int " << stack_counter  << " = -1;\n";
    g.auxiliaries << "static int " << stack << "[CASADI_MAX_NUM_THREADS];\n";
    g.auxiliaries << "static " << codegen_mem_type() <<
               " " << mem_array << "[CASADI_MAX_NUM_THREADS];\n\n";
 
    if (g.thread_safe()) {
      Function F = shared_from_this<Function>();
      g.define_local_mutex(F, name + "_mem_mutex");
      std::string mem_mutex = g.local_mutex(F, name + "_mem_mutex");
      g << "CASADI_MUTEX_LOCK(&" << mem_mutex << ");\n";
      g.scope_add_cleanup("CASADI_MUTEX_UNLOCK(&" + mem_mutex + ");\n");
    }
 
    g.local("mid", "int");
 
    g << "if (" << stack_counter << ">=0) {\n";
    g.scope_return(stack + "[" + stack_counter + "--]");
    g << "} else {\n";
    g << "if (" << mem_counter << "==CASADI_MAX_NUM_THREADS) {\n";
    g.scope_return("-1");
    g << "}\n";
    g << "mid = " << alloc_mem << "();\n";
    g << "if (mid<0) {\n";
    g.scope_return("-1");
    g << "}\n";
    g << "if (" << init_mem << "(mid)) {\n";
    g.scope_return("-1");
    g << "}\n";
    g.scope_return("mid");
    g << "}\n";
  }
 
  void FunctionInternal::codegen_release(CodeGenerator& g) const {
    std::string name = codegen_name(g, false);
    std::string stack_counter = g.shorthand(name + "_unused_stack_counter");
    std::string stack = g.shorthand(name + "_unused_stack");
 
    if (g.thread_safe()) {
      Function F = shared_from_this<Function>();
      std::string mem_mutex = g.local_mutex(F, name + "_mem_mutex");
      g << "CASADI_MUTEX_LOCK(&" << mem_mutex << ");\n";
      g.scope_add_cleanup("CASADI_MUTEX_UNLOCK(&" + mem_mutex + ");\n");
    }
 
    g << stack << "[++" << stack_counter << "] = mem;\n";
    g.scope_return();
  }
 
  void FunctionInternal::codegen_sparsities(CodeGenerator& g) const {
    g.add_io_sparsities(name_, sparsity_in_, sparsity_out_);
  }
 
  void FunctionInternal::codegen_meta(CodeGenerator& g) const {
    bool needs_mem = codegen_needs_mem();
    std::string name = codegen_name(g, false);
 
    // Checkout/release routines
    g << g.declare("int " + name_ + "_checkout(void)") << " {\n";
    if (needs_mem) {
      std::string checkout = g.shorthand(name + "_checkout");
      g << "return " << checkout << "();\n";
    } else {
      g << "return 0;\n";
    }
    g << "}\n\n";
 
    if (needs_mem) {
      g << g.declare("void " + name_ + "_release(int mem)") << " {\n";
      std::string release = g.shorthand(name + "_release");
      g << release << "(mem);\n";
    } else {
      g << g.declare("void " + name_ + "_release(int mem)") << " {\n";
    }
    g << "}\n\n";
 
    // Reference counter routines
    g << g.declare("void " + name_ + "_incref(void)") << " {\n";
    if (has_refcount_in_deps_) {
      std::string incref = g.shorthand(name + "_incref");
      g << incref << "();\n";
    }
    g << "}\n\n"
      << g.declare("void " + name_ + "_decref(void)") << " {\n";
    if (has_refcount_in_deps_) {
      std::string decref = g.shorthand(name + "_decref");
      g << decref << "();\n";
    }
    g << "}\n\n";
 
    // Number of inputs and outptus
    g << g.declare("casadi_int " + name_ + "_n_in(void)")
      << " { return " << n_in_ << ";}\n\n"
      << g.declare("casadi_int " + name_ + "_n_out(void)")
      << " { return " << n_out_ << ";}\n\n";
 
    // Default inputs
    g << g.declare("casadi_real " + name_ + "_default_in(casadi_int i)") << " {\n"
      << "switch (i) {\n";
    for (casadi_int i=0; i<n_in_; ++i) {
      double def = get_default_in(i);
      if (def!=0) g << "case " << i << ": return " << g.constant(def) << ";\n";
    }
    g << "default: return 0;\n}\n"
      << "}\n\n";
 
    // Input names
    g << g.declare("const char* " + name_ + "_name_in(casadi_int i)") << " {\n"
      << "switch (i) {\n";
    for (casadi_int i=0; i<n_in_; ++i) {
      g << "case " << i << ": return \"" << name_in_[i] << "\";\n";
    }
    g << "default: return 0;\n}\n"
      << "}\n\n";
 
    // Output names
    g << g.declare("const char* " + name_ + "_name_out(casadi_int i)") << " {\n"
      << "switch (i) {\n";
    for (casadi_int i=0; i<n_out_; ++i) {
      g << "case " << i << ": return \"" << name_out_[i] << "\";\n";
    }
    g << "default: return 0;\n}\n"
      << "}\n\n";
 
    // Codegen sparsities
    codegen_sparsities(g);
 
    // Function that returns work vector lengths
    g << g.declare(
        "int " + name_ + "_work(casadi_int *sz_arg, casadi_int* sz_res, "
        "casadi_int *sz_iw, casadi_int *sz_w)")
      << " {\n"
      << "if (sz_arg) *sz_arg = " << codegen_sz_arg(g) << ";\n"
      << "if (sz_res) *sz_res = " << codegen_sz_res(g) << ";\n"
      << "if (sz_iw) *sz_iw = " << codegen_sz_iw(g) << ";\n"
      << "if (sz_w) *sz_w = " << codegen_sz_w(g) << ";\n"
      << "return 0;\n"
      << "}\n\n";
 
    // Function that returns work vector lengths in bytes
    g << g.declare(
        "int " + name_ + "_work_bytes(casadi_int *sz_arg, casadi_int* sz_res, "
        "casadi_int *sz_iw, casadi_int *sz_w)")
      << " {\n"
      << "if (sz_arg) *sz_arg = " << codegen_sz_arg(g) << "*sizeof(const casadi_real*);\n"
      << "if (sz_res) *sz_res = " << codegen_sz_res(g) << "*sizeof(casadi_real*);\n"
      << "if (sz_iw) *sz_iw = " << codegen_sz_iw(g) << "*sizeof(casadi_int);\n"
      << "if (sz_w) *sz_w = " << codegen_sz_w(g) << "*sizeof(casadi_real);\n"
      << "return 0;\n"
      << "}\n\n";
 
    // Also add to header file to allow getting
     if (g.with_header) {
      g.header
        << "#define " << name_ << "_SZ_ARG " << codegen_sz_arg(g) << "\n"
        << "#define " << name_ << "_SZ_RES " << codegen_sz_res(g) << "\n"
        << "#define " << name_ << "_SZ_IW " << codegen_sz_iw(g) << "\n"
        << "#define " << name_ << "_SZ_W " << codegen_sz_w(g) << "\n";
     }
 
    // Which inputs are differentiable
    if (!all(is_diff_in_)) {
      g << g.declare("int " + name_ + "_diff_in(casadi_int i)") << " {\n"
        << "switch (i) {\n";
      for (casadi_int i=0; i<n_in_; ++i) {
        g << "case " << i << ": return " << is_diff_in_[i] << ";\n";
      }
      g << "default: return -1;\n}\n"
        << "}\n\n";
    }
 
    // Which outputs are differentiable
    if (!all(is_diff_out_)) {
      g << g.declare("int " + name_ + "_diff_out(casadi_int i)") << " {\n"
        << "switch (i) {\n";
      for (casadi_int i=0; i<n_out_; ++i) {
        g << "case " << i << ": return " << is_diff_out_[i] << ";\n";
      }
      g << "default: return -1;\n}\n"
        << "}\n\n";
    }
 
    // Generate mex gateway for the function
    if (g.mex) {
      // Begin conditional compilation
      g << "#ifdef MATLAB_MEX_FILE\n";
 
      // Declare wrapper
      g << "void mex_" << name_
        << "(int resc, mxArray *resv[], int argc, const mxArray *argv[]) {\n"
        << "casadi_int i;\n";
      g << "int mem;\n";
      // Work vectors, including input and output buffers
      casadi_int i_nnz = nnz_in(), o_nnz = nnz_out();
      size_t sz_w = this->sz_w();
      for (casadi_int i=0; i<n_in_; ++i) {
        const Sparsity& s = sparsity_in_[i];
        sz_w = std::max(sz_w, static_cast<size_t>(s.size1())); // To be able to copy a column
        sz_w = std::max(sz_w, static_cast<size_t>(s.size2())); // To be able to copy a row
      }
      sz_w += i_nnz + o_nnz;
      g << CodeGenerator::array("casadi_real", "w", sz_w);
      g << CodeGenerator::array("casadi_int", "iw", sz_iw());
      std::string fw = "w+" + str(i_nnz + o_nnz);
 
      // Copy inputs to buffers
      casadi_int offset=0;
      g << CodeGenerator::array("const casadi_real*", "arg", sz_arg(), "{0}");
 
      // Allocate output buffers
      g << "casadi_real* res[" << sz_res() << "] = {0};\n";
 
      // Check arguments
      g << "if (argc>" << n_in_ << ") mexErrMsgIdAndTxt(\"Casadi:RuntimeError\","
        << "\"Evaluation of \\\"" << name_ << "\\\" failed. Too many input arguments "
        << "(%d, max " << n_in_ << ")\", argc);\n";
 
      g << "if (resc>" << n_out_ << ") mexErrMsgIdAndTxt(\"Casadi:RuntimeError\","
        << "\"Evaluation of \\\"" << name_ << "\\\" failed. "
        << "Too many output arguments (%d, max " << n_out_ << ")\", resc);\n";
 
      for (casadi_int i=0; i<n_in_; ++i) {
        std::string p = "argv[" + str(i) + "]";
        g << "if (--argc>=0) arg[" << i << "] = "
          << g.from_mex(p, "w", offset, sparsity_in_[i], fw) << "\n";
        offset += nnz_in(i);
      }
 
      for (casadi_int i=0; i<n_out_; ++i) {
        if (i==0) {
          // if i==0, always store output (possibly ans output)
          g << "--resc;\n";
        } else {
          // Store output, if it exists
          g << "if (--resc>=0) ";
        }
        // Create and get pointer
        g << g.res(i) << " = w+" << str(offset) << ";\n";
        offset += nnz_out(i);
      }
      g << name_ << "_incref();\n";
      g << "mem = " << name_ << "_checkout();\n";
 
      // Call the function
      g << "i = " << name_ << "(arg, res, iw, " << fw << ", mem);\n"
        << "if (i) mexErrMsgIdAndTxt(\"Casadi:RuntimeError\",\"Evaluation of \\\"" << name_
        << "\\\" failed.\");\n";
      g << name_ << "_release(mem);\n";
      g << name_ << "_decref();\n";
 
      // Save results
      for (casadi_int i=0; i<n_out_; ++i) {
        g << "if (" << g.res(i) << ") resv[" << i << "] = "
          << g.to_mex(sparsity_out_[i], g.res(i)) << "\n";
      }
 
      // End conditional compilation and function
      g << "}\n"
        << "#endif\n\n";
    }
 
    if (g.main) {
      // Declare wrapper
      g << "casadi_int main_" << name_ << "(casadi_int argc, char* argv[]) {\n";
 
      g << "casadi_int j;\n";
      g << "casadi_real* a;\n";
      g << "const casadi_real* r;\n";
      g << "casadi_int flag;\n";
      if (needs_mem) g << "int mem;\n";
 
 
 
      // Work vectors and input and output buffers
      size_t nr = sz_w() + nnz_in() + nnz_out();
      g << CodeGenerator::array("casadi_int", "iw", sz_iw())
        << CodeGenerator::array("casadi_real", "w", nr);
 
      // Input buffers
      g << "const casadi_real* arg[" << sz_arg() << "];\n";
 
      // Output buffers
      g << "casadi_real* res[" << sz_res() << "];\n";
 
      casadi_int off=0;
      for (casadi_int i=0; i<n_in_; ++i) {
        g << "arg[" << i << "] = w+" << off << ";\n";
        off += nnz_in(i);
      }
      for (casadi_int i=0; i<n_out_; ++i) {
        g << "res[" << i << "] = w+" << off << ";\n";
        off += nnz_out(i);
      }
 
      // TODO(@jaeandersson): Read inputs from file. For now; read from stdin
      g << "a = w;\n"
        << "for (j=0; j<" << nnz_in() << "; ++j) "
        << "if (scanf(\"%lg\", a++)<=0) return 2;\n";
 
      if (has_refcount_in_deps_) {
        g << name_ << "_incref();\n";
      }
 
      if (needs_mem) {
        g << "mem = " << name_ << "_checkout();\n";
      }
 
      // Call the function
      g << "flag = " << name_ << "(arg, res, iw, w+" << off << ", ";
      if (needs_mem) {
        g << "mem";
      } else {
        g << "0";
      }
      g << ");\n";
      if (needs_mem) {
        g << name_ << "_release(mem);\n";
      }
 
      if (has_refcount_in_deps_) {
        g << name_ << "_decref();\n";
      }
 
      g << "if (flag) return flag;\n";
 
      // TODO(@jaeandersson): Write outputs to file. For now: print to stdout
      g << "r = w+" << nnz_in() << ";\n"
        << "for (j=0; j<" << nnz_out() << "; ++j) "
        << g.printf("%.16e ", "*r++") << "\n";
 
      // End with newline
      g << g.printf("\\n") << "\n";
 
      // Finalize function
      g << "return 0;\n"
        << "}\n\n";
    }
 
    if (g.with_mem) {
      // Allocate memory
      g << g.declare("casadi_functions* " + name_ + "_functions(void)") << " {\n"
        << "static casadi_functions fun = {\n"
        << name_ << "_incref,\n"
        << name_ << "_decref,\n"
        << name_ << "_checkout,\n"
        << name_ << "_release,\n"
        << name_ << "_default_in,\n"
        << name_ << "_n_in,\n"
        << name_ << "_n_out,\n"
        << name_ << "_name_in,\n"
        << name_ << "_name_out,\n"
        << name_ << "_sparsity_in,\n"
        << name_ << "_sparsity_out,\n"
        << name_ << "_work,\n"
        << name_ << "\n"
        << "};\n"
        << "return &fun;\n"
        << "}\n";
    }
    // Flush
    g.flush(g.body);
  }
 
  std::string FunctionInternal::codegen_name(const CodeGenerator& g, bool ns) const {
    if (ns) {
      // Get the index of the function
      for (auto&& e : g.added_functions_) {
        if (e.f.get()==this) return e.codegen_name;
      }
    } else {
      for (casadi_int i=0;i<g.added_functions_.size();++i) {
        const auto & e = g.added_functions_[i];
        if (e.f.get()==this) return "f" + str(i);
      }
    }
    casadi_error("Function '" + name_ + "' not found");
  }
 
  std::string FunctionInternal::codegen_mem(CodeGenerator& g, const std::string& index) const {
    std::string name = codegen_name(g, false);
    std::string mem_array = g.shorthand(name + "_mem");
    return mem_array+"[" + index + "]";
  }
 
  void FunctionInternal::codegen_declarations(CodeGenerator& g) const {
    // Nothing to declare
  }
 
  void FunctionInternal::codegen_body(CodeGenerator& g) const {
    casadi_warning("The function \"" + name_ + "\", which is of type \""
                   + class_name() + "\" cannot be code generated. The generation "
                   "will proceed, but compilation of the code will not be possible.");
    g << "#error Code generation not supported for " << class_name() << "\n";
  }
 
  std::string FunctionInternal::
  generate_dependencies(const std::string& fname, const Dict& opts) const {
    casadi_error("'generate_dependencies' not defined for " + class_name());
  }
 
  int FunctionInternal::
  eval_activity(const bvec_t** arg, bvec_t** res, casadi_int* iw, bvec_t* w, void* mem) const {
    // Sound fallback: we cannot prove any output zero, so mark everything active
    for (casadi_int oind=0; oind<n_out_; ++oind) {
      if (res[oind]==nullptr) continue;
      std::fill_n(res[oind], nnz_out(oind), ~static_cast<bvec_t>(0));
    }
    return 0;
  }
 
  int FunctionInternal::
  sp_forward(const bvec_t** arg, bvec_t** res, casadi_int* iw, bvec_t* w, void* mem) const {
    // Loop over outputs
    for (casadi_int oind=0; oind<n_out_; ++oind) {
      // Skip if nothing to assign
      if (res[oind]==nullptr || nnz_out(oind)==0) continue;
      // Clear result
      casadi_clear(res[oind], nnz_out(oind));
      // Loop over inputs
      for (casadi_int iind=0; iind<n_in_; ++iind) {
        // Skip if no seeds
        if (arg[iind]==nullptr || nnz_in(iind)==0) continue;
        // Propagate sparsity for the specific block
        if (sp_forward_block(arg, res, iw, w, mem, oind, iind)) return 1;
      }
    }
    return 0;
  }
 
  int FunctionInternal::sp_forward_block(const bvec_t** arg, bvec_t** res,
      casadi_int* iw, bvec_t* w, void* mem, casadi_int oind, casadi_int iind) const {
    // Get the sparsity of the Jacobian block
    Sparsity sp = jac_sparsity(oind, iind, true, false);
    if (sp.is_null() || sp.nnz() == 0) return 0; // Skip if zero
    // Carry out the sparse matrix-vector multiplication
    casadi_int d1 = sp.size2();
    const casadi_int *colind = sp.colind(), *row = sp.row();
    for (casadi_int cc=0; cc<d1; ++cc) {
      for (casadi_int el = colind[cc]; el < colind[cc+1]; ++el) {
        res[oind][row[el]] |= arg[iind][cc];
      }
    }
    return 0;
  }
 
  int FunctionInternal::
  sp_reverse(bvec_t** arg, bvec_t** res, casadi_int* iw, bvec_t* w, void* mem) const {
    // Loop over outputs
    for (casadi_int oind=0; oind<n_out_; ++oind) {
      // Skip if nothing to assign
      if (res[oind]==nullptr || nnz_out(oind)==0) continue;
 
      // Loop over inputs
      for (casadi_int iind=0; iind<n_in_; ++iind) {
        // Skip if no seeds
        if (arg[iind]==nullptr || nnz_in(iind)==0) continue;
 
        // Get the sparsity of the Jacobian block
        Sparsity sp = jac_sparsity(oind, iind, true, false);
        if (sp.is_null() || sp.nnz() == 0) continue; // Skip if zero
 
        // Carry out the sparse matrix-vector multiplication
        casadi_int d1 = sp.size2();
        const casadi_int *colind = sp.colind(), *row = sp.row();
        for (casadi_int cc=0; cc<d1; ++cc) {
          for (casadi_int el = colind[cc]; el < colind[cc+1]; ++el) {
            arg[iind][cc] |= res[oind][row[el]];
          }
        }
      }
 
      // Clear seeds
      casadi_clear(res[oind], nnz_out(oind));
    }
    return 0;
  }
 
  void FunctionInternal::sz_work(size_t& sz_arg, size_t& sz_res,
                                 size_t& sz_iw, size_t& sz_w) const {
    sz_arg = this->sz_arg();
    sz_res = this->sz_res();
    sz_iw = this->sz_iw();
    sz_w = this->sz_w();
  }
 
  size_t FunctionInternal::codegen_sz_arg(const CodeGenerator& g) const {
    return sz_arg();
  }
  size_t FunctionInternal::codegen_sz_res(const CodeGenerator& g) const {
    return sz_res();
  }
  size_t FunctionInternal::codegen_sz_iw(const CodeGenerator& g) const {
    return sz_iw();
  }
  size_t FunctionInternal::codegen_sz_w(const CodeGenerator& g) const {
    return sz_w();
  }
 
  void FunctionInternal::alloc_arg(size_t sz_arg, bool persistent) {
    if (persistent) {
      sz_arg_per_ += sz_arg;
    } else {
      sz_arg_tmp_ = std::max(sz_arg_tmp_, sz_arg);
    }
  }
 
  void FunctionInternal::alloc_res(size_t sz_res, bool persistent) {
    if (persistent) {
      sz_res_per_ += sz_res;
    } else {
      sz_res_tmp_ = std::max(sz_res_tmp_, sz_res);
    }
  }
 
  void FunctionInternal::alloc_iw(size_t sz_iw, bool persistent) {
    if (persistent) {
      sz_iw_per_ += sz_iw;
    } else {
      sz_iw_tmp_ = std::max(sz_iw_tmp_, sz_iw);
    }
  }
 
  void FunctionInternal::alloc_w(size_t sz_w, bool persistent) {
    if (persistent) {
      sz_w_per_ += sz_w;
    } else {
      sz_w_tmp_ = std::max(sz_w_tmp_, sz_w);
    }
  }
 
  void FunctionInternal::alloc(const Function& f, bool persistent, int num_threads) {
    if (f.is_null()) return;
    size_t sz_arg, sz_res, sz_iw, sz_w;
    f.sz_work(sz_arg, sz_res, sz_iw, sz_w);
    alloc_arg(sz_arg*num_threads, persistent);
    alloc_res(sz_res*num_threads, persistent);
    alloc_iw(sz_iw*num_threads, persistent);
    alloc_w(sz_w*num_threads, persistent);
    registered_functions_.push_back(f);
  }
 
  Dict ProtoFunction::get_stats(void* mem) const {
    auto *m = static_cast<ProtoFunctionMemory*>(mem);
    // Add timing statistics
    Dict stats;
    for (const auto& s : m->fstats) {
      stats["n_call_" +s.first] = s.second.n_call;
      stats["t_wall_" +s.first] = s.second.t_wall;
      stats["t_proc_" +s.first] = s.second.t_proc;
    }
    return stats;
  }
 
  Dict FunctionInternal::get_stats(void* mem) const {
    Dict stats = ProtoFunction::get_stats(mem);
    auto *m = static_cast<FunctionMemory*>(mem);
    casadi_assert(m->stats_available,
      "No stats available: Function '" + name_ + "' not set up. "
      "To get statistics, first evaluate it numerically.");
    return stats;
  }
 
  bool FunctionInternal::has_derivative() const {
    return enable_forward_ || enable_reverse_ || enable_jacobian_ || enable_fd_;
  }
 
  bool FunctionInternal::fwdViaJac(casadi_int nfwd) const {
    if (!enable_forward_ && !enable_fd_) return true;
    if (jac_penalty_==-1) return false;
 
    // Heuristic 1: Jac calculated via forward mode likely cheaper
    if (jac_penalty_*static_cast<double>(nnz_in())<nfwd) return true;
 
    // Heuristic 2: Jac calculated via reverse mode likely cheaper
    double w = ad_weight();
    if (enable_reverse_ &&
        jac_penalty_*(1-w)*static_cast<double>(nnz_out())<w*static_cast<double>(nfwd))
      return true; // NOLINT
 
    return false;
  }
 
  bool FunctionInternal::adjViaJac(casadi_int nadj) const {
    if (!enable_reverse_) return true;
    if (jac_penalty_==-1) return false;
 
    // Heuristic 1: Jac calculated via reverse mode likely cheaper
    if (jac_penalty_*static_cast<double>(nnz_out())<nadj) return true;
 
    // Heuristic 2: Jac calculated via forward mode likely cheaper
    double w = ad_weight();
    if ((enable_forward_ || enable_fd_) &&
        jac_penalty_*w*static_cast<double>(nnz_in())<(1-w)*static_cast<double>(nadj))
      return true; // NOLINT
 
    return false;
  }
 
  Dict FunctionInternal::info() const {
    return Dict();
  }
 
  void FunctionInternal::
  call_forward(const std::vector<MX>& arg, const std::vector<MX>& res,
             const std::vector<std::vector<MX> >& fseed,
             std::vector<std::vector<MX> >& fsens,
             bool always_inline, bool never_inline) const {
    casadi_assert(!(always_inline && never_inline), "Inconsistent options");
    casadi_assert(!always_inline, "Class " + class_name() +
                          " cannot be inlined in an MX expression");
 
    // Derivative information must be available
    casadi_assert(has_derivative(),
                          "Derivatives cannot be calculated for " + name_);
 
    // Number of directional derivatives
    casadi_int nfwd = fseed.size();
    fsens.resize(nfwd);
 
    // Quick return if no seeds
    if (nfwd==0) return;
 
    // Check if seeds need to have dimensions corrected
    casadi_int npar = 1;
    for (auto&& r : fseed) {
      if (!matching_arg(r, npar)) {
        FunctionInternal::call_forward(arg, res, replace_fseed(fseed, npar),
                                       fsens, always_inline, never_inline);
        return;
      }
    }
 
    // Calculating full Jacobian and then multiplying
    if (fwdViaJac(nfwd)) {
      // Multiply the Jacobian from the right
      std::vector<MX> darg = arg;
      darg.insert(darg.end(), res.begin(), res.end());
      std::vector<MX> J = jacobian()(darg);
      // Join forward seeds
      std::vector<MX> v(nfwd), all_fseed(n_in_);
      for (size_t i = 0; i < n_in_; ++i) {
        for (size_t d = 0; d < nfwd; ++d) v[d] = vec(fseed.at(d).at(i));
        all_fseed[i] = horzcat(v);
      }
      // Calculate forward sensitivities
      std::vector<MX> all_fsens(n_out_);
      std::vector<MX>::const_iterator J_it = J.begin();
      for (size_t oind = 0; oind < n_out_; ++oind) {
        for (size_t iind = 0; iind < n_in_; ++iind) {
          // Add contribution
          MX a = mtimes(*J_it++, all_fseed[iind]);
          all_fsens[oind] = all_fsens[oind].is_empty(true) ? a : all_fsens[oind] + a;
        }
      }
      // Split forward sensitivities
      for (size_t d = 0; d < nfwd; ++d) fsens[d].resize(n_out_);
      for (size_t i = 0; i < n_out_; ++i) {
        v = horzsplit(all_fsens[i]);
        casadi_assert_dev(v.size() == nfwd);
        for (size_t d = 0; d < nfwd; ++d) fsens[d][i] = reshape(v[d], size_out(i));
      }
    } else {
      // Evaluate in batches
      casadi_assert_dev(enable_forward_ || enable_fd_);
      casadi_int max_nfwd = max_num_dir_;
      if (!enable_fd_) {
        while (!has_forward(max_nfwd)) max_nfwd/=2;
      }
      casadi_int offset = 0;
      while (offset<nfwd) {
        // Number of derivatives, in this batch
        casadi_int nfwd_batch = std::min(nfwd-offset, max_nfwd);
 
        // All inputs and seeds
        std::vector<MX> darg;
        darg.reserve(n_in_ + n_out_ + n_in_);
        darg.insert(darg.end(), arg.begin(), arg.end());
        darg.insert(darg.end(), res.begin(), res.end());
        std::vector<MX> v(nfwd_batch);
        for (casadi_int i=0; i<n_in_; ++i) {
          for (casadi_int d=0; d<nfwd_batch; ++d) v[d] = fseed[offset+d][i];
          darg.push_back(horzcat(v));
        }
 
        // Create the evaluation node
        Function dfcn = self().forward(nfwd_batch);
        std::vector<MX> x = dfcn(darg);
 
        casadi_assert_dev(x.size()==n_out_);
 
        // Retrieve sensitivities
        for (casadi_int d=0; d<nfwd_batch; ++d) fsens[offset+d].resize(n_out_);
        for (casadi_int i=0; i<n_out_; ++i) {
          if (size2_out(i)>0) {
            v = horzsplit(x[i], size2_out(i));
            casadi_assert_dev(v.size()==nfwd_batch);
          } else {
            v = std::vector<MX>(nfwd_batch, MX(size_out(i)));
          }
          for (casadi_int d=0; d<nfwd_batch; ++d) fsens[offset+d][i] = v[d];
        }
 
        // Update offset
        offset += nfwd_batch;
      }
    }
  }
 
  void FunctionInternal::
  call_reverse(const std::vector<MX>& arg, const std::vector<MX>& res,
             const std::vector<std::vector<MX> >& aseed,
             std::vector<std::vector<MX> >& asens,
             bool always_inline, bool never_inline) const {
    casadi_assert(!(always_inline && never_inline), "Inconsistent options");
    casadi_assert(!always_inline, "Class " + class_name() +
                          " cannot be inlined in an MX expression");
 
    // Derivative information must be available
    casadi_assert(has_derivative(),
                          "Derivatives cannot be calculated for " + name_);
 
    // Number of directional derivatives
    casadi_int nadj = aseed.size();
    asens.resize(nadj);
 
    // Quick return if no seeds
    if (nadj==0) return;
 
    // Check if seeds need to have dimensions corrected
    casadi_int npar = 1;
    for (auto&& r : aseed) {
      if (!matching_res(r, npar)) {
        FunctionInternal::call_reverse(arg, res, replace_aseed(aseed, npar),
                                       asens, always_inline, never_inline);
        return;
      }
    }
 
    // Calculating full Jacobian and then multiplying likely cheaper
    if (adjViaJac(nadj)) {
      // Multiply the transposed Jacobian from the right
      std::vector<MX> darg = arg;
      darg.insert(darg.end(), res.begin(), res.end());
      std::vector<MX> J = jacobian()(darg);
      // Join adjoint seeds
      std::vector<MX> v(nadj), all_aseed(n_out_);
      for (size_t i = 0; i < n_out_; ++i) {
        for (size_t d = 0; d < nadj; ++d) v[d] = vec(aseed.at(d).at(i));
        all_aseed[i] = horzcat(v);
      }
      // Calculate adjoint sensitivities
      std::vector<MX> all_asens(n_in_);
      std::vector<MX>::const_iterator J_it = J.begin();
      for (size_t oind = 0; oind < n_out_; ++oind) {
        for (size_t iind = 0; iind < n_in_; ++iind) {
          // Add contribution
          MX a = mtimes((*J_it++).T(), all_aseed[oind]);
          all_asens[iind] = all_asens[iind].is_empty(true) ? a : all_asens[iind] + a;
        }
      }
      // Split adjoint sensitivities
      for (size_t d = 0; d < nadj; ++d) asens[d].resize(n_in_);
      for (size_t i = 0; i < n_in_; ++i) {
        v = horzsplit(all_asens[i]);
        casadi_assert_dev(v.size() == nadj);
        for (size_t d = 0; d < nadj; ++d) {
          if (asens[d][i].is_empty(true)) {
            asens[d][i] = reshape(v[d], size_in(i));
          } else {
            asens[d][i] += reshape(v[d], size_in(i));
          }
        }
      }
    } else {
      // Evaluate in batches
      casadi_assert_dev(enable_reverse_);
      casadi_int max_nadj = max_num_dir_;
 
      while (!has_reverse(max_nadj)) max_nadj/=2;
      casadi_int offset = 0;
      while (offset<nadj) {
        // Number of derivatives, in this batch
        casadi_int nadj_batch =  std::min(nadj-offset, max_nadj);
 
        // All inputs and seeds
        std::vector<MX> darg;
        darg.reserve(n_in_ + n_out_ + n_out_);
        darg.insert(darg.end(), arg.begin(), arg.end());
        darg.insert(darg.end(), res.begin(), res.end());
        std::vector<MX> v(nadj_batch);
        for (casadi_int i=0; i<n_out_; ++i) {
          for (casadi_int d=0; d<nadj_batch; ++d) v[d] = aseed[offset+d][i];
          darg.push_back(horzcat(v));
        }
 
        // Create the evaluation node
        Function dfcn = self().reverse(nadj_batch);
        std::vector<MX> x = dfcn(darg);
        casadi_assert_dev(x.size()==n_in_);
 
        // Retrieve sensitivities
        for (casadi_int d=0; d<nadj_batch; ++d) asens[offset+d].resize(n_in_);
        for (casadi_int i=0; i<n_in_; ++i) {
          if (size2_in(i)>0) {
            v = horzsplit(x[i], size2_in(i));
            casadi_assert_dev(v.size()==nadj_batch);
          } else {
            v = std::vector<MX>(nadj_batch, MX(size_in(i)));
          }
          for (casadi_int d=0; d<nadj_batch; ++d) {
            if (asens[offset+d][i].is_empty(true)) {
              asens[offset+d][i] = v[d];
            } else {
              asens[offset+d][i] += v[d];
            }
          }
        }
        // Update offset
        offset += nadj_batch;
      }
    }
  }
 
  void FunctionInternal::
  call_forward(const std::vector<SX>& arg, const std::vector<SX>& res,
             const std::vector<std::vector<SX> >& fseed,
             std::vector<std::vector<SX> >& fsens,
             bool always_inline, bool never_inline) const {
    casadi_assert(!(always_inline && never_inline), "Inconsistent options");
    if (fseed.empty()) { // Quick return if no seeds
      fsens.clear();
      return;
    }
    casadi_error("'forward' (SX) not defined for " + class_name());
  }
 
  void FunctionInternal::
  call_reverse(const std::vector<SX>& arg, const std::vector<SX>& res,
             const std::vector<std::vector<SX> >& aseed,
             std::vector<std::vector<SX> >& asens,
             bool always_inline, bool never_inline) const {
    casadi_assert(!(always_inline && never_inline), "Inconsistent options");
    if (aseed.empty()) { // Quick return if no seeds
      asens.clear();
      return;
    }
    casadi_error("'reverse' (SX) not defined for " + class_name());
  }
 
  double FunctionInternal::ad_weight() const {
    // If reverse mode derivatives unavailable, use forward
    if (!enable_reverse_) return 0;
 
    // If forward mode derivatives unavailable, use reverse
    if (!enable_forward_ && !enable_fd_) return 1;
 
    // Use the (potentially user set) option
    return ad_weight_;
  }
 
  double FunctionInternal::sp_weight() const {
    // If reverse mode propagation unavailable, use forward
    if (!has_sprev()) return 0;
 
    // If forward mode propagation unavailable, use reverse
    if (!has_spfwd()) return 1;
 
    // Use the (potentially user set) option
    return ad_weight_sp_;
  }
 
  const SX FunctionInternal::sx_in(casadi_int ind) const {
    return SX::sym(name_in_.at(ind), sparsity_in(ind));
  }
 
  const SX FunctionInternal::sx_out(casadi_int ind) const {
    return SX::sym(name_out_.at(ind), sparsity_out(ind));
  }
 
  const DM FunctionInternal::dm_in(casadi_int ind) const {
    return DM::zeros(sparsity_in(ind));
  }
 
  const DM FunctionInternal::dm_out(casadi_int ind) const {
    return DM::zeros(sparsity_out(ind));
  }
 
  const std::vector<SX> FunctionInternal::sx_in() const {
    std::vector<SX> ret(n_in_);
    for (casadi_int i=0; i<ret.size(); ++i) {
      ret[i] = sx_in(i);
    }
    return ret;
  }
 
  const std::vector<SX> FunctionInternal::sx_out() const {
    std::vector<SX> ret(n_out_);
    for (casadi_int i=0; i<ret.size(); ++i) {
      ret[i] = sx_out(i);
    }
    return ret;
  }
 
  const std::vector<DM> FunctionInternal::dm_in() const {
    std::vector<DM> ret(n_in_);
    for (casadi_int i=0; i<ret.size(); ++i) {
      ret[i] = dm_in(i);
    }
    return ret;
  }
 
  const std::vector<DM> FunctionInternal::dm_out() const {
    std::vector<DM> ret(n_out_);
    for (casadi_int i=0; i<ret.size(); ++i) {
      ret[i] = dm_out(i);
    }
    return ret;
  }
 
  const MX FunctionInternal::mx_in(casadi_int ind) const {
    return MX::sym(name_in_.at(ind), sparsity_in(ind));
  }
 
  const MX FunctionInternal::mx_out(casadi_int ind) const {
    return MX::sym(name_out_.at(ind), sparsity_out(ind));
  }
 
  const std::vector<MX> FunctionInternal::mx_in() const {
    std::vector<MX> ret(n_in_);
    for (casadi_int i=0; i<ret.size(); ++i) {
      ret[i] = mx_in(i);
    }
    return ret;
  }
 
  const std::vector<MX> FunctionInternal::mx_out() const {
    std::vector<MX> ret(n_out_);
    for (casadi_int i=0; i<ret.size(); ++i) {
      ret[i] = mx_out(i);
    }
    return ret;
  }
 
  bool FunctionInternal::is_a(const std::string& type, bool recursive) const {
    return type == "FunctionInternal";
  }
 
  void FunctionInternal::merge(const std::vector<MX>& arg,
    std::vector<MX>& subs_from, std::vector<MX>& subs_to) const {
     }
 
  std::vector<MX> FunctionInternal::free_mx() const {
    casadi_error("'free_mx' only defined for 'MXFunction'");
  }
 
  std::vector<SX> FunctionInternal::free_sx() const {
    casadi_error("'free_sx' only defined for 'SXFunction'");
  }
 
  void FunctionInternal::generate_lifted(Function& vdef_fcn,
                                         Function& vinit_fcn) const {
    casadi_error("'generate_lifted' only defined for 'MXFunction'");
  }
 
  casadi_int FunctionInternal::n_instructions() const {
    casadi_error("'n_instructions' not defined for " + class_name());
  }
 
  casadi_int FunctionInternal::instruction_id(casadi_int k) const {
    casadi_error("'instruction_id' not defined for " + class_name());
  }
 
  std::vector<casadi_int> FunctionInternal::instruction_input(casadi_int k) const {
    casadi_error("'instruction_input' not defined for " + class_name());
  }
 
  double FunctionInternal::instruction_constant(casadi_int k) const {
    casadi_error("'instruction_constant' not defined for " + class_name());
  }
 
  std::vector<casadi_int> FunctionInternal::instruction_output(casadi_int k) const {
    casadi_error("'instruction_output' not defined for " + class_name());
  }
 
  MX FunctionInternal::instruction_MX(casadi_int k) const {
    casadi_error("'instruction_MX' not defined for " + class_name());
  }
 
  SX FunctionInternal::instructions_sx() const {
    casadi_error("'instructions_sx' not defined for " + class_name());
  }
 
  casadi_int FunctionInternal::n_nodes() const {
    casadi_error("'n_nodes' not defined for " + class_name());
  }
 
  std::vector<MX>
  FunctionInternal::mapsum_mx(const std::vector<MX > &x,
                              const std::string& parallelization) {
    if (x.empty()) return x;
    // Check number of arguments
    casadi_assert(x.size()==n_in_, "mapsum_mx: Wrong number_i of arguments");
    // Number of parallel calls
    casadi_int npar = 1;
    // Check/replace arguments
    std::vector<MX> x_mod(x.size());
    for (casadi_int i=0; i<n_in_; ++i) {
      if (check_mat(x[i].sparsity(), sparsity_in_[i], npar)) {
        x_mod[i] = replace_mat(x[i], sparsity_in_[i], npar);
      } else {
        // Mismatching sparsity: The following will throw an error message
        npar = 0;
        check_arg(x, npar);
      }
    }
 
    casadi_int n = 1;
    for (casadi_int i=0; i<x_mod.size(); ++i) {
      n = std::max(x_mod[i].size2() / size2_in(i), n);
    }
 
    std::vector<casadi_int> reduce_in;
    for (casadi_int i=0; i<x_mod.size(); ++i) {
      if (x_mod[i].size2()/size2_in(i)!=n) {
        reduce_in.push_back(i);
      }
    }
 
    Function ms = self().map("mapsum", parallelization, n, reduce_in, range(n_out_));
 
    // Call the internal function
    return ms(x_mod);
  }
 
  bool FunctionInternal::check_mat(const Sparsity& arg, const Sparsity& inp, casadi_int& npar) {
    // Matching dimensions
    if (arg.size()==inp.size()) return true;
    // Calling with a scalar - set all
    if (arg.is_scalar()) return true;
    // Vectors that are transposes of each other
    if (arg.is_vector() && inp.size()==std::make_pair(arg.size2(), arg.size1())) return true;
    // Horizontal repmat
    if (arg.size1()==inp.size1() && arg.size2()>0 && inp.size2()>0
        && inp.size2()%arg.size2()==0) return true;
    // Evaluate with multiple arguments
    if (npar!=-1 && arg.size1()==inp.size1() && arg.size2()>0 && inp.size2()>0
        && arg.size2()%(npar*inp.size2())==0) {
      npar *= arg.size2()/(npar*inp.size2());
      return true;
    }
    // Calling with empty matrix - set all to zero (after the structured branches above,
    // so that a 0-by-N argument can still be recognised as a parallel/repmat call)
    if (arg.is_empty()) return true;
    // No match
    return false;
  }
 
  std::vector<DM> FunctionInternal::nz_in(const std::vector<double>& arg) const {
    casadi_assert(nnz_in()==arg.size(),
      "Dimension mismatch. Expecting " + str(nnz_in()) +
      ", got " + str(arg.size()) + " instead.");
 
    std::vector<DM> ret = dm_in();
    casadi_int offset = 0;
    for (casadi_int i=0;i<n_in_;++i) {
      DM& r = ret.at(i);
      std::copy(arg.begin()+offset, arg.begin()+offset+nnz_in(i), r.ptr());
      offset+= nnz_in(i);
    }
    return ret;
  }
 
  std::vector<DM> FunctionInternal::nz_out(const std::vector<double>& res) const {
    casadi_assert(nnz_out()==res.size(),
      "Dimension mismatch. Expecting " + str(nnz_out()) +
      ", got " + str(res.size()) + " instead.");
 
    std::vector<DM> ret = dm_out();
    casadi_int offset = 0;
    for (casadi_int i=0;i<n_out_;++i) {
      DM& r = ret.at(i);
      std::copy(res.begin()+offset, res.begin()+offset+nnz_out(i), r.ptr());
      offset+= nnz_out(i);
    }
    return ret;
  }
 
  std::vector<double> FunctionInternal::nz_in(const std::vector<DM>& arg) const {
    // Disallow parallel inputs
    casadi_int npar = -1;
    if (!matching_arg(arg, npar)) {
      return nz_in(replace_arg(arg, npar));
    }
 
    std::vector<DM> arg2 = project_arg(arg, 1);
    std::vector<double> ret(nnz_in());
    casadi_int offset = 0;
    for (casadi_int i=0;i<n_in_;++i) {
      const double* e = arg2.at(i).ptr();
      std::copy(e, e+nnz_in(i), ret.begin()+offset);
      offset+= nnz_in(i);
    }
    return ret;
  }
 
  std::vector<double> FunctionInternal::nz_out(const std::vector<DM>& res) const {
    // Disallow parallel inputs
    casadi_int npar = -1;
    if (!matching_res(res, npar)) {
      return nz_out(replace_res(res, npar));
    }
 
    std::vector<DM> res2 = project_res(res, 1);
    std::vector<double> ret(nnz_out());
    casadi_int offset = 0;
    for (casadi_int i=0;i<n_out_;++i) {
      const double* e = res2.at(i).ptr();
      std::copy(e, e+nnz_out(i), ret.begin()+offset);
      offset+= nnz_out(i);
    }
    return ret;
  }
 
  void FunctionInternal::setup(void* mem, const double** arg, double** res,
                               casadi_int* iw, double* w) const {
    set_work(mem, arg, res, iw, w);
    set_temp(mem, arg, res, iw, w);
    auto *m = static_cast<FunctionMemory*>(mem);
    m->stats_available = true;
  }
 
  void ProtoFunction::clear_mem() {
    for (auto&& i : mem_) {
      if (i!=nullptr) free_mem(i);
    }
    mem_.clear();
  }
 
  size_t FunctionInternal::get_n_in() {
    if (!derivative_of_.is_null()) {
      std::string n = derivative_of_.name();
      if (name_ == "jac_" + n) {
        return derivative_of_.n_in() + derivative_of_.n_out();
      } else if (name_ == "adj1_" + n) {
        return derivative_of_.n_in() + derivative_of_.n_out() + derivative_of_.n_out();
      }
    }
    // One by default
    return 1;
  }
 
  size_t FunctionInternal::get_n_out() {
    if (!derivative_of_.is_null()) {
      std::string n = derivative_of_.name();
      if (name_ == "jac_" + n) {
        return derivative_of_.n_in() * derivative_of_.n_out();
      } else if (name_ == "adj1_" + n) {
        return derivative_of_.n_in();
      }
    }
    // One by default
    return 1;
  }
 
  Sparsity FunctionInternal::get_sparsity_in(casadi_int i) {
    if (!derivative_of_.is_null()) {
      std::string n = derivative_of_.name();
      if (name_ == "jac_" + n || name_ == "adj1_" + n) {
        if (i < derivative_of_.n_in()) {
          // Input of nondifferentiated function
          return derivative_of_.sparsity_in(i);
        } else if (i < derivative_of_.n_in() + derivative_of_.n_out()) {
          // Output of nondifferentiated function, if needed
          return uses_output() ? derivative_of_.sparsity_out(i - derivative_of_.n_in()) :
            Sparsity(derivative_of_.size_out(i - derivative_of_.n_in()));
        } else {
          // Adjoint seeds
          return derivative_of_.sparsity_out(i - derivative_of_.n_in() - derivative_of_.n_out());
        }
      }
    }
    // Scalar by default
    return Sparsity::scalar();
  }
 
  Sparsity FunctionInternal::get_sparsity_out(casadi_int i) {
    if (!derivative_of_.is_null()) {
      std::string n = derivative_of_.name();
      if (name_ == "jac_" + n) {
        // Get Jacobian block
        casadi_int oind = i / derivative_of_.n_in(), iind = i % derivative_of_.n_in();
        const Sparsity& sp_in = derivative_of_.sparsity_in(iind);
        const Sparsity& sp_out = derivative_of_.sparsity_out(oind);
        // Handle Jacobian blocks corresponding to non-differentiable inputs or outputs
        if (!derivative_of_.is_diff_out(oind) || !derivative_of_.is_diff_in(iind)) {
          return Sparsity(sp_out.numel(), sp_in.numel());
        }
        // Is there a routine for calculating the Jacobian?
        if (derivative_of_->has_jac_sparsity(oind, iind)) {
          return derivative_of_.jac_sparsity(oind, iind);
        }
        // Construct sparsity pattern
        std::vector<casadi_int> row, colind;
        row.reserve(sp_out.nnz() * sp_in.nnz());
        colind.reserve(sp_in.numel() + 1);
        // Loop over input nonzeros
        for (casadi_int c1 = 0; c1 < sp_in.size2(); ++c1) {
          for (casadi_int k1 = sp_in.colind(c1); k1 < sp_in.colind(c1 + 1); ++k1) {
            casadi_int e1 = sp_in.row(k1) + sp_in.size1() * c1;
            // Update column offsets
            colind.resize(e1 + 1, row.size());
            // Add nonzeros corresponding to all nonzero outputs
            for (casadi_int c2 = 0; c2 < sp_out.size2(); ++c2) {
              for (casadi_int k2 = sp_out.colind(c2); k2 < sp_out.colind(c2 + 1); ++k2) {
                row.push_back(sp_out.row(k2) + sp_out.size1() * c2);
              }
            }
          }
        }
        // Finish column offsets
        colind.resize(sp_in.numel() + 1, row.size());
        // Assemble and return sparsity pattern
        return Sparsity(sp_out.numel(), sp_in.numel(), colind, row);
      } else if (name_ == "adj1_" + n) {
        // Adjoint sensitivity
        return derivative_of_.sparsity_in(i);
      }
    }
    // Scalar by default
    return Sparsity::scalar();
  }
 
  void* ProtoFunction::memory(int ind) const {
#ifdef CASADI_WITH_THREAD
    std::lock_guard<std::mutex> lock(mtx_);
#endif //CASADI_WITH_THREAD
    return mem_.at(ind);
  }
 
  bool ProtoFunction::has_memory(int ind) const {
    return ind<mem_.size();
  }
 
  int ProtoFunction::checkout() const {
#ifdef CASADI_WITH_THREAD
    std::lock_guard<std::mutex> lock(mtx_);
#endif //CASADI_WITH_THREAD
    if (unused_.empty()) {
      check_mem_count(mem_.size()+1);
      // Allocate a new memory object
      void* m = alloc_mem();
      mem_.push_back(m);
      if (init_mem(m)) {
        casadi_error("Failed to create or initialize memory object");
      }
      return static_cast<int>(mem_.size()) - 1;
    } else {
      // Use an unused memory object
      int m = unused_.top();
      unused_.pop();
      return m;
    }
  }
 
  void ProtoFunction::release(int mem) const {
#ifdef CASADI_WITH_THREAD
    std::lock_guard<std::mutex> lock(mtx_);
#endif //CASADI_WITH_THREAD
    unused_.push(mem);
  }
 
  Function FunctionInternal::
  factory(const std::string& name,
          const std::vector<std::string>& s_in,
          const std::vector<std::string>& s_out,
          const Function::AuxOut& aux,
          const Dict& opts) const {
    return wrap().factory(name, s_in, s_out, aux, opts);
  }
 
  std::vector<std::string> FunctionInternal::get_function() const {
    // No functions
    return std::vector<std::string>();
  }
 
  bool FunctionInternal::has_function(const std::string& fname) const {
    std::vector<std::string> fnames = get_function();
    return std::find(fnames.begin(), fnames.end(), fname)!=fnames.end();
  }
 
  const Function& FunctionInternal::get_function(const std::string &name) const {
    casadi_error("'get_function' not defined for " + class_name());
    static Function singleton;
    return singleton;
  }
 
  void FunctionInternal::add_embedded(
        std::map<FunctionInternal*, std::pair<Function, size_t> >& all_fun,
      const Function& dep, casadi_int max_depth) const {
    // Add, if not already in graph and not null
    if (!dep.is_null() && all_fun.find(dep.get()) == all_fun.end()) {
      size_t index = all_fun.size();
      all_fun[dep.get()] = std::make_pair(dep, index);
      // Also add its dependencies
      if (max_depth > 0) dep->find(all_fun, max_depth - 1);
    }
  }
 
  void FunctionInternal::find(std::map<FunctionInternal*, std::pair<Function, size_t> >& all_fun,
    casadi_int max_depth) const {
    for (auto&& f : registered_functions_) {
      add_embedded(all_fun, f, max_depth);
    }
  }
 
  std::vector<bool> FunctionInternal::
  which_depends(const std::string& s_in, const std::vector<std::string>& s_out,
      casadi_int order, bool tr) const {
    Function f = shared_from_this<Function>();
    f = f.wrap();
    return f.which_depends(s_in, s_out, order, tr);
  }
 
  Function FunctionInternal::simplify_passes(
      const std::vector<std::pair<std::string, casadi_int> >& tasks) const {
    casadi_assert(tasks.empty(), "simplify passes not supported for " + class_name());
    return self();
  }
 
  const Function& FunctionInternal::oracle() const {
    casadi_error("'oracle' not defined for " + class_name());
    static Function singleton;
    return singleton;
  }
 
  Function FunctionInternal::slice(const std::string& name,
        const std::vector<casadi_int>& order_in,
        const std::vector<casadi_int>& order_out, const Dict& opts) const {
    return wrap().slice(name, order_in, order_out, opts);
  }
 
  bool FunctionInternal::all_scalar() const {
    // Check inputs
    for (casadi_int i=0; i<n_in_; ++i) {
      if (!sparsity_in_[i].is_scalar()) return false;
    }
    // Check outputs
    for (casadi_int i=0; i<n_out_; ++i) {
      if (!sparsity_out_[i].is_scalar()) return false;
    }
    // All are scalar
    return true;
  }
 
  void FunctionInternal::set_jac_sparsity(casadi_int oind, casadi_int iind, const Sparsity& sp) {
#ifdef CASADI_WITH_THREADSAFE_SYMBOLICS
    // Safe access to jac_sparsity_
    std::lock_guard<std::mutex> lock(jac_sparsity_mtx_);
#endif // CASADI_WITH_THREADSAFE_SYMBOLICS
    casadi_int ind = iind + oind * n_in_;
    jac_sparsity_[false].resize(n_in_ * n_out_);
    jac_sparsity_[false].at(ind) = sp;
    jac_sparsity_[true].resize(n_in_ * n_out_);
    jac_sparsity_[true].at(ind) = to_compact(oind, iind, sp);
  }
 
  int FunctionInternal::
  eval(const double** arg, double** res, casadi_int* iw, double* w, void* mem) const {
    if (has_eval_dm()) {
      // Evaluate via eval_dm (less efficient)
      try {
        // Allocate input matrices
        std::vector<DM> argv(n_in_);
        for (casadi_int i=0; i<n_in_; ++i) {
          argv[i] = DM(sparsity_in_[i]);
          casadi_copy(arg[i], argv[i].nnz(), argv[i].ptr());
        }
 
        // Try to evaluate using eval_dm
        std::vector<DM> resv = eval_dm(argv);
 
        // Check number of outputs
        casadi_assert(resv.size()==n_out_,
          "Expected " + str(n_out_) + " outputs, got " + str(resv.size()) + ".");
 
        // Get outputs
        for (casadi_int i=0; i<n_out_; ++i) {
          if (resv[i].sparsity()!=sparsity_out_[i]) {
            if (resv[i].size()==size_out(i)) {
              resv[i] = project(resv[i], sparsity_out_[i]);
            } else {
              casadi_error("Shape mismatch for output " + str(i) + ": got " + resv[i].dim() + ", "
                           "expected " + sparsity_out_[i].dim() + ".");
            }
          }
          if (res[i]) casadi_copy(resv[i].ptr(), resv[i].nnz(), res[i]);
        }
      } catch (KeyboardInterruptException&) {
        throw;
      } catch(std::exception& e) {
        casadi_error("Failed to evaluate 'eval_dm' for " + name_ + ":\n" + e.what());
      }
      // Successful return
      return 0;
    } else {
      casadi_error("'eval' not defined for " + class_name());
    }
  }
 
 
  void ProtoFunction::print_time(const std::map<std::string, FStats>& fstats) const {
    if (!print_time_) return;
    // Length of the name being printed
    size_t name_len=0;
    for (auto &&s : fstats) {
      name_len = std::max(s.first.size(), name_len);
    }
    name_len = std::max(name_.size(), name_len);
 
    // Print name with a given length. Format: "%NNs "
    char namefmt[10];
    sprint(namefmt, sizeof(namefmt), "%%%ds ", static_cast<casadi_int>(name_len));
 
    // Print header
    print(namefmt, name_.c_str());
 
    print(" : %8s %10s %8s %10s %9s\n", "t_proc", "(avg)", "t_wall", "(avg)", "n_eval");
 
 
    char buffer_proc[10];
    char buffer_wall[10];
    char buffer_proc_avg[10];
    char buffer_wall_avg[10];
 
    // Print keys
    for (const auto &s : fstats) {
      if (s.second.n_call!=0) {
        print(namefmt, s.first.c_str());
        format_time(buffer_proc, s.second.t_proc);
        format_time(buffer_wall, s.second.t_wall);
        format_time(buffer_proc_avg, s.second.t_proc/s.second.n_call);
        format_time(buffer_wall_avg, s.second.t_wall/s.second.n_call);
        print(" | %s (%s) %s (%s) %9d\n",
          buffer_proc, buffer_proc_avg,
          buffer_wall, buffer_wall_avg, s.second.n_call);
      }
    }
  }
 
  void ProtoFunction::format_time(char* buffer, double time) const {
    // Always of width 8
    casadi_assert_dev(time>=0);
    double log_time = log10(time);
    int magn = static_cast<int>(floor(log_time));
    int iprefix = static_cast<int>(floor(log_time/3));
    if (iprefix<-4) {
      sprint(buffer, 10, "       0");
      return;
    }
    if (iprefix>=5) {
      sprint(buffer, 10, "     inf");
      return;
    }
    char prefixes[] = "TGMk munp";
    char prefix = prefixes[4-iprefix];
 
    int rem = magn-3*iprefix;
    double time_normalized = time/pow(10, 3*iprefix);
 
    if (rem==0) {
      sprint(buffer, 10, "  %1.2f%cs", time_normalized, prefix);
    } else if (rem==1) {
      sprint(buffer, 10, " %2.2f%cs", time_normalized, prefix);
    } else {
      sprint(buffer, 10, "%3.2f%cs", time_normalized, prefix);
    }
  }
 
  void ProtoFunction::sprint(char* buf, size_t buf_sz, const char* fmt, ...) const {
    // Variable number of arguments
    va_list args;
    va_start(args, fmt);
    // Print to buffer
    casadi_int n = vsnprintf(buf, buf_sz, fmt, args);
    // Cleanup
    va_end(args);
    // Throw error if failure
    casadi_assert(n>=0 && n<buf_sz, "Print failure while processing '" + std::string(fmt) + "'");
  }
 
  void ProtoFunction::print(const char* fmt, ...) const {
    // Variable number of arguments
    va_list args;
    va_start(args, fmt);
    // Static & dynamic buffers
    char buf[256];
    size_t buf_sz = sizeof(buf);
    char* buf_dyn = nullptr;
    // Try to print with a small buffer
    casadi_int n = vsnprintf(buf, buf_sz, fmt, args);
    // Need a larger buffer?
    if (n>static_cast<casadi_int>(buf_sz)) {
      buf_sz = static_cast<size_t>(n+1);
      buf_dyn = new char[buf_sz];
      n = vsnprintf(buf_dyn, buf_sz, fmt, args);
    }
    // Print buffer content
    if (n>=0) uout() << (buf_dyn ? buf_dyn : buf) << std::flush;
    // Cleanup
    delete[] buf_dyn;
    va_end(args);
    // Throw error if failure
    casadi_assert(n>=0, "Print failure while processing '" + std::string(fmt) + "'");
  }
 
  void FunctionInternal::
  call_gen(const MXVector& arg, MXVector& res, casadi_int npar,
           bool always_inline, bool never_inline) const {
    if (npar==1) {
      eval_mx(arg, res, always_inline, never_inline);
    } else {
      // Split it up arguments
      std::vector<std::vector<MX>> v(npar, arg);
      std::vector<MX> t;
      for (int i=0; i<n_in_; ++i) {
        if (arg[i].size2()!=size2_in(i)) {
          t = horzsplit(arg[i], size2_in(i));
          casadi_assert_dev(t.size()==npar);
          for (int p=0; p<npar; ++p) v[p][i] = t[p];
        }
      }
      // Unroll the loop
      for (int p=0; p<npar; ++p) {
        eval_mx(v[p], t, always_inline, never_inline);
        v[p] = t;
      }
      // Concatenate results
      t.resize(npar);
      res.resize(n_out_);
      for (int i=0; i<n_out_; ++i) {
        for (int p=0; p<npar; ++p) t[p] = v[p][i];
        res[i] = horzcat(t);
      }
    }
  }
 
  std::string FunctionInternal::string_from_UnifiedReturnStatus(UnifiedReturnStatus status) {
    switch (status) {
      case SOLVER_RET_LIMITED:  return "SOLVER_RET_LIMITED";
      case SOLVER_RET_NAN:  return "SOLVER_RET_NAN";
      case SOLVER_RET_SUCCESS:  return "SOLVER_RET_SUCCESS";
      default: return "SOLVER_RET_UNKNOWN";
    }
  }
 
  void ProtoFunction::serialize_body(SerializingStream& s) const {
    s.version("ProtoFunction", 2);
    s.pack("ProtoFunction::name", name_);
    s.pack("ProtoFunction::verbose", verbose_);
    s.pack("ProtoFunction::print_time", print_time_);
    s.pack("ProtoFunction::record_time", record_time_);
    s.pack("ProtoFunction::regularity_check", regularity_check_);
    s.pack("ProtoFunction::error_on_fail", error_on_fail_);
  }
 
  ProtoFunction::ProtoFunction(DeserializingStream& s) {
    int version = s.version("ProtoFunction", 1, 2);
    s.unpack("ProtoFunction::name", name_);
    s.unpack("ProtoFunction::verbose", verbose_);
    s.unpack("ProtoFunction::print_time", print_time_);
    s.unpack("ProtoFunction::record_time", record_time_);
    if (version >= 2) s.unpack("ProtoFunction::regularity_check", regularity_check_);
    if (version >= 2) s.unpack("ProtoFunction::error_on_fail", error_on_fail_);
  }
 
  void FunctionInternal::serialize_type(SerializingStream &s) const {
    s.pack("FunctionInternal::base_function", serialize_base_function());
  }
 
  void FunctionInternal::serialize_body(SerializingStream& s) const {
    ProtoFunction::serialize_body(s);
    s.version("FunctionInternal", 9);
    s.pack("FunctionInternal::is_diff_in", is_diff_in_);
    s.pack("FunctionInternal::is_diff_out", is_diff_out_);
    s.pack("FunctionInternal::sp_in", sparsity_in_);
    s.pack("FunctionInternal::sp_out", sparsity_out_);
    s.pack("FunctionInternal::name_in", name_in_);
    s.pack("FunctionInternal::name_out", name_out_);
 
    s.pack("FunctionInternal::jit", jit_);
    s.pack("FunctionInternal::jit_cleanup", jit_cleanup_);
    s.pack("FunctionInternal::jit_serialize", jit_serialize_);
    if (jit_serialize_=="link" || jit_serialize_=="embed") {
      s.pack("FunctionInternal::jit_library", compiler_.library());
      if (jit_serialize_=="embed") {
        auto binary_ptr =
          Filesystem::ifstream_ptr(compiler_.library(), std::ios_base::binary, true);
        casadi_assert(binary_ptr, "Could not open library '" + compiler_.library() + "'.");
        s.pack("FunctionInternal::jit_binary", *binary_ptr);
      }
    }
    s.pack("FunctionInternal::jit_temp_suffix", jit_temp_suffix_);
    s.pack("FunctionInternal::jit_base_name", jit_base_name_);
    s.pack("FunctionInternal::jit_options", jit_options_);
    s.pack("FunctionInternal::codegen_options", codegen_options_);
    s.pack("FunctionInternal::compiler_plugin", compiler_plugin_);
    s.pack("FunctionInternal::has_refcount", has_refcount_);
 
    s.pack("FunctionInternal::cache_init", cache_init_);
 
    s.pack("FunctionInternal::derivative_of", derivative_of_);
 
    s.pack("FunctionInternal::jac_penalty", jac_penalty_);
 
    s.pack("FunctionInternal::enable_forward", enable_forward_);
    s.pack("FunctionInternal::enable_reverse", enable_reverse_);
    s.pack("FunctionInternal::enable_jacobian", enable_jacobian_);
    s.pack("FunctionInternal::enable_fd", enable_fd_);
    s.pack("FunctionInternal::enable_forward_op", enable_forward_op_);
    s.pack("FunctionInternal::enable_reverse_op", enable_reverse_op_);
    s.pack("FunctionInternal::enable_jacobian_op", enable_jacobian_op_);
    s.pack("FunctionInternal::enable_fd_op", enable_fd_op_);
 
    s.pack("FunctionInternal::ad_weight", ad_weight_);
    s.pack("FunctionInternal::ad_weight_sp", ad_weight_sp_);
    s.pack("FunctionInternal::always_inline", always_inline_);
    s.pack("FunctionInternal::never_inline", never_inline_);
 
    s.pack("FunctionInternal::max_num_dir", max_num_dir_);
 
    s.pack("FunctionInternal::inputs_check", inputs_check_);
 
    s.pack("FunctionInternal::fd_step", fd_step_);
 
    s.pack("FunctionInternal::fd_method", fd_method_);
    s.pack("FunctionInternal::print_in", print_in_);
    s.pack("FunctionInternal::print_out", print_out_);
    s.pack("FunctionInternal::print_canonical", print_canonical_);
    s.pack("FunctionInternal::max_io", max_io_);
    s.pack("FunctionInternal::dump_in", dump_in_);
    s.pack("FunctionInternal::dump_out", dump_out_);
    s.pack("FunctionInternal::dump_dir", dump_dir_);
    s.pack("FunctionInternal::dump_format", dump_format_);
    s.pack("FunctionInternal::forward_options", forward_options_);
    s.pack("FunctionInternal::reverse_options", reverse_options_);
    s.pack("FunctionInternal::jacobian_options", jacobian_options_);
    s.pack("FunctionInternal::der_options", der_options_);
    s.pack("FunctionInternal::custom_jacobian", custom_jacobian_);
    s.pack("FunctionInternal::registered_functions", registered_functions_);
 
    s.pack("FunctionInternal::sz_arg_per", sz_arg_per_);
    s.pack("FunctionInternal::sz_res_per", sz_res_per_);
    s.pack("FunctionInternal::sz_iw_per", sz_iw_per_);
    s.pack("FunctionInternal::sz_w_per", sz_w_per_);
    s.pack("FunctionInternal::sz_arg_tmp", sz_arg_tmp_);
    s.pack("FunctionInternal::sz_res_tmp", sz_res_tmp_);
    s.pack("FunctionInternal::sz_iw_tmp", sz_iw_tmp_);
    s.pack("FunctionInternal::sz_w_tmp", sz_w_tmp_);
  }
 
  FunctionInternal::FunctionInternal(DeserializingStream& s) : ProtoFunction(s) {
    eval_ = nullptr;
    checkout_ = nullptr;
    release_ = nullptr;
    incref_ = nullptr;
    decref_ = nullptr;
    int version = s.version("FunctionInternal", 1, 9);
    s.unpack("FunctionInternal::is_diff_in", is_diff_in_);
    s.unpack("FunctionInternal::is_diff_out", is_diff_out_);
    s.unpack("FunctionInternal::sp_in", sparsity_in_);
    s.unpack("FunctionInternal::sp_out", sparsity_out_);
    s.unpack("FunctionInternal::name_in", name_in_);
    s.unpack("FunctionInternal::name_out", name_out_);
 
    s.unpack("FunctionInternal::jit", jit_);
    s.unpack("FunctionInternal::jit_cleanup", jit_cleanup_);
    if (version < 2) {
      jit_serialize_ = "source";
    } else {
      s.unpack("FunctionInternal::jit_serialize", jit_serialize_);
    }
    if (jit_serialize_=="link" || jit_serialize_=="embed") {
      std::string library;
      s.unpack("FunctionInternal::jit_library", library);
      if (jit_serialize_=="embed") {
        // If file already exist
        auto binary_ptr = Filesystem::ifstream_ptr(library, std::ios_base::binary, false);
        if (binary_ptr) { // library exists
          // Ignore packed contents
          std::stringstream ss;
          s.unpack("FunctionInternal::jit_binary", ss);
        } else { // library does not exist
          auto binary_ptr = Filesystem::ofstream_ptr(library, std::ios_base::binary);
          s.unpack("FunctionInternal::jit_binary", *binary_ptr);
        }
      }
      compiler_ = Importer(library, "dll");
    }
    s.unpack("FunctionInternal::jit_temp_suffix", jit_temp_suffix_);
    s.unpack("FunctionInternal::jit_base_name", jit_base_name_);
    s.unpack("FunctionInternal::jit_options", jit_options_);
    if (version >= 9) {
      s.unpack("FunctionInternal::codegen_options", codegen_options_);
    }
    s.unpack("FunctionInternal::compiler_plugin", compiler_plugin_);
    s.unpack("FunctionInternal::has_refcount", has_refcount_);
 
    if (version >= 6) {
      s.unpack("FunctionInternal::cache_init", cache_init_);
    }
 
    s.unpack("FunctionInternal::derivative_of", derivative_of_);
 
    s.unpack("FunctionInternal::jac_penalty", jac_penalty_);
 
    s.unpack("FunctionInternal::enable_forward", enable_forward_);
    s.unpack("FunctionInternal::enable_reverse", enable_reverse_);
    s.unpack("FunctionInternal::enable_jacobian", enable_jacobian_);
    s.unpack("FunctionInternal::enable_fd", enable_fd_);
    s.unpack("FunctionInternal::enable_forward_op", enable_forward_op_);
    s.unpack("FunctionInternal::enable_reverse_op", enable_reverse_op_);
    s.unpack("FunctionInternal::enable_jacobian_op", enable_jacobian_op_);
    s.unpack("FunctionInternal::enable_fd_op", enable_fd_op_);
 
    s.unpack("FunctionInternal::ad_weight", ad_weight_);
    s.unpack("FunctionInternal::ad_weight_sp", ad_weight_sp_);
    s.unpack("FunctionInternal::always_inline", always_inline_);
    s.unpack("FunctionInternal::never_inline", never_inline_);
 
    s.unpack("FunctionInternal::max_num_dir", max_num_dir_);
 
    if (version < 3) s.unpack("FunctionInternal::regularity_check", regularity_check_);
 
    s.unpack("FunctionInternal::inputs_check", inputs_check_);
 
    s.unpack("FunctionInternal::fd_step", fd_step_);
 
    s.unpack("FunctionInternal::fd_method", fd_method_);
    s.unpack("FunctionInternal::print_in", print_in_);
    s.unpack("FunctionInternal::print_out", print_out_);
    if (version >= 7) {
      s.unpack("FunctionInternal::print_canonical", print_canonical_);
    } else {
      print_canonical_ = false;
    }
    if (version >= 4) {
      s.unpack("FunctionInternal::max_io", max_io_);
    } else {
      max_io_ = 10000;
    }
    s.unpack("FunctionInternal::dump_in", dump_in_);
    s.unpack("FunctionInternal::dump_out", dump_out_);
    s.unpack("FunctionInternal::dump_dir", dump_dir_);
    s.unpack("FunctionInternal::dump_format", dump_format_);
    // Makes no sense to dump a Function that is being deserialized
    dump_ = false;
    s.unpack("FunctionInternal::forward_options", forward_options_);
    s.unpack("FunctionInternal::reverse_options", reverse_options_);
    if (version>=5) {
      s.unpack("FunctionInternal::jacobian_options", jacobian_options_);
      s.unpack("FunctionInternal::der_options", der_options_);
    }
    s.unpack("FunctionInternal::custom_jacobian", custom_jacobian_);
    if (version >= 8) {
      s.unpack("FunctionInternal::registered_functions", registered_functions_);
    }
    if (!custom_jacobian_.is_null()) {
      casadi_assert_dev(custom_jacobian_.name() == "jac_" + name_);
      tocache(custom_jacobian_);
    }
    s.unpack("FunctionInternal::sz_arg_per", sz_arg_per_);
    s.unpack("FunctionInternal::sz_res_per", sz_res_per_);
    s.unpack("FunctionInternal::sz_iw_per", sz_iw_per_);
    s.unpack("FunctionInternal::sz_w_per", sz_w_per_);
    s.unpack("FunctionInternal::sz_arg_tmp", sz_arg_tmp_);
    s.unpack("FunctionInternal::sz_res_tmp", sz_res_tmp_);
    s.unpack("FunctionInternal::sz_iw_tmp", sz_iw_tmp_);
    s.unpack("FunctionInternal::sz_w_tmp", sz_w_tmp_);
 
    n_in_ = sparsity_in_.size();
    n_out_ = sparsity_out_.size();
    eval_ = nullptr;
    checkout_ = nullptr;
    release_ = nullptr;
    dump_count_ = 0;
  }
 
  void ProtoFunction::serialize(SerializingStream& s) const {
    serialize_type(s);
    serialize_body(s);
  }
 
  Function FunctionInternal::deserialize(DeserializingStream& s) {
    std::string base_function;
    s.unpack("FunctionInternal::base_function", base_function);
    auto it = FunctionInternal::deserialize_map.find(base_function);
    casadi_assert(it!=FunctionInternal::deserialize_map.end(),
      "FunctionInternal::deserialize: not found '" + base_function + "'");
 
    Function ret;
    ret.own(it->second(s));
    ret->finalize();
    return ret;
  }
 
  /*
  * Keys are given by serialize_base_function()
  */
  std::map<std::string, ProtoFunction* (*)(DeserializingStream&)>
      FunctionInternal::deserialize_map = {
    {"MXFunction", MXFunction::deserialize},
    {"SXFunction", SXFunction::deserialize},
    {"Interpolant", Interpolant::deserialize},
    {"Switch", Switch::deserialize},
    {"ForwardDiff", ForwardDiff::deserialize},
    {"BackwardDiff", BackwardDiff::deserialize},
    {"CentralDiff", CentralDiff::deserialize},
    {"Smoothing", Smoothing::deserialize},
 
    {"Map", Map::deserialize},
    {"MapSum", MapSum::deserialize},
    {"Nlpsol", Nlpsol::deserialize},
    {"Rootfinder", Rootfinder::deserialize},
    {"Integrator", Integrator::deserialize},
    {"External", External::deserialize},
    {"Conic", Conic::deserialize},
    {"FmuFunction", FmuFunction::deserialize},
    {"BlazingSplineFunction", BlazingSplineFunction::deserialize},
    {"Onnx", OnnxFunction::deserialize}
  };
 
} // namespace casadi