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/* ia64-gen.c -- Generate a shrunk set of opcode tables
   Copyright 1999, 2000, 2001, 2002, 2004, 2005, 2006
   Free Software Foundation, Inc.
   Written by Bob Manson, Cygnus Solutions, <manson@cygnus.com>

   This file is part of GDB, GAS, and the GNU binutils.

   GDB, GAS, and the GNU binutils are free software; you can redistribute
   them and/or modify them under the terms of the GNU General Public
   License as published by the Free Software Foundation; either version
   2, or (at your option) any later version.

   GDB, GAS, and the GNU binutils are distributed in the hope that they
   will be useful, but WITHOUT ANY WARRANTY; without even the implied
   warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See
   the GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this file; see the file COPYING.  If not, write to the
   Free Software Foundation, 51 Franklin Street - Fifth Floor, Boston, MA
   02110-1301, USA.  */

/* While the ia64-opc-* set of opcode tables are easy to maintain,
   they waste a tremendous amount of space.  ia64-gen rearranges the
   instructions into a directed acyclic graph (DAG) of instruction opcodes and 
   their possible completers, as well as compacting the set of strings used.  

   The disassembler table consists of a state machine that does
   branching based on the bits of the opcode being disassembled.  The
   state encodings have been chosen to minimize the amount of space
   required.  

   The resource table is constructed based on some text dependency tables, 
   which are also easier to maintain than the final representation.  */

#include <stdio.h>
#include <stdarg.h>
#include <errno.h>

#include "ansidecl.h"
#include "libiberty.h"
#include "safe-ctype.h"
#include "sysdep.h"
#include "getopt.h"
#include "ia64-opc.h"
#include "ia64-opc-a.c"
#include "ia64-opc-i.c"
#include "ia64-opc-m.c"
#include "ia64-opc-b.c"
#include "ia64-opc-f.c"
#include "ia64-opc-x.c"
#include "ia64-opc-d.c"

#include <libintl.h>
#define _(String) gettext (String)

/* This is a copy of fprintf_vma from bfd/bfd-in2.h.  We have to use this
   always, because we might be compiled without BFD64 defined, if configured
   for a 32-bit target and --enable-targets=all is used.  This will work for
   both 32-bit and 64-bit hosts.  */
#define _opcode_int64_low(x) ((unsigned long) (((x) & 0xffffffff)))
#define _opcode_int64_high(x) ((unsigned long) (((x) >> 32) & 0xffffffff))
#define opcode_fprintf_vma(s,x) \
  fprintf ((s), "%08lx%08lx", _opcode_int64_high (x), _opcode_int64_low (x))

const char * program_name = NULL;
int debug = 0;

#define NELEMS(a) (sizeof (a) / sizeof ((a)[0]))
#define tmalloc(X) (X *) xmalloc (sizeof (X))

/* The main opcode table entry.  Each entry is a unique combination of
   name and flags (no two entries in the table compare as being equal
   via opcodes_eq).  */
struct main_entry
{
  /* The base name of this opcode.  The names of its completers are
     appended to it to generate the full instruction name.  */
  struct string_entry *name;
  /* The base opcode entry.  Which one to use is a fairly arbitrary choice;
     it uses the first one passed to add_opcode_entry.  */
  struct ia64_opcode *opcode;
  /* The list of completers that can be applied to this opcode.  */
  struct completer_entry *completers;
  /* Next entry in the chain.  */
  struct main_entry *next;
  /* Index in the  main table.  */
  int main_index;
} *maintable, **ordered_table;

int otlen = 0;
int ottotlen = 0;
int opcode_count = 0;

/* The set of possible completers for an opcode.  */
struct completer_entry
{
  /* This entry's index in the ia64_completer_table[] array.  */
  int num;

  /* The name of the completer.  */
  struct string_entry *name;

  /* This entry's parent.  */
  struct completer_entry *parent;

  /* Set if this is a terminal completer (occurs at the end of an
     opcode).  */
  int is_terminal;

  /* An alternative completer.  */
  struct completer_entry *alternative;

  /* Additional completers that can be appended to this one.  */
  struct completer_entry *addl_entries;

  /* Before compute_completer_bits () is invoked, this contains the actual
     instruction opcode for this combination of opcode and completers.
     Afterwards, it contains those bits that are different from its
     parent opcode.  */
  ia64_insn bits;

  /* Bits set to 1 correspond to those bits in this completer's opcode
     that are different from its parent completer's opcode (or from
     the base opcode if the entry is the root of the opcode's completer
     list).  This field is filled in by compute_completer_bits ().  */
  ia64_insn mask;

  /* Index into the opcode dependency list, or -1 if none.  */
  int dependencies;

  /* Remember the order encountered in the opcode tables.  */
  int order;
};

/* One entry in the disassembler name table.  */
struct disent
{
  /* The index into the ia64_name_dis array for this entry.  */
  int ournum;

  /* The index into the main_table[] array.  */
  int insn;

  /* The disassmbly priority of this entry.  */
  int priority;

  /* The completer_index value for this entry.  */
  int completer_index;

  /* How many other entries share this decode.  */
  int nextcnt;

  /* The next entry sharing the same decode.  */
  struct disent *nexte;

  /* The next entry in the name list.  */
  struct disent *next_ent;
} *disinsntable = NULL;

/* A state machine that will eventually be used to generate the
   disassembler table.  */
struct bittree
{
  struct disent *disent;
  struct bittree *bits[3]; /* 0, 1, and X (don't care).  */
  int bits_to_skip;
  int skip_flag;
} *bittree;

/* The string table contains all opcodes and completers sorted in
   alphabetical order.  */

/* One entry in the string table.  */
struct string_entry 
{
  /* The index in the ia64_strings[] array for this entry.  */
  int num;
  /* And the string.  */
  char *s;
} **string_table = NULL;

int strtablen = 0;
int strtabtotlen = 0;


/* Resource dependency entries.  */
struct rdep
{
  char *name;                       /* Resource name.  */
  unsigned 
    mode:2,                         /* RAW, WAW, or WAR.  */
    semantics:3;                    /* Dependency semantics.  */
  char *extra;                      /* Additional semantics info.  */
  int nchks;                   
  int total_chks;                   /* Total #of terminal insns.  */
  int *chks;                        /* Insn classes which read (RAW), write
                                       (WAW), or write (WAR) this rsrc.  */
  int *chknotes;                    /* Dependency notes for each class.  */
  int nregs;
  int total_regs;                   /* Total #of terminal insns.  */
  int *regs;                        /* Insn class which write (RAW), write2
                                       (WAW), or read (WAR) this rsrc.  */
  int *regnotes;                    /* Dependency notes for each class.  */

  int waw_special;                  /* Special WAW dependency note.  */
} **rdeps = NULL;

static int rdepslen = 0;
static int rdepstotlen = 0;

/* Array of all instruction classes.  */
struct iclass
{ 
  char *name;                       /* Instruction class name.  */
  int is_class;                     /* Is a class, not a terminal.  */
  int nsubs;                        
  int *subs;                        /* Other classes within this class.  */
  int nxsubs;                       
  int xsubs[4];                     /* Exclusions.  */
  char *comment;                    /* Optional comment.  */
  int note;                         /* Optional note.  */
  int terminal_resolved;            /* Did we match this with anything?  */
  int orphan;                       /* Detect class orphans.  */
} **ics = NULL;

static int iclen = 0;
static int ictotlen = 0;

/* An opcode dependency (chk/reg pair of dependency lists).  */
struct opdep
{
  int chk;                          /* index into dlists */
  int reg;                          /* index into dlists */
} **opdeps;

static int opdeplen = 0;
static int opdeptotlen = 0;

/* A generic list of dependencies w/notes encoded.  These may be shared.  */
struct deplist
{
  int len;
  unsigned short *deps;
} **dlists;

static int dlistlen = 0;
static int dlisttotlen = 0;


static void fail (const char *, ...) ATTRIBUTE_PRINTF_1;
static void warn (const char *, ...) ATTRIBUTE_PRINTF_1;
static struct rdep * insert_resource (const char *, enum ia64_dependency_mode);
static int  deplist_equals (struct deplist *, struct deplist *);
static short insert_deplist (int, unsigned short *);
static short insert_dependencies (int, unsigned short *, int, unsigned short *);
static void  mark_used (struct iclass *, int);
static int  fetch_insn_class (const char *, int);
static int  sub_compare (const void *, const void *);
static void load_insn_classes (void);
static void parse_resource_users (const char *, int **, int *, int **);
static int  parse_semantics (char *);
static void add_dep (const char *, const char *, const char *, int, int, char *, int);
static void load_depfile (const char *, enum ia64_dependency_mode);
static void load_dependencies (void);
static int  irf_operand (int, const char *);
static int  in_iclass_mov_x (struct ia64_opcode *, struct iclass *, const char *, const char *);
static int  in_iclass (struct ia64_opcode *, struct iclass *, const char *, const char *, int *);
static int  lookup_regindex (const char *, int);
static int  lookup_specifier (const char *);
static void print_dependency_table (void);
static struct string_entry * insert_string (char *);
static void gen_dis_table (struct bittree *);
static void print_dis_table (void);
static void generate_disassembler (void);
static void print_string_table (void);
static int  completer_entries_eq (struct completer_entry *, struct completer_entry *);
static struct completer_entry * insert_gclist (struct completer_entry *);
static int  get_prefix_len (const char *);
static void compute_completer_bits (struct main_entry *, struct completer_entry *);
static void collapse_redundant_completers (void);
static int  insert_opcode_dependencies (struct ia64_opcode *, struct completer_entry *);
static void insert_completer_entry (struct ia64_opcode *, struct main_entry *, int);
static void print_completer_entry (struct completer_entry *);
static void print_completer_table (void);
static int  opcodes_eq (struct ia64_opcode *, struct ia64_opcode *);
static void add_opcode_entry (struct ia64_opcode *);
static void print_main_table (void);
static void shrink (struct ia64_opcode *);
static void print_version (void);
static void usage (FILE *, int);
static void finish_distable (void);
static void insert_bit_table_ent (struct bittree *, int, ia64_insn, ia64_insn, int, int, int);
static void add_dis_entry (struct bittree *, ia64_insn, ia64_insn, int, struct completer_entry *, int);
static void compact_distree (struct bittree *);
static struct bittree * make_bittree_entry (void);
static struct disent * add_dis_table_ent (struct disent *, int, int, int);


static void
fail (const char *message, ...)
{
  va_list args;
  
  va_start (args, message);
  fprintf (stderr, _("%s: Error: "), program_name);
  vfprintf (stderr, message, args);
  va_end (args);
  xexit (1);
}

static void
warn (const char *message, ...)
{
  va_list args;

  va_start (args, message);

  fprintf (stderr, _("%s: Warning: "), program_name);
  vfprintf (stderr, message, args);
  va_end (args);
}

/* Add NAME to the resource table, where TYPE is RAW or WAW.  */
static struct rdep *
insert_resource (const char *name, enum ia64_dependency_mode type)
{
  if (rdepslen == rdepstotlen)
    {
      rdepstotlen += 20;
      rdeps = (struct rdep **)
        xrealloc (rdeps, sizeof(struct rdep **) * rdepstotlen);
    }
  rdeps[rdepslen] = tmalloc(struct rdep);
  memset((void *)rdeps[rdepslen], 0, sizeof(struct rdep));
  rdeps[rdepslen]->name = xstrdup (name);
  rdeps[rdepslen]->mode = type;
  rdeps[rdepslen]->waw_special = 0;
  
  return rdeps[rdepslen++];
}

/* Are the lists of dependency indexes equivalent?  */
static int
deplist_equals (struct deplist *d1, struct deplist *d2)
{
  int i;

  if (d1->len != d2->len)
    return 0;

  for (i = 0; i < d1->len; i++)
    if (d1->deps[i] != d2->deps[i])
      return 0;

  return 1;
}

/* Add the list of dependencies to the list of dependency lists.  */
static short
insert_deplist (int count, unsigned short *deps)
{
  /* Sort the list, then see if an equivalent list exists already.
     this results in a much smaller set of dependency lists.  */
  struct deplist *list;
  char set[0x10000];
  int i;

  memset ((void *)set, 0, sizeof (set));
  for (i = 0; i < count; i++)
    set[deps[i]] = 1;

  count = 0;
  for (i = 0; i < (int) sizeof (set); i++)
    if (set[i])
      ++count;

  list = tmalloc (struct deplist);
  list->len = count;
  list->deps = (unsigned short *) malloc (sizeof (unsigned short) * count);

  for (i = 0, count = 0; i < (int) sizeof (set); i++)
    if (set[i])
      list->deps[count++] = i;

  /* Does this list exist already?  */
  for (i = 0; i < dlistlen; i++)
    if (deplist_equals (list, dlists[i]))
      {
	free (list->deps);
	free (list);
	return i;
      }

  if (dlistlen == dlisttotlen)
    {
      dlisttotlen += 20;
      dlists = (struct deplist **)
        xrealloc (dlists, sizeof(struct deplist **) * dlisttotlen);
    }
  dlists[dlistlen] = list;

  return dlistlen++;
}

/* Add the given pair of dependency lists to the opcode dependency list.  */
static short
insert_dependencies (int nchks, unsigned short *chks, 
                     int nregs, unsigned short *regs)
{
  struct opdep *pair;
  int i;
  int regind = -1;
  int chkind = -1;

  if (nregs > 0)
    regind = insert_deplist (nregs, regs);
  if (nchks > 0)
    chkind = insert_deplist (nchks, chks);

  for (i = 0; i < opdeplen; i++)
    if (opdeps[i]->chk == chkind 
	&& opdeps[i]->reg == regind)
      return i;

  pair = tmalloc (struct opdep);
  pair->chk = chkind;
  pair->reg = regind;
  
  if (opdeplen == opdeptotlen)
    {
      opdeptotlen += 20;
      opdeps = (struct opdep **)
        xrealloc (opdeps, sizeof(struct opdep **) * opdeptotlen);
    }
  opdeps[opdeplen] = pair;

  return opdeplen++;
}

static void 
mark_used (struct iclass *ic, int clear_terminals)
{
  int i;

  ic->orphan = 0;
  if (clear_terminals)
    ic->terminal_resolved = 1;

  for (i = 0; i < ic->nsubs; i++)
    mark_used (ics[ic->subs[i]], clear_terminals);

  for (i = 0; i < ic->nxsubs; i++)
    mark_used (ics[ic->xsubs[i]], clear_terminals);
}

/* Look up an instruction class; if CREATE make a new one if none found;
   returns the index into the insn class array.  */
static int
fetch_insn_class (const char *full_name, int create)
{
  char *name;
  char *notestr;
  char *xsect;
  char *comment;
  int i, note = 0;
  int ind;
  int is_class = 0;

  if (strncmp (full_name, "IC:", 3) == 0)
    {
      name = xstrdup (full_name + 3);
      is_class = 1;
    }
  else
    name = xstrdup (full_name);

  if ((xsect = strchr(name, '\\')) != NULL)
    is_class = 1;
  if ((comment = strchr(name, '[')) != NULL)
    is_class = 1;
  if ((notestr = strchr(name, '+')) != NULL)
    is_class = 1;

  /* If it is a composite class, then ignore comments and notes that come after
     the '\\', since they don't apply to the part we are decoding now.  */
  if (xsect)
    {
      if (comment > xsect)
	comment = 0;
      if (notestr > xsect)
	notestr = 0;
    }

  if (notestr)
    {
      char *nextnotestr;

      note = atoi (notestr + 1);
      if ((nextnotestr = strchr (notestr + 1, '+')) != NULL)
        {
          if (strcmp (notestr, "+1+13") == 0)
            note = 13;
          else if (!xsect || nextnotestr < xsect)
            warn (_("multiple note %s not handled\n"), notestr);
        }
    }

  /* If it's a composite class, leave the notes and comments in place so that
     we have a unique name for the composite class.  Otherwise, we remove
     them.  */
  if (!xsect)
    {
      if (notestr)
        *notestr = 0;
      if (comment)
        *comment = 0;
    }

  for (i = 0; i < iclen; i++)
    if (strcmp (name, ics[i]->name) == 0
        && ((comment == NULL && ics[i]->comment == NULL)
            || (comment != NULL && ics[i]->comment != NULL
                && strncmp (ics[i]->comment, comment, 
                            strlen (ics[i]->comment)) == 0))
        && note == ics[i]->note)
      return i;

  if (!create)
    return -1;

  /* Doesn't exist, so make a new one.  */
  if (iclen == ictotlen)
    {
      ictotlen += 20;
      ics = (struct iclass **)
        xrealloc (ics, (ictotlen) * sizeof (struct iclass *));
    }

  ind = iclen++;
  ics[ind] = tmalloc (struct iclass);
  memset ((void *)ics[ind], 0, sizeof (struct iclass));
  ics[ind]->name = xstrdup (name);
  ics[ind]->is_class = is_class;
  ics[ind]->orphan = 1;

  if (comment)
    {
      ics[ind]->comment = xstrdup (comment + 1);
      ics[ind]->comment[strlen (ics[ind]->comment)-1] = 0;
    }

  if (notestr)
    ics[ind]->note = note;

  /* If it's a composite class, there's a comment or note, look for an
     existing class or terminal with the same name.  */
  if ((xsect || comment || notestr) && is_class)
    {
      /* First, populate with the class we're based on.  */
      char *subname = name;

      if (xsect)
        *xsect = 0;
      else if (comment)
        *comment = 0;
      else if (notestr)
        *notestr = 0;

      ics[ind]->nsubs = 1;
      ics[ind]->subs = tmalloc(int);
      ics[ind]->subs[0] = fetch_insn_class (subname, 1);;
    }

  while (xsect)
    {
      char *subname = xsect + 1;

      xsect = strchr (subname, '\\');
      if (xsect)
        *xsect = 0;
      ics[ind]->xsubs[ics[ind]->nxsubs] = fetch_insn_class (subname,1);
      ics[ind]->nxsubs++;
    }
  free (name);

  return ind;
}

/* For sorting a class's sub-class list only; make sure classes appear before
   terminals.  */
static int
sub_compare (const void *e1, const void *e2)
{
  struct iclass *ic1 = ics[*(int *)e1];
  struct iclass *ic2 = ics[*(int *)e2];

  if (ic1->is_class)
    {
      if (!ic2->is_class)
        return -1;
    }
  else if (ic2->is_class)
    return 1;

  return strcmp (ic1->name, ic2->name);
}

static void
load_insn_classes (void)
{
  FILE *fp = fopen ("ia64-ic.tbl", "r");
  char buf[2048];

  if (fp == NULL)
    fail (_("can't find ia64-ic.tbl for reading\n"));

  /* Discard first line.  */
  fgets (buf, sizeof(buf), fp);

  while (!feof (fp))
    {
      int iclass;
      char *name;
      char *tmp;
      
      if (fgets (buf, sizeof (buf), fp) == NULL)
        break;
      
      while (ISSPACE (buf[strlen (buf) - 1]))
        buf[strlen (buf) - 1] = '\0';

      name = tmp = buf;
      while (*tmp != ';')
        {
          ++tmp;
          if (tmp == buf + sizeof (buf))
            abort ();
        }
      *tmp++ = '\0';

      iclass = fetch_insn_class (name, 1);
      ics[iclass]->is_class = 1;

      if (strcmp (name, "none") == 0)
        {
          ics[iclass]->is_class = 0;
          ics[iclass]->terminal_resolved = 1;
          continue;
        }

      /* For this class, record all sub-classes.  */
      while (*tmp)
        {
          char *subname;
          int sub;

          while (*tmp && ISSPACE (*tmp))
            {
              ++tmp;
              if (tmp == buf + sizeof (buf))
                abort ();
            }
          subname = tmp;
          while (*tmp && *tmp != ',')
            {
              ++tmp;
              if (tmp == buf + sizeof (buf))
                abort ();
            }
          if (*tmp == ',')
            *tmp++ = '\0';
          
          ics[iclass]->subs = (int *)
            xrealloc ((void *)ics[iclass]->subs, 
		      (ics[iclass]->nsubs + 1) * sizeof (int));

          sub = fetch_insn_class (subname, 1);
          ics[iclass]->subs = (int *)
            xrealloc (ics[iclass]->subs, (ics[iclass]->nsubs + 1) * sizeof (int));
          ics[iclass]->subs[ics[iclass]->nsubs++] = sub;
        }

      /* Make sure classes come before terminals.  */
      qsort ((void *)ics[iclass]->subs, 
             ics[iclass]->nsubs, sizeof(int), sub_compare);
    }
  fclose (fp);

  if (debug)
    printf ("%d classes\n", iclen);
}

/* Extract the insn classes from the given line.  */
static void
parse_resource_users (ref, usersp, nusersp, notesp)
  const char *ref;
  int **usersp;
  int *nusersp;
  int **notesp;
{
  int c;
  char *line = xstrdup (ref);
  char *tmp = line;
  int *users = *usersp;
  int count = *nusersp;
  int *notes = *notesp;

  c = *tmp;
  while (c != 0)
    {
      char *notestr;
      int note;
      char *xsect;
      int iclass;
      int create = 0;
      char *name;
      
      while (ISSPACE (*tmp))
        ++tmp;
      name = tmp;
      while (*tmp && *tmp != ',')
        ++tmp;
      c = *tmp;
      *tmp++ = '\0';
      
      xsect = strchr (name, '\\');
      if ((notestr = strstr (name, "+")) != NULL)
        {
          char *nextnotestr;

          note = atoi (notestr + 1);
          if ((nextnotestr = strchr (notestr + 1, '+')) != NULL)
            {
              /* Note 13 always implies note 1.  */
              if (strcmp (notestr, "+1+13") == 0)
                note = 13;
              else if (!xsect || nextnotestr < xsect)
                warn (_("multiple note %s not handled\n"), notestr);
            }
          if (!xsect)
            *notestr = '\0';
        }
      else 
        note = 0;

      /* All classes are created when the insn class table is parsed;
         Individual instructions might not appear until the dependency tables
         are read.  Only create new classes if it's *not* an insn class,
         or if it's a composite class (which wouldn't necessarily be in the IC
         table).  */
      if (strncmp (name, "IC:", 3) != 0 || xsect != NULL)
        create = 1;
      
      iclass = fetch_insn_class (name, create);
      if (iclass != -1)
        {
          users = (int *)
            xrealloc ((void *) users,(count + 1) * sizeof (int));
          notes = (int *)
            xrealloc ((void *) notes,(count + 1) * sizeof (int));
          notes[count] = note;
          users[count++] = iclass;
          mark_used (ics[iclass], 0);
        }
      else if (debug)
	printf("Class %s not found\n", name);
    }
  /* Update the return values.  */
  *usersp = users;
  *nusersp = count;
  *notesp = notes;

  free (line);
}

static int
parse_semantics (char *sem)
{
  if (strcmp (sem, "none") == 0)
    return IA64_DVS_NONE;
  else if (strcmp (sem, "implied") == 0)
    return IA64_DVS_IMPLIED;
  else if (strcmp (sem, "impliedF") == 0)
    return IA64_DVS_IMPLIEDF;
  else if (strcmp (sem, "data") == 0)
    return IA64_DVS_DATA;
  else if (strcmp (sem, "instr") == 0)
    return IA64_DVS_INSTR;
  else if (strcmp (sem, "specific") == 0)
    return IA64_DVS_SPECIFIC;
  else if (strcmp (sem, "stop") == 0)
    return IA64_DVS_STOP;
  else 
    return IA64_DVS_OTHER;
}

static void
add_dep (const char *name, const char *chk, const char *reg,
         int semantics, int mode, char *extra, int flag)
{
  struct rdep *rs;

  rs = insert_resource (name, mode);

  parse_resource_users (chk, &rs->chks, &rs->nchks, &rs->chknotes);
  parse_resource_users (reg, &rs->regs, &rs->nregs, &rs->regnotes);

  rs->semantics = semantics;
  rs->extra = extra;
  rs->waw_special = flag;
}

static void
load_depfile (const char *filename, enum ia64_dependency_mode mode)
{
  FILE *fp = fopen (filename, "r");
  char buf[1024];

  if (fp == NULL)
    fail (_("can't find %s for reading\n"), filename);

  fgets (buf, sizeof(buf), fp);
  while (!feof (fp))
    {
      char *name, *tmp;
      int semantics;
      char *extra;
      char *regp, *chkp;

      if (fgets (buf, sizeof(buf), fp) == NULL)
        break;

      while (ISSPACE (buf[strlen (buf) - 1]))
        buf[strlen (buf) - 1] = '\0';

      name = tmp = buf;
      while (*tmp != ';')
        ++tmp;
      *tmp++ = '\0';
      
      while (ISSPACE (*tmp))
        ++tmp;
      regp = tmp;
      tmp = strchr (tmp, ';');
      if (!tmp)
        abort ();
      *tmp++ = 0;
      while (ISSPACE (*tmp))
        ++tmp;
      chkp = tmp;
      tmp = strchr (tmp, ';');
      if (!tmp)
        abort ();
      *tmp++ = 0;
      while (ISSPACE (*tmp))
        ++tmp;
      semantics = parse_semantics (tmp);
      extra = semantics == IA64_DVS_OTHER ? xstrdup (tmp) : NULL;

      /* For WAW entries, if the chks and regs differ, we need to enter the
         entries in both positions so that the tables will be parsed properly,
         without a lot of extra work.  */
      if (mode == IA64_DV_WAW && strcmp (regp, chkp) != 0)
        {
          add_dep (name, chkp, regp, semantics, mode, extra, 0);
          add_dep (name, regp, chkp, semantics, mode, extra, 1);
        }
      else
        {
          add_dep (name, chkp, regp, semantics, mode, extra, 0);
        }
    }
  fclose (fp);
}

static void
load_dependencies (void)
{
  load_depfile ("ia64-raw.tbl", IA64_DV_RAW);
  load_depfile ("ia64-waw.tbl", IA64_DV_WAW);
  load_depfile ("ia64-war.tbl", IA64_DV_WAR);

  if (debug)
    printf ("%d RAW/WAW/WAR dependencies\n", rdepslen);
}

/* Is the given operand an indirect register file operand?  */
static int 
irf_operand (int op, const char *field)
{
  if (!field)
    {
      return op == IA64_OPND_RR_R3 || op == IA64_OPND_DBR_R3
        || op == IA64_OPND_IBR_R3  || op == IA64_OPND_PKR_R3
	|| op == IA64_OPND_PMC_R3  || op == IA64_OPND_PMD_R3
	|| op == IA64_OPND_MSR_R3 || op == IA64_OPND_CPUID_R3;
    }
  else
    {
      return ((op == IA64_OPND_RR_R3 && strstr (field, "rr"))
              || (op == IA64_OPND_DBR_R3 && strstr (field, "dbr"))
              || (op == IA64_OPND_IBR_R3 && strstr (field, "ibr"))
              || (op == IA64_OPND_PKR_R3 && strstr (field, "pkr"))
              || (op == IA64_OPND_PMC_R3 && strstr (field, "pmc"))
              || (op == IA64_OPND_PMD_R3 && strstr (field, "pmd"))
              || (op == IA64_OPND_MSR_R3 && strstr (field, "msr"))
              || (op == IA64_OPND_CPUID_R3 && strstr (field, "cpuid")));
    }
}

/* Handle mov_ar, mov_br, mov_cr, mov_indirect, mov_ip, mov_pr, mov_psr, and
   mov_um insn classes.  */
static int
in_iclass_mov_x (struct ia64_opcode *idesc, struct iclass *ic, 
                 const char *format, const char *field)
{
  int plain_mov = strcmp (idesc->name, "mov") == 0;

  if (!format)
    return 0;

  switch (ic->name[4])
    {
    default:
      abort ();
    case 'a':
      {
        int i = strcmp (idesc->name, "mov.i") == 0;
        int m = strcmp (idesc->name, "mov.m") == 0;
        int i2627 = i && idesc->operands[0] == IA64_OPND_AR3;
        int i28 = i && idesc->operands[1] == IA64_OPND_AR3;
        int m2930 = m && idesc->operands[0] == IA64_OPND_AR3;
        int m31 = m && idesc->operands[1] == IA64_OPND_AR3;
        int pseudo0 = plain_mov && idesc->operands[1] == IA64_OPND_AR3;
        int pseudo1 = plain_mov && idesc->operands[0] == IA64_OPND_AR3;

        /* IC:mov ar */
        if (i2627)
          return strstr (format, "I26") || strstr (format, "I27");
        if (i28)
          return strstr (format, "I28") != NULL;
        if (m2930)
          return strstr (format, "M29") || strstr (format, "M30");
        if (m31)
          return strstr (format, "M31") != NULL;
        if (pseudo0 || pseudo1)
          return 1;
      }
      break;
    case 'b':
      {
        int i21 = idesc->operands[0] == IA64_OPND_B1;
        int i22 = plain_mov && idesc->operands[1] == IA64_OPND_B2;
        if (i22)
          return strstr (format, "I22") != NULL;
        if (i21)
          return strstr (format, "I21") != NULL;
      }
      break;
    case 'c':
      {
        int m32 = plain_mov && idesc->operands[0] == IA64_OPND_CR3;
        int m33 = plain_mov && idesc->operands[1] == IA64_OPND_CR3;
        if (m32)
          return strstr (format, "M32") != NULL;
        if (m33)
          return strstr (format, "M33") != NULL;
      }
      break;
    case 'i':
      if (ic->name[5] == 'n')
        {
          int m42 = plain_mov && irf_operand (idesc->operands[0], field);
          int m43 = plain_mov && irf_operand (idesc->operands[1], field);
          if (m42)
            return strstr (format, "M42") != NULL;
          if (m43)
            return strstr (format, "M43") != NULL;
        }
      else if (ic->name[5] == 'p')
        {
          return idesc->operands[1] == IA64_OPND_IP;
        }
      else
        abort ();
      break;
    case 'p':
      if (ic->name[5] == 'r')
        {
          int i25 = plain_mov && idesc->operands[1] == IA64_OPND_PR;
          int i23 = plain_mov && idesc->operands[0] == IA64_OPND_PR;
          int i24 = plain_mov && idesc->operands[0] == IA64_OPND_PR_ROT;
          if (i23)
            return strstr (format, "I23") != NULL;
          if (i24)
            return strstr (format, "I24") != NULL;
          if (i25)
            return strstr (format, "I25") != NULL;
        }
      else if (ic->name[5] == 's')
        {
          int m35 = plain_mov && idesc->operands[0] == IA64_OPND_PSR_L;
          int m36 = plain_mov && idesc->operands[1] == IA64_OPND_PSR;
          if (m35)
            return strstr (format, "M35") != NULL;
          if (m36)
            return strstr (format, "M36") != NULL;
        }
      else
        abort ();
      break;
    case 'u':
      {
        int m35 = plain_mov && idesc->operands[0] == IA64_OPND_PSR_UM;
        int m36 = plain_mov && idesc->operands[1] == IA64_OPND_PSR_UM;
        if (m35)
          return strstr (format, "M35") != NULL;
        if (m36)
          return strstr (format, "M36") != NULL;
      }
      break;
    }
  return 0;
}

/* Is the given opcode in the given insn class?  */
static int
in_iclass (struct ia64_opcode *idesc, struct iclass *ic, 
	   const char *format, const char *field, int *notep)
{
  int i;
  int resolved = 0;

  if (ic->comment)
    {
      if (!strncmp (ic->comment, "Format", 6))
        {
          /* Assume that the first format seen is the most restrictive, and
             only keep a later one if it looks like it's more restrictive.  */
          if (format)
            {
              if (strlen (ic->comment) < strlen (format))
                {
                  warn (_("most recent format '%s'\nappears more restrictive than '%s'\n"),
			ic->comment, format);
                  format = ic->comment; 
                }
            }
          else
            format = ic->comment;
        }
      else if (!strncmp (ic->comment, "Field", 5))
        {
          if (field)
            warn (_("overlapping field %s->%s\n"),
		  ic->comment, field);
          field = ic->comment;
        }
    }

  /* An insn class matches anything that is the same followed by completers,
     except when the absence and presence of completers constitutes different
     instructions.  */
  if (ic->nsubs == 0 && ic->nxsubs == 0)
    {
      int is_mov = strncmp (idesc->name, "mov", 3) == 0;
      int plain_mov = strcmp (idesc->name, "mov") == 0;
      int len = strlen(ic->name);

      resolved = ((strncmp (ic->name, idesc->name, len) == 0)
                  && (idesc->name[len] == '\0' 
                      || idesc->name[len] == '.'));

      /* All break, nop, and hint variations must match exactly.  */
      if (resolved &&
          (strcmp (ic->name, "break") == 0
           || strcmp (ic->name, "nop") == 0
	   || strcmp (ic->name, "hint") == 0))
        resolved = strcmp (ic->name, idesc->name) == 0;

      /* Assume restrictions in the FORMAT/FIELD negate resolution,
         unless specifically allowed by clauses in this block.  */
      if (resolved && field)
        {
          /* Check Field(sf)==sN against opcode sN.  */
          if (strstr(field, "(sf)==") != NULL)
            {
              char *sf;

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/* ----------------------------------------------------------------------
* Copyright (C) 2010-2015 ARM Limited. All rights reserved.
*
* $Date:        20. October 2015
* $Revision:    V1.4.5 b
*
* Project:      CMSIS DSP Library
* Title:        arm_math.h
*
* Description:  Public header file for CMSIS DSP Library
*
* Target Processor: Cortex-M7/Cortex-M4/Cortex-M3/Cortex-M0
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*   - Redistributions of source code must retain the above copyright
*     notice, this list of conditions and the following disclaimer.
*   - Redistributions in binary form must reproduce the above copyright
*     notice, this list of conditions and the following disclaimer in
*     the documentation and/or other materials provided with the
*     distribution.
*   - Neither the name of ARM LIMITED nor the names of its contributors
*     may be used to endorse or promote products derived from this
*     software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
 * -------------------------------------------------------------------- */

/**
   \mainpage CMSIS DSP Software Library
   *
   * Introduction
   * ------------
   *
   * This user manual describes the CMSIS DSP software library,
   * a suite of common signal processing functions for use on Cortex-M processor based devices.
   *
   * The library is divided into a number of functions each covering a specific category:
   * - Basic math functions
   * - Fast math functions
   * - Complex math functions
   * - Filters
   * - Matrix functions
   * - Transforms
   * - Motor control functions
   * - Statistical functions
   * - Support functions
   * - Interpolation functions
   *
   * The library has separate functions for operating on 8-bit integers, 16-bit integers,
   * 32-bit integer and 32-bit floating-point values.
   *
   * Using the Library
   * ------------
   *
   * The library installer contains prebuilt versions of the libraries in the <code>Lib</code> folder.
   * - arm_cortexM7lfdp_math.lib (Little endian and Double Precision Floating Point Unit on Cortex-M7)
   * - arm_cortexM7bfdp_math.lib (Big endian and Double Precision Floating Point Unit on Cortex-M7)
   * - arm_cortexM7lfsp_math.lib (Little endian and Single Precision Floating Point Unit on Cortex-M7)
   * - arm_cortexM7bfsp_math.lib (Big endian and Single Precision Floating Point Unit on Cortex-M7)
   * - arm_cortexM7l_math.lib (Little endian on Cortex-M7)
   * - arm_cortexM7b_math.lib (Big endian on Cortex-M7)
   * - arm_cortexM4lf_math.lib (Little endian and Floating Point Unit on Cortex-M4)
   * - arm_cortexM4bf_math.lib (Big endian and Floating Point Unit on Cortex-M4)
   * - arm_cortexM4l_math.lib (Little endian on Cortex-M4)
   * - arm_cortexM4b_math.lib (Big endian on Cortex-M4)
   * - arm_cortexM3l_math.lib (Little endian on Cortex-M3)
   * - arm_cortexM3b_math.lib (Big endian on Cortex-M3)
   * - arm_cortexM0l_math.lib (Little endian on Cortex-M0 / CortexM0+)
   * - arm_cortexM0b_math.lib (Big endian on Cortex-M0 / CortexM0+)
   *
   * The library functions are declared in the public file <code>arm_math.h</code> which is placed in the <code>Include</code> folder.
   * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single
   * public header file <code> arm_math.h</code> for Cortex-M7/M4/M3/M0/M0+ with little endian and big endian. Same header file will be used for floating point unit(FPU) variants.
   * Define the appropriate pre processor MACRO ARM_MATH_CM7 or ARM_MATH_CM4 or  ARM_MATH_CM3 or
   * ARM_MATH_CM0 or ARM_MATH_CM0PLUS depending on the target processor in the application.
   *
   * Examples
   * --------
   *
   * The library ships with a number of examples which demonstrate how to use the library functions.
   *
   * Toolchain Support
   * ------------
   *
   * The library has been developed and tested with MDK-ARM version 5.14.0.0
   * The library is being tested in GCC and IAR toolchains and updates on this activity will be made available shortly.
   *
   * Building the Library
   * ------------
   *
   * The library installer contains a project file to re build libraries on MDK-ARM Tool chain in the <code>CMSIS\\DSP_Lib\\Source\\ARM</code> folder.
   * - arm_cortexM_math.uvprojx
   *
   *
   * The libraries can be built by opening the arm_cortexM_math.uvprojx project in MDK-ARM, selecting a specific target, and defining the optional pre processor MACROs detailed above.
   *
   * Pre-processor Macros
   * ------------
   *
   * Each library project have differant pre-processor macros.
   *
   * - UNALIGNED_SUPPORT_DISABLE:
   *
   * Define macro UNALIGNED_SUPPORT_DISABLE, If the silicon does not support unaligned memory access
   *
   * - ARM_MATH_BIG_ENDIAN:
   *
   * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets.
   *
   * - ARM_MATH_MATRIX_CHECK:
   *
   * Define macro ARM_MATH_MATRIX_CHECK for checking on the input and output sizes of matrices
   *
   * - ARM_MATH_ROUNDING:
   *
   * Define macro ARM_MATH_ROUNDING for rounding on support functions
   *
   * - ARM_MATH_CMx:
   *
   * Define macro ARM_MATH_CM4 for building the library on Cortex-M4 target, ARM_MATH_CM3 for building library on Cortex-M3 target
   * and ARM_MATH_CM0 for building library on Cortex-M0 target, ARM_MATH_CM0PLUS for building library on Cortex-M0+ target, and
   * ARM_MATH_CM7 for building the library on cortex-M7.
   *
   * - __FPU_PRESENT:
   *
   * Initialize macro __FPU_PRESENT = 1 when building on FPU supported Targets. Enable this macro for M4bf and M4lf libraries
   *
   * <hr>
   * CMSIS-DSP in ARM::CMSIS Pack
   * -----------------------------
   *
   * The following files relevant to CMSIS-DSP are present in the <b>ARM::CMSIS</b> Pack directories:
   * |File/Folder                   |Content                                                                 |
   * |------------------------------|------------------------------------------------------------------------|
   * |\b CMSIS\\Documentation\\DSP  | This documentation                                                     |
   * |\b CMSIS\\DSP_Lib             | Software license agreement (license.txt)                               |
   * |\b CMSIS\\DSP_Lib\\Examples   | Example projects demonstrating the usage of the library functions      |
   * |\b CMSIS\\DSP_Lib\\Source     | Source files for rebuilding the library                                |
   *
   * <hr>
   * Revision History of CMSIS-DSP
   * ------------
   * Please refer to \ref ChangeLog_pg.
   *
   * Copyright Notice
   * ------------
   *
   * Copyright (C) 2010-2015 ARM Limited. All rights reserved.
   */


/**
 * @defgroup groupMath Basic Math Functions
 */

/**
 * @defgroup groupFastMath Fast Math Functions
 * This set of functions provides a fast approximation to sine, cosine, and square root.
 * As compared to most of the other functions in the CMSIS math library, the fast math functions
 * operate on individual values and not arrays.
 * There are separate functions for Q15, Q31, and floating-point data.
 *
 */

/**
 * @defgroup groupCmplxMath Complex Math Functions
 * This set of functions operates on complex data vectors.
 * The data in the complex arrays is stored in an interleaved fashion
 * (real, imag, real, imag, ...).
 * In the API functions, the number of samples in a complex array refers
 * to the number of complex values; the array contains twice this number of
 * real values.
 */

/**
 * @defgroup groupFilters Filtering Functions
 */

/**
 * @defgroup groupMatrix Matrix Functions
 *
 * This set of functions provides basic matrix math operations.
 * The functions operate on matrix data structures.  For example,
 * the type
 * definition for the floating-point matrix structure is shown
 * below:
 * <pre>
 *     typedef struct
 *     {
 *       uint16_t numRows;     // number of rows of the matrix.
 *       uint16_t numCols;     // number of columns of the matrix.
 *       float32_t *pData;     // points to the data of the matrix.
 *     } arm_matrix_instance_f32;
 * </pre>
 * There are similar definitions for Q15 and Q31 data types.
 *
 * The structure specifies the size of the matrix and then points to
 * an array of data.  The array is of size <code>numRows X numCols</code>
 * and the values are arranged in row order.  That is, the
 * matrix element (i, j) is stored at:
 * <pre>
 *     pData[i*numCols + j]
 * </pre>
 *
 * \par Init Functions
 * There is an associated initialization function for each type of matrix
 * data structure.
 * The initialization function sets the values of the internal structure fields.
 * Refer to the function <code>arm_mat_init_f32()</code>, <code>arm_mat_init_q31()</code>
 * and <code>arm_mat_init_q15()</code> for floating-point, Q31 and Q15 types,  respectively.
 *
 * \par
 * Use of the initialization function is optional. However, if initialization function is used
 * then the instance structure cannot be placed into a const data section.
 * To place the instance structure in a const data
 * section, manually initialize the data structure.  For example:
 * <pre>
 * <code>arm_matrix_instance_f32 S = {nRows, nColumns, pData};</code>
 * <code>arm_matrix_instance_q31 S = {nRows, nColumns, pData};</code>
 * <code>arm_matrix_instance_q15 S = {nRows, nColumns, pData};</code>
 * </pre>
 * where <code>nRows</code> specifies the number of rows, <code>nColumns</code>
 * specifies the number of columns, and <code>pData</code> points to the
 * data array.
 *
 * \par Size Checking
 * By default all of the matrix functions perform size checking on the input and
 * output matrices.  For example, the matrix addition function verifies that the
 * two input matrices and the output matrix all have the same number of rows and
 * columns.  If the size check fails the functions return:
 * <pre>
 *     ARM_MATH_SIZE_MISMATCH
 * </pre>
 * Otherwise the functions return
 * <pre>
 *     ARM_MATH_SUCCESS
 * </pre>
 * There is some overhead associated with this matrix size checking.
 * The matrix size checking is enabled via the \#define
 * <pre>
 *     ARM_MATH_MATRIX_CHECK
 * </pre>
 * within the library project settings.  By default this macro is defined
 * and size checking is enabled.  By changing the project settings and
 * undefining this macro size checking is eliminated and the functions
 * run a bit faster.  With size checking disabled the functions always
 * return <code>ARM_MATH_SUCCESS</code>.
 */

/**
 * @defgroup groupTransforms Transform Functions
 */

/**
 * @defgroup groupController Controller Functions
 */

/**
 * @defgroup groupStats Statistics Functions
 */
/**
 * @defgroup groupSupport Support Functions
 */

/**
 * @defgroup groupInterpolation Interpolation Functions
 * These functions perform 1- and 2-dimensional interpolation of data.
 * Linear interpolation is used for 1-dimensional data and
 * bilinear interpolation is used for 2-dimensional data.
 */

/**
 * @defgroup groupExamples Examples
 */
#ifndef _ARM_MATH_H
#define _ARM_MATH_H

/* ignore some GCC warnings */
#if defined ( __GNUC__ )
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wsign-conversion"
#pragma GCC diagnostic ignored "-Wconversion"
#pragma GCC diagnostic ignored "-Wunused-parameter"
#endif

#define __CMSIS_GENERIC         /* disable NVIC and Systick functions */

#if defined(ARM_MATH_CM7)
  #include "core_cm7.h"
#elif defined (ARM_MATH_CM4)
  #include "core_cm4.h"
#elif defined (ARM_MATH_CM3)
  #include "core_cm3.h"
#elif defined (ARM_MATH_CM0)
  #include "core_cm0.h"
  #define ARM_MATH_CM0_FAMILY
#elif defined (ARM_MATH_CM0PLUS)
  #include "core_cm0plus.h"
  #define ARM_MATH_CM0_FAMILY
#else
  #error "Define according the used Cortex core ARM_MATH_CM7, ARM_MATH_CM4, ARM_MATH_CM3, ARM_MATH_CM0PLUS or ARM_MATH_CM0"
#endif

#undef  __CMSIS_GENERIC         /* enable NVIC and Systick functions */
#include "string.h"
#include "math.h"
#ifdef   __cplusplus
extern "C"
{
#endif


  /**
   * @brief Macros required for reciprocal calculation in Normalized LMS
   */

#define DELTA_Q31          (0x100)
#define DELTA_Q15          0x5
#define INDEX_MASK         0x0000003F
#ifndef PI
#define PI                 3.14159265358979f
#endif

  /**
   * @brief Macros required for SINE and COSINE Fast math approximations
   */

#define FAST_MATH_TABLE_SIZE  512
#define FAST_MATH_Q31_SHIFT   (32 - 10)
#define FAST_MATH_Q15_SHIFT   (16 - 10)
#define CONTROLLER_Q31_SHIFT  (32 - 9)
#define TABLE_SIZE  256
#define TABLE_SPACING_Q31     0x400000
#define TABLE_SPACING_Q15     0x80

  /**
   * @brief Macros required for SINE and COSINE Controller functions
   */
  /* 1.31(q31) Fixed value of 2/360 */
  /* -1 to +1 is divided into 360 values so total spacing is (2/360) */
#define INPUT_SPACING         0xB60B61

  /**
   * @brief Macro for Unaligned Support
   */
#ifndef UNALIGNED_SUPPORT_DISABLE
    #define ALIGN4
#else
  #if defined  (__GNUC__)
    #define ALIGN4 __attribute__((aligned(4)))
  #else
    #define ALIGN4 __align(4)
  #endif
#endif   /* #ifndef UNALIGNED_SUPPORT_DISABLE */

  /**
   * @brief Error status returned by some functions in the library.
   */

  typedef enum
  {
    ARM_MATH_SUCCESS = 0,                /**< No error */
    ARM_MATH_ARGUMENT_ERROR = -1,        /**< One or more arguments are incorrect */
    ARM_MATH_LENGTH_ERROR = -2,          /**< Length of data buffer is incorrect */
    ARM_MATH_SIZE_MISMATCH = -3,         /**< Size of matrices is not compatible with the operation. */
    ARM_MATH_NANINF = -4,                /**< Not-a-number (NaN) or infinity is generated */
    ARM_MATH_SINGULAR = -5,              /**< Generated by matrix inversion if the input matrix is singular and cannot be inverted. */
    ARM_MATH_TEST_FAILURE = -6           /**< Test Failed  */
  } arm_status;

  /**
   * @brief 8-bit fractional data type in 1.7 format.
   */
  typedef int8_t q7_t;

  /**
   * @brief 16-bit fractional data type in 1.15 format.
   */
  typedef int16_t q15_t;

  /**
   * @brief 32-bit fractional data type in 1.31 format.
   */
  typedef int32_t q31_t;

  /**
   * @brief 64-bit fractional data type in 1.63 format.
   */
  typedef int64_t q63_t;

  /**
   * @brief 32-bit floating-point type definition.
   */
  typedef float float32_t;

  /**
   * @brief 64-bit floating-point type definition.
   */
  typedef double float64_t;

  /**
   * @brief definition to read/write two 16 bit values.
   */
#if defined __CC_ARM
  #define __SIMD32_TYPE int32_t __packed
  #define CMSIS_UNUSED __attribute__((unused))

#elif defined(__ARMCC_VERSION) && (__ARMCC_VERSION >= 6010050)
  #define __SIMD32_TYPE int32_t
  #define CMSIS_UNUSED __attribute__((unused))

#elif defined __GNUC__
  #define __SIMD32_TYPE int32_t
  #define CMSIS_UNUSED __attribute__((unused))

#elif defined __ICCARM__
  #define __SIMD32_TYPE int32_t __packed
  #define CMSIS_UNUSED

#elif defined __CSMC__
  #define __SIMD32_TYPE int32_t
  #define CMSIS_UNUSED

#elif defined __TASKING__
  #define __SIMD32_TYPE __unaligned int32_t
  #define CMSIS_UNUSED

#else
  #error Unknown compiler
#endif

#define __SIMD32(addr)        (*(__SIMD32_TYPE **) & (addr))
#define __SIMD32_CONST(addr)  ((__SIMD32_TYPE *)(addr))
#define _SIMD32_OFFSET(addr)  (*(__SIMD32_TYPE *)  (addr))
#define __SIMD64(addr)        (*(int64_t **) & (addr))

#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)
  /**
   * @brief definition to pack two 16 bit values.
   */
#define __PKHBT(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0x0000FFFF) | \
                                         (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
#define __PKHTB(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0xFFFF0000) | \
                                         (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF)  )

#endif


   /**
   * @brief definition to pack four 8 bit values.
   */
#ifndef ARM_MATH_BIG_ENDIAN

#define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) <<  0) & (int32_t)0x000000FF) | \
                                (((int32_t)(v1) <<  8) & (int32_t)0x0000FF00) | \
                                (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) | \
                                (((int32_t)(v3) << 24) & (int32_t)0xFF000000)  )
#else

#define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) <<  0) & (int32_t)0x000000FF) | \
                                (((int32_t)(v2) <<  8) & (int32_t)0x0000FF00) | \
                                (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) | \
                                (((int32_t)(v0) << 24) & (int32_t)0xFF000000)  )

#endif


  /**
   * @brief Clips Q63 to Q31 values.
   */
  static __INLINE q31_t clip_q63_to_q31(
  q63_t x)
  {
    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
      ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x;
  }

  /**
   * @brief Clips Q63 to Q15 values.
   */
  static __INLINE q15_t clip_q63_to_q15(
  q63_t x)
  {
    return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
      ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15);
  }

  /**
   * @brief Clips Q31 to Q7 values.
   */
  static __INLINE q7_t clip_q31_to_q7(
  q31_t x)
  {
    return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ?
      ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x;
  }

  /**
   * @brief Clips Q31 to Q15 values.
   */
  static __INLINE q15_t clip_q31_to_q15(
  q31_t x)
  {
    return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ?
      ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x;
  }

  /**
   * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format.
   */

  static __INLINE q63_t mult32x64(
  q63_t x,
  q31_t y)
  {
    return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
            (((q63_t) (x >> 32) * y)));
  }

/*
  #if defined (ARM_MATH_CM0_FAMILY) && defined ( __CC_ARM   )
  #define __CLZ __clz
  #endif
 */
/* note: function can be removed when all toolchain support __CLZ for Cortex-M0 */
#if defined (ARM_MATH_CM0_FAMILY) && ((defined (__ICCARM__))  )
  static __INLINE uint32_t __CLZ(
  q31_t data);

  static __INLINE uint32_t __CLZ(
  q31_t data)
  {
    uint32_t count = 0;
    uint32_t mask = 0x80000000;

    while((data & mask) == 0)
    {
      count += 1u;
      mask = mask >> 1u;
    }

    return (count);
  }
#endif

  /**
   * @brief Function to Calculates 1/in (reciprocal) value of Q31 Data type.
   */

  static __INLINE uint32_t arm_recip_q31(
  q31_t in,
  q31_t * dst,
  q31_t * pRecipTable)
  {
    q31_t out;
    uint32_t tempVal;
    uint32_t index, i;
    uint32_t signBits;

    if(in > 0)
    {
      signBits = ((uint32_t) (__CLZ( in) - 1));
    }
    else
    {
      signBits = ((uint32_t) (__CLZ(-in) - 1));
    }

    /* Convert input sample to 1.31 format */
    in = (in << signBits);

    /* calculation of index for initial approximated Val */
    index = (uint32_t)(in >> 24);
    index = (index & INDEX_MASK);

    /* 1.31 with exp 1 */
    out = pRecipTable[index];

    /* calculation of reciprocal value */
    /* running approximation for two iterations */
    for (i = 0u; i < 2u; i++)
    {
      tempVal = (uint32_t) (((q63_t) in * out) >> 31);
      tempVal = 0x7FFFFFFFu - tempVal;
      /*      1.31 with exp 1 */
      /* out = (q31_t) (((q63_t) out * tempVal) >> 30); */
      out = clip_q63_to_q31(((q63_t) out * tempVal) >> 30);
    }

    /* write output */
    *dst = out;

    /* return num of signbits of out = 1/in value */
    return (signBits + 1u);
  }


  /**
   * @brief Function to Calculates 1/in (reciprocal) value of Q15 Data type.
   */
  static __INLINE uint32_t arm_recip_q15(
  q15_t in,
  q15_t * dst,
  q15_t * pRecipTable)
  {
    q15_t out = 0;
    uint32_t tempVal = 0;
    uint32_t index = 0, i = 0;
    uint32_t signBits = 0;

    if(in > 0)
    {
      signBits = ((uint32_t)(__CLZ( in) - 17));
    }
    else
    {
      signBits = ((uint32_t)(__CLZ(-in) - 17));
    }

    /* Convert input sample to 1.15 format */
    in = (in << signBits);

    /* calculation of index for initial approximated Val */
    index = (uint32_t)(in >>  8);
    index = (index & INDEX_MASK);

    /*      1.15 with exp 1  */
    out = pRecipTable[index];

    /* calculation of reciprocal value */
    /* running approximation for two iterations */
    for (i = 0u; i < 2u; i++)
    {
      tempVal = (uint32_t) (((q31_t) in * out) >> 15);
      tempVal = 0x7FFFu - tempVal;
      /*      1.15 with exp 1 */
      out = (q15_t) (((q31_t) out * tempVal) >> 14);
      /* out = clip_q31_to_q15(((q31_t) out * tempVal) >> 14); */
    }

    /* write output */
    *dst = out;

    /* return num of signbits of out = 1/in value */
    return (signBits + 1);
  }


  /*
   * @brief C custom defined intrinisic function for only M0 processors
   */
#if defined(ARM_MATH_CM0_FAMILY)
  static __INLINE q31_t __SSAT(
  q31_t x,
  uint32_t y)
  {
    int32_t posMax, negMin;
    uint32_t i;

    posMax = 1;
    for (i = 0; i < (y - 1); i++)
    {
      posMax = posMax * 2;
    }

    if(x > 0)
    {
      posMax = (posMax - 1);

      if(x > posMax)
      {
        x = posMax;
      }
    }
    else
    {
      negMin = -posMax;

      if(x < negMin)
      {
        x = negMin;
      }
    }
    return (x);
  }
#endif /* end of ARM_MATH_CM0_FAMILY */


  /*
   * @brief C custom defined intrinsic function for M3 and M0 processors
   */
#if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)

  /*
   * @brief C custom defined QADD8 for M3 and M0 processors
   */
  static __INLINE uint32_t __QADD8(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s, t, u;

    r = __SSAT(((((q31_t)x << 24) >> 24) + (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF;
    s = __SSAT(((((q31_t)x << 16) >> 24) + (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF;
    t = __SSAT(((((q31_t)x <<  8) >> 24) + (((q31_t)y <<  8) >> 24)), 8) & (int32_t)0x000000FF;
    u = __SSAT(((((q31_t)x      ) >> 24) + (((q31_t)y      ) >> 24)), 8) & (int32_t)0x000000FF;

    return ((uint32_t)((u << 24) | (t << 16) | (s <<  8) | (r      )));
  }


  /*
   * @brief C custom defined QSUB8 for M3 and M0 processors
   */
  static __INLINE uint32_t __QSUB8(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s, t, u;

    r = __SSAT(((((q31_t)x << 24) >> 24) - (((q31_t)y << 24) >> 24)), 8) & (int32_t)0x000000FF;
    s = __SSAT(((((q31_t)x << 16) >> 24) - (((q31_t)y << 16) >> 24)), 8) & (int32_t)0x000000FF;
    t = __SSAT(((((q31_t)x <<  8) >> 24) - (((q31_t)y <<  8) >> 24)), 8) & (int32_t)0x000000FF;
    u = __SSAT(((((q31_t)x      ) >> 24) - (((q31_t)y      ) >> 24)), 8) & (int32_t)0x000000FF;

    return ((uint32_t)((u << 24) | (t << 16) | (s <<  8) | (r      )));
  }


  /*
   * @brief C custom defined QADD16 for M3 and M0 processors
   */
  static __INLINE uint32_t __QADD16(
  uint32_t x,
  uint32_t y)
  {
/*  q31_t r,     s;  without initialisation 'arm_offset_q15 test' fails  but 'intrinsic' tests pass! for armCC */
    q31_t r = 0, s = 0;

    r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
    s = __SSAT(((((q31_t)x      ) >> 16) + (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;

    return ((uint32_t)((s << 16) | (r      )));
  }


  /*
   * @brief C custom defined SHADD16 for M3 and M0 processors
   */
  static __INLINE uint32_t __SHADD16(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s;

    r = (((((q31_t)x << 16) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
    s = (((((q31_t)x      ) >> 16) + (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;

    return ((uint32_t)((s << 16) | (r      )));
  }


  /*
   * @brief C custom defined QSUB16 for M3 and M0 processors
   */
  static __INLINE uint32_t __QSUB16(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s;

    r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;
    s = __SSAT(((((q31_t)x      ) >> 16) - (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;

    return ((uint32_t)((s << 16) | (r      )));
  }


  /*
   * @brief C custom defined SHSUB16 for M3 and M0 processors
   */
  static __INLINE uint32_t __SHSUB16(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s;

    r = (((((q31_t)x << 16) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;
    s = (((((q31_t)x      ) >> 16) - (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;

    return ((uint32_t)((s << 16) | (r      )));
  }


  /*
   * @brief C custom defined QASX for M3 and M0 processors
   */
  static __INLINE uint32_t __QASX(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s;

    r = __SSAT(((((q31_t)x << 16) >> 16) - (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
    s = __SSAT(((((q31_t)x      ) >> 16) + (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;

    return ((uint32_t)((s << 16) | (r      )));
  }


  /*
   * @brief C custom defined SHASX for M3 and M0 processors
   */
  static __INLINE uint32_t __SHASX(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s;

    r = (((((q31_t)x << 16) >> 16) - (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
    s = (((((q31_t)x      ) >> 16) + (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;

    return ((uint32_t)((s << 16) | (r      )));
  }


  /*
   * @brief C custom defined QSAX for M3 and M0 processors
   */
  static __INLINE uint32_t __QSAX(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s;

    r = __SSAT(((((q31_t)x << 16) >> 16) + (((q31_t)y      ) >> 16)), 16) & (int32_t)0x0000FFFF;
    s = __SSAT(((((q31_t)x      ) >> 16) - (((q31_t)y << 16) >> 16)), 16) & (int32_t)0x0000FFFF;

    return ((uint32_t)((s << 16) | (r      )));
  }


  /*
   * @brief C custom defined SHSAX for M3 and M0 processors
   */
  static __INLINE uint32_t __SHSAX(
  uint32_t x,
  uint32_t y)
  {
    q31_t r, s;

    r = (((((q31_t)x << 16) >> 16) + (((q31_t)y      ) >> 16)) >> 1) & (int32_t)0x0000FFFF;
    s = (((((q31_t)x      ) >> 16) - (((q31_t)y << 16) >> 16)) >> 1) & (int32_t)0x0000FFFF;

    return ((uint32_t)((s << 16) | (r      )));
  }


  /*
   * @brief C custom defined SMUSDX for M3 and M0 processors
   */
  static __INLINE uint32_t __SMUSDX(
  uint32_t x,
  uint32_t y)
  {
    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) -
                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16))   ));
  }

  /*
   * @brief C custom defined SMUADX for M3 and M0 processors
   */
  static __INLINE uint32_t __SMUADX(
  uint32_t x,
  uint32_t y)
  {
    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16))   ));
  }


  /*
   * @brief C custom defined QADD for M3 and M0 processors
   */
  static __INLINE int32_t __QADD(
  int32_t x,
  int32_t y)
  {
    return ((int32_t)(clip_q63_to_q31((q63_t)x + (q31_t)y)));
  }


  /*
   * @brief C custom defined QSUB for M3 and M0 processors
   */
  static __INLINE int32_t __QSUB(
  int32_t x,
  int32_t y)
  {
    return ((int32_t)(clip_q63_to_q31((q63_t)x - (q31_t)y)));
  }


  /*
   * @brief C custom defined SMLAD for M3 and M0 processors
   */
  static __INLINE uint32_t __SMLAD(
  uint32_t x,
  uint32_t y,
  uint32_t sum)
  {
    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16)) +
                       ( ((q31_t)sum    )                                  )   ));
  }


  /*
   * @brief C custom defined SMLADX for M3 and M0 processors
   */
  static __INLINE uint32_t __SMLADX(
  uint32_t x,
  uint32_t y,
  uint32_t sum)
  {
    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
                       ( ((q31_t)sum    )                                  )   ));
  }


  /*
   * @brief C custom defined SMLSDX for M3 and M0 processors
   */
  static __INLINE uint32_t __SMLSDX(
  uint32_t x,
  uint32_t y,
  uint32_t sum)
  {
    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) -
                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
                       ( ((q31_t)sum    )                                  )   ));
  }


  /*
   * @brief C custom defined SMLALD for M3 and M0 processors
   */
  static __INLINE uint64_t __SMLALD(
  uint32_t x,
  uint32_t y,
  uint64_t sum)
  {
/*  return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) + ((q15_t) x * (q15_t) y)); */
    return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16)) +
                       ( ((q63_t)sum    )                                  )   ));
  }


  /*
   * @brief C custom defined SMLALDX for M3 and M0 processors
   */
  static __INLINE uint64_t __SMLALDX(
  uint32_t x,
  uint32_t y,
  uint64_t sum)
  {
/*  return (sum + ((q15_t) (x >> 16) * (q15_t) y)) + ((q15_t) x * (q15_t) (y >> 16)); */
    return ((uint64_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y      ) >> 16)) +
                       ((((q31_t)x      ) >> 16) * (((q31_t)y << 16) >> 16)) +
                       ( ((q63_t)sum    )                                  )   ));
  }


  /*
   * @brief C custom defined SMUAD for M3 and M0 processors
   */
  static __INLINE uint32_t __SMUAD(
  uint32_t x,
  uint32_t y)
  {
    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) +
                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16))   ));
  }


  /*
   * @brief C custom defined SMUSD for M3 and M0 processors
   */
  static __INLINE uint32_t __SMUSD(
  uint32_t x,
  uint32_t y)
  {
    return ((uint32_t)(((((q31_t)x << 16) >> 16) * (((q31_t)y << 16) >> 16)) -
                       ((((q31_t)x      ) >> 16) * (((q31_t)y      ) >> 16))   ));
  }


  /*
   * @brief C custom defined SXTB16 for M3 and M0 processors
   */
  static __INLINE uint32_t __SXTB16(
  uint32_t x)
  {
    return ((uint32_t)(((((q31_t)x << 24) >> 24) & (q31_t)0x0000FFFF) |
                       ((((q31_t)x <<  8) >>  8) & (q31_t)0xFFFF0000)  ));
  }

#endif /* defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY) */


  /**
   * @brief Instance structure for the Q7 FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;        /**< number of filter coefficients in the filter. */
    q7_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q7_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
  } arm_fir_instance_q7;

  /**
   * @brief Instance structure for the Q15 FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;         /**< number of filter coefficients in the filter. */
    q15_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q15_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
  } arm_fir_instance_q15;

  /**
   * @brief Instance structure for the Q31 FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;         /**< number of filter coefficients in the filter. */
    q31_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    q31_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps. */
  } arm_fir_instance_q31;

  /**
   * @brief Instance structure for the floating-point FIR filter.
   */
  typedef struct
  {
    uint16_t numTaps;     /**< number of filter coefficients in the filter. */
    float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
    float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
  } arm_fir_instance_f32;


  /**
   * @brief Processing function for the Q7 FIR filter.
   * @param[in]  S          points to an instance of the Q7 FIR filter structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_fir_q7(
  const arm_fir_instance_q7 * S,
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q7 FIR filter.
   * @param[in,out] S          points to an instance of the Q7 FIR structure.
   * @param[in]     numTaps    Number of filter coefficients in the filter.
   * @param[in]     pCoeffs    points to the filter coefficients.
   * @param[in]     pState     points to the state buffer.
   * @param[in]     blockSize  number of samples that are processed.
   */
  void arm_fir_init_q7(
  arm_fir_instance_q7 * S,
  uint16_t numTaps,
  q7_t * pCoeffs,
  q7_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q15 FIR filter.
   * @param[in]  S          points to an instance of the Q15 FIR structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_fir_q15(
  const arm_fir_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Processing function for the fast Q15 FIR filter for Cortex-M3 and Cortex-M4.
   * @param[in]  S          points to an instance of the Q15 FIR filter structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_fir_fast_q15(
  const arm_fir_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q15 FIR filter.
   * @param[in,out] S          points to an instance of the Q15 FIR filter structure.
   * @param[in]     numTaps    Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
   * @param[in]     pCoeffs    points to the filter coefficients.
   * @param[in]     pState     points to the state buffer.
   * @param[in]     blockSize  number of samples that are processed at a time.
   * @return The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_ARGUMENT_ERROR if
   * <code>numTaps</code> is not a supported value.
   */
  arm_status arm_fir_init_q15(
  arm_fir_instance_q15 * S,
  uint16_t numTaps,
  q15_t * pCoeffs,
  q15_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q31 FIR filter.
   * @param[in]  S          points to an instance of the Q31 FIR filter structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_fir_q31(
  const arm_fir_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Processing function for the fast Q31 FIR filter for Cortex-M3 and Cortex-M4.
   * @param[in]  S          points to an instance of the Q31 FIR structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_fir_fast_q31(
  const arm_fir_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q31 FIR filter.
   * @param[in,out] S          points to an instance of the Q31 FIR structure.
   * @param[in]     numTaps    Number of filter coefficients in the filter.
   * @param[in]     pCoeffs    points to the filter coefficients.
   * @param[in]     pState     points to the state buffer.
   * @param[in]     blockSize  number of samples that are processed at a time.
   */
  void arm_fir_init_q31(
  arm_fir_instance_q31 * S,
  uint16_t numTaps,
  q31_t * pCoeffs,
  q31_t * pState,
  uint32_t blockSize);


  /**
   * @brief Processing function for the floating-point FIR filter.
   * @param[in]  S          points to an instance of the floating-point FIR structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_fir_f32(
  const arm_fir_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the floating-point FIR filter.
   * @param[in,out] S          points to an instance of the floating-point FIR filter structure.
   * @param[in]     numTaps    Number of filter coefficients in the filter.
   * @param[in]     pCoeffs    points to the filter coefficients.
   * @param[in]     pState     points to the state buffer.
   * @param[in]     blockSize  number of samples that are processed at a time.
   */
  void arm_fir_init_f32(
  arm_fir_instance_f32 * S,
  uint16_t numTaps,
  float32_t * pCoeffs,
  float32_t * pState,
  uint32_t blockSize);


  /**
   * @brief Instance structure for the Q15 Biquad cascade filter.
   */
  typedef struct
  {
    int8_t numStages;        /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    q15_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
    q15_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
    int8_t postShift;        /**< Additional shift, in bits, applied to each output sample. */
  } arm_biquad_casd_df1_inst_q15;

  /**
   * @brief Instance structure for the Q31 Biquad cascade filter.
   */
  typedef struct
  {
    uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    q31_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
    q31_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
    uint8_t postShift;       /**< Additional shift, in bits, applied to each output sample. */
  } arm_biquad_casd_df1_inst_q31;

  /**
   * @brief Instance structure for the floating-point Biquad cascade filter.
   */
  typedef struct
  {
    uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
    float32_t *pState;       /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
    float32_t *pCoeffs;      /**< Points to the array of coefficients.  The array is of length 5*numStages. */
  } arm_biquad_casd_df1_inst_f32;


  /**
   * @brief Processing function for the Q15 Biquad cascade filter.
   * @param[in]  S          points to an instance of the Q15 Biquad cascade structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_biquad_cascade_df1_q15(
  const arm_biquad_casd_df1_inst_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q15 Biquad cascade filter.
   * @param[in,out] S          points to an instance of the Q15 Biquad cascade structure.
   * @param[in]     numStages  number of 2nd order stages in the filter.
   * @param[in]     pCoeffs    points to the filter coefficients.
   * @param[in]     pState     points to the state buffer.
   * @param[in]     postShift  Shift to be applied to the output. Varies according to the coefficients format
   */
  void arm_biquad_cascade_df1_init_q15(
  arm_biquad_casd_df1_inst_q15 * S,
  uint8_t numStages,
  q15_t * pCoeffs,
  q15_t * pState,
  int8_t postShift);


  /**
   * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
   * @param[in]  S          points to an instance of the Q15 Biquad cascade structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_biquad_cascade_df1_fast_q15(
  const arm_biquad_casd_df1_inst_q15 * S,
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Processing function for the Q31 Biquad cascade filter
   * @param[in]  S          points to an instance of the Q31 Biquad cascade structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_biquad_cascade_df1_q31(
  const arm_biquad_casd_df1_inst_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
   * @param[in]  S          points to an instance of the Q31 Biquad cascade structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_biquad_cascade_df1_fast_q31(
  const arm_biquad_casd_df1_inst_q31 * S,
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the Q31 Biquad cascade filter.
   * @param[in,out] S          points to an instance of the Q31 Biquad cascade structure.
   * @param[in]     numStages  number of 2nd order stages in the filter.
   * @param[in]     pCoeffs    points to the filter coefficients.
   * @param[in]     pState     points to the state buffer.
   * @param[in]     postShift  Shift to be applied to the output. Varies according to the coefficients format
   */
  void arm_biquad_cascade_df1_init_q31(
  arm_biquad_casd_df1_inst_q31 * S,
  uint8_t numStages,
  q31_t * pCoeffs,
  q31_t * pState,
  int8_t postShift);


  /**
   * @brief Processing function for the floating-point Biquad cascade filter.
   * @param[in]  S          points to an instance of the floating-point Biquad cascade structure.
   * @param[in]  pSrc       points to the block of input data.
   * @param[out] pDst       points to the block of output data.
   * @param[in]  blockSize  number of samples to process.
   */
  void arm_biquad_cascade_df1_f32(
  const arm_biquad_casd_df1_inst_f32 * S,
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Initialization function for the floating-point Biquad cascade filter.
   * @param[in,out] S          points to an instance of the floating-point Biquad cascade structure.
   * @param[in]     numStages  number of 2nd order stages in the filter.
   * @param[in]     pCoeffs    points to the filter coefficients.
   * @param[in]     pState     points to the state buffer.
   */
  void arm_biquad_cascade_df1_init_f32(
  arm_biquad_casd_df1_inst_f32 * S,
  uint8_t numStages,
  float32_t * pCoeffs,
  float32_t * pState);


  /**
   * @brief Instance structure for the floating-point matrix structure.
   */
  typedef struct
  {
    uint16_t numRows;     /**< number of rows of the matrix.     */
    uint16_t numCols;     /**< number of columns of the matrix.  */
    float32_t *pData;     /**< points to the data of the matrix. */
  } arm_matrix_instance_f32;


  /**
   * @brief Instance structure for the floating-point matrix structure.
   */
  typedef struct
  {
    uint16_t numRows;     /**< number of rows of the matrix.     */
    uint16_t numCols;     /**< number of columns of the matrix.  */
    float64_t *pData;     /**< points to the data of the matrix. */
  } arm_matrix_instance_f64;

  /**
   * @brief Instance structure for the Q15 matrix structure.
   */
  typedef struct
  {
    uint16_t numRows;     /**< number of rows of the matrix.     */
    uint16_t numCols;     /**< number of columns of the matrix.  */
    q15_t *pData;         /**< points to the data of the matrix. */
  } arm_matrix_instance_q15;

  /**
   * @brief Instance structure for the Q31 matrix structure.
   */
  typedef struct
  {
    uint16_t numRows;     /**< number of rows of the matrix.     */
    uint16_t numCols;     /**< number of columns of the matrix.  */
    q31_t *pData;         /**< points to the data of the matrix. */
  } arm_matrix_instance_q31;


  /**
   * @brief Floating-point matrix addition.
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_add_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);


  /**
   * @brief Q15 matrix addition.
   * @param[in]   pSrcA  points to the first input matrix structure
   * @param[in]   pSrcB  points to the second input matrix structure
   * @param[out]  pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_add_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst);


  /**
   * @brief Q31 matrix addition.
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_add_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Floating-point, complex, matrix multiplication.
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_cmplx_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);


  /**
   * @brief Q15, complex,  matrix multiplication.
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_cmplx_mult_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst,
  q15_t * pScratch);


  /**
   * @brief Q31, complex, matrix multiplication.
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_cmplx_mult_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Floating-point matrix transpose.
   * @param[in]  pSrc  points to the input matrix
   * @param[out] pDst  points to the output matrix
   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_trans_f32(
  const arm_matrix_instance_f32 * pSrc,
  arm_matrix_instance_f32 * pDst);


  /**
   * @brief Q15 matrix transpose.
   * @param[in]  pSrc  points to the input matrix
   * @param[out] pDst  points to the output matrix
   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_trans_q15(
  const arm_matrix_instance_q15 * pSrc,
  arm_matrix_instance_q15 * pDst);


  /**
   * @brief Q31 matrix transpose.
   * @param[in]  pSrc  points to the input matrix
   * @param[out] pDst  points to the output matrix
   * @return    The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_trans_q31(
  const arm_matrix_instance_q31 * pSrc,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Floating-point matrix multiplication
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_mult_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);


  /**
   * @brief Q15 matrix multiplication
   * @param[in]  pSrcA   points to the first input matrix structure
   * @param[in]  pSrcB   points to the second input matrix structure
   * @param[out] pDst    points to output matrix structure
   * @param[in]  pState  points to the array for storing intermediate results
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_mult_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst,
  q15_t * pState);


  /**
   * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
   * @param[in]  pSrcA   points to the first input matrix structure
   * @param[in]  pSrcB   points to the second input matrix structure
   * @param[out] pDst    points to output matrix structure
   * @param[in]  pState  points to the array for storing intermediate results
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_mult_fast_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst,
  q15_t * pState);


  /**
   * @brief Q31 matrix multiplication
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_mult_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_mult_fast_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Floating-point matrix subtraction
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_sub_f32(
  const arm_matrix_instance_f32 * pSrcA,
  const arm_matrix_instance_f32 * pSrcB,
  arm_matrix_instance_f32 * pDst);


  /**
   * @brief Q15 matrix subtraction
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_sub_q15(
  const arm_matrix_instance_q15 * pSrcA,
  const arm_matrix_instance_q15 * pSrcB,
  arm_matrix_instance_q15 * pDst);


  /**
   * @brief Q31 matrix subtraction
   * @param[in]  pSrcA  points to the first input matrix structure
   * @param[in]  pSrcB  points to the second input matrix structure
   * @param[out] pDst   points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_sub_q31(
  const arm_matrix_instance_q31 * pSrcA,
  const arm_matrix_instance_q31 * pSrcB,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief Floating-point matrix scaling.
   * @param[in]  pSrc   points to the input matrix
   * @param[in]  scale  scale factor
   * @param[out] pDst   points to the output matrix
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_scale_f32(
  const arm_matrix_instance_f32 * pSrc,
  float32_t scale,
  arm_matrix_instance_f32 * pDst);


  /**
   * @brief Q15 matrix scaling.
   * @param[in]  pSrc        points to input matrix
   * @param[in]  scaleFract  fractional portion of the scale factor
   * @param[in]  shift       number of bits to shift the result by
   * @param[out] pDst        points to output matrix
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_scale_q15(
  const arm_matrix_instance_q15 * pSrc,
  q15_t scaleFract,
  int32_t shift,
  arm_matrix_instance_q15 * pDst);


  /**
   * @brief Q31 matrix scaling.
   * @param[in]  pSrc        points to input matrix
   * @param[in]  scaleFract  fractional portion of the scale factor
   * @param[in]  shift       number of bits to shift the result by
   * @param[out] pDst        points to output matrix structure
   * @return     The function returns either
   * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   */
  arm_status arm_mat_scale_q31(
  const arm_matrix_instance_q31 * pSrc,
  q31_t scaleFract,
  int32_t shift,
  arm_matrix_instance_q31 * pDst);


  /**
   * @brief  Q31 matrix initialization.
   * @param[in,out] S         points to an instance of the floating-point matrix structure.
   * @param[in]     nRows     number of rows in the matrix.
   * @param[in]     nColumns  number of columns in the matrix.
   * @param[in]     pData     points to the matrix data array.
   */
  void arm_mat_init_q31(
  arm_matrix_instance_q31 * S,
  uint16_t nRows,
  uint16_t nColumns,
  q31_t * pData);


  /**
   * @brief  Q15 matrix initialization.
   * @param[in,out] S         points to an instance of the floating-point matrix structure.
   * @param[in]     nRows     number of rows in the matrix.
   * @param[in]     nColumns  number of columns in the matrix.
   * @param[in]     pData     points to the matrix data array.
   */
  void arm_mat_init_q15(
  arm_matrix_instance_q15 * S,
  uint16_t nRows,
  uint16_t nColumns,
  q15_t * pData);


  /**
   * @brief  Floating-point matrix initialization.
   * @param[in,out] S         points to an instance of the floating-point matrix structure.
   * @param[in]     nRows     number of rows in the matrix.
   * @param[in]     nColumns  number of columns in the matrix.
   * @param[in]     pData     points to the matrix data array.
   */
  void arm_mat_init_f32(
  arm_matrix_instance_f32 * S,
  uint16_t nRows,
  uint16_t nColumns,
  float32_t * pData);



  /**
   * @brief Instance structure for the Q15 PID Control.
   */
  typedef struct
  {
    q15_t A0;           /**< The derived gain, A0 = Kp + Ki + Kd . */
#ifdef ARM_MATH_CM0_FAMILY
    q15_t A1;
    q15_t A2;
#else
    q31_t A1;           /**< The derived gain A1 = -Kp - 2Kd | Kd.*/
#endif
    q15_t state[3];     /**< The state array of length 3. */
    q15_t Kp;           /**< The proportional gain. */
    q15_t Ki;           /**< The integral gain. */
    q15_t Kd;           /**< The derivative gain. */
  } arm_pid_instance_q15;

  /**
   * @brief Instance structure for the Q31 PID Control.
   */
  typedef struct
  {
    q31_t A0;            /**< The derived gain, A0 = Kp + Ki + Kd . */
    q31_t A1;            /**< The derived gain, A1 = -Kp - 2Kd. */
    q31_t A2;            /**< The derived gain, A2 = Kd . */
    q31_t state[3];      /**< The state array of length 3. */
    q31_t Kp;            /**< The proportional gain. */
    q31_t Ki;            /**< The integral gain. */
    q31_t Kd;            /**< The derivative gain. */
  } arm_pid_instance_q31;

  /**
   * @brief Instance structure for the floating-point PID Control.
   */
  typedef struct
  {
    float32_t A0;          /**< The derived gain, A0 = Kp + Ki + Kd . */
    float32_t A1;          /**< The derived gain, A1 = -Kp - 2Kd. */
    float32_t A2;          /**< The derived gain, A2 = Kd . */
    float32_t state[3];    /**< The state array of length 3. */
    float32_t Kp;          /**< The proportional gain. */
    float32_t Ki;          /**< The integral gain. */
    float32_t Kd;          /**< The derivative gain. */
  } arm_pid_instance_f32;



  /**
   * @brief  Initialization function for the floating-point PID Control.
   * @param[in,out] S               points to an instance of the PID structure.
   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   */
  void arm_pid_init_f32(
  arm_pid_instance_f32 * S,
  int32_t resetStateFlag);


  /**
   * @brief  Reset function for the floating-point PID Control.
   * @param[in,out] S  is an instance of the floating-point PID Control structure
   */
  void arm_pid_reset_f32(
  arm_pid_instance_f32 * S);


  /**
   * @brief  Initialization function for the Q31 PID Control.
   * @param[in,out] S               points to an instance of the Q15 PID structure.
   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   */
  void arm_pid_init_q31(
  arm_pid_instance_q31 * S,
  int32_t resetStateFlag);


  /**
   * @brief  Reset function for the Q31 PID Control.
   * @param[in,out] S   points to an instance of the Q31 PID Control structure
   */

  void arm_pid_reset_q31(
  arm_pid_instance_q31 * S);


  /**
   * @brief  Initialization function for the Q15 PID Control.
   * @param[in,out] S               points to an instance of the Q15 PID structure.
   * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   */
  void arm_pid_init_q15(
  arm_pid_instance_q15 * S,
  int32_t resetStateFlag);


  /**
   * @brief  Reset function for the Q15 PID Control.
   * @param[in,out] S  points to an instance of the q15 PID Control structure
   */
  void arm_pid_reset_q15(
  arm_pid_instance_q15 * S);


  /**
   * @brief Instance structure for the floating-point Linear Interpolate function.
   */
  typedef struct
  {
    uint32_t nValues;           /**< nValues */
    float32_t x1;               /**< x1 */
    float32_t xSpacing;         /**< xSpacing */
    float32_t *pYData;          /**< pointer to the table of Y values */
  } arm_linear_interp_instance_f32;

  /**
   * @brief Instance structure for the floating-point bilinear interpolation function.
   */
  typedef struct
  {
    uint16_t numRows;   /**< number of rows in the data table. */
    uint16_t numCols;   /**< number of columns in the data table. */
    float32_t *pData;   /**< points to the data table. */
  } arm_bilinear_interp_instance_f32;

   /**
   * @brief Instance structure for the Q31 bilinear interpolation function.
   */
  typedef struct
  {
    uint16_t numRows;   /**< number of rows in the data table. */
    uint16_t numCols;   /**< number of columns in the data table. */
    q31_t *pData;       /**< points to the data table. */
  } arm_bilinear_interp_instance_q31;

   /**
   * @brief Instance structure for the Q15 bilinear interpolation function.
   */
  typedef struct
  {
    uint16_t numRows;   /**< number of rows in the data table. */
    uint16_t numCols;   /**< number of columns in the data table. */
    q15_t *pData;       /**< points to the data table. */
  } arm_bilinear_interp_instance_q15;

   /**
   * @brief Instance structure for the Q15 bilinear interpolation function.
   */
  typedef struct
  {
    uint16_t numRows;   /**< number of rows in the data table. */
    uint16_t numCols;   /**< number of columns in the data table. */
    q7_t *pData;        /**< points to the data table. */
  } arm_bilinear_interp_instance_q7;


  /**
   * @brief Q7 vector multiplication.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_mult_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q15 vector multiplication.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_mult_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q31 vector multiplication.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_mult_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Floating-point vector multiplication.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_mult_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Instance structure for the Q15 CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                 /**< length of the FFT. */
    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    q15_t *pTwiddle;                 /**< points to the Sin twiddle factor table. */
    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
  } arm_cfft_radix2_instance_q15;

/* Deprecated */
  arm_status arm_cfft_radix2_init_q15(
  arm_cfft_radix2_instance_q15 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_q15(
  const arm_cfft_radix2_instance_q15 * S,
  q15_t * pSrc);


  /**
   * @brief Instance structure for the Q15 CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                 /**< length of the FFT. */
    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    q15_t *pTwiddle;                 /**< points to the twiddle factor table. */
    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
  } arm_cfft_radix4_instance_q15;

/* Deprecated */
  arm_status arm_cfft_radix4_init_q15(
  arm_cfft_radix4_instance_q15 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix4_q15(
  const arm_cfft_radix4_instance_q15 * S,
  q15_t * pSrc);

  /**
   * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                 /**< length of the FFT. */
    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    q31_t *pTwiddle;                 /**< points to the Twiddle factor table. */
    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
  } arm_cfft_radix2_instance_q31;

/* Deprecated */
  arm_status arm_cfft_radix2_init_q31(
  arm_cfft_radix2_instance_q31 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_q31(
  const arm_cfft_radix2_instance_q31 * S,
  q31_t * pSrc);

  /**
   * @brief Instance structure for the Q31 CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                 /**< length of the FFT. */
    uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    q31_t *pTwiddle;                 /**< points to the twiddle factor table. */
    uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
  } arm_cfft_radix4_instance_q31;

/* Deprecated */
  void arm_cfft_radix4_q31(
  const arm_cfft_radix4_instance_q31 * S,
  q31_t * pSrc);

/* Deprecated */
  arm_status arm_cfft_radix4_init_q31(
  arm_cfft_radix4_instance_q31 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

  /**
   * @brief Instance structure for the floating-point CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
    uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
    float32_t onebyfftLen;             /**< value of 1/fftLen. */
  } arm_cfft_radix2_instance_f32;

/* Deprecated */
  arm_status arm_cfft_radix2_init_f32(
  arm_cfft_radix2_instance_f32 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix2_f32(
  const arm_cfft_radix2_instance_f32 * S,
  float32_t * pSrc);

  /**
   * @brief Instance structure for the floating-point CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
    uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
    float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
    uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
    uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
    float32_t onebyfftLen;             /**< value of 1/fftLen. */
  } arm_cfft_radix4_instance_f32;

/* Deprecated */
  arm_status arm_cfft_radix4_init_f32(
  arm_cfft_radix4_instance_f32 * S,
  uint16_t fftLen,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

/* Deprecated */
  void arm_cfft_radix4_f32(
  const arm_cfft_radix4_instance_f32 * S,
  float32_t * pSrc);

  /**
   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    const q15_t *pTwiddle;             /**< points to the Twiddle factor table. */
    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
    uint16_t bitRevLength;             /**< bit reversal table length. */
  } arm_cfft_instance_q15;

void arm_cfft_q15(
    const arm_cfft_instance_q15 * S,
    q15_t * p1,
    uint8_t ifftFlag,
    uint8_t bitReverseFlag);

  /**
   * @brief Instance structure for the fixed-point CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    const q31_t *pTwiddle;             /**< points to the Twiddle factor table. */
    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
    uint16_t bitRevLength;             /**< bit reversal table length. */
  } arm_cfft_instance_q31;

void arm_cfft_q31(
    const arm_cfft_instance_q31 * S,
    q31_t * p1,
    uint8_t ifftFlag,
    uint8_t bitReverseFlag);

  /**
   * @brief Instance structure for the floating-point CFFT/CIFFT function.
   */
  typedef struct
  {
    uint16_t fftLen;                   /**< length of the FFT. */
    const float32_t *pTwiddle;         /**< points to the Twiddle factor table. */
    const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
    uint16_t bitRevLength;             /**< bit reversal table length. */
  } arm_cfft_instance_f32;

  void arm_cfft_f32(
  const arm_cfft_instance_f32 * S,
  float32_t * p1,
  uint8_t ifftFlag,
  uint8_t bitReverseFlag);

  /**
   * @brief Instance structure for the Q15 RFFT/RIFFT function.
   */
  typedef struct
  {
    uint32_t fftLenReal;                      /**< length of the real FFT. */
    uint8_t ifftFlagR;                        /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
    uint8_t bitReverseFlagR;                  /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
    uint32_t twidCoefRModifier;               /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    q15_t *pTwiddleAReal;                     /**< points to the real twiddle factor table. */
    q15_t *pTwiddleBReal;                     /**< points to the imag twiddle factor table. */
    const arm_cfft_instance_q15 *pCfft;       /**< points to the complex FFT instance. */
  } arm_rfft_instance_q15;

  arm_status arm_rfft_init_q15(
  arm_rfft_instance_q15 * S,
  uint32_t fftLenReal,
  uint32_t ifftFlagR,
  uint32_t bitReverseFlag);

  void arm_rfft_q15(
  const arm_rfft_instance_q15 * S,
  q15_t * pSrc,
  q15_t * pDst);

  /**
   * @brief Instance structure for the Q31 RFFT/RIFFT function.
   */
  typedef struct
  {
    uint32_t fftLenReal;                        /**< length of the real FFT. */
    uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
    uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
    uint32_t twidCoefRModifier;                 /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    q31_t *pTwiddleAReal;                       /**< points to the real twiddle factor table. */
    q31_t *pTwiddleBReal;                       /**< points to the imag twiddle factor table. */
    const arm_cfft_instance_q31 *pCfft;         /**< points to the complex FFT instance. */
  } arm_rfft_instance_q31;

  arm_status arm_rfft_init_q31(
  arm_rfft_instance_q31 * S,
  uint32_t fftLenReal,
  uint32_t ifftFlagR,
  uint32_t bitReverseFlag);

  void arm_rfft_q31(
  const arm_rfft_instance_q31 * S,
  q31_t * pSrc,
  q31_t * pDst);

  /**
   * @brief Instance structure for the floating-point RFFT/RIFFT function.
   */
  typedef struct
  {
    uint32_t fftLenReal;                        /**< length of the real FFT. */
    uint16_t fftLenBy2;                         /**< length of the complex FFT. */
    uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
    uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
    uint32_t twidCoefRModifier;                     /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
    float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
    float32_t *pTwiddleBReal;                   /**< points to the imag twiddle factor table. */
    arm_cfft_radix4_instance_f32 *pCfft;        /**< points to the complex FFT instance. */
  } arm_rfft_instance_f32;

  arm_status arm_rfft_init_f32(
  arm_rfft_instance_f32 * S,
  arm_cfft_radix4_instance_f32 * S_CFFT,
  uint32_t fftLenReal,
  uint32_t ifftFlagR,
  uint32_t bitReverseFlag);

  void arm_rfft_f32(
  const arm_rfft_instance_f32 * S,
  float32_t * pSrc,
  float32_t * pDst);

  /**
   * @brief Instance structure for the floating-point RFFT/RIFFT function.
   */
typedef struct
  {
    arm_cfft_instance_f32 Sint;      /**< Internal CFFT structure. */
    uint16_t fftLenRFFT;             /**< length of the real sequence */
    float32_t * pTwiddleRFFT;        /**< Twiddle factors real stage  */
  } arm_rfft_fast_instance_f32 ;

arm_status arm_rfft_fast_init_f32 (
   arm_rfft_fast_instance_f32 * S,
   uint16_t fftLen);

void arm_rfft_fast_f32(
  arm_rfft_fast_instance_f32 * S,
  float32_t * p, float32_t * pOut,
  uint8_t ifftFlag);

  /**
   * @brief Instance structure for the floating-point DCT4/IDCT4 function.
   */
  typedef struct
  {
    uint16_t N;                          /**< length of the DCT4. */
    uint16_t Nby2;                       /**< half of the length of the DCT4. */
    float32_t normalize;                 /**< normalizing factor. */
    float32_t *pTwiddle;                 /**< points to the twiddle factor table. */
    float32_t *pCosFactor;               /**< points to the cosFactor table. */
    arm_rfft_instance_f32 *pRfft;        /**< points to the real FFT instance. */
    arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */
  } arm_dct4_instance_f32;


  /**
   * @brief  Initialization function for the floating-point DCT4/IDCT4.
   * @param[in,out] S          points to an instance of floating-point DCT4/IDCT4 structure.
   * @param[in]     S_RFFT     points to an instance of floating-point RFFT/RIFFT structure.
   * @param[in]     S_CFFT     points to an instance of floating-point CFFT/CIFFT structure.
   * @param[in]     N          length of the DCT4.
   * @param[in]     Nby2       half of the length of the DCT4.
   * @param[in]     normalize  normalizing factor.
   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length.
   */
  arm_status arm_dct4_init_f32(
  arm_dct4_instance_f32 * S,
  arm_rfft_instance_f32 * S_RFFT,
  arm_cfft_radix4_instance_f32 * S_CFFT,
  uint16_t N,
  uint16_t Nby2,
  float32_t normalize);


  /**
   * @brief Processing function for the floating-point DCT4/IDCT4.
   * @param[in]     S              points to an instance of the floating-point DCT4/IDCT4 structure.
   * @param[in]     pState         points to state buffer.
   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
   */
  void arm_dct4_f32(
  const arm_dct4_instance_f32 * S,
  float32_t * pState,
  float32_t * pInlineBuffer);


  /**
   * @brief Instance structure for the Q31 DCT4/IDCT4 function.
   */
  typedef struct
  {
    uint16_t N;                          /**< length of the DCT4. */
    uint16_t Nby2;                       /**< half of the length of the DCT4. */
    q31_t normalize;                     /**< normalizing factor. */
    q31_t *pTwiddle;                     /**< points to the twiddle factor table. */
    q31_t *pCosFactor;                   /**< points to the cosFactor table. */
    arm_rfft_instance_q31 *pRfft;        /**< points to the real FFT instance. */
    arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */
  } arm_dct4_instance_q31;


  /**
   * @brief  Initialization function for the Q31 DCT4/IDCT4.
   * @param[in,out] S          points to an instance of Q31 DCT4/IDCT4 structure.
   * @param[in]     S_RFFT     points to an instance of Q31 RFFT/RIFFT structure
   * @param[in]     S_CFFT     points to an instance of Q31 CFFT/CIFFT structure
   * @param[in]     N          length of the DCT4.
   * @param[in]     Nby2       half of the length of the DCT4.
   * @param[in]     normalize  normalizing factor.
   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
   */
  arm_status arm_dct4_init_q31(
  arm_dct4_instance_q31 * S,
  arm_rfft_instance_q31 * S_RFFT,
  arm_cfft_radix4_instance_q31 * S_CFFT,
  uint16_t N,
  uint16_t Nby2,
  q31_t normalize);


  /**
   * @brief Processing function for the Q31 DCT4/IDCT4.
   * @param[in]     S              points to an instance of the Q31 DCT4 structure.
   * @param[in]     pState         points to state buffer.
   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
   */
  void arm_dct4_q31(
  const arm_dct4_instance_q31 * S,
  q31_t * pState,
  q31_t * pInlineBuffer);


  /**
   * @brief Instance structure for the Q15 DCT4/IDCT4 function.
   */
  typedef struct
  {
    uint16_t N;                          /**< length of the DCT4. */
    uint16_t Nby2;                       /**< half of the length of the DCT4. */
    q15_t normalize;                     /**< normalizing factor. */
    q15_t *pTwiddle;                     /**< points to the twiddle factor table. */
    q15_t *pCosFactor;                   /**< points to the cosFactor table. */
    arm_rfft_instance_q15 *pRfft;        /**< points to the real FFT instance. */
    arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */
  } arm_dct4_instance_q15;


  /**
   * @brief  Initialization function for the Q15 DCT4/IDCT4.
   * @param[in,out] S          points to an instance of Q15 DCT4/IDCT4 structure.
   * @param[in]     S_RFFT     points to an instance of Q15 RFFT/RIFFT structure.
   * @param[in]     S_CFFT     points to an instance of Q15 CFFT/CIFFT structure.
   * @param[in]     N          length of the DCT4.
   * @param[in]     Nby2       half of the length of the DCT4.
   * @param[in]     normalize  normalizing factor.
   * @return      arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
   */
  arm_status arm_dct4_init_q15(
  arm_dct4_instance_q15 * S,
  arm_rfft_instance_q15 * S_RFFT,
  arm_cfft_radix4_instance_q15 * S_CFFT,
  uint16_t N,
  uint16_t Nby2,
  q15_t normalize);


  /**
   * @brief Processing function for the Q15 DCT4/IDCT4.
   * @param[in]     S              points to an instance of the Q15 DCT4 structure.
   * @param[in]     pState         points to state buffer.
   * @param[in,out] pInlineBuffer  points to the in-place input and output buffer.
   */
  void arm_dct4_q15(
  const arm_dct4_instance_q15 * S,
  q15_t * pState,
  q15_t * pInlineBuffer);


  /**
   * @brief Floating-point vector addition.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_add_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q7 vector addition.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_add_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q15 vector addition.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_add_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q31 vector addition.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_add_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Floating-point vector subtraction.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_sub_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q7 vector subtraction.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_sub_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q15 vector subtraction.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_sub_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q31 vector subtraction.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_sub_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Multiplies a floating-point vector by a scalar.
   * @param[in]  pSrc       points to the input vector
   * @param[in]  scale      scale factor to be applied
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in the vector
   */
  void arm_scale_f32(
  float32_t * pSrc,
  float32_t scale,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Multiplies a Q7 vector by a scalar.
   * @param[in]  pSrc        points to the input vector
   * @param[in]  scaleFract  fractional portion of the scale value
   * @param[in]  shift       number of bits to shift the result by
   * @param[out] pDst        points to the output vector
   * @param[in]  blockSize   number of samples in the vector
   */
  void arm_scale_q7(
  q7_t * pSrc,
  q7_t scaleFract,
  int8_t shift,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Multiplies a Q15 vector by a scalar.
   * @param[in]  pSrc        points to the input vector
   * @param[in]  scaleFract  fractional portion of the scale value
   * @param[in]  shift       number of bits to shift the result by
   * @param[out] pDst        points to the output vector
   * @param[in]  blockSize   number of samples in the vector
   */
  void arm_scale_q15(
  q15_t * pSrc,
  q15_t scaleFract,
  int8_t shift,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Multiplies a Q31 vector by a scalar.
   * @param[in]  pSrc        points to the input vector
   * @param[in]  scaleFract  fractional portion of the scale value
   * @param[in]  shift       number of bits to shift the result by
   * @param[out] pDst        points to the output vector
   * @param[in]  blockSize   number of samples in the vector
   */
  void arm_scale_q31(
  q31_t * pSrc,
  q31_t scaleFract,
  int8_t shift,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q7 vector absolute value.
   * @param[in]  pSrc       points to the input buffer
   * @param[out] pDst       points to the output buffer
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_abs_q7(
  q7_t * pSrc,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Floating-point vector absolute value.
   * @param[in]  pSrc       points to the input buffer
   * @param[out] pDst       points to the output buffer
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_abs_f32(
  float32_t * pSrc,
  float32_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q15 vector absolute value.
   * @param[in]  pSrc       points to the input buffer
   * @param[out] pDst       points to the output buffer
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_abs_q15(
  q15_t * pSrc,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Q31 vector absolute value.
   * @param[in]  pSrc       points to the input buffer
   * @param[out] pDst       points to the output buffer
   * @param[in]  blockSize  number of samples in each vector
   */
  void arm_abs_q31(
  q31_t * pSrc,
  q31_t * pDst,
  uint32_t blockSize);


  /**
   * @brief Dot product of floating-point vectors.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[in]  blockSize  number of samples in each vector
   * @param[out] result     output result returned here
   */
  void arm_dot_prod_f32(
  float32_t * pSrcA,
  float32_t * pSrcB,
  uint32_t blockSize,
  float32_t * result);


  /**
   * @brief Dot product of Q7 vectors.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[in]  blockSize  number of samples in each vector
   * @param[out] result     output result returned here
   */
  void arm_dot_prod_q7(
  q7_t * pSrcA,
  q7_t * pSrcB,
  uint32_t blockSize,
  q31_t * result);


  /**
   * @brief Dot product of Q15 vectors.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[in]  blockSize  number of samples in each vector
   * @param[out] result     output result returned here
   */
  void arm_dot_prod_q15(
  q15_t * pSrcA,
  q15_t * pSrcB,
  uint32_t blockSize,
  q63_t * result);


  /**
   * @brief Dot product of Q31 vectors.
   * @param[in]  pSrcA      points to the first input vector
   * @param[in]  pSrcB      points to the second input vector
   * @param[in]  blockSize  number of samples in each vector
   * @param[out] result     output result returned here
   */
  void arm_dot_prod_q31(
  q31_t * pSrcA,
  q31_t * pSrcB,
  uint32_t blockSize,
  q63_t * result);


  /**
   * @brief  Shifts the elements of a Q7 vector a specified number of bits.
   * @param[in]  pSrc       points to the input vector
   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in the vector
   */
  void arm_shift_q7(
  q7_t * pSrc,
  int8_t shiftBits,
  q7_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Shifts the elements of a Q15 vector a specified number of bits.
   * @param[in]  pSrc       points to the input vector
   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in the vector
   */
  void arm_shift_q15(
  q15_t * pSrc,
  int8_t shiftBits,
  q15_t * pDst,
  uint32_t blockSize);


  /**
   * @brief  Shifts the elements of a Q31 vector a specified number of bits.
   * @param[in]  pSrc       points to the input vector
   * @param[in]  shiftBits  number of bits to shift.  A positive value shifts left; a negative value shifts right.
   * @param[out] pDst       points to the output vector
   * @param[in]  blockSize  number of samples in the vector
   */
  void arm_shift_q31(
  q31_t * pSrc,
  int8_t shif