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 * Copyright (c) 2003, 2006 Matteo Frigo
 * Copyright (c) 2003, 2006 Massachusetts Institute of Technology
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * GNU General Public License for more details.
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

/* $Id: ifftw.h,v 1.281 2006-02-10 14:18:39 athena Exp $ */

/* FFTW internal header file */
#ifndef __IFFTW_H__
#define __IFFTW_H__

#include "config.h"

#include <stdlib.h>           /* size_t */
#include <stdarg.h>           /* va_list */
#include <stddef.h>             /* ptrdiff_t */

# include <sys/types.h>

#if defined(_WIN32) && !defined(FREE_WINDOWS)

#ifdef _WIN64
typedef __int64 intptr_t;
typedef long intptr_t;

#ifdef _WIN64
typedef unsigned __int64 uintptr_t;
typedef unsigned long uintptr_t;

#elif defined(__linux__)

      /* Linux-i386, Linux-Alpha, Linux-ppc */
#include <stdint.h>

#elif defined (__APPLE__)

#include <inttypes.h>

#elif defined(FREE_WINDOWS)

#include <stdint.h>


      /* FreeBSD, Irix, Solaris */
#include <sys/types.h>

#endif /* ifdef platform for types */

/* Windows annoyances -- since tests/hook.c uses some internal
   FFTW functions, we need to given them the dllexport attribute
   under Windows when compiling as a DLL (see api/fftw3.h). */
#if defined(FFTW_EXTERN)
#elif (defined(FFTW_DLL) || defined(DLL_EXPORT)) \
 && (defined(_WIN32) || defined(__WIN32__))
#  define IFFTW_EXTERN extern __declspec(dllexport)
#  define IFFTW_EXTERN extern

/* determine precision and name-mangling scheme */
#define CONCAT(prefix, name) prefix ## name
#if defined(FFTW_SINGLE)
  typedef float R;
# define X(name) CONCAT(fftwf_, name)
#elif defined(FFTW_LDOUBLE)
  typedef long double R;
# define X(name) CONCAT(fftwl_, name)
  typedef double R;
# define X(name) CONCAT(fftw_, name)

  integral type large enough to contain a stride (what ``int'' should
  have been in the first place.
typedef ptrdiff_t INT;

/* dummy use of unused parameters to silence compiler warnings */
#define UNUSED(x) (void)x

#define FFT_SIGN (-1)  /* sign convention for forward transforms */

#define REGISTER_SOLVER(p, s) X(solver_register)(p, s)

#define STRINGIZEx(x) #x

#ifndef HAVE_K7
#define HAVE_K7 0

#if defined(HAVE_SSE) || defined(HAVE_SSE2) || defined(HAVE_ALTIVEC)
#define HAVE_SIMD 1
#define HAVE_SIMD 0

/* forward declarations */
typedef struct problem_s problem;
typedef struct plan_s plan;
typedef struct solver_s solver;
typedef struct planner_s planner;
typedef struct printer_s printer;
typedef struct scanner_s scanner;

/* alloca: */
#define MIN_ALIGNMENT 16

   /* use alloca if available */

#ifndef alloca
#ifdef __GNUC__
# define alloca __builtin_alloca
# ifdef _MSC_VER
#  include <malloc.h>
#  define alloca _alloca
# else
#   include <alloca.h>
#  else
#   ifdef _AIX
 #pragma alloca
#   else
#    ifndef alloca /* predefined by HP cc +Olibcalls */
void *alloca(size_t);
#    endif
#   endif
#  endif
# endif

#    define STACK_MALLOC(T, p, x)                     \
     {                                                \
         p = (T)alloca((x) + MIN_ALIGNMENT);                \
         p = (T)(((uintptr_t)p + (MIN_ALIGNMENT - 1)) &     \
               (~(uintptr_t)(MIN_ALIGNMENT - 1)));          \
#    define STACK_FREE(x) 
#  else /* HAVE_ALLOCA && !defined(MIN_ALIGNMENT) */
#    define STACK_MALLOC(T, p, x) p = (T)alloca(x) 
#    define STACK_FREE(x) 
#  endif

#else /* ! HAVE_ALLOCA */
   /* use malloc instead of alloca */
#  define STACK_MALLOC(T, p, x) p = (T)MALLOC(x, OTHER)
#  define STACK_FREE(x) X(ifree)(x)
#endif /* ! HAVE_ALLOCA */

/* define uintptr_t if it is not already defined */

#  if SIZEOF_VOID_P == 0
#    error sizeof void* is unknown!
     typedef unsigned int uintptr_t;
     typedef unsigned long uintptr_t;
     typedef unsigned long long uintptr_t;
#  else
#    error no unsigned integer type matches void* sizeof!
#  endif

/* We can do an optimization for copying pairs of (aligned) floats
   when in single precision if 2*float = double. */

#define FFTW_2R_IS_DOUBLE (defined(FFTW_SINGLE) \
                           && SIZEOF_FLOAT != 0 \
                           && SIZEOF_DOUBLE == 2*SIZEOF_FLOAT)

#define DOUBLE_ALIGNED(p) ((((uintptr_t)(p)) % sizeof(double)) == 0)

/* assert.c: */
IFFTW_EXTERN void X(assertion_failed)(const char *s, 
                              int line, const char *file);

/* always check */
#define CK(ex)                                   \
      (void)((ex) || (X(assertion_failed)(#ex, __LINE__, __FILE__), 0))

/* check only if debug enabled */
#define A(ex)                                    \
      (void)((ex) || (X(assertion_failed)(#ex, __LINE__, __FILE__), 0))
#define A(ex) /* nothing */

extern void X(debug)(const char *format, ...);
#define D X(debug)

/* kalloc.c: */
extern void *X(kernel_malloc)(size_t n);
extern void X(kernel_free)(void *p);

/* alloc.c: */

/* objects allocated by malloc, for statistical purposes */
enum malloc_tag {
     MALLOC_WHAT_LAST         /* must be last */

IFFTW_EXTERN void X(ifree)(void *ptr);
extern void X(ifree0)(void *ptr);


IFFTW_EXTERN void *X(malloc_debug)(size_t n, enum malloc_tag what,
                       const char *file, int line);
#define MALLOC(n, what) X(malloc_debug)(n, what, __FILE__, __LINE__)
#define NATIVE_MALLOC(n, what) MALLOC(n, what)
IFFTW_EXTERN void X(malloc_print_minfo)(int vrbose);

#else /* ! FFTW_DEBUG_MALLOC */

IFFTW_EXTERN void *X(malloc_plain)(size_t sz);
#define MALLOC(n, what)  X(malloc_plain)(n)
#define NATIVE_MALLOC(n, what) malloc(n)


#if defined(FFTW_DEBUG) && defined(FFTW_DEBUG_MALLOC) && defined(HAVE_THREADS)
extern int X(in_thread);
#  define IN_THREAD X(in_thread)
#  define THREAD_ON { int in_thread_save = X(in_thread); X(in_thread) = 1
#  define THREAD_OFF X(in_thread) = in_thread_save; }
#  define IN_THREAD 0
#  define THREAD_ON 
#  define THREAD_OFF 

/* low-resolution clock */

# include <sys/time.h>
# include <time.h>
#  include <sys/time.h>
# else
#  include <time.h>
# endif

#define gettimeofday BSDgettimeofday

typedef struct timeval crude_time;
typedef clock_t crude_time;

crude_time X(get_crude_time)(void);
double X(elapsed_since)(crude_time t0); /* time in seconds since t0 */

/* ops.c: */
 * ops counter.  The total number of additions is add + fma
 * and the total number of multiplications is mul + fma.
 * Total flops = add + mul + 2 * fma
typedef struct {
     double add;
     double mul;
     double fma;
     double other;
} opcnt;

void X(ops_zero)(opcnt *dst);
void X(ops_other)(INT o, opcnt *dst);
void X(ops_cpy)(const opcnt *src, opcnt *dst);

void X(ops_add)(const opcnt *a, const opcnt *b, opcnt *dst);
void X(ops_add2)(const opcnt *a, opcnt *dst);

/* dst = m * a + b */
void X(ops_madd)(INT m, const opcnt *a, const opcnt *b, opcnt *dst);

/* dst += m * a */
void X(ops_madd2)(INT m, const opcnt *a, opcnt *dst);

/* minmax.c: */
INT X(imax)(INT a, INT b);
INT X(imin)(INT a, INT b);

/* iabs.c: */
INT X(iabs)(INT a);

/* inline version */
#define IABS(x) (((x) < 0) ? (0 - (x)) : (x))

/* md5.c */

typedef unsigned int md5uint;
typedef unsigned long md5uint; /* at least 32 bits as per C standard */

typedef md5uint md5sig[4];

typedef struct {
     md5sig s; /* state and signature */

     /* fields not meant to be used outside md5.c: */
     unsigned char c[64]; /* stuff not yet processed */
     unsigned l;  /* total length.  Should be 64 bits long, but this is
                 good enough for us */
} md5;

void X(md5begin)(md5 *p);
void X(md5putb)(md5 *p, const void *d_, size_t len);
void X(md5puts)(md5 *p, const char *s);
void X(md5putc)(md5 *p, unsigned char c);
void X(md5int)(md5 *p, int i);
void X(md5INT)(md5 *p, INT i);
void X(md5unsigned)(md5 *p, unsigned i);
void X(md5end)(md5 *p);

/* tensor.c: */
#undef STRUCT_HACK_C99

typedef struct {
     INT n;
     INT is;                  /* input stride */
     INT os;                  /* output stride */
} iodim;

typedef struct {
     int rnk;
#if defined(STRUCT_HACK_KR)
     iodim dims[1];
#elif defined(STRUCT_HACK_C99)
     iodim dims[];
     iodim *dims;
} tensor;

  Definition of rank -infinity.
  This definition has the property that if you want rank 0 or 1,
  you can simply test for rank <= 1.  This is a common case.
  A tensor of rank -infinity has size 0.
#define RNK_MINFTY  ((int)(((unsigned) -1) >> 1))
#define FINITE_RNK(rnk) ((rnk) != RNK_MINFTY)

typedef enum { INPLACE_IS, INPLACE_OS } inplace_kind;

tensor *X(mktensor)(int rnk);
tensor *X(mktensor_0d)(void);
tensor *X(mktensor_1d)(INT n, INT is, INT os);
tensor *X(mktensor_2d)(INT n0, INT is0, INT os0,
                   INT n1, INT is1, INT os1);
tensor *X(mktensor_3d)(INT n0, INT is0, INT os0,
                   INT n1, INT is1, INT os1,
                   INT n2, INT is2, INT os2);
INT X(tensor_sz)(const tensor *sz);
void X(tensor_md5)(md5 *p, const tensor *t);
INT X(tensor_max_index)(const tensor *sz);
INT X(tensor_min_istride)(const tensor *sz);
INT X(tensor_min_ostride)(const tensor *sz);
INT X(tensor_min_stride)(const tensor *sz);
int X(tensor_inplace_strides)(const tensor *sz);
int X(tensor_inplace_strides2)(const tensor *a, const tensor *b);
int X(tensor_strides_decrease)(const tensor *sz, const tensor *vecsz,
                               inplace_kind k);
tensor *X(tensor_copy)(const tensor *sz);
int X(tensor_kosherp)(const tensor *x);

tensor *X(tensor_copy_inplace)(const tensor *sz, inplace_kind k);
tensor *X(tensor_copy_except)(const tensor *sz, int except_dim);
tensor *X(tensor_copy_sub)(const tensor *sz, int start_dim, int rnk);
tensor *X(tensor_compress)(const tensor *sz);
tensor *X(tensor_compress_contiguous)(const tensor *sz);
tensor *X(tensor_append)(const tensor *a, const tensor *b);
void X(tensor_split)(const tensor *sz, tensor **a, int a_rnk, tensor **b);
int X(tensor_tornk1)(const tensor *t, INT *n, INT *is, INT *os);
void X(tensor_destroy)(tensor *sz);
void X(tensor_destroy2)(tensor *a, tensor *b);
void X(tensor_destroy4)(tensor *a, tensor *b, tensor *c, tensor *d);
void X(tensor_print)(const tensor *sz, printer *p);
int X(dimcmp)(const iodim *a, const iodim *b);

/* problem.c: */
enum { 

typedef struct {
     int problem_kind;
     void (*hash) (const problem *ego, md5 *p);
     void (*zero) (const problem *ego);
     void (*print) (problem *ego, printer *p);
     void (*destroy) (problem *ego);
} problem_adt;

struct problem_s {
     const problem_adt *adt;

problem *X(mkproblem)(size_t sz, const problem_adt *adt);
void X(problem_destroy)(problem *ego);

/* print.c */
struct printer_s {
     void (*print)(printer *p, const char *format, ...);
     void (*vprint)(printer *p, const char *format, va_list ap);
     void (*putchr)(printer *p, char c);
     void (*cleanup)(printer *p);
     int indent;
     int indent_incr;

printer *X(mkprinter)(size_t size, 
                  void (*putchr)(printer *p, char c),
                  void (*cleanup)(printer *p));
IFFTW_EXTERN void X(printer_destroy)(printer *p);

/* scan.c */
struct scanner_s {
     int (*scan)(scanner *sc, const char *format, ...);
     int (*vscan)(scanner *sc, const char *format, va_list ap);
     int (*getchr)(scanner *sc);
     int ungotc;

scanner *X(mkscanner)(size_t size, int (*getchr)(scanner *sc));
void X(scanner_destroy)(scanner *sc);

/* plan.c: */

enum wakefulness {

typedef struct {
     void (*solve)(const plan *ego, const problem *p);
     void (*awake)(plan *ego, enum wakefulness wakefulness);
     void (*print)(const plan *ego, printer *p);
     void (*destroy)(plan *ego);
} plan_adt;

struct plan_s {
     const plan_adt *adt;
     opcnt ops;
     double pcost;
     enum wakefulness wakefulness; /* used for debugging only */
     int could_prune_now_p;

plan *X(mkplan)(size_t size, const plan_adt *adt);
void X(plan_destroy_internal)(plan *ego);
IFFTW_EXTERN void X(plan_awake)(plan *ego, enum wakefulness wakefulness);
void X(plan_null_destroy)(plan *ego);

/* solver.c: */
typedef struct {
     int problem_kind;
     plan *(*mkplan)(const solver *ego, const problem *p, planner *plnr);
} solver_adt;

struct solver_s {
     const solver_adt *adt;
     int refcnt;

solver *X(mksolver)(size_t size, const solver_adt *adt);
void X(solver_use)(solver *ego);
void X(solver_destroy)(solver *ego);
void X(solver_register)(planner *plnr, solver *s);

/* shorthand */
#define MKSOLVER(type, adt) (type *)X(mksolver)(sizeof(type), adt)

/* planner.c */

typedef struct slvdesc_s {
     solver *slv;
     const char *reg_nam;
     unsigned nam_hash;
     int reg_id;
     int next_for_same_problem_kind;
} slvdesc;

typedef struct solution_s solution; /* opaque */

/* interpretation of L and U: 

   - if it returns a plan, the planner guarantees that all applicable
     plans at least as impatient as U have been tried, and that each
     plan in the solution is at least as impatient as L.
   - if it returns 0, the planner guarantees to have tried all solvers
     at least as impatient as L, and that none of them was applicable.

   The structure is packed to fit into 64 bits.

typedef struct {
     unsigned l:20;
     unsigned hash_info:3;
#    define BITS_FOR_TIMELIMIT 9
     unsigned timelimit_impatience:BITS_FOR_TIMELIMIT;
     unsigned u:20;
     /* abstraction break: we store the solver here to pad the
      structure to 64 bits.  Otherwise, the struct is padded to 64
      bits anyway, and another word is allocated for slvndx. */
#    define BITS_FOR_SLVNDX 12
     unsigned slvndx:BITS_FOR_SLVNDX;
} flags_t;

/* impatience flags  */
enum {
     BELIEVE_PCOST = 0x0001,
     ESTIMATE = 0x0002,
     NO_DFT_R2HC = 0x0004,
     NO_SLOW = 0x0008,
     NO_VRECURSE = 0x0010,
     NO_INDIRECT_OP = 0x0020,
     NO_LARGE_GENERIC = 0x0040,
     NO_RANK_SPLITS = 0x0080,
     NO_VRANK_SPLITS = 0x0100,
     NO_NONTHREADED = 0x0200,
     NO_BUFFERING = 0x0400,
     NO_FIXED_RADIX_LARGE_N = 0x0800,
     NO_DESTROY_INPUT = 0x1000,
     NO_SIMD = 0x2000,
     CONSERVE_MEMORY = 0x4000,
     NO_DHT_R2HC = 0x8000,
     NO_UGLY = 0x10000,
     ALLOW_PRUNING = 0x20000

/* hashtable information */
enum {
     BLESSING = 0x1,   /* save this entry */
     H_VALID = 0x2,    /* valid hastable entry */
     H_LIVE = 0x4      /* entry is nonempty, implies H_VALID */

#define PLNR_L(plnr) ((plnr)->flags.l)
#define PLNR_U(plnr) ((plnr)->flags.u)
#define PLNR_TIMELIMIT_IMPATIENCE(plnr) ((plnr)->flags.timelimit_impatience)

#define ESTIMATEP(plnr) (PLNR_U(plnr) & ESTIMATE)

#define NO_INDIRECT_OP_P(plnr) (PLNR_L(plnr) & NO_INDIRECT_OP)
#define NO_RANK_SPLITSP(plnr) (PLNR_L(plnr) & NO_RANK_SPLITS)
#define NO_VRECURSEP(plnr) (PLNR_L(plnr) & NO_VRECURSE)
#define NO_DFT_R2HCP(plnr) (PLNR_L(plnr) & NO_DFT_R2HC)
#define NO_SLOWP(plnr) (PLNR_L(plnr) & NO_SLOW)
#define NO_UGLYP(plnr) (PLNR_L(plnr) & NO_UGLY)
#define NO_FIXED_RADIX_LARGE_NP(plnr) \
#define NO_NONTHREADEDP(plnr) \
  ((PLNR_L(plnr) & NO_NONTHREADED) && (plnr)->nthr > 1)

#define NO_SIMDP(plnr) (PLNR_L(plnr) & NO_SIMD)
#define NO_DHT_R2HCP(plnr) (PLNR_L(plnr) & NO_DHT_R2HC)
#define NO_BUFFERINGP(plnr) (PLNR_L(plnr) & NO_BUFFERING)

typedef enum { FORGET_ACCURSED, FORGET_EVERYTHING } amnesia;

typedef enum { 
     /* WISDOM_NORMAL: planner may or may not use wisdom */

     /* WISDOM_ONLY: planner must use wisdom and must avoid searching */

     /* WISDOM_IS_BOGUS: planner must return 0 as quickly as possible */

     /* WISDOM_IGNORE_INFEASIBLE: planner ignores infeasible wisdom */

     /* WISDOM_IGNORE_ALL: planner ignores all */
} wisdom_state_t;

typedef struct {
     void (*register_solver)(planner *ego, solver *s);
     plan *(*mkplan)(planner *ego, problem *p);
     void (*forget)(planner *ego, amnesia a);
     void (*exprt)(planner *ego, printer *p); /* ``export'' is a reserved
                                     word in C++. */
     int (*imprt)(planner *ego, scanner *sc);
} planner_adt;

/* hash table of solutions */
typedef struct {
     solution *solutions;
     unsigned hashsiz, nelem;

     /* statistics */
     int lookup, succ_lookup, lookup_iter;
     int insert, insert_iter, insert_unknown;
     int nrehash;
} hashtab;

struct planner_s {
     const planner_adt *adt;
     void (*hook)(struct planner_s *plnr, plan *pln, 
              const problem *p, int optimalp);

     /* solver descriptors */
     slvdesc *slvdescs;
     unsigned nslvdesc, slvdescsiz;
     const char *cur_reg_nam;
     int cur_reg_id;
     int slvdescs_for_problem_kind[PROBLEM_LAST];

     wisdom_state_t wisdom_state;

     hashtab htab_blessed;
     hashtab htab_unblessed;

     int nthr;
     flags_t flags;

     crude_time start_time;
     double timelimit; /* elapsed_since(start_time) at which to bail out */
     int timed_out; /* whether most recent search timed out */
     int need_timeout_check;

     /* various statistics */
     int nplan;    /* number of plans evaluated */
     double pcost, epcost; /* total pcost of measured/estimated plans */
     int nprob;    /* number of problems evaluated */

planner *X(mkplanner)(void);
void X(planner_destroy)(planner *ego);

  Iterate over all solvers.   Read:
  @article{ baker93iterators,
  author = "Henry G. Baker, Jr.",
  title = "Iterators: Signs of Weakness in Object-Oriented Languages",
  journal = "{ACM} {OOPS} Messenger",
  volume = "4",
  number = "3",
  pages = "18--25"
#define FORALL_SOLVERS(ego, s, p, what)               \
{                                         \
     unsigned _cnt;                             \
     for (_cnt = 0; _cnt < ego->nslvdesc; ++_cnt) {   \
        slvdesc *p = ego->slvdescs + _cnt;            \
        solver *s = p->slv;                     \
        what;                                   \
     }                                          \

#define FORALL_SOLVERS_OF_KIND(kind, ego, s, p, what)       \
{                                               \
     int _cnt = ego->slvdescs_for_problem_kind[kind];             \
     while (_cnt >= 0) {                              \
        slvdesc *p = ego->slvdescs + _cnt;                  \
        solver *s = p->slv;                           \
        what;                                         \
        _cnt = p->next_for_same_problem_kind;               \
     }                                                \

/* make plan, destroy problem */
plan *X(mkplan_d)(planner *ego, problem *p);
plan *X(mkplan_f_d)(planner *ego, problem *p, 
                unsigned l_set, unsigned u_set, unsigned u_reset);

/* stride.c: */

/* If PRECOMPUTE_ARRAY_INDICES is defined, precompute all strides. */
#if (defined(__i386__) || defined(__x86_64__) || _M_IX86 >= 500) && !HAVE_K7 && !defined(FFTW_LDOUBLE)

typedef INT *stride;
#define WS(stride, i)  (stride[i])
extern stride X(mkstride)(INT n, INT s);
void X(stride_destroy)(stride p);
#define MAKE_VOLATILE_STRIDE(x) (void)0 /* a no-op in expession context */

typedef INT stride;
#define WS(stride, i)  (stride * i)
#define fftwf_mkstride(n, stride) stride
#define fftw_mkstride(n, stride) stride
#define fftwl_mkstride(n, stride) stride
#define fftwf_stride_destroy(p) ((void) p)
#define fftw_stride_destroy(p) ((void) p)
#define fftwl_stride_destroy(p) ((void) p)

/* hackery to prevent the compiler from ``optimizing'' induction
   variables in codelet loops. */
extern const stride X(a_stride_guaranteed_to_be_zero);
#define MAKE_VOLATILE_STRIDE(x) (x) = (x) ^ X(a_stride_guaranteed_to_be_zero)


/* solvtab.c */

struct solvtab_s { void (*reg)(planner *); const char *reg_nam; };
typedef struct solvtab_s solvtab[];
void X(solvtab_exec)(const solvtab tbl, planner *p);
#define SOLVTAB(s) { s, STRINGIZE(s) }
#define SOLVTAB_END { 0, 0 }

/* pickdim.c */
int X(pickdim)(int which_dim, const int *buddies, int nbuddies,
             const tensor *sz, int oop, int *dp);

/* twiddle.c */
/* little language to express twiddle factors computation */
enum { TW_COS = 0, TW_SIN = 1, TW_CEXP = 2, TW_NEXT = 3, 
       TW_FULL = 4, TW_HALF = 5 };

typedef struct {
     unsigned char op;
     signed char v;
     short i;
} tw_instr;

typedef struct twid_s {
     R *W;                     /* array of twiddle factors */
     INT n, r, m;                /* transform order, radix, # twiddle rows */
     int refcnt;
     const tw_instr *instr;
     struct twid_s *cdr;
     enum wakefulness wakefulness;
} twid;

INT X(twiddle_length)(INT r, const tw_instr *p);
void X(twiddle_awake)(enum wakefulness wakefulness,
                  twid **pp, const tw_instr *instr, INT n, INT r, INT m);
const R *X(twiddle_shift)(const twid *p, INT mstart);

/* trig.c */
   typedef long double trigreal;
   typedef double trigreal;

typedef struct triggen_s triggen;

struct triggen_s {
     void (*cexp)(triggen *t, INT m, R *result);
     void (*cexpl)(triggen *t, INT m, trigreal *result);
     void (*rotate)(triggen *p, INT m, R xr, R xi, R *res);

     INT twshft;
     INT twradix;
     INT twmsk;
     trigreal *W0, *W1;
     INT n;

triggen *X(mktriggen)(enum wakefulness wakefulness, INT n);
void X(triggen_destroy)(triggen *p);

/* primes.c: */

#define MULMOD(x, y, p) \
   (((x) <= 92681 - (y)) ? ((x) * (y)) % (p) : X(safe_mulmod)(x, y, p))

INT X(safe_mulmod)(INT x, INT y, INT p);
INT X(power_mod)(INT n, INT m, INT p);
INT X(find_generator)(INT p);
INT X(first_divisor)(INT n);
int X(is_prime)(INT n);
INT X(next_prime)(INT n);
int X(factors_into)(INT n, const INT *primes);
INT X(choose_radix)(INT r, INT n);
INT X(isqrt)(INT n);

#define GENERIC_MIN_BAD 173 /* min prime for which generic becomes bad */

/* rader.c: */
typedef struct rader_tls rader_tl;

void X(rader_tl_insert)(INT k1, INT k2, INT k3, R *W, rader_tl **tl);
R *X(rader_tl_find)(INT k1, INT k2, INT k3, rader_tl *t);
void X(rader_tl_delete)(R *W, rader_tl **tl);

/* copy/transposition routines */

/* lower bound to the cache size, for tiled routines */
#define CACHESIZE 8192

INT X(compute_tilesz)(INT vl, int how_many_tiles_in_cache);

void X(tile2d)(INT n0l, INT n0u, INT n1l, INT n1u, INT tilesz,
             void (*f)(INT n0l, INT n0u, INT n1l, INT n1u, void *args),
             void *args);
void X(cpy1d)(R *I, R *O, INT n0, INT is0, INT os0, INT vl);
void X(cpy2d)(R *I, R *O,
            INT n0, INT is0, INT os0,
            INT n1, INT is1, INT os1,
            INT vl);
void X(cpy2d_ci)(R *I, R *O,
             INT n0, INT is0, INT os0,
             INT n1, INT is1, INT os1,
             INT vl);
void X(cpy2d_co)(R *I, R *O,
             INT n0, INT is0, INT os0,
             INT n1, INT is1, INT os1,
             INT vl);
void X(cpy2d_tiled)(R *I, R *O,
                INT n0, INT is0, INT os0,
                INT n1, INT is1, INT os1, 
                INT vl);
void X(cpy2d_tiledbuf)(R *I, R *O,
                   INT n0, INT is0, INT os0,
                   INT n1, INT is1, INT os1, 
                   INT vl);
void X(cpy2d_pair)(R *I0, R *I1, R *O0, R *O1,
               INT n0, INT is0, INT os0,
               INT n1, INT is1, INT os1);
void X(cpy2d_pair_ci)(R *I0, R *I1, R *O0, R *O1,
                  INT n0, INT is0, INT os0,
                  INT n1, INT is1, INT os1);
void X(cpy2d_pair_co)(R *I0, R *I1, R *O0, R *O1,
                  INT n0, INT is0, INT os0,
                  INT n1, INT is1, INT os1);

void X(transpose)(R *I, INT n, INT s0, INT s1, INT vl);
void X(transpose_tiled)(R *I, INT n, INT s0, INT s1, INT vl);
void X(transpose_tiledbuf)(R *I, INT n, INT s0, INT s1, INT vl);

typedef void (*transpose_func)(R *I, INT n, INT s0, INT s1, INT vl);
typedef void (*cpy2d_func)(R *I, R *O,
                     INT n0, INT is0, INT os0,
                     INT n1, INT is1, INT os1,
                     INT vl);

/* misc stuff */
void X(null_awake)(plan *ego, enum wakefulness wakefulness);
double X(iestimate_cost)(const plan *pln);
double X(measure_execution_time)(plan *pln, const problem *p);
int X(alignment_of)(R *p);
unsigned X(hash)(const char *s);
INT X(compute_nbuf)(INT n, INT vl, INT nbuf, INT maxbufsz);
int X(ct_uglyp)(INT min_n, INT n, INT r);

R *X(taint)(R *p, INT s);
R *X(join_taint)(R *p1, R *p2);
#define TAINT(p, s) X(taint)(p, s)
#define UNTAINT(p) ((R *) (((uintptr_t) (p)) & ~(uintptr_t)3))
#define TAINTOF(p) (((uintptr_t)(p)) & 3)
#define JOIN_TAINT(p1, p2) X(join_taint)(p1, p2)
#define TAINT(p, s) (p)
#define UNTAINT(p) (p)
#define TAINTOF(p) 0
#define JOIN_TAINT(p1, p2) p1

#  define ASSERT_ALIGNED_DOUBLE {         \
     double __foo;                        \
     CK(!(((uintptr_t) &__foo) & 0x7));         \

/* macros used in codelets to reduce source code size */

typedef R E;  /* internal precision of codelets. */

#  define K(x) ((E) x##L)
#  define K(x) ((E) x)
#define DK(name, value) const E name = K(value)

/* FMA macros */

#if defined(__GNUC__) && (defined(__powerpc__) || defined(__ppc__) || defined(_POWER))
/* The obvious expression a * b + c does not work.  If both x = a * b
   + c and y = a * b - c appear in the source, gcc computes t = a * b,
   x = t + c, y = t - c, thus destroying the fma.

   This peculiar coding seems to do the right thing on all of
   gcc-2.95, gcc-3.1, gcc-3.2, and gcc-3.3.  It does the right thing
   on gcc-3.4 -fno-web (because the ``web'' pass splits the variable
   `x' for the single-assignment form).

   However, gcc-4.0 is a formidable adversary which succeeds in
   pessimizing two fma's into one multiplication and two additions.
   It does it very early in the game---before the optimization passes
   even start.  The only real workaround seems to use fake inline asm
   such as

     asm ("# confuse gcc %0" : "=f"(a) : "0"(a));
     return a * b + c;
   in each of the FMA, FMS, FNMA, and FNMS functions.  However, this
   does not solve the problem either, because two equal asm statements
   count as a common subexpression!  One must use *different* fake asm

   in FMA:
     asm ("# confuse gcc for fma %0" : "=f"(a) : "0"(a));

   in FMS:
     asm ("# confuse gcc for fms %0" : "=f"(a) : "0"(a));


   After these changes, gcc recalcitrantly generates the fma that was
   in the source to begin with.  However, the extra asm() cruft
   confuses other passes of gcc, notably the instruction scheduler.
   (Of course, one could also generate the fma directly via inline
   asm, but this confuses the scheduler even more.)

   Steven and I have submitted more than one bug report to the gcc
   mailing list over the past few years, to no effect.  Thus, I give
   up.  gcc-4.0 can go to hell.  I'll wait at least until gcc-4.3 is
   out before touching this crap again.
static __inline__ E FMA(E a, E b, E c)
     E x = a * b;
     x = x + c;
     return x;

static __inline__ E FMS(E a, E b, E c)
     E x = a * b;
     x = x - c;
     return x;

static __inline__ E FNMA(E a, E b, E c)
     E x = a * b;
     x = - (x + c);
     return x;

static __inline__ E FNMS(E a, E b, E c)
     E x = a * b;
     x = - (x - c);
     return x;
#define FMA(a, b, c) (((a) * (b)) + (c))
#define FMS(a, b, c) (((a) * (b)) - (c))
#define FNMA(a, b, c) (- (((a) * (b)) + (c)))
#define FNMS(a, b, c) ((c) - ((a) * (b)))

/* stack-alignment hackery */
#ifdef __ICC /* Intel's compiler for ia32 */
#define WITH_ALIGNED_STACK(what)                      \
{                                               \
     /*                                               \
      * Simply calling alloca seems to do the right thing.  \
      * The size of the allocated block seems to be irrelevant.   \
      */                                        \
     _alloca(16);                               \
     what                                       \

#if defined(__GNUC__) && defined(__i386__) && !defined(WITH_ALIGNED_STACK) \
    && !(defined(__MACOSX__) || defined(__APPLE__)) /* OSX ABI is aligned */
 * horrible hack to align the stack to a 16-byte boundary.
 * We assume a gcc version >= 2.95 so that
 * -mpreferred-stack-boundary works.  Otherwise, all bets are
 * off.  However, -mpreferred-stack-boundary does not create a
 * stack alignment, but it only preserves it.  Unfortunately,
 * many versions of libc on linux call main() with the wrong
 * initial stack alignment, with the result that the code is now
 * pessimally aligned instead of having a 50% chance of being
 * correct.

#define WITH_ALIGNED_STACK(what)                      \
{                                               \
     /*                                               \
      * Use alloca to allocate some memory on the stack.    \
      * This alerts gcc that something funny is going       \
      * on, so that it does not omit the frame pointer            \
      * etc.                                          \
      */                                        \
     (void)__builtin_alloca(16);                      \
     /*                                               \
      * Now align the stack pointer                   \
      */                                        \
     __asm__ __volatile__ ("andl $-16, %esp");              \
     what                                       \

#define WITH_ALIGNED_STACK(what) what

#endif /* __IFFTW_H__ */

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