infft.h
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/*
* Copyright (c) 2002, 2017 Jens Keiner, Stefan Kunis, Daniel Potts
*
* 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 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 program; if not, write to the Free Software Foundation, Inc., 51
* Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#ifndef __INFFT_H__
#define __INFFT_H__
#include "config.h"
#include <math.h>
#include <float.h>
#ifdef HAVE_COMPLEX_H
#include <complex.h>
#endif
#include <stdio.h>
#include <string.h>
#include <stdlib.h> /* size_t */
#include <stdarg.h> /* va_list */
#include <stddef.h> /* ptrdiff_t */
#if HAVE_SYS_TYPES_H
#include <sys/types.h>
#endif
#if HAVE_STDINT_H
#include <stdint.h> /* uintptr_t, maybe */
#endif
#if HAVE_INTTYPES_H
#include <inttypes.h> /* uintptr_t, maybe */
#endif
#include <fftw3.h>
#include "ticks.h"
/* Determine precision and name-mangling scheme. */
#define CONCAT(prefix, name) prefix ## name
#if defined(NFFT_SINGLE)
typedef float R;
typedef float _Complex C;
#define Y(name) CONCAT(nfftf_,name)
#define FFTW(name) CONCAT(fftwf_,name)
#define NFFT(name) CONCAT(nfftf_,name)
#define NFCT(name) CONCAT(nfctf_,name)
#define NFST(name) CONCAT(nfstf_,name)
#define NFSFT(name) CONCAT(nfsftf_,name)
#define SOLVER(name) CONCAT(solverf_,name)
#elif defined(NFFT_LDOUBLE)
typedef long double R;
typedef long double _Complex C;
#define Y(name) CONCAT(nfftl_,name)
#define FFTW(name) CONCAT(fftwl_,name)
#define NFFT(name) CONCAT(nfftl_,name)
#define NFCT(name) CONCAT(nfctl_,name)
#define NFST(name) CONCAT(nfstl_,name)
#define NFSFT(name) CONCAT(nfsftl_,name)
#define SOLVER(name) CONCAT(solverl_,name)
#else
typedef double R;
typedef double _Complex C;
#define Y(name) CONCAT(nfft_,name)
#define FFTW(name) CONCAT(fftw_,name)
#define NFFT(name) CONCAT(nfft_,name)
#define NFCT(name) CONCAT(nfct_,name)
#define NFST(name) CONCAT(nfst_,name)
#define NFSFT(name) CONCAT(nfsft_,name)
#define SOLVER(name) CONCAT(solver_,name)
#endif
#define X(name) Y(name)
#define STRINGIZEx(x) #x
#define STRINGIZE(x) STRINGIZEx(x)
#ifdef NFFT_LDOUBLE
# define K(x) ((R) x##L)
#else
# define K(x) ((R) x)
#endif
#define DK(name, value) const R name = K(value)
#if defined __CYGWIN32__ && !defined __CYGWIN__
/* For backwards compatibility with Cygwin b19 and
earlier, we define __CYGWIN__ here, so that
we can rely on checking just for that macro. */
# define __CYGWIN__ __CYGWIN32__
#endif
/* Integral type large enough to contain a stride (what ``int'' should have been
* in the first place) */
typedef ptrdiff_t INT;
#define KPI K(3.1415926535897932384626433832795028841971693993751)
#define K2PI K(6.2831853071795864769252867665590057683943387987502)
#define K4PI K(12.5663706143591729538505735331180115367886775975004)
#define KE K(2.7182818284590452353602874713526624977572470937000)
#define IF(x,a,b) ((x)?(a):(b))
#define MIN(a,b) (((a)<(b))?(a):(b))
#define MAX(a,b) (((a)>(b))?(a):(b))
#define ABS(x) (((x)>K(0.0))?(x):(-(x)))
#define SIGN(a) (((a)>=0)?1:-1)
#define SIGN(a) (((a)>=0)?1:-1)
#define SIGNF(a) IF((a)<K(0.0),K(-1.0),K(1.0))
/* Size of array. */
#define SIZE(x) sizeof(x)/sizeof(x[0])
#define CSWAP(x,y) {C* NFFT_SWAP_temp__; \
NFFT_SWAP_temp__=(x); (x)=(y); (y)=NFFT_SWAP_temp__;}
#define RSWAP(x,y) {R* NFFT_SWAP_temp__; NFFT_SWAP_temp__=(x); \
(x)=(y); (y)=NFFT_SWAP_temp__;}
/* macros for window functions */
#if defined(DIRAC_DELTA)
#define PHI_HUT(n,k,d) K(1.0)
#define PHI(n,x,d) IF(FABS((x)) < K(10E-8),K(1.0),K(0.0))
#define WINDOW_HELP_INIT(d)
#define WINDOW_HELP_FINALIZE
#define WINDOW_HELP_ESTIMATE_m 0
#elif defined(GAUSSIAN)
#define PHI_HUT(n,k,d) ((R)EXP(-(POW(KPI*(k)/n,K(2.0))*ths->b[d])))
#define PHI(n,x,d) ((R)EXP(-POW((x)*((R)n),K(2.0)) / \
ths->b[d])/SQRT(KPI*ths->b[d]))
#define WINDOW_HELP_INIT \
{ \
int WINDOW_idx; \
ths->b = (R*) Y(malloc)(ths->d*sizeof(R)); \
for (WINDOW_idx = 0; WINDOW_idx < ths->d; WINDOW_idx++) \
ths->b[WINDOW_idx]=(K(2.0)*ths->sigma[WINDOW_idx]) / \
(K(2.0)*ths->sigma[WINDOW_idx] - K(1.0)) * (((R)ths->m) / KPI); \
}
#define WINDOW_HELP_FINALIZE {Y(free)(ths->b);}
#if defined(NFFT_LDOUBLE)
#define WINDOW_HELP_ESTIMATE_m 17
#elif defined(NFFT_SINGLE)
#define WINDOW_HELP_ESTIMATE_m 5
#else
#define WINDOW_HELP_ESTIMATE_m 13
#endif
#elif defined(B_SPLINE)
#define PHI_HUT(n,k,d) ((R)(((k) == 0) ? K(1.0) / n : \
POW(SIN((k) * KPI / n) / ((k) * KPI / n), \
K(2.0) * ths->m)/n))
#define PHI(n,x,d) (Y(bsplines)(2*ths->m,((x)*n) + \
(R)ths->m) / n)
#define WINDOW_HELP_INIT
#define WINDOW_HELP_FINALIZE
#if defined(NFFT_LDOUBLE)
#define WINDOW_HELP_ESTIMATE_m 11
#elif defined(NFFT_SINGLE)
#define WINDOW_HELP_ESTIMATE_m 11
#else
#define WINDOW_HELP_ESTIMATE_m 11
#endif
#elif defined(SINC_POWER)
#define PHI_HUT(n,k,d) (Y(bsplines)(2 * ths->m, (K(2.0) * ths->m*(k)) / \
((K(2.0) * ths->sigma[(d)] - 1) * n / \
ths->sigma[(d)]) + (R)ths->m))
#define PHI(n,x,d) ((R)(n / ths->sigma[(d)] * \
(K(2.0) * ths->sigma[(d)] - K(1.0))/ (K(2.0)*ths->m) * \
POW(Y(sinc)(KPI * n / ths->sigma[(d)] * (x) * \
(K(2.0) * ths->sigma[(d)] - K(1.0)) / (K(2.0)*ths->m)) , 2*ths->m) / \
n))
#define WINDOW_HELP_INIT
#define WINDOW_HELP_FINALIZE
#if defined(NFFT_LDOUBLE)
#define WINDOW_HELP_ESTIMATE_m 13
#elif defined(NFFT_SINGLE)
#define WINDOW_HELP_ESTIMATE_m 11
#else
#define WINDOW_HELP_ESTIMATE_m 11
#endif
#else /* Kaiser-Bessel is the default. */
#define PHI_HUT(n,k,d) (Y(bessel_i0)((R)(ths->m) * SQRT(ths->b[d] * ths->b[d] - (K(2.0) * KPI * (R)(k) / (R)(n)) * (K(2.0) * KPI * (R)(k) / (R)(n)))))
#define PHI(n,x,d) ( (((R)(ths->m) * (R)(ths->m) - (x) * (R)(n) * (x) * (R)(n)) > K(0.0)) \
? SINH(ths->b[d] * SQRT((R)(ths->m) * (R)(ths->m) - (x) * (R)(n) * (x) * (R)(n))) \
/ (KPI * SQRT((R)(ths->m) * (R)(ths->m) - (x) * (R)(n) * (x) * (R)(n))) \
: ((((R)(ths->m) * (R)(ths->m) - (x) * (R)(n) * (x) * (R)(n)) < K(0.0)) \
? SIN(ths->b[d] * SQRT((x) * (R)(n) * (x) * (R)(n) - (R)(ths->m) * (R)(ths->m))) \
/ (KPI * SQRT((x) * (R)(n) * (x) * (R)(n) - (R)(ths->m) * (R)(ths->m))) \
: ths->b[d] / KPI))
#define WINDOW_HELP_INIT \
{ \
int WINDOW_idx; \
ths->b = (R*) Y(malloc)((size_t)(ths->d) * sizeof(R)); \
for (WINDOW_idx = 0; WINDOW_idx < ths->d; WINDOW_idx++) \
ths->b[WINDOW_idx] = (KPI * (K(2.0) - K(1.0) / ths->sigma[WINDOW_idx])); \
}
#define WINDOW_HELP_FINALIZE {Y(free)(ths->b);}
#if defined(NFFT_LDOUBLE)
#define WINDOW_HELP_ESTIMATE_m 9
#elif defined(NFFT_SINGLE)
#define WINDOW_HELP_ESTIMATE_m 4
#else
#define WINDOW_HELP_ESTIMATE_m 8
#endif
#endif
/* window.c */
INT Y(m2K)(const INT m);
#if defined(NFFT_LDOUBLE)
#if HAVE_DECL_COPYSIGNL == 0
extern long double copysignl(long double, long double);
#endif
#if HAVE_DECL_NEXTAFTERL == 0
extern long double nextafterl(long double, long double);
#endif
#if HAVE_DECL_NANL == 0
extern long double nanl(const char *tag);
#endif
#if HAVE_DECL_CEILL == 0
extern long double ceill(long double);
#endif
#if HAVE_DECL_FLOORL == 0
extern long double floorl(long double);
#endif
#if HAVE_DECL_NEARBYINTL == 0
extern long double nearbyintl(long double);
#endif
#if HAVE_DECL_RINTL == 0
extern long double rintl(long double);
#endif
#if HAVE_DECL_ROUNDL == 0
extern long double roundl(long double);
#endif
#if HAVE_DECL_LRINTL == 0
extern long int lrintl(long double);
#endif
#if HAVE_DECL_LROUNDL == 0
extern long int lroundl(long double);
#endif
#if HAVE_DECL_LLRINTL == 0
extern long long int llrintl(long double);
#endif
#if HAVE_DECL_LLROUNDL == 0
extern long long int llroundl(long double);
#endif
#if HAVE_DECL_TRUNCL == 0
extern long double truncl(long double);
#endif
#if HAVE_DECL_FMODL == 0
extern long double fmodl(long double, long double);
#endif
#if HAVE_DECL_REMAINDERL == 0
extern long double remainderl(long double, long double);
#endif
#if HAVE_DECL_REMQUOL == 0
extern long double remquol(long double x, long double y, int *);
#endif
#if HAVE_DECL_FDIML == 0
extern long double fdiml(long double, long double);
#endif
#if HAVE_DECL_FMAXL == 0
extern long double fmaxl(long double, long double);
#endif
#if HAVE_DECL_FMINL == 0
extern long double fminl(long double, long double);
#endif
#if HAVE_DECL_FMAL == 0
extern long double fmal(long double x, long double y, long double z);
#endif
#if HAVE_DECL_FABSL == 0
extern long double fabsl(long double);
#endif
#if HAVE_DECL_SQRTL == 0
extern long double sqrtl(long double);
#endif
#if HAVE_DECL_CBRTL == 0
extern long double cbrtl(long double);
#endif
#if HAVE_DECL_HYPOTL == 0
extern long double hypotl(long double, long double);
#endif
#if HAVE_DECL_EXPL == 0
extern long double expl(long double);
#endif
#if HAVE_DECL_EXP2L == 0
extern long double exp2l(long double);
#endif
#if HAVE_DECL_EXPM1L == 0
extern long double expm1l(long double);
#endif
#if HAVE_DECL_LOGL == 0
extern long double logl(long double);
#endif
#if HAVE_DECL_LOG2L == 0
extern long double log2l(long double);
#endif
#if HAVE_DECL_LOG10L == 0
extern long double log10l(long double);
#endif
#if HAVE_DECL_LOG1PL == 0
extern long double log1pl(long double);
#endif
#if HAVE_DECL_LOGBL == 0
extern long double logbl(long double);
#endif
#if HAVE_DECL_ILOGBL == 0
extern int ilogbl(long double);
#endif
#if HAVE_DECL_MODFL == 0
extern long double modfl(long double, long double *);
#endif
#if HAVE_DECL_FREXPL == 0
extern long double frexpl(long double, int *);
#endif
#if HAVE_DECL_LDEXPL == 0
extern long double ldexpl(long double, int);
#endif
#if HAVE_DECL_SCALBNL == 0
extern long double scalbnl(long double, int);
#endif
#if HAVE_DECL_SCALBLNL == 0
extern long double scalblnl(long double, long int);
#endif
#if HAVE_DECL_POWL == 0
extern long double powl(long double, long double);
#endif
#if HAVE_DECL_COSL == 0
extern long double cosl(long double);
#endif
#if HAVE_DECL_SINL == 0
extern long double sinl(long double);
#endif
#if HAVE_DECL_TANL == 0
extern long double tanl(long double);
#endif
#if HAVE_DECL_COSHL == 0
extern long double coshl(long double);
#endif
#if HAVE_DECL_SINHL == 0
extern long double sinhl(long double);
#endif
#if HAVE_DECL_TANHL == 0
extern long double tanhl(long double);
#endif
#if HAVE_DECL_ACOSL == 0
extern long double acosl(long double);
#endif
#if HAVE_DECL_ASINL == 0
extern long double asinl(long double);
#endif
#if HAVE_DECL_ATANL == 0
extern long double atanl(long double);
#endif
#if HAVE_DECL_ATAN2L == 0
extern long double atan2l(long double, long double);
#endif
#if HAVE_DECL_ACOSHL == 0
extern long double acoshl(long double);
#endif
#if HAVE_DECL_ASINHL == 0
extern long double asinhl(long double);
#endif
#if HAVE_DECL_ATANHL == 0
extern long double atanhl(long double);
#endif
#if HAVE_DECL_TGAMMAL == 0
extern long double tgammal(long double);
#endif
#if HAVE_DECL_LGAMMAL == 0
extern long double lgammal(long double);
#endif
#if HAVE_DECL_J0L == 0
extern long double j0l(long double);
#endif
#if HAVE_DECL_J1L == 0
extern long double j1l(long double);
#endif
#if HAVE_DECL_JNL == 0
extern long double jnl(int, long double);
#endif
#if HAVE_DECL_Y0L == 0
extern long double y0l(long double);
#endif
#if HAVE_DECL_Y1L == 0
extern long double y1l(long double);
#endif
#if HAVE_DECL_YNL == 0
extern long double ynl(int, long double);
#endif
#if HAVE_DECL_ERFL == 0
extern long double erfl(long double);
#endif
#if HAVE_DECL_ERFCL == 0
extern long double erfcl(long double);
#endif
#if HAVE_DECL_CREALL == 0
extern long double creall(long double _Complex z);
#endif
#if HAVE_DECL_CIMAGL == 0
extern long double cimagl(long double _Complex z);
#endif
#if HAVE_DECL_CABSL == 0
extern long double cabsl(long double _Complex z);
#endif
#if HAVE_DECL_CARGL == 0
extern long double cargl(long double _Complex z);
#endif
#if HAVE_DECL_CONJL == 0
extern long double _Complex conjl(long double _Complex z);
#endif
#if HAVE_DECL_CPROJL == 0
extern long double _Complex cprojl(long double _Complex z);
#endif
#if HAVE_DECL_CSQRTL == 0
extern long double _Complex csqrtl(long double _Complex z);
#endif
#if HAVE_DECL_CEXPL == 0
extern long double _Complex cexpl(long double _Complex z);
#endif
#if HAVE_DECL_CLOGL == 0
extern long double _Complex clogl(long double _Complex z);
#endif
#if HAVE_DECL_CPOWL == 0
extern long double _Complex cpowl(long double _Complex z, long double _Complex w);
#endif
#if HAVE_DECL_CSINL == 0
extern long double _Complex csinl(long double _Complex z);
#endif
#if HAVE_DECL_CCOSL == 0
extern long double _Complex ccosl(long double _Complex z);
#endif
#if HAVE_DECL_CTANL == 0
extern long double _Complex ctanl(long double _Complex z);
#endif
#if HAVE_DECL_CASINL == 0
extern long double _Complex casinl(long double _Complex z);
#endif
#if HAVE_DECL_CACOSL == 0
extern long double _Complex cacosl(long double _Complex z);
#endif
#if HAVE_DECL_CATANL == 0
extern long double _Complex catanl(long double _Complex z);
#endif
#if HAVE_DECL_CSINHL == 0
extern long double _Complex csinhl(long double _Complex z);
#endif
#if HAVE_DECL_CCOSHL == 0
extern long double _Complex ccoshl(long double _Complex z);
#endif
#if HAVE_DECL_CTANHL == 0
extern long double _Complex ctanhl(long double _Complex z);
#endif
#if HAVE_DECL_CASINHL == 0
extern long double _Complex casinhl(long double _Complex z);
#endif
#if HAVE_DECL_CACOSHL == 0
extern long double _Complex cacoshl(long double _Complex z);
#endif
#if HAVE_DECL_CATANHL == 0
extern long double _Complex catanhl(long double _Complex z);
#endif
#define COPYSIGN copysignl
#define NEXTAFTER nextafterl
#define MKNAN nanl
#define CEIL ceill
#define FLOOR floorl
#define NEARBYINT nearbyintl
#define RINT rintl
#define ROUND roundl
#define LRINT lrintl
#define LROUND lroundl
#define LLRINT llrintl
#define LLROUND llroundl
#define TRUNC truncl
#define FMOD fmodl
#define REMAINDER remainderl
#define REMQUO remquol
#define FDIM fdiml
#define FMAX fmaxl
#define FMIN fminl
#define FFMA fmal
#define FABS fabsl
#define SQRT sqrtl
#define CBRT cbrtl
#define HYPOT hypotl
#define EXP expl
#define EXP2 exp2l
#define EXPM1 expm1l
#define LOG logl
#define LOG2 log2l
#define LOG10 log10l
#define LOG1P log1pl
#define LOGB logbl
#define ILOGB ilogbl
#define MODF modfl
#define FREXP frexpl
#define LDEXP ldexpl
#define SCALBN scalbnl
#define SCALBLN scalblnl
#define POW powl
#define COS cosl
#define SIN sinl
#define TAN tanl
#define COSH coshl
#define SINH sinhl
#define TANH tanhl
#define ACOS acosl
#define ASIN asinl
#define ATAN atanl
#define ATAN2 atan2l
#define ACOSH acoshl
#define ASINH asinhl
#define ATANH atanhl
#define TGAMMA tgammal
#define LGAMMA lgammal
#define J0 j0l
#define J1 j1l
#define JN jnl
#define Y0 y0l
#define Y1 y1l
#define YN ynl
#define ERF erfl
#define ERFC erfcl
#define CREAL creall
#define CIMAG cimagl
#define CABS cabsl
#define CARG cargl
#define CONJ conjl
#define CPROJ cprojl
#define CSQRT csqrtl
#define CEXP cexpl
#define CLOG clogl
#define CPOW cpowl
#define CSIN csinl
#define CCOS ccosl
#define CTAN ctanl
#define CASIN casinl
#define CACOS cacosl
#define CATAN catanl
#define CSINH csinhl
#define CCOSH ccoshl
#define CTANH ctanhl
#define CASINH casinhl
#define CACOSH cacoshl
#define CATANH catanhl
#elif defined(NFFT_SINGLE)
#if HAVE_DECL_COPYSIGNF == 0
extern float copysignf(float, float);
#endif
#if HAVE_DECL_NEXTAFTERF == 0
extern float nextafterf(float, float);
#endif
#if HAVE_DECL_NANF == 0
extern float nanf(const char *tag);
#endif
#if HAVE_DECL_CEILF == 0
extern float ceilf(float);
#endif
#if HAVE_DECL_FLOORF == 0
extern float floorf(float);
#endif
#if HAVE_DECL_NEARBYINTF == 0
extern float nearbyintf(float);
#endif
#if HAVE_DECL_RINTF == 0
extern float rintf(float);
#endif
#if HAVE_DECL_ROUNDF == 0
extern float roundf(float);
#endif
#if HAVE_DECL_LRINTF == 0
extern long int lrintf(float);
#endif
#if HAVE_DECL_LROUNDF == 0
extern long int lroundf(float);
#endif
#if HAVE_DECL_LLRINTF == 0
extern long long int llrintf(float);
#endif
#if HAVE_DECL_LLROUNDF == 0
extern long long int llroundf(float);
#endif
#if HAVE_DECL_TRUNCF == 0
extern float truncf(float);
#endif
#if HAVE_DECL_FMODF == 0
extern float fmodf(float, float);
#endif
#if HAVE_DECL_REMAINDERF == 0
extern float remainderf(float, float);
#endif
#if HAVE_DECL_REMQUOF == 0
extern float remquof(float x, float y, int *);
#endif
#if HAVE_DECL_FDIMF == 0
extern float fdimf(float, float);
#endif
#if HAVE_DECL_FMAXF == 0
extern float fmaxf(float, float);
#endif
#if HAVE_DECL_FMINF == 0
extern float fminf(float, float);
#endif
#if HAVE_DECL_FMAF == 0
extern float fmaf(float x, float y, float z);
#endif
#if HAVE_DECL_FABSF == 0
extern float fabsf(float);
#endif
#if HAVE_DECL_SQRTF == 0
extern float sqrtf(float);
#endif
#if HAVE_DECL_CBRTF == 0
extern float cbrtf(float);
#endif
#if HAVE_DECL_HYPOTF == 0
extern float hypotf(float, float);
#endif
#if HAVE_DECL_EXPF == 0
extern float expf(float);
#endif
#if HAVE_DECL_EXP2F == 0
extern float exp2f(float);
#endif
#if HAVE_DECL_EXPM1F == 0
extern float expm1f(float);
#endif
#if HAVE_DECL_LOGF == 0
extern float logf(float);
#endif
#if HAVE_DECL_LOG2F == 0
extern float log2f(float);
#endif
#if HAVE_DECL_LOG10F == 0
extern float log10f(float);
#endif
#if HAVE_DECL_LOG1PF == 0
extern float log1pf(float);
#endif
#if HAVE_DECL_LOGBF == 0
extern float logbf(float);
#endif
#if HAVE_DECL_ILOGBF == 0
extern int ilogbf(float);
#endif
#if HAVE_DECL_MODFF == 0
extern float modff(float, float *);
#endif
#if HAVE_DECL_FREXPF == 0
extern float frexpf(float, int *);
#endif
#if HAVE_DECL_LDEXPF == 0
extern float ldexpf(float, int);
#endif
#if HAVE_DECL_SCALBNF == 0
extern float scalbnf(float, int);
#endif
#if HAVE_DECL_SCALBLNF == 0
extern float scalblnf(float, long int);
#endif
#if HAVE_DECL_POWF == 0
extern float powf(float, float);
#endif
#if HAVE_DECL_COSF == 0
extern float cosf(float);
#endif
#if HAVE_DECL_SINF == 0
extern float sinf(float);
#endif
#if HAVE_DECL_TANF == 0
extern float tanf(float);
#endif
#if HAVE_DECL_COSHF == 0
extern float coshf(float);
#endif
#if HAVE_DECL_SINHF == 0
extern float sinhf(float);
#endif
#if HAVE_DECL_TANHF == 0
extern float tanhf(float);
#endif
#if HAVE_DECL_ACOSF == 0
extern float acosf(float);
#endif
#if HAVE_DECL_ASINF == 0
extern float asinf(float);
#endif
#if HAVE_DECL_ATANF == 0
extern float atanf(float);
#endif
#if HAVE_DECL_ATAN2F == 0
extern float atan2f(float, float);
#endif
#if HAVE_DECL_ACOSHF == 0
extern float acoshf(float);
#endif
#if HAVE_DECL_ASINHF == 0
extern float asinhf(float);
#endif
#if HAVE_DECL_ATANHF == 0
extern float atanhf(float);
#endif
#if HAVE_DECL_TGAMMAF == 0
extern float tgammaf(float);
#endif
#if HAVE_DECL_LGAMMAF == 0
extern float lgammaf(float);
#endif
#if HAVE_DECL_J0F == 0
extern float j0f(float);
#endif
#if HAVE_DECL_J1F == 0
extern float j1f(float);
#endif
#if HAVE_DECL_JNF == 0
extern float jnf(int, float);
#endif
#if HAVE_DECL_Y0F == 0
extern float y0f(float);
#endif
#if HAVE_DECL_Y1F == 0
extern float y1f(float);
#endif
#if HAVE_DECL_YNF == 0
extern float ynf(int, float);
#endif
#if HAVE_DECL_ERFF == 0
extern float erff(float);
#endif
#if HAVE_DECL_ERFCF == 0
extern float erfcf(float);
#endif
#if HAVE_DECL_CREALF == 0
extern float crealf(float _Complex z);
#endif
#if HAVE_DECL_CIMAGF == 0
extern float cimagf(float _Complex z);
#endif
#if HAVE_DECL_CABSF == 0
extern float cabsf(float _Complex z);
#endif
#if HAVE_DECL_CARGF == 0
extern float cargf(float _Complex z);
#endif
#if HAVE_DECL_CONJF == 0
extern float _Complex conjf(float _Complex z);
#endif
#if HAVE_DECL_CPROJF == 0
extern float _Complex cprojf(float _Complex z);
#endif
#if HAVE_DECL_CSQRTF == 0
extern float _Complex csqrtf(float _Complex z);
#endif
#if HAVE_DECL_CEXPF == 0
extern float _Complex cexpf(float _Complex z);
#endif
#if HAVE_DECL_CLOGF == 0
extern float _Complex clogf(float _Complex z);
#endif
#if HAVE_DECL_CPOWF == 0
extern float _Complex cpowf(float _Complex z, float _Complex w);
#endif
#if HAVE_DECL_CSINF == 0
extern float _Complex csinf(float _Complex z);
#endif
#if HAVE_DECL_CCOSF == 0
extern float _Complex ccosf(float _Complex z);
#endif
#if HAVE_DECL_CTANF == 0
extern float _Complex ctanf(float _Complex z);
#endif
#if HAVE_DECL_CASINF == 0
extern float _Complex casinf(float _Complex z);
#endif
#if HAVE_DECL_CACOSF == 0
extern float _Complex cacosf(float _Complex z);
#endif
#if HAVE_DECL_CATANF == 0
extern float _Complex catanf(float _Complex z);
#endif
#if HAVE_DECL_CSINHF == 0
extern float _Complex csinhf(float _Complex z);
#endif
#if HAVE_DECL_CCOSHF == 0
extern float _Complex ccoshf(float _Complex z);
#endif
#if HAVE_DECL_CTANHF == 0
extern float _Complex ctanhf(float _Complex z);
#endif
#if HAVE_DECL_CASINHF == 0
extern float _Complex casinhf(float _Complex z);
#endif
#if HAVE_DECL_CACOSHF == 0
extern float _Complex cacoshf(float _Complex z);
#endif
#if HAVE_DECL_CATANHF == 0
extern float _Complex catanhf(float _Complex z);
#endif
#define COPYSIGN copysignf
#define NEXTAFTER nextafterf
#define MKNAN nanf
#define CEIL ceilf
#define FLOOR floorf
#define NEARBYINT nearbyintf
#define RINT rintf
#define ROUND roundf
#define LRINT lrintf
#define LROUND lroundf
#define LLRINT llrintf
#define LLROUND llroundf
#define TRUNC truncf
#define FMOD fmodf
#define REMAINDER remainderf
#define REMQUO remquof
#define FDIM fdimf
#define FMAX fmaxf
#define FMIN fminf
#define FFMA fmaf
#define FABS fabsf
#define SQRT sqrtf
#define CBRT cbrtf
#define HYPOT hypotf
#define EXP expf
#define EXP2 exp2f
#define EXPM1 expm1f
#define LOG logf
#define LOG2 log2f
#define LOG10 log10f
#define LOG1P log1pf
#define LOGB logbf
#define ILOGB ilogbf
#define MODF modff
#define FREXP frexpf
#define LDEXP ldexpf
#define SCALBN scalbnf
#define SCALBLN scalblnf
#define POW powf
#define COS cosf
#define SIN sinf
#define TAN tanf
#define COSH coshf
#define SINH sinhf
#define TANH tanhf
#define ACOS acosf
#define ASIN asinf
#define ATAN atanf
#define ATAN2 atan2f
#define ACOSH acoshf
#define ASINH asinhf
#define ATANH atanhf
#define TGAMMA tgammaf
#define LGAMMA lgammaf
#define J0 j0f
#define J1 j1f
#define JN jnf
#define Y0 y0f
#define Y1 y1f
#define YN ynf
#define ERF erff
#define ERFC erfcf
#define CREAL crealf
#define CIMAG cimagf
#define CABS cabsf
#define CARG cargf
#define CONJ conjf
#define CPROJ cprojf
#define CSQRT csqrtf
#define CEXP cexpf
#define CLOG clogf
#define CPOW cpowf
#define CSIN csinf
#define CCOS ccosf
#define CTAN ctanf
#define CASIN casinf
#define CACOS cacosf
#define CATAN catanf
#define CSINH csinhf
#define CCOSH ccoshf
#define CTANH ctanhf
#define CASINH casinhf
#define CACOSH cacoshf
#define CATANH catanhf
#else
#if HAVE_DECL_COPYSIGN == 0
extern double copysign(double, double);
#endif
#if HAVE_DECL_NEXTAFTER == 0
extern double nextafter(double, double);
#endif
#if HAVE_DECL_NAN == 0
extern double nan(const char *tag);
#endif
#if HAVE_DECL_CEIL == 0
extern double ceil(double);
#endif
#if HAVE_DECL_FLOOR == 0
extern double floor(double);
#endif
#if HAVE_DECL_NEARBYINT == 0
extern double nearbyint(double);
#endif
#if HAVE_DECL_RINT == 0
extern double rint(double);
#endif
#if HAVE_DECL_ROUND == 0
extern double round(double);
#endif
#if HAVE_DECL_LRINT == 0
extern long int lrint(double);
#endif
#if HAVE_DECL_LROUND == 0
extern long int lround(double);
#endif
#if HAVE_DECL_LLRINT == 0
extern long long int llrint(double);
#endif
#if HAVE_DECL_LLROUND == 0
extern long long int llround(double);
#endif
#if HAVE_DECL_TRUNC == 0
extern double trunc(double);
#endif
#if HAVE_DECL_FMOD == 0
extern double fmod(double, double);
#endif
#if HAVE_DECL_REMAINDER == 0
extern double remainder(double, double);
#endif
#if HAVE_DECL_REMQUO == 0
extern double remquo(double x, double y, int *);
#endif
#if HAVE_DECL_FDIM == 0
extern double fdim(double, double);
#endif
#if HAVE_DECL_FMAX == 0
extern double fmax(double, double);
#endif
#if HAVE_DECL_FMIN == 0
extern double fmin(double, double);
#endif
#if HAVE_DECL_FMA == 0
extern double fma(double x, double y, double z);
#endif
#if HAVE_DECL_FABS == 0
extern double fabs(double);
#endif
#if HAVE_DECL_SQRT == 0
extern double sqrt(double);
#endif
#if HAVE_DECL_CBRT == 0
extern double cbrt(double);
#endif
#if HAVE_DECL_HYPOT == 0
extern double hypot(double, double);
#endif
#if HAVE_DECL_EXP == 0
extern double exp(double);
#endif
#if HAVE_DECL_EXP2 == 0
extern double exp2(double);
#endif
#if HAVE_DECL_EXPM1 == 0
extern double expm1(double);
#endif
#if HAVE_DECL_LOG == 0
extern double log(double);
#endif
#if HAVE_DECL_LOG2 == 0
extern double log2(double);
#endif
#if HAVE_DECL_LOG10 == 0
extern double log10(double);
#endif
#if HAVE_DECL_LOG1P == 0
extern double log1p(double);
#endif
#if HAVE_DECL_LOGB == 0
extern double logb(double);
#endif
#if HAVE_DECL_ILOGB == 0
extern int ilogb(double);
#endif
#if HAVE_DECL_MODF == 0
extern double modf(double, double *);
#endif
#if HAVE_DECL_FREXP == 0
extern double frexp(double, int *);
#endif
#if HAVE_DECL_LDEXP == 0
extern double ldexp(double, int);
#endif
#if HAVE_DECL_SCALBN == 0
extern double scalbn(double, int);
#endif
#if HAVE_DECL_SCALBLN == 0
extern double scalbln(double, long int);
#endif
#if HAVE_DECL_POW == 0
extern double pow(double, double);
#endif
#if HAVE_DECL_COS == 0
extern double cos(double);
#endif
#if HAVE_DECL_SIN == 0
extern double sin(double);
#endif
#if HAVE_DECL_TAN == 0
extern double tan(double);
#endif
#if HAVE_DECL_COSH == 0
extern double cosh(double);
#endif
#if HAVE_DECL_SINH == 0
extern double sinh(double);
#endif
#if HAVE_DECL_TANH == 0
extern double tanh(double);
#endif
#if HAVE_DECL_ACOS == 0
extern double acos(double);
#endif
#if HAVE_DECL_ASIN == 0
extern double asin(double);
#endif
#if HAVE_DECL_ATAN == 0
extern double atan(double);
#endif
#if HAVE_DECL_ATAN2 == 0
extern double atan2(double, double);
#endif
#if HAVE_DECL_ACOSH == 0
extern double acosh(double);
#endif
#if HAVE_DECL_ASINH == 0
extern double asinh(double);
#endif
#if HAVE_DECL_ATANH == 0
extern double atanh(double);
#endif
#if HAVE_DECL_TGAMMA == 0
extern double tgamma(double);
#endif
#if HAVE_DECL_LGAMMA == 0
extern double lgamma(double);
#endif
#if HAVE_DECL_J0 == 0
extern double j0(double);
#endif
#if HAVE_DECL_J1 == 0
extern double j1(double);
#endif
#if HAVE_DECL_JN == 0
extern double jn(int, double);
#endif
#if HAVE_DECL_Y0 == 0
extern double y0(double);
#endif
#if HAVE_DECL_Y1 == 0
extern double y1(double);
#endif
#if HAVE_DECL_YN == 0
extern double yn(int, double);
#endif
#if HAVE_DECL_ERF == 0
extern double erf(double);
#endif
#if HAVE_DECL_ERFC == 0
extern double erfc(double);
#endif
#if HAVE_DECL_CREAL == 0
extern double creal(double _Complex z);
#endif
#if HAVE_DECL_CIMAG == 0
extern double cimag(double _Complex z);
#endif
#if HAVE_DECL_CABS == 0
extern double cabs(double _Complex z);
#endif
#if HAVE_DECL_CARG == 0
extern double carg(double _Complex z);
#endif
#if HAVE_DECL_CONJ == 0
extern double _Complex conj(double _Complex z);
#endif
#if HAVE_DECL_CPROJ == 0
extern double _Complex cproj(double _Complex z);
#endif
#if HAVE_DECL_CSQRT == 0
extern double _Complex csqrt(double _Complex z);
#endif
#if HAVE_DECL_CEXP == 0
extern double _Complex cexp(double _Complex z);
#endif
#if HAVE_DECL_CLOG == 0
extern double _Complex clog(double _Complex z);
#endif
#if HAVE_DECL_CPOW == 0
extern double _Complex cpow(double _Complex z, double _Complex w);
#endif
#if HAVE_DECL_CSIN == 0
extern double _Complex csin(double _Complex z);
#endif
#if HAVE_DECL_CCOS == 0
extern double _Complex ccos(double _Complex z);
#endif
#if HAVE_DECL_CTAN == 0
extern double _Complex ctan(double _Complex z);
#endif
#if HAVE_DECL_CASIN == 0
extern double _Complex casin(double _Complex z);
#endif
#if HAVE_DECL_CACOS == 0
extern double _Complex cacos(double _Complex z);
#endif
#if HAVE_DECL_CATAN == 0
extern double _Complex catan(double _Complex z);
#endif
#if HAVE_DECL_CSINH == 0
extern double _Complex csinh(double _Complex z);
#endif
#if HAVE_DECL_CCOSH == 0
extern double _Complex ccosh(double _Complex z);
#endif
#if HAVE_DECL_CTANH == 0
extern double _Complex ctanh(double _Complex z);
#endif
#if HAVE_DECL_CASINH == 0
extern double _Complex casinh(double _Complex z);
#endif
#if HAVE_DECL_CACOSH == 0
extern double _Complex cacosh(double _Complex z);
#endif
#if HAVE_DECL_CATANH == 0
extern double _Complex catanh(double _Complex z);
#endif
#define COPYSIGN copysign
#define NEXTAFTER nextafter
#define MKNAN nan
#define CEIL ceil
#define FLOOR floor
#define NEARBYINT nearbyint
#define RINT rint
#define ROUND round
#define LRINT lrint
#define LROUND lround
#define LLRINT llrint
#define LLROUND llround
#define TRUNC trunc
#define FMOD fmod
#define REMAINDER remainder
#define REMQUO remquo
#define FDIM fdim
#define FMAX fmax
#define FMIN fmin
#define FFMA fma
#define FABS fabs
#define SQRT sqrt
#define CBRT cbrt
#define HYPOT hypot
#define EXP exp
#define EXP2 exp2
#define EXPM1 expm1
#define LOG log
#define LOG2 log2
#define LOG10 log10
#define LOG1P log1p
#define LOGB logb
#define ILOGB ilogb
#define MODF modf
#define FREXP frexp
#define LDEXP ldexp
#define SCALBN scalbn
#define SCALBLN scalbln
#define POW pow
#define COS cos
#define SIN sin
#define TAN tan
#define COSH cosh
#define SINH sinh
#define TANH tanh
#define ACOS acos
#define ASIN asin
#define ATAN atan
#define ATAN2 atan2
#define ACOSH acosh
#define ASINH asinh
#define ATANH atanh
#define TGAMMA tgamma
#define LGAMMA lgamma
#define J0 j0
#define J1 j1
#define JN jn
#define Y0 y0
#define Y1 y1
#define YN yn
#define ERF erf
#define ERFC erfc
#define CREAL creal
#define CIMAG cimag
#define CABS cabs
#define CARG carg
#define CONJ conj
#define CPROJ cproj
#define CSQRT csqrt
#define CEXP cexp
#define CLOG clog
#define CPOW cpow
#define CSIN csin
#define CCOS ccos
#define CTAN ctan
#define CASIN casin
#define CACOS cacos
#define CATAN catan
#define CSINH csinh
#define CCOSH ccosh
#define CTANH ctanh
#define CASINH casinh
#define CACOSH cacosh
#define CATANH catanh
#endif
#if defined(NFFT_LDOUBLE)
#define MANT_DIG LDBL_MANT_DIG
#define MIN_EXP LDBL_MIN_EXP
#define MAX_EXP LDBL_MAX_EXP
#define EPSILON LDBL_EPSILON
#elif defined(NFFT_SINGLE)
#define MANT_DIG FLT_MANT_DIG
#define MIN_EXP FLT_MIN_EXP
#define MAX_EXP FLT_MAX_EXP
#define EPSILON FLT_EPSILON
#else
#define MANT_DIG DBL_MANT_DIG
#define MIN_EXP DBL_MIN_EXP
#define MAX_EXP DBL_MAX_EXP
#define EPSILON DBL_EPSILON
#endif
#if defined(FLT_ROUND)
#if FLT_ROUND != -1
#define FLTROUND 1.0
#else
#define FLTROUND 0.0
#endif
#else
#define FLTROUND 0.0
#endif
#if HAVE_DECL_DRAND48 == 0
extern double drand48(void);
#endif
#if HAVE_DECL_SRAND48 == 0
extern void srand48(long int);
#endif
#define R_RADIX FLT_RADIX
#define II _Complex_I
/* format strings */
#if defined(NFFT_LDOUBLE)
# define __FGS__ "Lg"
# define __FES__ "LE"
# define __FE__ "% 36.32LE"
# define __FI__ "%Lf"
# define __FIS__ "Lf"
# define __FR__ "%Le"
#elif defined(NFFT_SINGLE)
# define __FGS__ "g"
# define __FES__ "E"
# define __FE__ "% 12.8E"
# define __FI__ "%f"
# define __FIS__ "f"
# define __FR__ "%e"
#else
# define __FGS__ "lg"
# define __FES__ "lE"
# define __FE__ "% 20.16lE"
# define __FI__ "%lf"
# define __FIS__ "lf"
# define __FR__ "%le"
#endif
#define TRUE 1
#define FALSE 0
#if defined(_WIN32) || defined(_WIN64)
# define __D__ "%Id"
#else
# define __D__ "%td"
#endif
#define UNUSED(x) (void)x
#ifdef HAVE_ALLOCA
/* Use alloca if available. */
#ifndef alloca
#ifdef __GNUC__
/* No alloca defined but can use GCC's builtin version. */
#define alloca __builtin_alloca
#else
/* No alloca defined and not using GCC. */
#ifdef _MSC_VER
/* Using Microsoft's C compiler. Include header file and use _alloca
* defined therein. */
#include <malloc.h>
#define alloca _alloca
#else
/* Also not using Microsoft's C compiler. */
#if HAVE_ALLOCA_H
/* Alloca header is available. */
#include <alloca.h>
#else
/* No alloca header available. */
#ifdef _AIX
/* We're using the AIX C compiler. Use pragma. */
#pragma alloca
#else
/* Not using AIX compiler. */
#ifndef alloca /* HP's cc +Olibcalls predefines alloca. */
void *alloca(size_t);
#endif
#endif
#endif
#endif
#endif
#endif
/* So we have alloca. */
#define STACK_MALLOC(T, p, x) p = (T)alloca(x)
#define STACK_FREE(x) /* Nothing. Cleanup done automatically. */
#else /* ! HAVE_ALLOCA */
/* Use malloc instead of alloca. So we allocate memory on the heap instead of
* on the stack which is slower. */
#define STACK_MALLOC(T, p, x) p = (T)Y(malloc)(x)
#define STACK_FREE(x) Y(free)(x)
#endif /* ! HAVE_ALLOCA */
R Y(elapsed_seconds)(ticks t1, ticks t0);
#define UNUSED(x) (void)x
#ifdef MEASURE_TIME
int MEASURE_TIME_r;
double MEASURE_TIME_tt;
ticks MEASURE_TIME_t0, MEASURE_TIME_t1;
#define TIC(a) \
ths->MEASURE_TIME_t[(a)]=0; \
MEASURE_TIME_r=0; \
/* DISABLED LOOP due to code blocks causing segfault when repeatedly run */ \
/*while(ths->MEASURE_TIME_t[(a)]<0.01)*/ \
{ \
MEASURE_TIME_r++; \
MEASURE_TIME_t0 = getticks(); \
/* THE MEASURED FUNCTION IS CALLED REPEATEDLY */
#define TOC(a) \
MEASURE_TIME_t1 = getticks(); \
MEASURE_TIME_tt = Y(elapsed_seconds)(MEASURE_TIME_t1,MEASURE_TIME_t0);\
ths->MEASURE_TIME_t[(a)]+=MEASURE_TIME_tt; \
} \
ths->MEASURE_TIME_t[(a)]/=MEASURE_TIME_r; \
#else
#define TIC(a)
#define TOC(a)
#endif
#ifdef MEASURE_TIME_FFTW
#define TIC_FFTW(a) TIC(a)
#define TOC_FFTW(a) TOC(a)
#else
#define TIC_FFTW(a)
#define TOC_FFTW(a)
#endif
/* sinc.c: */
/* Sinus cardinalis. */
R Y(sinc)(R x);
/* lambda.c: */
/* lambda(z, eps) = gamma(z + eps) / gamma(z + 1) */
R Y(lambda)(R z, R eps);
/* lambda2(mu, nu) = sqrt(gamma(mu + nu + 1) / (gamma(mu + 1) * gamma(nu + 1))) */
R Y(lambda2)(R mu, R nu);
/* bessel_i0.c: */
R Y(bessel_i0)(R x);
/* bspline.c: */
R Y(bsplines)(const INT, const R x);
/* float.c: */
typedef enum {NFFT_EPSILON = 0, NFFT_SAFE__MIN = 1, NFFT_BASE = 2,
NFFT_PRECISION = 3, NFFT_MANT_DIG = 4, NFFT_FLTROUND = 5, NFFT_E_MIN = 6,
NFFT_R_MIN = 7, NFFT_E_MAX = 8, NFFT_R_MAX = 9 } float_property;
R Y(float_property)(float_property);
R Y(prod_real)(R *vec, INT d);
/* int.c: */
INT Y(log2i)(const INT m);
void Y(next_power_of_2_exp)(const INT N, INT *N2, INT *t);
void Y(next_power_of_2_exp_int)(const int N, int *N2, int *t);
/* error.c: */
/* not used */ R Y(error_l_infty_double)(const R *x, const R *y, const INT n);
/* not used */ R Y(error_l_infty_1_double)(const R *x, const R *y, const INT n, const R *z,
const INT m);
R Y(error_l_2_complex)(const C *x, const C *y, const INT n);
/* not used */ R Y(error_l_2_double)(const R *x, const R *y, const INT n);
/* sort.c: */
void Y(sort_node_indices_radix_msdf)(INT n, INT *keys0, INT *keys1, INT rhigh);
void Y(sort_node_indices_radix_lsdf)(INT n, INT *keys0, INT *keys1, INT rhigh);
/* assert.c */
void Y(assertion_failed)(const char *s, int line, const char *file);
/* vector1.c */
R Y(dot_double)(R *x, INT n);
R Y(dot_w_complex)(C *x, R *w, INT n);
R Y(dot_w_double)(R *x, R *w, INT n);
R Y(dot_w_w2_complex)(C *x, R *w, R *w2, INT n);
R Y(dot_w2_complex)(C *x, R *w2, INT n);
/* vector2.c */
void Y(cp_complex)(C *x, C *y, INT n);
void Y(cp_double)(R *x, R *y, INT n);
void Y(cp_a_complex)(C *x, R a, C *y, INT n);
void Y(cp_a_double)(R *x, R a, R *y, INT n);
void Y(cp_w_complex)(C *x, R *w, C *y, INT n);
void Y(cp_w_double)(R *x, R *w, R *y, INT n);
/* vector3.c */
void Y(upd_axpy_double)(R *x, R a, R *y, INT n);
void Y(upd_xpay_complex)(C *x, R a, C *y, INT n);
void Y(upd_xpay_double)(R *x, R a, R *y, INT n);
void Y(upd_axpby_complex)(C *x, R a, C *y, R b, INT n);
void Y(upd_axpby_double)(R *x, R a, R *y, R b, INT n);
void Y(upd_xpawy_complex)(C *x, R a, R *w, C *y, INT n);
void Y(upd_xpawy_double)(R *x, R a, R *w, R *y, INT n);
void Y(upd_axpwy_complex)(C *x, R a, R *w, C *y, INT n);
void Y(upd_axpwy_double)(R *x, R a, R *w, R *y, INT n);
/* voronoi.c */
void Y(voronoi_weights_1d)(R *w, R *x, const INT M);
/* damp.c */
R Y(modified_fejer)(const INT N, const INT kk);
R Y(modified_jackson2)(const INT N, const INT kk);
R Y(modified_jackson4)(const INT N, const INT kk);
R Y(modified_sobolev)(const R mu, const INT kk);
R Y(modified_multiquadric)(const R mu, const R c, const INT kk);
/* always check */
#define CK(ex) \
(void)((ex) || (Y(assertion_failed)(#ex, __LINE__, __FILE__), 0))
#ifdef NFFT_DEBUG
/* check only if debug enabled */
#define A(ex) \
(void)((ex) || (Y(assertion_failed)(#ex, __LINE__, __FILE__), 0))
#else
#define A(ex) /* nothing */
#endif
#endif