stats/src/fourier.c

/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 1998--2020  The R Core Team
 *  Copyright (C) 1995--1997  Robert Gentleman and Ross Ihaka
 *
 *  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, a copy is available at
 *  https://www.R-project.org/Licenses/
 */

/* These are the R interface routines to the plain FFT code
   fft_factor() & fft_work() in fft.c. */

#include <inttypes.h>
// for PRIu64

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <Defn.h>

#undef _
#ifdef ENABLE_NLS
#include <libintl.h>
#define _(String) dgettext ("stats", String)
#else
#define _(String) (String)
#endif


// workhorse routines from fft.c
void fft_factor(int n, int *pmaxf, int *pmaxp);
Rboolean fft_work(double *a, double *b, int nseg, int n, int nspn,
		  int isn, double *work, int *iwork);

#include "statsR.h"

/* Fourier Transform for Univariate Spatial and Time Series */

SEXP fft(SEXP z, SEXP inverse)
{
    SEXP d;
    int i, inv, maxf, maxmaxf, maxmaxp, maxp, n, ndims, nseg, nspn;
    double *work;
    int *iwork;
    size_t smaxf;
    size_t maxsize = ((size_t) -1) / 4;

    switch (TYPEOF(z)) {
    case INTSXP:
    case LGLSXP:
    case REALSXP:
	z = coerceVector(z, CPLXSXP);
	break;
    case CPLXSXP:
	if (MAYBE_REFERENCED(z)) z = duplicate(z);
	break;
    default:
	error(_("non-numeric argument"));
    }
    PROTECT(z);

    /* -2 for forward transform, complex values */
    /* +2 for backward transform, complex values */

    inv = asLogical(inverse);
    if (inv == NA_INTEGER || inv == 0)
	inv = -2;
    else
	inv = 2;

    if (LENGTH(z) > 1) {
	if (isNull(d = getAttrib(z, R_DimSymbol))) {  /* temporal transform */
	    n = length(z);
	    fft_factor(n, &maxf, &maxp);
	    if (maxf == 0)
		error(_("fft factorization error"));
	    smaxf = maxf;
	    if (smaxf > maxsize)
		error("fft too large");
	    work = (double*)R_alloc(4 * smaxf, sizeof(double));
	    iwork = (int*)R_alloc(maxp, sizeof(int));
	    fft_work(&(COMPLEX(z)[0].r), &(COMPLEX(z)[0].i),
		     1, n, 1, inv, work, iwork);
	}
	else {					     /* spatial transform */
	    maxmaxf = 1;
	    maxmaxp = 1;
	    ndims = LENGTH(d);
	    /* do whole loop just for error checking and maxmax[fp] .. */
	    for (i = 0; i < ndims; i++) {
		if (INTEGER(d)[i] > 1) {
		    fft_factor(INTEGER(d)[i], &maxf, &maxp);
		    if (maxf == 0)
			error(_("fft factorization error"));
		    if (maxf > maxmaxf)
			maxmaxf = maxf;
		    if (maxp > maxmaxp)
			maxmaxp = maxp;
		}
	    }
	    smaxf = maxmaxf;
	    if (smaxf > maxsize)
		error("fft too large");
	    work = (double*)R_alloc(4 * smaxf, sizeof(double));
	    iwork = (int*)R_alloc(maxmaxp, sizeof(int));
	    nseg = LENGTH(z);
	    n = 1;
	    nspn = 1;
	    for (i = 0; i < ndims; i++) {
		if (INTEGER(d)[i] > 1) {
		    nspn *= n;
		    n = INTEGER(d)[i];
		    nseg /= n;
		    fft_factor(n, &maxf, &maxp);
		    fft_work(&(COMPLEX(z)[0].r), &(COMPLEX(z)[0].i),
			     nseg, n, nspn, inv, work, iwork);
		}
	    }
	}
    }
    UNPROTECT(1);
    return z;
}

/* Fourier Transform for Vector-Valued ("multivariate") Series */
/* Not to be confused with the spatial case (in do_fft). */

SEXP mvfft(SEXP z, SEXP inverse)
{
    SEXP d;
    int i, inv, maxf, maxp, n, p;
    double *work;
    int *iwork;
    size_t smaxf;
    size_t maxsize = ((size_t) -1) / 4;

    d = getAttrib(z, R_DimSymbol);
    if (d == R_NilValue || length(d) > 2)
	error(_("vector-valued (multivariate) series required"));
    n = INTEGER(d)[0];
    p = INTEGER(d)[1];

    switch(TYPEOF(z)) {
    case INTSXP:
    case LGLSXP:
    case REALSXP:
	z = coerceVector(z, CPLXSXP);
	break;
    case CPLXSXP:
	if (MAYBE_REFERENCED(z)) z = duplicate(z);
	break;
    default:
	error(_("non-numeric argument"));
    }
    PROTECT(z);

    /* -2 for forward  transform, complex values */
    /* +2 for backward transform, complex values */

    inv = asLogical(inverse);
    if (inv == NA_INTEGER || inv == 0) inv = -2;
    else inv = 2;

    if (n > 1) {
	fft_factor(n, &maxf, &maxp);
	if (maxf == 0)
	    error(_("fft factorization error"));
	smaxf = maxf;
	if (smaxf > maxsize)
	    error("fft too large");
	work = (double*)R_alloc(4 * smaxf, sizeof(double));
	iwork = (int*)R_alloc(maxp, sizeof(int));
	for (i = 0; i < p; i++) {
	    fft_factor(n, &maxf, &maxp);
	    fft_work(&(COMPLEX(z)[i*n].r), &(COMPLEX(z)[i*n].i),
		     1, n, 1, inv, work, iwork);
	}
    }
    UNPROTECT(1);
    return z;
}

static Rboolean ok_n(int n, const int f[], int nf)
{
    for (int i = 0; i < nf; i++) {
	while(n % f[i] == 0) {
	    if ((n = n / f[i]) == 1)
		return TRUE;
	}
    }
    return n == 1;
}
static Rboolean ok_n_64(uint64_t n, const int f[], int nf)
{
    for (int i = 0; i < nf; i++) {
	while(n % f[i] == 0) {
	    if ((n = n / f[i]) == 1)
		return TRUE;
	}
    }
    return n == 1;
}

static int nextn0(int n, const int f[], int nf)
{
    while(!ok_n(n, f, nf) && n < INT_MAX)
	n++;
    if(n >= INT_MAX) {
	warning(_("nextn() found no solution < %d = INT_MAX (the maximal integer);"
		  " pass '0+ n' instead of 'n'"), // i.e. pass "double" type
		INT_MAX);
	return NA_INTEGER;
    } else
	return n;
}
static uint64_t nextn0_64(uint64_t n, const int f[], int nf)
{
    while(!ok_n_64(n, f, nf) && n < UINT64_MAX)
	n++;
    if(n >= UINT64_MAX) { // or give an error?  previously was much more problematic
	warning(_("nextn<64>() found no solution < %ld = UINT64_MAX (the maximal integer)"),
		UINT64_MAX);
	return 0; // no NA for this type
    } else  // FIXME: R has no 64 int --> The caller may *not* be able to coerce to REALSXP
	return n;
}


SEXP nextn(SEXP n, SEXP f)
{
    if(TYPEOF(n) == NILSXP) // NULL <==> integer(0) :
	return allocVector(INTSXP, 0);
    int nprot = 0;
    if(TYPEOF(f) != INTSXP) { PROTECT(f = coerceVector(f, INTSXP)); nprot++; }
    int nf = LENGTH(f), *f_ = INTEGER(f);
    /* check the factors */
    if (nf == 0) error(_("no factors"));
    if (nf <  0) error(_("too many factors")); // < 0 : from integer overflow
    for (int i = 0; i < nf; i++)
	if (f_[i] == NA_INTEGER || f_[i] <= 1)
	    error(_("invalid factors"));

    Rboolean use_int = TYPEOF(n) == INTSXP;
    if(!use_int && TYPEOF(n) != REALSXP)
	error(_("'n' must have typeof(.) \"integer\" or \"double\""));
    R_xlen_t nn = XLENGTH(n);
    if(!use_int && nn) {
	double *d_n = REAL(n), n_max = -1; // := max_i n[i]
	for (R_xlen_t i = 0; i < nn; i++) {
	    if (!ISNAN(d_n[i]) && d_n[i] > n_max) n_max = d_n[i];
	}
	if(n_max <= INT_MAX / f_[0]) { // maximal n[] should not be too large to find "next n"
	    use_int = TRUE;
	    n = PROTECT(n = coerceVector(n, INTSXP)); nprot++;
	}
    }
    SEXP ans = PROTECT(allocVector(use_int ? INTSXP : REALSXP, nn)); nprot++;
    if(nn == 0) {
	UNPROTECT(nprot);
	return(ans);
    }
    if(use_int) {
	int *n_ = INTEGER(n),
	    *r  = INTEGER(ans);
	for (R_xlen_t i = 0; i < nn; i++) {
	    if (n_[i] == NA_INTEGER)
		r[i] = NA_INTEGER;
	    else if (n_[i] <= 1)
		r[i] = 1;
	    else
		r[i] = nextn0(n_[i], f_, nf);
	}
    } else { // use "double" (as R has no int64 ..)
	double
	    *n_ = REAL(n),
	    *r  = REAL(ans);
	for (R_xlen_t i = 0; i < nn; i++) {
	    if (ISNAN(n_[i]))
		r[i] = NA_REAL;
	    else if (n_[i] <= 1)
		r[i] = 1;
	    else {
		const uint64_t max_dbl_int = 9007199254740992L; // = 2^53
		uint64_t n_n = nextn0_64((uint64_t)n_[i], f_, nf);
		if(n_n > max_dbl_int)
		    warning(_("nextn() = %" PRIu64
			      " > 2^53 may not be exactly representable in R (as \"double\")"),
			    n_n);
		r[i] = (double) n_n;
	    }
	}
    }
    UNPROTECT(nprot);
    return ans;
}