/*
 *  R : A Computer Language for Statistical Data Analysis
 *  Copyright (C) 1997--2021  The R Core Team
 *  Copyright (C) 2002--2009  The R Foundation
 *  Copyright (C) 1995, 1996  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 3 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/
 */

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

#include <Defn.h>   // Rexp10  (et al)
#include <float.h>  /* for DBL_MAX */
#include <Graphics.h>
#include <Print.h>
#include <Rmath.h> // for imax2

/* used in graphics and grid */
SEXP CreateAtVector(double axp[], const double usr[], int nint, Rboolean logflag)
{
/*	Create an  'at = ...' vector for  axis(.)
 *	i.e., the vector of tick mark locations,
 *	when none has been specified (= default).
 *
 *	axp[0:2] = (x1, x2, nInt), where x1..x2 are the extreme tick marks
 *		   {unless in log case, where nInt \in {1,2,3 ; -1,-2,....}
 *		    and the `nint' argument is used *instead*.}
 *
 * only if(logflag && axp[2] >= 0)
 *			usr[0:1] is used, additionally
 *
 *	The resulting REAL vector must have length >= 1, ideally >= 2
 */
    SEXP at = R_NilValue;/* -Wall*/
    double dn, rng, small;
    int i, n;
    // "arbitrary" threshold: |delta_tick| / SMALL  is "barely visible" in plot
#define SMALL_F 100.
    if (!logflag || axp[2] < 0) { /* --- linear axis --- Only use axp[] arg. */
	n = (int)(fabs(axp[2]) + 0.25);/* >= 0 */
	dn = imax2(1, n);
	rng = axp[1] - axp[0];
	at = allocVector(REALSXP, n + 1);
	double a_i;
	if(!R_FINITE(rng)) { // need to carefully work around overflow
	    double at_ = axp[0]/dn; // 2021-07: "/dn" avoids overflow
	    rng = axp[1]/dn - at_;
	    small = fabs(rng)/SMALL_F;
#ifdef DEBUG_axis
	    REprintf("CreateAtVector(axp=(%g,%g, %g), log=F, diff(*)=Inf: at_=%g, rng=%g, small=%g\n",
		     axp[0],axp[1], axp[2], at_, rng, small);
#endif
	    int n2 = n/2; // integer division
	    for (i = 0; i <= n2; i++) { // from the left
		a_i = axp[0] + i * rng;
		// REprintf(" at[i=%2d]=%g\n", i+1, a_i);
		REAL(at)[i] = (fabs(a_i) < small) ? 0. : a_i;
	    }
	    for (int i2 = 0; i2 < n-n2; i2++) { // from the right
		i = n-i2; // for(i in n:k) where k = n-(n-n2-1) = n2+1
		a_i = axp[1] - i2 * rng;
		// REprintf(" at[i=%2d]=%g\n", i+1, a_i);
		REAL(at)[i] = (fabs(a_i) < small) ? 0. : a_i;
	    }
	}
	else { // rng is finite (normal case):
	    small = fabs(rng)/SMALL_F/dn;
	    for (i = 0; i <= n; i++) {
		a_i = axp[0] + (i / dn) * rng;
		REAL(at)[i] = (fabs(a_i) < small) ? 0. : a_i;
	    }
	}
    }
    else { /* ------ log axis ----- */
	Rboolean reversed = FALSE;
	double
	    umin = usr[0],
	    umax = usr[1];
	n = (int)(axp[2] + 0.5);
	/* {xy}axp[2] for 'log': GLpretty() [./graphics.c] sets
	   n < 0: very small scale ==> linear axis, above, or
	   n = 1,2,3.  see switch() below */
#ifdef DEBUG_axis
	REprintf("CreateAtVector(axp=(%g,%g,%g), usr=(%g,%g), _log_):",
		 axp[0],axp[1],axp[2],  usr[0],usr[1]);
#endif
	if (umin > umax) {
	    reversed = (axp[0] > axp[1]);
	    if (reversed) {
		/* have *reversed* log axis -- whereas
		 * the switch(n) { .. } below assumes *increasing* values
		 * --> reverse axis direction here, and reverse back at end */
		umin = usr[1];
		umax = usr[0];
		dn = axp[0]; axp[0] = axp[1]; axp[1] = dn;
	    }
	    else {
		/* can the following still happen... ? */
		warning("CreateAtVector \"log\"(from axis()): "
			"usr[0] = %g > %g = usr[1] !", umin, umax);
	    }
	}
	/* allow a fuzz (iff we don't under-/over-flow) since we will do things like 0.2*dn >= umin */
	dn = 1 - 1e-12; if(fabs(umin*dn) >     0.  ) umin *= dn;
	dn = 1 + 1e-12; if(fabs(umax*dn) <= DBL_MAX) umax *= dn;

	dn = axp[0];
	if (dn < DBL_MIN) {/* was 1e-300; now seems too cautious */
	    if (dn <= 0) /* real trouble (once for Solaris) later on */
		error("CreateAtVector [log-axis()]: axp[0] = %g < 0!", dn);
	    else
		warning("CreateAtVector [log-axis()]: small axp[0] = %g", dn);
	}

	/* You get the 3 cases below by
	 *  for (y in 1e-5*c(1,2,8))  plot(y, log = "y")
	 */
	switch(n) {
	case 1: /* large range:	1	 * 10^k */
	{
	    i = (int)(floor(log10(axp[1])) - ceil(log10(axp[0])) + 0.25);
	    // want nint intervals, i.e. typically nint+1 breaks :
	    int ne = i / nint;
	    /* for nint breaks, i.e. typically nint-1 intervals, would be
	     * ne = i / imax2(1, nint - 1);  *PLUS* replace s/nint/nint-1/ below !! */
#ifdef DEBUG_axis
	    REprintf(" .. case 1: umin,umax= %g,%g;\n  (nint=%d, ne=%d); ",
		     umin, umax, nint, ne);
	    if (ne < 1) {
		REprintf("ne = %d <= 0 !!\n\t axp[0:1]=(%g,%g) ==> i = %d, nint = %d; ",
			 ne, axp[0],axp[1], i, nint);
	    }
#endif
	    double l10_max = log10(umax),
		d0 = l10_max - log10(dn);
#ifdef DEBUG_axis
	    REprintf("exponent diff d0=%g\n", d0);
#endif
	    if(ne < 1) ne = 1;
	    else // if ne is too large, i.e, the "final tick" is beyond umax, reduce it :
		while(ne > 1 && nint*ne > d0) {
		    ne--;
#ifdef DEBUG_axis
		    REprintf(" last > umax ==> ne--: ne=%d\n", ne);
#endif
		}
	    int k = 1 + ne / 308; // >= 1, typically == 1.
	    if(k > 1) {// i.e. ne > 308: 10^ne overflows; must split the multiplication
		ne = k*(ne/k); // <= ne_{previous}
#ifdef DEBUG_axis
		REprintf(" original ne > 308: split in k=%d parts; new ne=%d\n", k,ne);
#endif
	    }
	    /* Now, still in exponent-10 range: nint*ne <= d0 = l10_max - log10(dn)
	     * If difference (=: d1) is "large", say > 3, increase the first at[] =: d0
	     */
	    double d1 = d0 - nint*ne; // >= 0
#ifdef DEBUG_axis
	    REprintf("expo.diff d0 - nint*ne =: d1=%g\n", d1);
#endif
	    d0 = dn;

#define Large_D1 5
//              === was '3' all up into R 4.1.0
	    if(d1 > Large_D1) {
		d0 = dn * Rexp10(floor(d1/2));
#ifdef DEBUG_axis
		REprintf("large d1 => d0 := dn * 10 ^ fl(d1/2) = dn * 10^%d = %g\n",
			 (int)floor(d1/2), d0);
#endif
	    }
	    rng = Rexp10((double)ne/k); // = 10^(ne/k) >= 10
	    n=0;
	    dn=d0;
	    while(dn < umax) {
		for(int j=0; j < k; j++)
		    dn *= rng;
		n++;
	    }
#ifdef DEBUG_axis
	    REprintf(" rng:=10^(ne/(k=%d)) = %g => n=%d, final dn=%g\n", k, rng, n, dn);
#endif
	    if (!n)
		error("log - axis(), 'at' creation, _LARGE_ range: "
		      "invalid {xy}axp or par; nint=%d\n"
		      "	 axp[0:1]=(%g,%g), usr[0:1]=(%g,%g); i=%d, ni=%d",
		      nint, axp[0],axp[1], umin,umax, i,ne);
	    at = allocVector(REALSXP, n);
	    dn=d0;
	    for(int i=0; i < n; i++) {
		REAL(at)[i] = dn;
		for(int j=0; j < k; j++)
		    dn *= rng;
	    }
	    break;
	}
	case 2: /* medium range:  1, 5	  * 10^k */
	    n = 0;
	    if (0.5 * dn >= umin) n++;
#ifdef DEBUG_axis
	    REprintf(" .. case 2: (dn, umin,umax, n) = (%g, %g,%g, %d)\n",
		     dn, umin, umax, n);
#endif
	    for (;;) {
		if (dn > umax) break;
		n++;
		if (5 * dn > umax) break;
		n++;
		dn *= 10;
	    }
	    if (!n)
		error("log - axis(), 'at' creation, _MEDIUM_ range: "
		      "invalid {xy}axp or par;\n"
		      "	 axp[0]= %g, usr[0:1]=(%g,%g)",
		      axp[0], umin,umax);

	    at = allocVector(REALSXP, n);
	    dn = axp[0];
	    n = 0;
	    if (0.5 * dn >= umin) REAL(at)[n++] = 0.5 * dn;
	    for (;;) {
		if (dn > umax) break;
		REAL(at)[n++] = dn;
		if (5 * dn > umax) break;
		REAL(at)[n++] = 5 * dn;
		dn *= 10;
	    }
	    break;

	case 3: /* small range:	 1,2,5,10 * 10^k */
	    n = 0;
	    if (0.2 * dn >= umin) n++;
	    if (0.5 * dn >= umin) n++;
	    for (;;) {
		if (dn > umax) break;
		n++;
		if (2 * dn > umax) break;
		n++;
		if (5 * dn > umax) break;
		n++;
		dn *= 10;
	    }
#ifdef DEBUG_axis
	    REprintf(" .. case 3: (umin,umax)-usr[*] = (%g, %g); n=%d, dn=%g\n",
		     umin-usr[reversed? 1: 0],
		     umax-usr[reversed? 0: 1], n, dn);
#endif
	    if (!n)
		error("log - axis(), 'at' creation, _SMALL_ range: "
		      "invalid {xy}axp or par;\n"
		      "	 axp[0]= %g, usr[0:1]=(%g,%g)",
		      axp[0], umin,umax);
	    at = allocVector(REALSXP, n);
	    dn = axp[0];
	    n = 0;
	    if (0.2 * dn >= umin) REAL(at)[n++] = 0.2 * dn;
	    if (0.5 * dn >= umin) REAL(at)[n++] = 0.5 * dn;
	    for (;;) {
		if (dn > umax) break;
		REAL(at)[n++] = dn;
		if (2 * dn > umax) break;
		REAL(at)[n++] = 2 * dn;
		if (5 * dn > umax) break;
		REAL(at)[n++] = 5 * dn;
		dn *= 10;
	    }
	    break;
	default:
	    error("log - axis(), 'at' creation: INVALID {xy}axp[3] = %g",
		  axp[2]);
	}

	if (reversed) {/* reverse back again - last assignment was at[n++]= . */
	    for (i = 0; i < n/2; i++) { /* swap( at[i], at[n-i-1] ) : */
		dn = REAL(at)[i];
		     REAL(at)[i] = REAL(at)[n-i-1];
		                   REAL(at)[n-i-1] = dn;
	    }
	}
    } /* linear / log */
    return at;
}