The R Project SVN R

/*
 *  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;
}