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/* catdvi - get text from DVI files
Copyright (C) 2000-01 Bjoern Brill <brill@fs.math.uni-frankfurt.de>
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., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
#ifndef DENSITY_H
#define DENSITY_H
/* Implements a staircase (i.e. piecewise constant) density function
* on an interval [xmin, xmax].
*
* The domain can be integral or "real" (float, double), the range should
* be "real".
*
* The implementation is NOT numerically sophisticated, so don't expect
* miracles.
*/
/* There's no need to use these two typdefs in an application. They
* are here for logical clarity and easy customization and can be changed
* as needed.
*/
#include "bytesex.h" /* for sint32 */
typedef sint32 scdf_domain_t;
typedef double scdf_range_t;
/* convenience defs - c++ does this automatically */
#ifndef __cplusplus
typedef struct scdf_t scdf_t;
typedef struct scdf_step_t scdf_step_t;
#endif
/* The function is stored as a (singly) linked list of steps. Its value
* f(x) is step.f for x in the half-open interval [step.x, step.next->x) .
* For technical reasons, we keep a last step with last.x = xmax and
* last.next = NULL. last.f is not important since any value f(xmax) will
* give the same integral of f.
*
* Typical applications will traverse [xmin, xmax) as a union of subintervals
* [x0, x1) from left to right. We try to keep this direction efficient.
*/
struct scdf_step_t {
scdf_domain_t x;
scdf_range_t f;
scdf_step_t * next;
};
struct scdf_t {
scdf_domain_t xmin;
scdf_domain_t xmax;
scdf_step_t * head;
scdf_step_t * curr;
};
void scdf_init(
scdf_t * this,
scdf_domain_t xmin,
scdf_domain_t xmax,
scdf_range_t f /* The initial (constant) value of f - usually 0 */
);
void scdf_done(scdf_t * this);
/* Join neighbouring steps with the same f. This should be done at the
* end of a sequence of operations traversing [xmin, xmax] .
*/
void scdf_normalize(scdf_t * this);
/* Force the density function to have at least value fmin in the interval
* [x0, x1). Mathematically: let g have value fmin on [x0, x1) and value
* (-infinity) elsewhere, then f is replaced by the pointwise maximum of
* f and g.
*/
void scdf_force_min_value(
scdf_t * this,
scdf_domain_t x0,
scdf_domain_t x1,
scdf_range_t fmin
);
/* Force f to have at least integral Jmin on [x0, x1]. This is currently
* done by first checking if the integral is large enough anyway, and
* forcing f to have value at least Jmin / (x1 - x0) if not. More
* sophisticated (keeping f smaller in some cases) methods are possible.
* However, some experiments with real world data for the intended application
* (catdvi) have shown that:
* - Methods that tend to evenly distribute the density (like the
* one implemented here) do in almost all cases yield better results
* (both in terms of appearance of output and of shorter lines) than
* an exact "additive" method which gives rather uneven distributions.
* - Replacing Jmin / (x1 - x0) by a quantity deviating at most 1/128
* from the minimal possible value gains 1-3 columns for some lines
* and nothing most of the time.
* Since the currently implemented method is fast and seems to be nearly
* optimal for typical catdvi input, we'll probably stick with it.
*/
void scdf_force_min_integral(
scdf_t * this,
scdf_domain_t x0,
scdf_domain_t x1,
scdf_range_t Jmin
);
/* Find the value of f at x */
scdf_range_t scdf_eval(scdf_t * this, scdf_domain_t x);
/* Compute the integral of f on [x0, x1] */
scdf_range_t scdf_integral(scdf_t * this, scdf_domain_t x0, scdf_domain_t x1);
/* Solve the equation "integral of f on [x0, x1] = J" for x1;
* set errno = EDOM if this is not possible.
*
* The algorithm used has to do a conversion from scdf_range_t to
* scdf_domain_t, which is done by casting a _positive_ value of
* type scdf_range_t to scdf_domain_t. This should result in rounding
* the return value towards (-infinity) in cases where loss of precision
* occurs.
*/
scdf_domain_t scdf_solve_integral_for_x1(
scdf_t * this,
scdf_domain_t x0,
scdf_range_t J
);
/* Create new staircase function
* F(x) = floor(integral(f(t), t = f.xmin..x))
* on the heap; return pointer to it. Abort if OOM.
* F obviously has the same domain of definition as f.
*/
scdf_t * scdf_floor_of_integral(scdf_t * this);
/* Dump a textual representation of f to stderr */
void scdf_dump(scdf_t * this);
#endif
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