[deb_ffmpeg.git] / ffmpeg / libavutil / rational.c

/*
 * rational numbers
 * Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
 *
 * This file is part of FFmpeg.
 *
 * FFmpeg is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * FFmpeg 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
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with FFmpeg; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 */

/**
 * @file
 * rational numbers
 * @author Michael Niedermayer <michaelni@gmx.at>
 */

#include "avassert.h"
#include <limits.h>

#include "common.h"
#include "mathematics.h"
#include "rational.h"

int av_reduce(int *dst_num, int *dst_den,
              int64_t num, int64_t den, int64_t max)
{
    AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
    int sign = (num < 0) ^ (den < 0);
    int64_t gcd = av_gcd(FFABS(num), FFABS(den));

    if (gcd) {
        num = FFABS(num) / gcd;
        den = FFABS(den) / gcd;
    }
    if (num <= max && den <= max) {
        a1 = (AVRational) { num, den };
        den = 0;
    }

    while (den) {
        uint64_t x        = num / den;
        int64_t next_den  = num - den * x;
        int64_t a2n       = x * a1.num + a0.num;
        int64_t a2d       = x * a1.den + a0.den;

        if (a2n > max || a2d > max) {
            if (a1.num) x =          (max - a0.num) / a1.num;
            if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);

            if (den * (2 * x * a1.den + a0.den) > num * a1.den)
                a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
            break;
        }

        a0  = a1;
        a1  = (AVRational) { a2n, a2d };
        num = den;
        den = next_den;
    }
    av_assert2(av_gcd(a1.num, a1.den) <= 1U);

    *dst_num = sign ? -a1.num : a1.num;
    *dst_den = a1.den;

    return den == 0;
}

AVRational av_mul_q(AVRational b, AVRational c)
{
    av_reduce(&b.num, &b.den,
               b.num * (int64_t) c.num,
               b.den * (int64_t) c.den, INT_MAX);
    return b;
}

AVRational av_div_q(AVRational b, AVRational c)
{
    return av_mul_q(b, (AVRational) { c.den, c.num });
}

AVRational av_add_q(AVRational b, AVRational c) {
    av_reduce(&b.num, &b.den,
               b.num * (int64_t) c.den +
               c.num * (int64_t) b.den,
               b.den * (int64_t) c.den, INT_MAX);
    return b;
}

AVRational av_sub_q(AVRational b, AVRational c)
{
    return av_add_q(b, (AVRational) { -c.num, c.den });
}

AVRational av_d2q(double d, int max)
{
    AVRational a;
#define LOG2  0.69314718055994530941723212145817656807550013436025
    int exponent;
    int64_t den;
    if (isnan(d))
        return (AVRational) { 0,0 };
    if (fabs(d) > INT_MAX + 3LL)
        return (AVRational) { d < 0 ? -1 : 1, 0 };
    exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
    den = 1LL << (61 - exponent);
    // (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64
    av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
    if ((!a.num || !a.den) && d && max>0 && max<INT_MAX)
        av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);

    return a;
}

int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
{
    /* n/d is q, a/b is the median between q1 and q2 */
    int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
    int64_t b = 2 * (int64_t)q1.den * q2.den;

    /* rnd_up(a*d/b) > n => a*d/b > n */
    int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);

    /* rnd_down(a*d/b) < n => a*d/b < n */
    int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);

    return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
}

int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
{
    int i, nearest_q_idx = 0;
    for (i = 0; q_list[i].den; i++)
        if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
            nearest_q_idx = i;

    return nearest_q_idx;
}

#ifdef TEST
int main(void)
{
    AVRational a,b,r;
    for (a.num = -2; a.num <= 2; a.num++) {
        for (a.den = -2; a.den <= 2; a.den++) {
            for (b.num = -2; b.num <= 2; b.num++) {
                for (b.den = -2; b.den <= 2; b.den++) {
                    int c = av_cmp_q(a,b);
                    double d = av_q2d(a) == av_q2d(b) ?
                               0 : (av_q2d(a) - av_q2d(b));
                    if (d > 0)       d = 1;
                    else if (d < 0)  d = -1;
                    else if (d != d) d = INT_MIN;
                    if (c != d)
                        av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
                               a.den, b.num, b.den, c,d);
                    r = av_sub_q(av_add_q(b,a), b);
                    if(b.den && (r.num*a.den != a.num*r.den || !r.num != !a.num || !r.den != !a.den))
                        av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den);
                }
            }
        }
    }

    for (a.num = 1; a.num <= 10; a.num++) {
        for (a.den = 1; a.den <= 10; a.den++) {
            if (av_gcd(a.num, a.den) > 1)
                continue;
            for (b.num = 1; b.num <= 10; b.num++) {
                for (b.den = 1; b.den <= 10; b.den++) {
                    int start;
                    if (av_gcd(b.num, b.den) > 1)
                        continue;
                    if (av_cmp_q(b, a) < 0)
                        continue;
                    for (start = 0; start < 10 ; start++) {
                        int acc= start;
                        int i;

                        for (i = 0; i<100; i++) {
                            int exact = start + av_rescale_q(i+1, b, a);
                            acc = av_add_stable(a, acc, b, 1);
                            if (FFABS(acc - exact) > 2) {
                                av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num,
                                       a.den, b.num, b.den, acc, exact);
                                return 1;
                            }
                        }
                    }
                }
            }
        }
    }
    return 0;
}
#endif
Commit	Line	Data
2ba45a60 DM	1	/*
	2	* rational numbers
	3	* Copyright (c) 2003 Michael Niedermayer <michaelni@gmx.at>
	4	*
	5	* This file is part of FFmpeg.
	6	*
	7	* FFmpeg is free software; you can redistribute it and/or
	8	* modify it under the terms of the GNU Lesser General Public
	9	* License as published by the Free Software Foundation; either
	10	* version 2.1 of the License, or (at your option) any later version.
	11	*
	12	* FFmpeg is distributed in the hope that it will be useful,
	13	* but WITHOUT ANY WARRANTY; without even the implied warranty of
	14	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
	15	* Lesser General Public License for more details.
	16	*
	17	* You should have received a copy of the GNU Lesser General Public
	18	* License along with FFmpeg; if not, write to the Free Software
	19	* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
	20	*/
	21
	22	/**
	23	* @file
	24	* rational numbers
	25	* @author Michael Niedermayer <michaelni@gmx.at>
	26	*/
	27
	28	#include "avassert.h"
	29	#include <limits.h>
	30
	31	#include "common.h"
	32	#include "mathematics.h"
	33	#include "rational.h"
	34
	35	int av_reduce(int dst_num, int dst_den,
	36	int64_t num, int64_t den, int64_t max)
	37	{
	38	AVRational a0 = { 0, 1 }, a1 = { 1, 0 };
	39	int sign = (num < 0) ^ (den < 0);
	40	int64_t gcd = av_gcd(FFABS(num), FFABS(den));
	41
	42	if (gcd) {
	43	num = FFABS(num) / gcd;
	44	den = FFABS(den) / gcd;
	45	}
	46	if (num <= max && den <= max) {
	47	a1 = (AVRational) { num, den };
	48	den = 0;
	49	}
	50
	51	while (den) {
	52	uint64_t x = num / den;
	53	int64_t next_den = num - den * x;
	54	int64_t a2n = x * a1.num + a0.num;
	55	int64_t a2d = x * a1.den + a0.den;
	56
	57	if (a2n > max \|\| a2d > max) {
	58	if (a1.num) x = (max - a0.num) / a1.num;
	59	if (a1.den) x = FFMIN(x, (max - a0.den) / a1.den);
	60
	61	if (den * (2 * x * a1.den + a0.den) > num * a1.den)
	62	a1 = (AVRational) { x * a1.num + a0.num, x * a1.den + a0.den };
	63	break;
	64	}
65
66	a0 = a1;
67	a1 = (AVRational) { a2n, a2d };
68	num = den;
69	den = next_den;
70	}
71	av_assert2(av_gcd(a1.num, a1.den) <= 1U);
72
73	*dst_num = sign ? -a1.num : a1.num;
74	*dst_den = a1.den;
75
76	return den == 0;
77	}
78
79	AVRational av_mul_q(AVRational b, AVRational c)
80	{
81	av_reduce(&b.num, &b.den,
82	b.num * (int64_t) c.num,
83	b.den * (int64_t) c.den, INT_MAX);
84	return b;
85	}
86
87	AVRational av_div_q(AVRational b, AVRational c)
88	{
89	return av_mul_q(b, (AVRational) { c.den, c.num });
90	}
91
92	AVRational av_add_q(AVRational b, AVRational c) {
93	av_reduce(&b.num, &b.den,
94	b.num * (int64_t) c.den +
95	c.num * (int64_t) b.den,
96	b.den * (int64_t) c.den, INT_MAX);
97	return b;
98	}
99
100	AVRational av_sub_q(AVRational b, AVRational c)
101	{
102	return av_add_q(b, (AVRational) { -c.num, c.den });
103	}
104
105	AVRational av_d2q(double d, int max)
106	{
107	AVRational a;
108	#define LOG2 0.69314718055994530941723212145817656807550013436025
109	int exponent;
110	int64_t den;
111	if (isnan(d))
112	return (AVRational) { 0,0 };
113	if (fabs(d) > INT_MAX + 3LL)
114	return (AVRational) { d < 0 ? -1 : 1, 0 };
115	exponent = FFMAX( (int)(log(fabs(d) + 1e-20)/LOG2), 0);
116	den = 1LL << (61 - exponent);
117	// (int64_t)rint() and llrint() do not work with gcc on ia64 and sparc64
118	av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max);
119	if ((!a.num \|\| !a.den) && d && max>0 && max<INT_MAX)
120	av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, INT_MAX);
121
122	return a;
123	}
124
125	int av_nearer_q(AVRational q, AVRational q1, AVRational q2)
126	{
127	/* n/d is q, a/b is the median between q1 and q2 */
128	int64_t a = q1.num * (int64_t)q2.den + q2.num * (int64_t)q1.den;
129	int64_t b = 2 * (int64_t)q1.den * q2.den;
130
131	/* rnd_up(ad/b) > n => ad/b > n */
132	int64_t x_up = av_rescale_rnd(a, q.den, b, AV_ROUND_UP);
133
134	/* rnd_down(ad/b) < n => ad/b < n */
135	int64_t x_down = av_rescale_rnd(a, q.den, b, AV_ROUND_DOWN);
136
137	return ((x_up > q.num) - (x_down < q.num)) * av_cmp_q(q2, q1);
138	}
139
140	int av_find_nearest_q_idx(AVRational q, const AVRational* q_list)
141	{
142	int i, nearest_q_idx = 0;
143	for (i = 0; q_list[i].den; i++)
144	if (av_nearer_q(q, q_list[i], q_list[nearest_q_idx]) > 0)
145	nearest_q_idx = i;
146
147	return nearest_q_idx;
148	}
149
150	#ifdef TEST
151	int main(void)
152	{
153	AVRational a,b,r;
154	for (a.num = -2; a.num <= 2; a.num++) {
155	for (a.den = -2; a.den <= 2; a.den++) {
156	for (b.num = -2; b.num <= 2; b.num++) {
157	for (b.den = -2; b.den <= 2; b.den++) {
158	int c = av_cmp_q(a,b);
159	double d = av_q2d(a) == av_q2d(b) ?
160	0 : (av_q2d(a) - av_q2d(b));
161	if (d > 0) d = 1;
162	else if (d < 0) d = -1;
163	else if (d != d) d = INT_MIN;
164	if (c != d)
165	av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %f\n", a.num,
166	a.den, b.num, b.den, c,d);
167	r = av_sub_q(av_add_q(b,a), b);
168	if(b.den && (r.numa.den != a.numr.den \|\| !r.num != !a.num \|\| !r.den != !a.den))
169	av_log(NULL, AV_LOG_ERROR, "%d/%d ", r.num, r.den);
170	}
171	}
172	}
173	}
174
175	for (a.num = 1; a.num <= 10; a.num++) {
176	for (a.den = 1; a.den <= 10; a.den++) {
177	if (av_gcd(a.num, a.den) > 1)
178	continue;
179	for (b.num = 1; b.num <= 10; b.num++) {
180	for (b.den = 1; b.den <= 10; b.den++) {
181	int start;
182	if (av_gcd(b.num, b.den) > 1)
183	continue;
184	if (av_cmp_q(b, a) < 0)
185	continue;
186	for (start = 0; start < 10 ; start++) {
187	int acc= start;
188	int i;
189
190	for (i = 0; i<100; i++) {
191	int exact = start + av_rescale_q(i+1, b, a);
192	acc = av_add_stable(a, acc, b, 1);
193	if (FFABS(acc - exact) > 2) {
194	av_log(NULL, AV_LOG_ERROR, "%d/%d %d/%d, %d %d\n", a.num,
195	a.den, b.num, b.den, acc, exact);
196	return 1;
197	}
198	}
199	}
200	}
201	}
202	}
203	}
204	return 0;
205	}
206	#endif