| /* |
| * 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); |
| av_assert2(a1.num <= max && a1.den <= max); |
| |
| *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; |
| 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 }; |
| frexp(d, &exponent); |
| exponent = FFMAX(exponent-1, 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; |
| } |
| |
| uint32_t av_q2intfloat(AVRational q) { |
| int64_t n; |
| int shift; |
| int sign = 0; |
| |
| if (q.den < 0) { |
| q.den *= -1; |
| q.num *= -1; |
| } |
| if (q.num < 0) { |
| q.num *= -1; |
| sign = 1; |
| } |
| |
| if (!q.num && !q.den) return 0xFFC00000; |
| if (!q.num) return 0; |
| if (!q.den) return 0x7F800000 | (q.num & 0x80000000); |
| |
| shift = 23 + av_log2(q.den) - av_log2(q.num); |
| if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den); |
| else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift); |
| |
| shift -= n >= (1<<24); |
| shift += n < (1<<23); |
| |
| if (shift >= 0) n = av_rescale(q.num, 1LL<<shift, q.den); |
| else n = av_rescale(q.num, 1, ((int64_t)q.den) << -shift); |
| |
| av_assert1(n < (1<<24)); |
| av_assert1(n >= (1<<23)); |
| |
| return sign<<31 | (150-shift)<<23 | (n - (1<<23)); |
| } |
| |
| #ifdef TEST |
| |
| #include "integer.h" |
| |
| int main(void) |
| { |
| AVRational a,b,r; |
| int i,j,k; |
| static const int64_t numlist[] = { |
| INT64_MIN, INT64_MIN+1, INT64_MAX, INT32_MIN, INT32_MAX, 1,0,-1, |
| 123456789, INT32_MAX-1, INT32_MAX+1LL, UINT32_MAX-1, UINT32_MAX, UINT32_MAX+1LL |
| }; |
| |
| 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 (i = 0; i < FF_ARRAY_ELEMS(numlist); i++) { |
| int64_t a = numlist[i]; |
| |
| for (j = 0; j < FF_ARRAY_ELEMS(numlist); j++) { |
| int64_t b = numlist[j]; |
| if (b<=0) |
| continue; |
| for (k = 0; k < FF_ARRAY_ELEMS(numlist); k++) { |
| int64_t c = numlist[k]; |
| int64_t res; |
| AVInteger ai; |
| |
| if (c<=0) |
| continue; |
| res = av_rescale_rnd(a,b,c, AV_ROUND_ZERO); |
| |
| ai = av_mul_i(av_int2i(a), av_int2i(b)); |
| ai = av_div_i(ai, av_int2i(c)); |
| |
| if (av_cmp_i(ai, av_int2i(INT64_MAX)) > 0 && res == INT64_MIN) |
| continue; |
| if (av_cmp_i(ai, av_int2i(INT64_MIN)) < 0 && res == INT64_MIN) |
| continue; |
| if (av_cmp_i(ai, av_int2i(res)) == 0) |
| continue; |
| |
| // Special exception for INT64_MIN, remove this in case INT64_MIN is handled without off by 1 error |
| if (av_cmp_i(ai, av_int2i(res-1)) == 0 && a == INT64_MIN) |
| continue; |
| |
| av_log(NULL, AV_LOG_ERROR, "%"PRId64" * %"PRId64" / %"PRId64" = %"PRId64" or %"PRId64"\n", a,b,c, res, av_i2int(ai)); |
| } |
| } |
| } |
| |
| 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; |
| } |
| } |
| } |
| } |
| } |
| } |
| } |
| |
| for (a.den = 1; a.den < 0x100000000U/3; a.den*=3) { |
| for (a.num = -1; a.num < (1<<27); a.num += 1 + a.num/100) { |
| float f = av_int2float(av_q2intfloat(a)); |
| float f2 = av_q2d(a); |
| if (fabs(f - f2) > fabs(f)/5000000) { |
| av_log(NULL, AV_LOG_ERROR, "%d/%d %f %f\n", a.num, |
| a.den, f, f2); |
| return 1; |
| } |
| |
| } |
| } |
| |
| return 0; |
| } |
| #endif |
