/* * rational numbers * Copyright (c) 2003 Michael Niedermayer * * 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 */ #include "avassert.h" #include #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, // see Ticket2713 for affected gcc/glibc versions av_reduce(&a.num, &a.den, floor(d * den + 0.5), den, max); if ((!a.num || !a.den) && d && max>0 && max 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<= (1<<24); shift += n < (1<<23); if (shift >= 0) n = av_rescale(q.num, 1LL<= (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