14da117bc8
This fixes various rounding issues. Notably superclock to sample conversion must always round down when playing forward. `::process (start, end, speed = 1)` uses exclusive end. Processing begins at `start` and end ends just before `end`. Next cycle will begin with the current end. One example where this failed: - New session at 48kHz - Change tempo to 130 BPM - Enable snap to 1/8 note - Snap playhead to 1|3|0 - Enable Metronome - Play `assert (superclock_to_samples ((*i).sclock(), sample_rate()) < end);` end = 177231 samples == superclock 1042118280 A grid point is found at superclock 1042116920 (that is < 1042118280). However converting it back to samples rounded it to sample 177231 == end, while actual location is 1360 super-clock ticks before end. The metronome click has to be started this cycle, since the same position will not be found at the beginning of the next cycle, with start = 177232. Similarly a samplecnt_t t, converted to music-time and back must not be later than the given sample. ``` timepos_t tsc (t); assert (timepos_t::from_ticks (tsc.ticks ()).samples () <= t); ``` IOW. When playing forward, all super-clock time between 1|1|0 and 1|1|1 should round down to 1|1|0. "We have not yet reached the first tick".
132 lines
3.5 KiB
C++
132 lines
3.5 KiB
C++
/*
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Copyright (C) 2020 Paul Davis
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
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*/
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#ifndef __libpbd_integer_division_h__
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#define __libpbd_integer_division_h__
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#include <cstdint>
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#ifndef COMPILER_INT128_SUPPORT
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#include <boost/multiprecision/cpp_int.hpp>
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#include "pbd/error.h"
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#endif
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#define PBD_IDIV_ASR(x) ((x) < 0 ? -1 : 0) // Compiles into a (N-1)-bit arithmetic shift right
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/* The value of PBD_IDIV_ROUNDING will have the same sign as the dividend (x) and half
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* the magnitude of the divisor (y). Adding ROUNDING to the dividend thus
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* increases its magnitude before the integer division truncates the resulting
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* quotient.
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*/
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#define PBD_IDIV_ROUNDING(x,y) ( (y)/2 - (PBD_IDIV_ASR((x)^(y)) & (y)))
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template<typename T>
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T int_div_round (T x, T y)
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{
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/* essentially ((x + (y/2)) / y) but handles signed/negative values correcvtly */
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return (x + PBD_IDIV_ROUNDING(x,y)) / y ;
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}
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namespace PBD {
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/* this computes v * (n/d) where v, n and d are all 64 bit integers, without
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* overflow, and with appropriate rounding given that this is integer division.
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*/
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inline
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int64_t muldiv_round (int64_t v, int64_t n, int64_t d)
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{
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/* either n or d or both could be negative but for now we assume that
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only d could be (that is, n and d represent negative rational numbers of the
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form 1/-2 rather than -1/2). This follows the behavior of the
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ratio_t type in the temporal library.
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Consequently, we only use d in the rounding-signdness expression.
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*/
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const int64_t hd = PBD_IDIV_ROUNDING (v, d);
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#ifndef COMPILER_INT128_SUPPORT
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boost::multiprecision::int512_t bignum = v;
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bignum *= n;
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bignum += hd;
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bignum /= d;
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try {
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return bignum.convert_to<int64_t> ();
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} catch (...) {
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fatal << "arithmetic overflow in timeline math\n" << endmsg;
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/* NOTREACHED */
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return 0;
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}
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#else
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__int128 _n (n);
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__int128 _d (d);
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__int128 _v (v);
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/* this could overflow, but will not do so merely because we are
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* multiplying two int64_t together and storing the result in an
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* int64_t. Overflow will occur where (v*n)+hd > INT128_MAX (hard
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* limit) or where v * n / d > INT64_T (i.e. n > d)
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*/
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return(int64_t) (((_v * _n) + hd) / _d);
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#endif
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}
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inline
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int64_t muldiv_floor (int64_t v, int64_t n, int64_t d)
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{
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#ifndef COMPILER_INT128_SUPPORT
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boost::multiprecision::int512_t bignum = v;
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bignum *= n;
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bignum /= d;
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try {
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return bignum.convert_to<int64_t> ();
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} catch (...) {
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fatal << "arithmetic overflow in timeline math\n" << endmsg;
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/* NOTREACHED */
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return 0;
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}
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#else
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__int128 _n (n);
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__int128 _d (d);
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__int128 _v (v);
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/* this could overflow, but will not do so merely because we are
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* multiplying two int64_t together and storing the result in an
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* int64_t. Overflow will occur where (v*n)+hd > INT128_MAX (hard
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* limit) or where v * n / d > INT64_T (i.e. n > d)
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*/
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return(int64_t) ((_v * _n) / _d);
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#endif
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}
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} /* namespace */
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#endif /* __libpbd_integer_division_h___ */
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