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117cfc844b
The previous code only used the 1st multiplicand was use to determine the direction of rounding, breaking commutative property `muldiv_round (1, 3, 4) != muldiv_round (3, 1, 4)`
125 lines
3.2 KiB
C++
125 lines
3.2 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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#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 += PBD_IDIV_ROUNDING (bignum, d);
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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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__int128 vn (_v * _n);
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const int64_t hd = PBD_IDIV_ROUNDING (vn, d);
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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) ((vn + 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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