Mercurial > octave
view liboctave/array/Range.cc @ 30420:366aa563dd2e stable
style fixes for Range.h and Range.cc
* Range.h, Range.cc: Don't pass bool function arguments as const
reference. Do pass non-pod object function argumennts as const
reference where possible.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Thu, 02 Dec 2021 14:18:48 -0500 |
parents | 4736bc8e9804 |
children | 796f54d4ddbf |
line wrap: on
line source
//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1993-2021 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave 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 General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cmath> #include <istream> #include <limits> #include <ostream> #include "Array-util.h" #include "Range.h" #include "lo-error.h" #include "lo-mappers.h" #include "lo-utils.h" namespace octave { template <typename T> T xtfloor (T x, T ct) { // C---------FLOOR(X) is the largest integer algebraically less than // C or equal to X; that is, the unfuzzy FLOOR function. // DINT (X) = X - DMOD (X, 1.0); // FLOOR (X) = DINT (X) - DMOD (2.0 + DSIGN (1.0, X), 3.0); // C---------Hagerty's FL5 function follows... T q = 1; if (x < 0) q = 1 - ct; T rmax = q / (2 - ct); T t1 = 1 + std::floor (x); t1 = (ct / q) * (t1 < 0 ? -t1 : t1); t1 = (rmax < t1 ? rmax : t1); t1 = (ct > t1 ? ct : t1); t1 = std::floor (x + t1); if (x <= 0 || (t1 - x) < rmax) return t1; else return t1 - 1; } template <typename T> bool xteq (T u, T v, T ct = 3 * std::numeric_limits<T>::epsilon ()) { T tu = std::abs (u); T tv = std::abs (v); return std::abs (u - v) < ((tu > tv ? tu : tv) * ct); } template <typename T> octave_idx_type xnumel_internal (T base, T limit, T inc) { octave_idx_type retval = -1; if (! math::isfinite (base) || ! math::isfinite (inc) || math::isnan (limit)) retval = -2; else if (math::isinf (limit) && ((inc > 0 && limit > 0) || (inc < 0 && limit < 0))) retval = std::numeric_limits<octave_idx_type>::max () - 1; else if (inc == 0 || (limit > base && inc < 0) || (limit < base && inc > 0)) { retval = 0; } else { T ct = 3 * std::numeric_limits<T>::epsilon (); T tmp = xtfloor ((limit - base + inc) / inc, ct); octave_idx_type n_elt = (tmp > 0 ? static_cast<octave_idx_type> (tmp) : 0); // If the final element that we would compute for the range is // equal to the limit of the range, or is an adjacent floating // point number, accept it. Otherwise, try a range with one // fewer element. If that fails, try again with one more // element. // // I'm not sure this is very good, but it seems to work better // than just using tfloor as above. For example, without it, // the expression 1.8:0.05:1.9 fails to produce the expected // result of [1.8, 1.85, 1.9]. if (! xteq (base + (n_elt - 1) * inc, limit)) { if (xteq (base + (n_elt - 2) * inc, limit)) n_elt--; else if (xteq (base + n_elt * inc, limit)) n_elt++; } retval = (n_elt < std::numeric_limits<octave_idx_type>::max () - 1 ? n_elt : -1); } return retval; } template <typename T> bool xall_elements_are_ints (T base, T inc, T final_val, octave_idx_type nel) { // If the range is empty or NaN then there are no elements so there // can be no int elements. if (nel == 0 || math::isnan (final_val)) return false; // If the base and increment are ints, all elements will be // integers. if (math::nint_big (base) == base && math::nint_big (inc) == inc) return true; // If the range has only one element, then the base needs to be an // integer. if (nel == 1 && math::nint_big (base)) return true; return false; } template <typename T> T xfinal_value (T base, T limit, T inc, octave_idx_type nel) { T retval = T (0); if (nel <= 1) return base; // If increment is 0, then numel should also be zero. retval = base + (nel - 1) * inc; // On some machines (x86 with extended precision floating point // arithmetic, for example) it is possible that we can overshoot // the limit by approximately the machine precision even though // we were very careful in our calculation of the number of // elements. Therefore, we clip the result to the limit if it // overshoots. // NOTE: The test also includes equality (>= limit) to have // expressions such as -5:1:-0 result in a -0 endpoint. if ((inc > T (0) && retval >= limit) || (inc < T (0) && retval <= limit)) retval = limit; // If all elements are integers, then ensure the final value is. // Note that we pass the preliminary computed final value to // xall_elements_are_ints, but it only checks whether that value is // NaN. if (xall_elements_are_ints (base, inc, retval, nel)) retval = std::round (retval); return retval; } template <typename T> void xinit (T base, T limit, T inc, bool reverse, T& final_val, octave_idx_type& nel) { // Catch obvious NaN ranges. if (math::isnan (base) || math::isnan (limit) || math::isnan (inc)) { final_val = numeric_limits<T>::NaN (); nel = 1; return; } // Floating point numbers are always signed if (reverse) inc = -inc; // Catch empty ranges. if (inc == 0 || (limit < base && inc > 0) || (limit > base && inc < 0)) { nel = 0; return; } // The following case also catches Inf values for increment when // there will be only one element. if ((limit <= base && base + inc < limit) || (limit >= base && base + inc > limit)) { final_val = base; nel = 1; return; } // Any other calculations with Inf will give us either a NaN range // or an infinite nember of elements. T dnel = (limit - base) / inc; if (math::isnan (dnel)) { nel = 1; final_val = numeric_limits<T>::NaN (); return; } if (dnel > 0 && math::isinf (dnel)) { // FIXME: Should this be an immediate error? nel = std::numeric_limits<octave_idx_type>::max (); // FIXME: Will this do the right thing in all cases? final_val = xfinal_value (base, limit, inc, nel); return; } // Now that we have handled all the special cases, we can compute // the number of elements and the final value in a way that attempts // to avoid rounding errors as much as possible. nel = xnumel_internal (base, limit, inc); final_val = xfinal_value (base, limit, inc, nel); } template <typename T> void xinit (const octave_int<T>& base, const octave_int<T>& limit, const octave_int<T>& inc, bool reverse, octave_int<T>& final_val, octave_idx_type& nel) { // We need an integer division that is truncating decimals instead // of rounding. So, use underlying C++ types instead of // octave_int<T>. // FIXME: The numerator might underflow or overflow. Add checks for // that. if (reverse) { nel = ((inc == octave_int<T> (0) || (limit > base && inc > octave_int<T> (0)) || (limit < base && inc < octave_int<T> (0))) ? 0 : (base.value () - limit.value () + inc.value ()) / inc.value ()); final_val = base - (nel - 1) * inc; } else { nel = ((inc == octave_int<T> (0) || (limit > base && inc < octave_int<T> (0)) || (limit < base && inc > octave_int<T> (0))) ? 0 : (limit.value () - base.value () + inc.value ()) / inc.value ()); final_val = base + (nel - 1) * inc; } } template <typename T> bool xis_storable (T base, T limit, octave_idx_type nel) { return ! (nel > 1 && (math::isinf (base) || math::isinf (limit))); } template <> bool range<double>::all_elements_are_ints (void) const { return xall_elements_are_ints (m_base, m_increment, m_final, m_numel); } template <> bool range<float>::all_elements_are_ints (void) const { return xall_elements_are_ints (m_base, m_increment, m_final, m_numel); } template <> void range<double>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<float>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<octave_int8>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<octave_int16>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<octave_int32>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<octave_int64>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<octave_uint8>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<octave_uint16>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<octave_uint32>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> void range<octave_uint64>::init (void) { xinit (m_base, m_limit, m_increment, m_reverse, m_final, m_numel); } template <> bool range<double>::is_storable (void) const { return xis_storable (m_base, m_limit, m_numel); } template <> bool range<float>::is_storable (void) const { return xis_storable (m_base, m_limit, m_numel); } template <typename T> octave_idx_type xnnz (T base, T limit, T inc, T final_val, octave_idx_type nel) { // Note that the order of the following checks matters. // If there are no elements, there can be no non-zero elements. if (nel == 0) return 0; // All elements have the same sign, hence there are no zeros. if ((base > 0 && limit > 0) || (base < 0 && limit < 0)) return nel; // All elements are equal (inc = 0) but we know from the previous // condition that they are not positive or negative, therefore all // elements are zero. if (inc == 0) return 0; // Exactly one zero at beginning or end of range. if (base == 0 || final_val == 0) return nel - 1; // Range crosses negative/positive without hitting zero. // FIXME: Is this test sufficiently tolerant or do we need to be // more careful? if (math::mod (-base, inc) != 0) return nel; // Range crosses negative/positive and hits zero. return nel - 1; } template <> octave_idx_type range<double>::nnz (void) const { return xnnz (m_base, m_limit, m_increment, m_final, m_numel); } template <> octave_idx_type range<float>::nnz (void) const { return xnnz (m_base, m_limit, m_increment, m_final, m_numel); } } bool Range::all_elements_are_ints (void) const { // If the base and increment are ints, the final value in the range will also // be an integer, even if the limit is not. If there is one or fewer // elements only the base needs to be an integer. return (! (octave::math::isnan (m_base) || octave::math::isnan (m_inc)) && (octave::math::nint_big (m_base) == m_base || m_numel < 1) && (octave::math::nint_big (m_inc) == m_inc || m_numel <= 1)); } octave_idx_type Range::nnz (void) const { octave_idx_type retval = 0; if (! isempty ()) { if ((m_base > 0.0 && m_limit > 0.0) || (m_base < 0.0 && m_limit < 0.0)) { // All elements have the same sign, hence there are no zeros. retval = m_numel; } else if (m_inc != 0.0) { if (m_base == 0.0 || m_limit == 0.0) // Exactly one zero at beginning or end of range. retval = m_numel - 1; else if ((m_base / m_inc) != std::floor (m_base / m_inc)) // Range crosses negative/positive without hitting zero. retval = m_numel; else // Range crosses negative/positive and hits zero. retval = m_numel - 1; } else { // All elements are equal (m_inc = 0) but not positive or negative, // therefore all elements are zero. retval = 0; } } return retval; } Matrix Range::matrix_value (void) const { Matrix retval (1, m_numel); if (m_numel > 0) { // The first element must always be *exactly* the base. // E.g, -0 would otherwise become +0 in the loop (-0 + 0*increment). retval(0) = m_base; double b = m_base; double increment = m_inc; for (octave_idx_type i = 1; i < m_numel - 1; i++) retval.xelem (i) = b + i * increment; retval.xelem (m_numel - 1) = m_limit; } return retval; } double Range::checkelem (octave_idx_type i) const { if (i < 0 || i >= m_numel) octave::err_index_out_of_range (2, 2, i+1, m_numel, dims ()); if (i == 0) return m_base; else if (i < m_numel - 1) return m_base + i * m_inc; else return m_limit; } double Range::checkelem (octave_idx_type i, octave_idx_type j) const { // Ranges are *always* row vectors. if (i != 0) octave::err_index_out_of_range (1, 1, i+1, m_numel, dims ()); return checkelem (j); } double Range::elem (octave_idx_type i) const { if (i == 0) return m_base; else if (i < m_numel - 1) return m_base + i * m_inc; else return m_limit; } Array<double> Range::index (const octave::idx_vector& idx) const { Array<double> retval; octave_idx_type n = m_numel; if (idx.is_colon ()) { retval = matrix_value ().reshape (dim_vector (m_numel, 1)); } else { if (idx.extent (n) != n) octave::err_index_out_of_range (1, 1, idx.extent (n), n, dims ()); // throws dim_vector idx_dims = idx.orig_dimensions (); octave_idx_type idx_len = idx.length (n); // taken from Array.cc. if (n != 1 && idx_dims.isvector ()) idx_dims = dim_vector (1, idx_len); retval.clear (idx_dims); // Loop over all values in IDX, executing the lambda expression // for each index value. double *array = retval.fortran_vec (); idx.loop (n, [=, &array] (idx_vector i) { if (i == 0) *array++ = m_base; else if (i < m_numel - 1) *array++ = m_base + i * m_inc; else *array++ = m_limit; }); } return retval; } // NOTE: max and min only return useful values if numel > 0. // do_minmax_body() in max.cc avoids calling Range::min/max if numel == 0. double Range::min (void) const { double retval = 0.0; if (m_numel > 0) { if (m_inc > 0) retval = m_base; else { retval = m_base + (m_numel - 1) * m_inc; // Require '<=' test. See note in max (). if (retval <= m_limit) retval = m_limit; } } return retval; } double Range::max (void) const { double retval = 0.0; if (m_numel > 0) { if (m_inc > 0) { retval = m_base + (m_numel - 1) * m_inc; // On some machines (x86 with extended precision floating point // arithmetic, for example) it is possible that we can overshoot the // limit by approximately the machine precision even though we were // very careful in our calculation of the number of elements. // Therefore, we clip the result to the limit if it overshoots. // The test also includes equality (>= m_limit) to have expressions // such as -5:1:-0 result in a -0 endpoint. if (retval >= m_limit) retval = m_limit; } else retval = m_base; } return retval; } void Range::sort_internal (bool ascending) { if ((ascending && m_base > m_limit && m_inc < 0.0) || (! ascending && m_base < m_limit && m_inc > 0.0)) { std::swap (m_base, m_limit); m_inc = -m_inc; } } void Range::sort_internal (Array<octave_idx_type>& sidx, bool ascending) { octave_idx_type nel = numel (); sidx.resize (dim_vector (1, nel)); octave_idx_type *psidx = sidx.fortran_vec (); bool reverse = false; if ((ascending && m_base > m_limit && m_inc < 0.0) || (! ascending && m_base < m_limit && m_inc > 0.0)) { std::swap (m_base, m_limit); m_inc = -m_inc; reverse = true; } octave_idx_type tmp = (reverse ? nel - 1 : 0); octave_idx_type stp = (reverse ? -1 : 1); for (octave_idx_type i = 0; i < nel; i++, tmp += stp) psidx[i] = tmp; } Matrix Range::diag (octave_idx_type k) const { return matrix_value ().diag (k); } Range Range::sort (octave_idx_type dim, sortmode mode) const { Range retval = *this; if (dim == 1) { if (mode == ASCENDING) retval.sort_internal (true); else if (mode == DESCENDING) retval.sort_internal (false); } else if (dim != 0) (*current_liboctave_error_handler) ("Range::sort: invalid dimension"); return retval; } Range Range::sort (Array<octave_idx_type>& sidx, octave_idx_type dim, sortmode mode) const { Range retval = *this; if (dim == 1) { if (mode == ASCENDING) retval.sort_internal (sidx, true); else if (mode == DESCENDING) retval.sort_internal (sidx, false); } else if (dim != 0) (*current_liboctave_error_handler) ("Range::sort: invalid dimension"); return retval; } sortmode Range::issorted (sortmode mode) const { if (m_numel > 1 && m_inc > 0) mode = (mode == DESCENDING) ? UNSORTED : ASCENDING; else if (m_numel > 1 && m_inc < 0) mode = (mode == ASCENDING) ? UNSORTED : DESCENDING; else mode = (mode == UNSORTED) ? ASCENDING : mode; return mode; } void Range::set_base (double b) { if (m_base != b) { m_base = b; init (); } } void Range::set_limit (double l) { if (m_limit != l) { m_limit = l; init (); } } void Range::set_inc (double i) { if (m_inc != i) { m_inc = i; init (); } } std::ostream& operator << (std::ostream& os, const Range& a) { double b = a.base (); double increment = a.increment (); octave_idx_type nel = a.numel (); if (nel > 1) { // First element must be the base *exactly* (e.g., -0). os << b << ' '; for (octave_idx_type i = 1; i < nel-1; i++) os << b + i * increment << ' '; } // Print out the last element exactly, rather than a calculated last element. os << a.m_limit << "\n"; return os; } std::istream& operator >> (std::istream& is, Range& a) { is >> a.m_base; if (is) { double tmp_limit; is >> tmp_limit; if (is) is >> a.m_inc; // Clip the m_limit to the true limit, rebuild numel, clear cache a.set_limit (tmp_limit); } return is; } // DEPRECATED in Octave 7. Range operator - (const Range& r) { return Range (-r.base (), -r.limit (), -r.increment (), r.numel ()); } // DEPRECATED in Octave 7. Range operator + (double x, const Range& r) { return Range (x + r.base (), x + r.limit (), r.increment (), r.numel ()); } // DEPRECATED in Octave 7. Range operator + (const Range& r, double x) { return Range (r.base () + x, r.limit () + x, r.increment (), r.numel ()); } // DEPRECATED in Octave 7. Range operator - (double x, const Range& r) { return Range (x - r.base (), x - r.limit (), -r.increment (), r.numel ()); } // DEPRECATED in Octave 7. Range operator - (const Range& r, double x) { return Range (r.base () - x, r.limit () - x, r.increment (), r.numel ()); } // DEPRECATED in Octave 7. Range operator * (double x, const Range& r) { return Range (x * r.base (), x * r.limit (), x * r.increment (), r.numel ()); } // DEPRECATED in Octave 7. Range operator * (const Range& r, double x) { return Range (r.base () * x, r.limit () * x, r.increment () * x, r.numel ()); } // C See Knuth, Art Of Computer Programming, Vol. 1, Problem 1.2.4-5. // C // C===Tolerant FLOOR function. // C // C X - is given as a Double Precision argument to be operated on. // C It is assumed that X is represented with M mantissa bits. // C CT - is given as a Comparison Tolerance such that // C 0.LT.CT.LE.3-SQRT(5)/2. If the relative difference between // C X and A whole number is less than CT, then TFLOOR is // C returned as this whole number. By treating the // C floating-point numbers as a finite ordered set note that // C the heuristic EPS=2.**(-(M-1)) and CT=3*EPS causes // C arguments of TFLOOR/TCEIL to be treated as whole numbers // C if they are exactly whole numbers or are immediately // C adjacent to whole number representations. Since EPS, the // C "distance" between floating-point numbers on the unit // C interval, and M, the number of bits in X'S mantissa, exist // C on every floating-point computer, TFLOOR/TCEIL are // C consistently definable on every floating-point computer. // C // C For more information see the following references: // C (1) P. E. Hagerty, "More On Fuzzy Floor And Ceiling," APL QUOTE // C QUAD 8(4):20-24, June 1978. Note that TFLOOR=FL5. // C (2) L. M. Breed, "Definitions For Fuzzy Floor And Ceiling", APL // C QUOTE QUAD 8(3):16-23, March 1978. This paper cites FL1 through // C FL5, the history of five years of evolutionary development of // C FL5 - the seven lines of code below - by open collaboration // C and corroboration of the mathematical-computing community. // C // C Penn State University Center for Academic Computing // C H. D. Knoble - August, 1978. static inline double tfloor (double x, double ct) { // C---------FLOOR(X) is the largest integer algebraically less than // C or equal to X; that is, the unfuzzy FLOOR function. // DINT (X) = X - DMOD (X, 1.0); // FLOOR (X) = DINT (X) - DMOD (2.0 + DSIGN (1.0, X), 3.0); // C---------Hagerty's FL5 function follows... double q = 1.0; if (x < 0.0) q = 1.0 - ct; double rmax = q / (2.0 - ct); double t1 = 1.0 + std::floor (x); t1 = (ct / q) * (t1 < 0.0 ? -t1 : t1); t1 = (rmax < t1 ? rmax : t1); t1 = (ct > t1 ? ct : t1); t1 = std::floor (x + t1); if (x <= 0.0 || (t1 - x) < rmax) return t1; else return t1 - 1.0; } static inline bool teq (double u, double v, double ct = 3.0 * std::numeric_limits<double>::epsilon ()) { double tu = std::abs (u); double tv = std::abs (v); return std::abs (u - v) < ((tu > tv ? tu : tv) * ct); } octave_idx_type Range::numel_internal (void) const { octave_idx_type retval = -1; if (! octave::math::isfinite (m_base) || ! octave::math::isfinite (m_inc) || octave::math::isnan (m_limit)) retval = -2; else if (octave::math::isinf (m_limit) && ((m_inc > 0 && m_limit > 0) || (m_inc < 0 && m_limit < 0))) retval = std::numeric_limits<octave_idx_type>::max () - 1; else if (m_inc == 0 || (m_limit > m_base && m_inc < 0) || (m_limit < m_base && m_inc > 0)) { retval = 0; } else { double ct = 3.0 * std::numeric_limits<double>::epsilon (); double tmp = tfloor ((m_limit - m_base + m_inc) / m_inc, ct); octave_idx_type n_elt = (tmp > 0.0 ? static_cast<octave_idx_type> (tmp) : 0); // If the final element that we would compute for the range is equal to // the limit of the range, or is an adjacent floating point number, // accept it. Otherwise, try a range with one fewer element. If that // fails, try again with one more element. // // I'm not sure this is very good, but it seems to work better than just // using tfloor as above. For example, without it, the expression // 1.8:0.05:1.9 fails to produce the expected result of [1.8, 1.85, 1.9]. if (! teq (m_base + (n_elt - 1) * m_inc, m_limit)) { if (teq (m_base + (n_elt - 2) * m_inc, m_limit)) n_elt--; else if (teq (m_base + n_elt * m_inc, m_limit)) n_elt++; } retval = ((n_elt < std::numeric_limits<octave_idx_type>::max ()) ? n_elt : -1); } return retval; } double Range::limit_internal (void) const { double new_limit = m_inc > 0 ? max () : min (); // If result must be an integer then force the new_limit to be one. if (all_elements_are_ints ()) new_limit = std::round (new_limit); return new_limit; } void Range::init (void) { m_numel = numel_internal (); if (! octave::math::isinf (m_limit)) m_limit = limit_internal (); }