mirror of
https://github.com/gcc-mirror/gcc.git
synced 2026-05-06 14:59:39 +02:00
083b7f2833
libstdc++-v3/ChangeLog:
* libsupc++/typeinfo: Switch to bits/version.h for
__cpp_lib_constexpr_typeinfo.
* libsupc++/new: Switch to bits/version.h for
__cpp_lib_{launder,hardware_interference_size,destroying_delete}.
(launder): Guard behind __cpp_lib_launder.
(hardware_destructive_interference_size)
(hardware_constructive_interference_size): Guard behind
__cpp_lib_hardware_interference_size.
* libsupc++/exception: Switch to bits/version.h for
__cpp_lib_uncaught_exceptions.
(uncaught_exceptions): Guard behind __cpp_lib_uncaught_exceptions.
* libsupc++/compare: Switch to bits/version.h for
__cpp_lib_three_way_comparison.
(three_way_comparable, three_way_comparable_with)
(compare_three_way, weak_order, strong_order, partial_order):
Guard behind __cpp_lib_three_way_comparison >= 201907L.
* include/std/chrono: Drop __cpp_lib_chrono definition.
* include/std/vector: Switch to bits/version.h for
__cpp_lib_erase_if.
(erase, erase_if): Guard behind __cpp_lib_erase_if.
* include/std/variant: Switch to bits/version.h for
__cpp_lib_variant. Guard whole header behind that FTM.
* include/std/utility: Switch to bits/version.h for
__cpp_lib_{exchange_function,constexpr_algorithms,as_const},
__cpp_lib_{integer_comparison_functions,to_underlying}, and
__cpp_lib_unreachable.
(exchange): Guard behind __cpp_lib_exchange_function.
(cmp_equal, cmp_not_equal, cmp_less, cmp_greater, cmp_less_equal)
(cmp_greater_equal, in_range): Guard behind
__cpp_lib_integer_comparison_functions.
(to_underlying): Guard behind __cpp_lib_to_underlying.
(unreachable): Guard behind __cpp_lib_unreachable.
* include/std/type_traits: Switch to bits/version.h for
__cpp_lib_is_{null_pointer,final,nothrow_convertible,aggregate},
__cpp_lib_is_{constant_evaluated,invocable,layout_compatible},
__cpp_lib_is_{pointer_interconvertible,scoped_enum,swappable},
__cpp_lib_{logical_traits,reference_from_temporary,remove_cvref},
__cpp_lib_{result_of_sfinae,transformation_trait_aliases},
__cpp_lib_{type_identity,type_trait_variable_templates},
__cpp_lib_{unwrap_ref,void_t,integral_constant_callable},
__cpp_lib_{bool_constant,bounded_array_traits}, and
__cpp_lib_has_unique_object_representations.
(integral_constant::operator()): Guard behind
__cpp_lib_integral_constant_callable.
(bool_constant): Guard behind __cpp_lib_bool_constant.
(conjunction, disjunction, negation, conjunction_v, disjunction_v)
(negation_v): Guard behind __cpp_lib_logical_traits.
(is_null_pointer): Guard behind __cpp_lib_is_null_pointer.
(is_final): Guard behind __cpp_lib_is_final.
(is_nothrow_convertible, is_nothrow_convertible_v): Guard behind
__cpp_lib_is_nothrow_convertible.
(remove_const_t, remove_volatile_t, remove_cv_t)
(add_const_t, add_volatile_t, add_cv_t): Guard behind
__cpp_lib_transformation_trait_aliases.
(void_t): Guard behind __cpp_lib_void_t.
(is_swappable_with_v, is_nothrow_swappable_with_v)
(is_swappable_with, is_nothrow_swappable_with): Guard behind
__cpp_lib_is_swappable.
(is_nothrow_invocable_r, is_invocable_r, invoke_result)
(is_invocable, invoke_result_t): Guard behind
__cpp_lib_is_invocable.
(alignment_of_v, extent_v, has_virtual_destructor_v)
(is_abstract_v, is_arithmetic_v, is_array_v)
(is_assignable_v, is_base_of_v, is_class_v, is_compound_v)
(is_constructible_v, is_const_v, is_convertible_v)
(is_copy_assignable_v, is_copy_constructible_v)
(is_default_constructible_v, is_destructible_v)
(is_empty_v, is_enum_v, is_final_v, is_floating_point_v)
(is_function_v, is_fundamental_v, is_integral_v)
(is_invocable_r_v, is_invocable_v, is_literal_type_v)
(is_lvalue_reference_v, is_member_function_pointer_v)
(is_member_object_pointer_v, is_member_pointer_v)
(is_move_assignable_v, is_move_constructible_v)
(is_nothrow_assignable_v, is_nothrow_constructible_v)
(is_nothrow_copy_assignable_v, is_nothrow_copy_constructible_v)
(is_nothrow_default_constructible_v, is_nothrow_destructible_v)
(is_nothrow_invocable_r_v, is_nothrow_invocable_v)
(is_nothrow_move_assignable_v, is_nothrow_move_constructible_v)
(is_null_pointer_v, is_object_v, is_pod_v, is_pointer_v)
(is_polymorphic_v, is_reference_v, is_rvalue_reference_v)
(is_same_v, is_scalar_v, is_signed_v, is_standard_layout_v)
(is_trivially_assignable_v, is_trivially_constructible_v)
(is_trivially_copyable_v, is_trivially_copy_assignable_v)
(is_trivially_copy_constructible_v)
(is_trivially_default_constructible_v)
(is_trivially_destructible_v, is_trivially_move_assignable_v)
(is_trivially_move_constructible_v, is_trivial_v, is_union_v)
(is_unsigned_v, is_void_v, is_volatile_v, rank_v, as variadic):
Guard behind __cpp_lib_type_trait_variable_templates.
(has_unique_object_representations)
(has_unique_object_representations_v): Guard behind
__cpp_lib_has_unique_object_representation.
(is_aggregate): Guard behind __cpp_lib_is_aggregate.
(remove_cvref, remove_cvref_t): Guard behind
__cpp_lib_remove_cvref.
(type_identity, type_identity_t): Guard behind
__cpp_lib_type_identity.
(unwrap_reference, unwrap_reference_t, unwrap_ref_decay)
(unwrap_ref_decay_t): Guard behind __cpp_lib_unwrap_ref.
(is_bounded_array_v, is_unbounded_array_v, is_bounded_array)
(is_unbounded_array): Guard behind __cpp_lib_bounded_array_traits.
(is_scoped_enum, is_scoped_enum_v): Guard behind
__cpp_lib_is_scoped_enum.
(reference_constructs_from_temporary)
(reference_constructs_from_temporary_v): Guard behind
__cpp_lib_reference_from_temporary.
* include/std/tuple: Switch to bits/version.h for
__cpp_lib_{constexpr_tuple,tuple_by_type,apply_make_from_tuple}.
(get<T>): Guard behind __cpp_lib_tuple_by_type.
(apply): Guard behind __cpp_lib_apply.
(make_from_tuple): Guard behind __cpp_lib_make_from_tuple.
* include/std/syncstream: Switch to bits/version.h for
__cpp_lib_syncbuf. Guard header behind that FTM.
* include/std/string_view: Switch to bits/version.h for
__cpp_lib_{string_{view,contains},constexpr_string_view} and
__cpp_lib_starts_ends_with.
(basic_string_view::starts_with, basic_string_view::ends_with):
Guard behind __cpp_lib_starts_ends_with.
[C++23 && _GLIBCXX_HOSTED && !defined(__cpp_lib_string_contains)]:
Assert as impossible ithout a bug in C++23.
* include/std/string: Switch to bits/version.h for
__cpp_lib_erase_if.
(erase, erase_if): Guard behind __cpp_lib_erase_if.
* include/std/thread: Switch to bits/version.h for
__cpp_lib_jthread.
* include/std/stop_token: Switch to bits/version.h for
__cpp_lib_jthread.
* include/std/spanstream: Switch to bits/version.h for
__cpp_lib_spanstream. Guard header behind that FTM.
* include/std/span: Switch to bits/version.h for __cpp_lib_span.
Guard header behind that FTM.
* include/std/source_location: Switch to bits/version.h for
__cpp_lib_source_location. Guard header with that FTM.
* include/std/shared_mutex: Switch to bits/version.h for
__cpp_lib_shared{,_timed}_mutex.
(shared_mutex): Guard behind __cpp_lib_shared_mutex.
* include/std/semaphore: Switch to bits/version.h for
__cpp_lib_semaphore. Guard header behind that FTM.
* include/std/ranges: Switch to bits/version.h for
__cpp_lib_ranges_{zip,chunk{,_by},slide,join_with},
__cpp_lib_ranges_{repeat_stride,cartesian_product,as_rvalue},
and __cpp_lib_ranges_{as_const,enumerate,iota}.
(ranges::zip et al, ranges::chunk et al, ranges::slide et al)
(ranges::chunk_by et al, ranges::join_with et al)
(ranges::stride et al, ranges::cartesian_product et al)
(ranges::as_rvalue et al, ranges::as_const et al)
(ranges::enumerate et al): Guard behind appropriate FTM.
* include/std/optional: Switch to bits/version.h for
__cpp_lib_optional. Guard header behind that FTM.
* include/std/numeric: Switch to bits/version.h for
__cpp_lib_{gcd{,_lcm},lcm,constexpr_numeric,interpolate}
and __cpp_lib_parallel_algorithm.
(gcd, lcm): Guard behind __cpp_lib_gcd_lcm.
(midpoint): Guard behind __cpp_lib_interpolate.
* include/std/numbers: Switch to bits/version.h for
__cpp_lib_math_constants. Guard header behind that FTM.
* include/std/mutex: Switch to bits/version.h for
__cpp_lib_scoped_lock.
(scoped_Lock): Guard behind __cpp_lib_scoped_lock.
* include/std/memory_resource: Switch to bits/version.h for
__cpp_lib_{polymorphic_allocator,memory_resource}.
(synchronized_pool_resource): Guard behind
__cpp_lib_memory_resource >= 201603L.
(polymorphic_allocator): Guard behind
__cpp_lib_polymorphic_allocator.
* include/std/memory: Switch to bits/version.h for
__cpp_lib_{parallel_algorithm,atomic_value_initialization}.
* include/std/list: Switch to bits/version.h for
__cpp_lib_erase_if.
(erase, erase_if): Guard behind __cpp_lib_erase_if.
* include/std/latch: Switch to bits/version.h for __cpp_lib_latch.
Guard header behind that FTM.
* include/std/iterator: Switch to bits/version.h for
__cpp_lib_null_iterators.
* include/std/iomanip: Switch to bits/version.h for
__cpp_lib_quoted_string_io.
(quoted): Guard behind __cpp_lib_quoted_string_io.
* include/std/functional: Switch to bits/version.h for
__cpp_lib_{invoke{,_r},constexpr_functional,bind_front} and
__cpp_lib_{not_fn,booyer_moore_searcher}.
(invoke): Guard behind __cpp_lib_invoke.
(invoke_r): Guard behind __cpp_lib_invoke_r.
(bind_front): Guard behind __cpp_lib_bind_front.
(not_fn): Guard behind __cpp_lib_not_fn.
(boyer_moore_searcher, boyer_moore_horspool_searcher): Guard
definition behind __cpp_lib_boyer_moore_searcher.
* include/std/forward_list: Switch to bits/version.h for
__cpp_lib_erase_if.
(erase, erase_if): Guard behind __cpp_lib_erase_if.
* include/std/format: Switch to bits/version.h for
__cpp_lib_format. Guard header behind that FTM.
* include/std/filesystem: Switch to bits/version.h for
__cpp_lib_filesystem. Guard header behind that FTM.
* include/std/expected: Switch to bits/version.h for
__cpp_lib_expected. Guard header behind it.
* include/std/execution: Switch to bits/version.h for
__cpp_lib_{execution,parallel_algorithm}. Guard header behind
either.
* include/std/deque: Switch to bits/version.h for
__cpp_lib_erase_if.
(erase, erase_if): Guard behind __cpp_lib_erase_if.
* include/std/coroutine: Switch to bits/version.h for
__cpp_lib_coroutine. Guard header behind that FTM.
* include/std/concepts: Switch to bits/version.h for
__cpp_lib_concepts. Guard header behind that FTM.
* include/std/complex: Switch to bits/version.h for
__cpp_lib_{complex_udls,constexpr_complex}.
(operator""if, operator""i, operator""il): Guard behind
__cpp_lib_complex_udls.
* include/std/charconv: Swtich to bits/version.h for
__cpp_lib_{to_chars,constexpr_charconv}.
* include/std/bitset: Switch to bits/version.h for
__cpp_lib_constexpr_bitset.
* include/std/bit: Switch to bits/version.h for
__cpp_lib_{bit_cast,byteswap,bitops,int_pow2,endian}.
(bit_cast): Guard behind __cpp_lib_bit_cast.
(byteswap): Guard behind __cpp_lib_byteswap.
(rotl, rotr, countl_zero, countl_one, countr_zero, countr_one)
(popcount): Guard behind __cpp_lib_bitops.
(has_single_bit, bit_ceil, bit_floor, bit_width): Guard behind
__cpp_lib_int_pow2.
(endian): Guard behind __cpp_lib_endian.
* include/std/barrier: Switch to bits/version.h for
__cpp_lib_barrier. Guard header behind that FTM.
* include/std/atomic: Switch to bits/version.h for
__cpp_lib_atomic_{is_always_lock_free,float,ref}
and __cpp_lib_lock_free_type_aliases.
(*::is_always_lock_free): Guard behind
__cpp_lib_atomic_is_always_lock_free.
(atomic<float>): Guard behind __cpp_lib_atomic_float.
(atomic_ref): Guard behind __cpp_lib_atomic_ref.
(atomic_signed_lock_free, atomic_unsigned_lock_free): Guard behind
__cpp_lib_atomic_lock_free_type_aliases.
* include/std/array: Switch to bits/version.h for
__cpp_lib_to_array.
(to_array): Guard behind __cpp_lib_to_array.
* include/std/any: Switch to bits/version.h for __cpp_lib_any.
Guard header behind that FTM.
* include/std/algorithm: Switch to bits/version.h for
__cpp_lib_parallel_algorithm.
* include/c_global/cstddef: Switch to bits/version.h for
__cpp_lib_byte.
(byte): Guard behind __cpp_lib_byte.
* include/c_global/cmath: Switch to bits/version.h for
__cpp_lib_{hypot,interpolate}.
(hypot3): Guard behind __cpp_lib_hypot.
(lerp): Guard behind __cpp_lib_interpolate.
* include/c_compatibility/stdatomic.h: Switch to
bits/stl_version.h for __cpp_lib_atomic. Guard header behind that
FTM.
* include/bits/utility.h: Switch to bits/version.h for
__cpp_lib_{tuple_element_t,integer_sequence,ranges_zip}.
(tuple_element_t): Guard behind __cpp_lib_tuple_element_t.
(integer_sequence et al): Guard behind __cpp_lib_integer_sequence.
* include/bits/uses_allocator_args.h: Switch to bits/version.h for
__cpp_lib_make_obj_using_allocator. Guard header behind that FTM.
* include/bits/unordered_map.h: Switch to bits/version.h for
__cpp_lib_unordered_map_try_emplace.
(try_emplace): Guard behind __cpp_lib_unordered_map_try_emplace.
* include/bits/unique_ptr.h: Switch to bits/version.h for
__cpp_lib_{constexpr_memory,make_unique}.
(make_unique): Guard behind __cpp_lib_make_unique.
* include/bits/stl_vector.h: Switch to bits/version.h for
__cpp_lib_constexpr_vector.
* include/bits/stl_uninitialized.h: Switch to bits/version.h for
__cpp_lib_raw_memory_algorithms.
(uninitialized_default_construct)
(uninitialized_default_construct_n, uninitialized_move)
(uninitialized_move_n, uninitialized_value_construct)
(uninitialized_value_construct_n): Guard behind
__cpp_lib_raw_memory_algorithms.
* include/bits/stl_tree.h: Switch to bits/version.h for
__cpp_lib_generic_associative_lookup.
* include/bits/stl_stack.h: Switch to bits/version.h for
__cpp_lib_adaptor_iterator_pair_constructor.
(stack): Guard iterator-pair constructor behind
__cpp_lib_adaptor_iterator_pair_constructor.
* include/bits/stl_queue.h: Switch to bits/version.h for
__cpp_lib_adaptor_iterator_pair_constructor.
(queue): Guard iterator-pair constructor behind
__cpp_lib_adaptor_iterator_pair_constructor.
* include/bits/stl_pair.h: Switch to bits/version.h for
__cpp_lib_{concepts,tuples_by_type}.
(get): Guard type-getting overloads behind
__cpp_lib_tuples_by_type.
* include/bits/stl_map.h: Switch to bits/version.h for
__cpp_lib_map_try_emplace.
(map<>::try_emplace): Guard behind __cpp_lib_map_try_emplace.
* include/bits/stl_list.h: Switch to bits/version.h for
__cpp_lib_list_remove_return_type.
(__remove_return_type, _GLIBCXX_LIST_REMOVE_RETURN_TYPE_TAG)
[C++20]: guard behind __cpp_lib_list_remove_return_type instead.
* include/bits/stl_iterator.h: Switch to bits/version.h for
__cpp_lib_{constexpr_iterator,array_constexpr} and
__cpp_lib_{make_reverse_iterator,move_iterator_concept}.
(make_reverse_iterator): Guard behind
__cpp_lib_make_reverse_iterator.
(iterator_concept et al): Guard __cpp_lib_move_iterator_concept
changes behind that FTM.
* include/bits/stl_function.h: Switch to bits/version.h for
__cpp_lib_transparent_operators.
(equal_to, not_equal_to, greater, less, greater_equal)
(less_equal, bit_and, bit_or, bit_xor, bit_not, logical_and)
(logical_or, logical_not, plus, minus, multiplies, divides)
(modulus, negate): Guard '= void' fwdecls behind
__cpp_lib_transparent_operators.
(plus<void>, minus<void>, multiplies<void>, divides<void>)
(modulus<void>, negate<void>, logical_and<void>, logical_or<void>)
(logical_not<void>, bit_and<void>, bit_or<void>, bit_xor<void>)
(equal_to<void>, not_equal_to<void>, greater<void>, less<void>)
(greater_equal<void>, less_equal<void>, bit_not<void>)
(__has_is_transparent): Guard behind
__cpp_lib_transparent_operators.
* include/bits/stl_algobase.h: Switch to bits/version.h for
__cpp_lib_robust_nonmodifying_seq_ops.
(robust equal, mismatch): Guard behind
__cpp_lib_nonmember_container_access.
* include/bits/stl_algo.h: Swtich to bits/version.h for
__cpp_lib_{clamp,sample}.
(clamp): Guard behind __cpp_lib_clamp.
(sample): Guard behind __cpp_lib_sample.
* include/bits/specfun.h: Switch to bits/version.h for
__cpp_lib_math_special_functions and __STDCPP_MATH_SPEC_FUNCS__.
* include/bits/shared_ptr_base.h: Switch to bits/version.h for
__cpp_lib_{smart_ptr_for_overwrite,shared_ptr_arrays}.
(_Sp_overwrite_tag): Guard behind
__cpp_lib_smart_ptr_for_overwrite.
* include/bits/shared_ptr_atomic.h: Switch to bits/version.h for
__cpp_lib_atomic_shared_ptr.
* include/bits/shared_ptr.h: Switch to bits/version.h for
__cpp_lib_{enable_shared_from_this,shared_ptr_weak_type}.
(shared_ptr<T>::weak_type): Guard behind
__cpp_lib_shared_ptr_weak_type.
(enable_shared_from_this<T>::weak_from_this): Guard behind
__cpp_lib_enable_shared_from_this.
* include/bits/ranges_cmp.h: Switch to bits/version.h for
__cpp_lib_ranges.
* include/bits/ranges_algo.h: Switch to bits/version.h for
__cpp_lib_{shift,ranges_{contains,find_last,fold,iota}}.
* include/bits/range_access.h: Switch to bits/version.h for
__cpp_lib_nonmember_container_access
(size, empty, data): Guard behind
__cpp_lib_nonmember_container_access.
(ssize): Guard behind __cpp_lib_ssize.
* include/bits/ptr_traits.h: Switch to bits/version.h. for
__cpp_lib_{constexpr_memory,to_address}.
(to_address): Guard behind __cpp_lib_to_address.
* include/bits/node_handle.h: Switch to bits/version.h for
__cpp_lib_node_extract. Guard header behind that FTM.
* include/bits/move_only_function.h: Switch to bits/version.h for
__cpp_lib_move_only_function. Guard header behind that FTM.
* include/bits/move.h: Switch to bits/version.h for
__cpp_lib_addressof_constexpr.
* include/bits/ios_base.h: Switch to bits/version.h for
__cpp_lib_ios_noreplace.
(noreplace): Guard with __cpp_lib_ios_noreplace.
* include/bits/hashtable.h: Switch to bits/version.h for
__cpp_lib_generic_unordered_lookup.
(_M_equal_range_tr, _M_count_tr, _M_find_tr): Guard behind
__cpp_lib_generic_unordered_lookup.
* include/bits/forward_list.h: Switch to bits/version.h for
__cpp_lib_list_remove_return_type.
(__remove_return_type): Guard behind
__cpp_lib_list_remove_return_type.
* include/bits/erase_if.h: Switch to bits/version.h for
__cpp_lib_erase_if.
* include/bits/cow_string.h: Switch to bits/version.h for
__cpp_lib_constexpr_string.
* include/bits/chrono.h: Swtich to bits/version.h for
__cpp_lib_chrono{,_udls}.
(ceil): Guard behind __cpp_lib_chrono.
(operator""ns et al): Guard behind __cpp_lib_chrono_udls.
* include/bits/char_traits.h: Switch to bits/version.h for
__cpp_lib_constexpr_char_traits.
* include/bits/basic_string.h: Switch to bits/version.h for
__cpp_lib_{constexpr_string,string_{resize_and_overwrite,udls}}.
(resize_and_overwrite): Guard behind
__cpp_lib_string_resize_and_overwrite.
(operator""s): Guard behind __cpp_lib_string_udls.
* include/bits/atomic_wait.h: Switch to bits/version.h for
__cpp_lib_atomic_wait. Guard header behind that FTM.
* include/bits/atomic_base.h: Switch to bits/version.h for
__cpp_lib_atomic_value_initialization and
__cpp_lib_atomic_flag_test.
(atomic_flag::test): Guard behind __cpp_lib_atomic_flag_test,
rather than C++20.
* include/bits/allocator.h: Switch to bits/version.h for
__cpp_lib_incomplete_container_elements.
* include/bits/alloc_traits.h: Switch to using bits/version.h for
__cpp_lib_constexpr_dynamic_alloc and
__cpp_lib_allocator_traits_is_always_equal.
* include/bits/align.h: Switch to bits/version.h for defining
__cpp_lib_assume_aligned.
(assume_aligned): Guard with __cpp_lib_assume_aligned.
* include/bits/algorithmfwd.h: Switch to bits/version.h for
defining __cpp_lib_constexpr_algorithms.
* include/std/stacktrace: Switch to bits/version.h for
__cpp_lib_stacktrace. Guard header behind that FTM.
* testsuite/23_containers/array/tuple_interface/get_neg.cc:
Update line numbers.
2654 lines
75 KiB
C++
2654 lines
75 KiB
C++
// The template and inlines for the -*- C++ -*- complex number classes.
|
|
|
|
// Copyright (C) 1997-2023 Free Software Foundation, Inc.
|
|
//
|
|
// This file is part of the GNU ISO C++ Library. This library 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, or (at your option)
|
|
// any later version.
|
|
|
|
// This library 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.
|
|
|
|
// Under Section 7 of GPL version 3, you are granted additional
|
|
// permissions described in the GCC Runtime Library Exception, version
|
|
// 3.1, as published by the Free Software Foundation.
|
|
|
|
// You should have received a copy of the GNU General Public License and
|
|
// a copy of the GCC Runtime Library Exception along with this program;
|
|
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
|
|
// <http://www.gnu.org/licenses/>.
|
|
|
|
/** @file include/complex
|
|
* This is a Standard C++ Library header.
|
|
*/
|
|
|
|
//
|
|
// ISO C++ 14882: 26.2 Complex Numbers
|
|
// Note: this is not a conforming implementation.
|
|
// Initially implemented by Ulrich Drepper <drepper@cygnus.com>
|
|
// Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
|
|
//
|
|
|
|
#ifndef _GLIBCXX_COMPLEX
|
|
#define _GLIBCXX_COMPLEX 1
|
|
|
|
#pragma GCC system_header
|
|
|
|
#include <bits/c++config.h>
|
|
#include <bits/cpp_type_traits.h>
|
|
#include <ext/type_traits.h>
|
|
#include <cmath>
|
|
#include <sstream>
|
|
|
|
// Get rid of a macro possibly defined in <complex.h>
|
|
#undef complex
|
|
|
|
#ifdef __clang__
|
|
#pragma clang diagnostic push
|
|
#pragma clang diagnostic ignored "-Wc99-extensions"
|
|
#endif
|
|
|
|
#define __glibcxx_want_constexpr_complex
|
|
#define __glibcxx_want_complex_udls
|
|
#include <bits/version.h>
|
|
|
|
namespace std _GLIBCXX_VISIBILITY(default)
|
|
{
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
|
|
|
/**
|
|
* @defgroup complex_numbers Complex Numbers
|
|
* @ingroup numerics
|
|
*
|
|
* Classes and functions for complex numbers.
|
|
* @{
|
|
*/
|
|
|
|
// Forward declarations.
|
|
template<typename _Tp> class complex;
|
|
template<> class complex<float>;
|
|
template<> class complex<double>;
|
|
template<> class complex<long double>;
|
|
|
|
/// Return magnitude of @a z.
|
|
template<typename _Tp> _Tp abs(const complex<_Tp>&);
|
|
/// Return phase angle of @a z.
|
|
template<typename _Tp> _Tp arg(const complex<_Tp>&);
|
|
/// Return @a z magnitude squared.
|
|
template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&);
|
|
|
|
/// Return complex conjugate of @a z.
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&);
|
|
/// Return complex with magnitude @a rho and angle @a theta.
|
|
template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
|
|
|
|
// Transcendentals:
|
|
/// Return complex cosine of @a z.
|
|
template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
|
|
/// Return complex hyperbolic cosine of @a z.
|
|
template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
|
|
/// Return complex base e exponential of @a z.
|
|
template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
|
|
/// Return complex natural logarithm of @a z.
|
|
template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
|
|
/// Return complex base 10 logarithm of @a z.
|
|
template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
|
|
/// Return @a x to the @a y'th power.
|
|
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
|
|
/// Return @a x to the @a y'th power.
|
|
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
|
|
/// Return @a x to the @a y'th power.
|
|
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
|
|
const complex<_Tp>&);
|
|
/// Return @a x to the @a y'th power.
|
|
template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
|
|
/// Return complex sine of @a z.
|
|
template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
|
|
/// Return complex hyperbolic sine of @a z.
|
|
template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
|
|
/// Return complex square root of @a z.
|
|
template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
|
|
/// Return complex tangent of @a z.
|
|
template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
|
|
/// Return complex hyperbolic tangent of @a z.
|
|
template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
|
|
|
|
|
|
// 26.2.2 Primary template class complex
|
|
/**
|
|
* Template to represent complex numbers.
|
|
*
|
|
* Specializations for float, double, and long double are part of the
|
|
* library. Results with any other type are not guaranteed.
|
|
*
|
|
* @param Tp Type of real and imaginary values.
|
|
*/
|
|
template<typename _Tp>
|
|
class complex
|
|
{
|
|
public:
|
|
/// Value typedef.
|
|
typedef _Tp value_type;
|
|
|
|
/// Default constructor. First parameter is x, second parameter is y.
|
|
/// Unspecified parameters default to 0.
|
|
_GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
|
|
: _M_real(__r), _M_imag(__i) { }
|
|
|
|
// Let the compiler synthesize the copy constructor
|
|
#if __cplusplus >= 201103L
|
|
constexpr complex(const complex&) = default;
|
|
#endif
|
|
|
|
/// Converting constructor.
|
|
template<typename _Up>
|
|
#if __cplusplus > 202002L
|
|
explicit(!requires(_Up __u) { _Tp{__u}; })
|
|
#endif
|
|
_GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
|
|
: _M_real(_Tp(__z.real())), _M_imag(_Tp(__z.imag())) { }
|
|
|
|
#if __cplusplus >= 201103L
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
_GLIBCXX_ABI_TAG_CXX11
|
|
constexpr _Tp
|
|
real() const { return _M_real; }
|
|
|
|
_GLIBCXX_ABI_TAG_CXX11
|
|
constexpr _Tp
|
|
imag() const { return _M_imag; }
|
|
#else
|
|
/// Return real part of complex number.
|
|
_Tp&
|
|
real() { return _M_real; }
|
|
|
|
/// Return real part of complex number.
|
|
const _Tp&
|
|
real() const { return _M_real; }
|
|
|
|
/// Return imaginary part of complex number.
|
|
_Tp&
|
|
imag() { return _M_imag; }
|
|
|
|
/// Return imaginary part of complex number.
|
|
const _Tp&
|
|
imag() const { return _M_imag; }
|
|
#endif
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
_GLIBCXX20_CONSTEXPR void
|
|
real(_Tp __val) { _M_real = __val; }
|
|
|
|
_GLIBCXX20_CONSTEXPR void
|
|
imag(_Tp __val) { _M_imag = __val; }
|
|
|
|
/// Assign a scalar to this complex number.
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&);
|
|
|
|
/// Add a scalar to this complex number.
|
|
// 26.2.5/1
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
operator+=(const _Tp& __t)
|
|
{
|
|
_M_real += __t;
|
|
return *this;
|
|
}
|
|
|
|
/// Subtract a scalar from this complex number.
|
|
// 26.2.5/3
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
operator-=(const _Tp& __t)
|
|
{
|
|
_M_real -= __t;
|
|
return *this;
|
|
}
|
|
|
|
/// Multiply this complex number by a scalar.
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&);
|
|
/// Divide this complex number by a scalar.
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&);
|
|
|
|
// Let the compiler synthesize the copy assignment operator
|
|
#if __cplusplus >= 201103L
|
|
_GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default;
|
|
#endif
|
|
|
|
/// Assign another complex number to this one.
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&);
|
|
/// Add another complex number to this one.
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&);
|
|
/// Subtract another complex number from this one.
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&);
|
|
/// Multiply this complex number by another.
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&);
|
|
/// Divide this complex number by another.
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&);
|
|
|
|
_GLIBCXX_CONSTEXPR complex __rep() const
|
|
{ return *this; }
|
|
|
|
private:
|
|
_Tp _M_real;
|
|
_Tp _M_imag;
|
|
};
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
complex<_Tp>::operator=(const _Tp& __t)
|
|
{
|
|
_M_real = __t;
|
|
_M_imag = _Tp();
|
|
return *this;
|
|
}
|
|
|
|
// 26.2.5/5
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
complex<_Tp>::operator*=(const _Tp& __t)
|
|
{
|
|
_M_real *= __t;
|
|
_M_imag *= __t;
|
|
return *this;
|
|
}
|
|
|
|
// 26.2.5/7
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
complex<_Tp>::operator/=(const _Tp& __t)
|
|
{
|
|
_M_real /= __t;
|
|
_M_imag /= __t;
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
complex<_Tp>::operator=(const complex<_Up>& __z)
|
|
{
|
|
_M_real = __z.real();
|
|
_M_imag = __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
// 26.2.5/9
|
|
template<typename _Tp>
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
complex<_Tp>::operator+=(const complex<_Up>& __z)
|
|
{
|
|
_M_real += __z.real();
|
|
_M_imag += __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
// 26.2.5/11
|
|
template<typename _Tp>
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
complex<_Tp>::operator-=(const complex<_Up>& __z)
|
|
{
|
|
_M_real -= __z.real();
|
|
_M_imag -= __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
// 26.2.5/13
|
|
// XXX: This is a grammar school implementation.
|
|
template<typename _Tp>
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
complex<_Tp>::operator*=(const complex<_Up>& __z)
|
|
{
|
|
const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
|
|
_M_imag = _M_real * __z.imag() + _M_imag * __z.real();
|
|
_M_real = __r;
|
|
return *this;
|
|
}
|
|
|
|
// 26.2.5/15
|
|
// XXX: This is a grammar school implementation.
|
|
template<typename _Tp>
|
|
template<typename _Up>
|
|
_GLIBCXX20_CONSTEXPR complex<_Tp>&
|
|
complex<_Tp>::operator/=(const complex<_Up>& __z)
|
|
{
|
|
const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
|
|
const _Tp __n = std::norm(__z);
|
|
_M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
|
|
_M_real = __r / __n;
|
|
return *this;
|
|
}
|
|
|
|
// Operators:
|
|
///@{
|
|
/// Return new complex value @a x plus @a y.
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r += __y;
|
|
return __r;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator+(const complex<_Tp>& __x, const _Tp& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r += __y;
|
|
return __r;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator+(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __r = __y;
|
|
__r += __x;
|
|
return __r;
|
|
}
|
|
///@}
|
|
|
|
///@{
|
|
/// Return new complex value @a x minus @a y.
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r -= __y;
|
|
return __r;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator-(const complex<_Tp>& __x, const _Tp& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r -= __y;
|
|
return __r;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator-(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __r = -__y;
|
|
__r += __x;
|
|
return __r;
|
|
}
|
|
///@}
|
|
|
|
///@{
|
|
/// Return new complex value @a x times @a y.
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r *= __y;
|
|
return __r;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator*(const complex<_Tp>& __x, const _Tp& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r *= __y;
|
|
return __r;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator*(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __r = __y;
|
|
__r *= __x;
|
|
return __r;
|
|
}
|
|
///@}
|
|
|
|
///@{
|
|
/// Return new complex value @a x divided by @a y.
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r /= __y;
|
|
return __r;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator/(const complex<_Tp>& __x, const _Tp& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r /= __y;
|
|
return __r;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator/(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
complex<_Tp> __r = __x;
|
|
__r /= __y;
|
|
return __r;
|
|
}
|
|
///@}
|
|
|
|
/// Return @a x.
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator+(const complex<_Tp>& __x)
|
|
{ return __x; }
|
|
|
|
/// Return complex negation of @a x.
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
operator-(const complex<_Tp>& __x)
|
|
{ return complex<_Tp>(-__x.real(), -__x.imag()); }
|
|
|
|
///@{
|
|
/// Return true if @a x is equal to @a y.
|
|
template<typename _Tp>
|
|
inline _GLIBCXX_CONSTEXPR bool
|
|
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return __x.real() == __y.real() && __x.imag() == __y.imag(); }
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX_CONSTEXPR bool
|
|
operator==(const complex<_Tp>& __x, const _Tp& __y)
|
|
{ return __x.real() == __y && __x.imag() == _Tp(); }
|
|
|
|
#if !(__cpp_impl_three_way_comparison >= 201907L)
|
|
template<typename _Tp>
|
|
inline _GLIBCXX_CONSTEXPR bool
|
|
operator==(const _Tp& __x, const complex<_Tp>& __y)
|
|
{ return __x == __y.real() && _Tp() == __y.imag(); }
|
|
///@}
|
|
|
|
///@{
|
|
/// Return false if @a x is equal to @a y.
|
|
template<typename _Tp>
|
|
inline _GLIBCXX_CONSTEXPR bool
|
|
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return __x.real() != __y.real() || __x.imag() != __y.imag(); }
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX_CONSTEXPR bool
|
|
operator!=(const complex<_Tp>& __x, const _Tp& __y)
|
|
{ return __x.real() != __y || __x.imag() != _Tp(); }
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX_CONSTEXPR bool
|
|
operator!=(const _Tp& __x, const complex<_Tp>& __y)
|
|
{ return __x != __y.real() || _Tp() != __y.imag(); }
|
|
#endif
|
|
///@}
|
|
|
|
/// Extraction operator for complex values.
|
|
template<typename _Tp, typename _CharT, class _Traits>
|
|
basic_istream<_CharT, _Traits>&
|
|
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
|
|
{
|
|
bool __fail = true;
|
|
_CharT __ch;
|
|
if (__is >> __ch)
|
|
{
|
|
if (_Traits::eq(__ch, __is.widen('(')))
|
|
{
|
|
_Tp __u;
|
|
if (__is >> __u >> __ch)
|
|
{
|
|
const _CharT __rparen = __is.widen(')');
|
|
if (_Traits::eq(__ch, __rparen))
|
|
{
|
|
__x = __u;
|
|
__fail = false;
|
|
}
|
|
else if (_Traits::eq(__ch, __is.widen(',')))
|
|
{
|
|
_Tp __v;
|
|
if (__is >> __v >> __ch)
|
|
{
|
|
if (_Traits::eq(__ch, __rparen))
|
|
{
|
|
__x = complex<_Tp>(__u, __v);
|
|
__fail = false;
|
|
}
|
|
else
|
|
__is.putback(__ch);
|
|
}
|
|
}
|
|
else
|
|
__is.putback(__ch);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
__is.putback(__ch);
|
|
_Tp __u;
|
|
if (__is >> __u)
|
|
{
|
|
__x = __u;
|
|
__fail = false;
|
|
}
|
|
}
|
|
}
|
|
if (__fail)
|
|
__is.setstate(ios_base::failbit);
|
|
return __is;
|
|
}
|
|
|
|
/// Insertion operator for complex values.
|
|
template<typename _Tp, typename _CharT, class _Traits>
|
|
basic_ostream<_CharT, _Traits>&
|
|
operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
|
|
{
|
|
basic_ostringstream<_CharT, _Traits> __s;
|
|
__s.flags(__os.flags());
|
|
__s.imbue(__os.getloc());
|
|
__s.precision(__os.precision());
|
|
__s << '(' << __x.real() << ',' << __x.imag() << ')';
|
|
return __os << __s.str();
|
|
}
|
|
|
|
// Values
|
|
#if __cplusplus >= 201103L
|
|
template<typename _Tp>
|
|
constexpr _Tp
|
|
real(const complex<_Tp>& __z)
|
|
{ return __z.real(); }
|
|
|
|
template<typename _Tp>
|
|
constexpr _Tp
|
|
imag(const complex<_Tp>& __z)
|
|
{ return __z.imag(); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline _Tp&
|
|
real(complex<_Tp>& __z)
|
|
{ return __z.real(); }
|
|
|
|
template<typename _Tp>
|
|
inline const _Tp&
|
|
real(const complex<_Tp>& __z)
|
|
{ return __z.real(); }
|
|
|
|
template<typename _Tp>
|
|
inline _Tp&
|
|
imag(complex<_Tp>& __z)
|
|
{ return __z.imag(); }
|
|
|
|
template<typename _Tp>
|
|
inline const _Tp&
|
|
imag(const complex<_Tp>& __z)
|
|
{ return __z.imag(); }
|
|
#endif
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline _Float16
|
|
__complex_abs(__complex__ _Float16 __z)
|
|
{ return _Float16(__builtin_cabsf(__z)); }
|
|
|
|
inline _Float16
|
|
__complex_arg(__complex__ _Float16 __z)
|
|
{ return _Float16(__builtin_cargf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_cos(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_ccosf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_cosh(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_ccoshf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_exp(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_cexpf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_log(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_clogf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_sin(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_csinf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_sinh(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_csinhf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_sqrt(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_csqrtf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_tan(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_ctanf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_tanh(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_ctanhf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_pow(__complex__ _Float16 __x, __complex__ _Float16 __y)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_cpowf(__x, __y)); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline _Float32
|
|
__complex_abs(__complex__ _Float32 __z) { return __builtin_cabsf(__z); }
|
|
|
|
inline _Float32
|
|
__complex_arg(__complex__ _Float32 __z) { return __builtin_cargf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_cos(__complex__ _Float32 __z) { return __builtin_ccosf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_cosh(__complex__ _Float32 __z) { return __builtin_ccoshf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_exp(__complex__ _Float32 __z) { return __builtin_cexpf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_log(__complex__ _Float32 __z) { return __builtin_clogf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_sin(__complex__ _Float32 __z) { return __builtin_csinf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_sinh(__complex__ _Float32 __z) { return __builtin_csinhf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_sqrt(__complex__ _Float32 __z) { return __builtin_csqrtf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_tan(__complex__ _Float32 __z) { return __builtin_ctanf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_tanh(__complex__ _Float32 __z) { return __builtin_ctanhf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_pow(__complex__ _Float32 __x, __complex__ _Float32 __y)
|
|
{ return __builtin_cpowf(__x, __y); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
|
|
inline _Float64
|
|
__complex_abs(__complex__ _Float64 __z) { return __builtin_cabs(__z); }
|
|
|
|
inline _Float64
|
|
__complex_arg(__complex__ _Float64 __z) { return __builtin_carg(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_cos(__complex__ _Float64 __z) { return __builtin_ccos(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_cosh(__complex__ _Float64 __z) { return __builtin_ccosh(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_exp(__complex__ _Float64 __z) { return __builtin_cexp(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_log(__complex__ _Float64 __z) { return __builtin_clog(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_sin(__complex__ _Float64 __z) { return __builtin_csin(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_sinh(__complex__ _Float64 __z) { return __builtin_csinh(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_sqrt(__complex__ _Float64 __z) { return __builtin_csqrt(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_tan(__complex__ _Float64 __z) { return __builtin_ctan(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_tanh(__complex__ _Float64 __z) { return __builtin_ctanh(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_pow(__complex__ _Float64 __x, __complex__ _Float64 __y)
|
|
{ return __builtin_cpow(__x, __y); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
|
|
inline _Float128
|
|
__complex_abs(__complex__ _Float128 __z) { return __builtin_cabsl(__z); }
|
|
|
|
inline _Float128
|
|
__complex_arg(__complex__ _Float128 __z) { return __builtin_cargl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_cos(__complex__ _Float128 __z) { return __builtin_ccosl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_cosh(__complex__ _Float128 __z) { return __builtin_ccoshl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_exp(__complex__ _Float128 __z) { return __builtin_cexpl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_log(__complex__ _Float128 __z) { return __builtin_clogl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_sin(__complex__ _Float128 __z) { return __builtin_csinl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_sinh(__complex__ _Float128 __z) { return __builtin_csinhl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_sqrt(__complex__ _Float128 __z) { return __builtin_csqrtl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_tan(__complex__ _Float128 __z) { return __builtin_ctanl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_tanh(__complex__ _Float128 __z) { return __builtin_ctanhl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_pow(__complex__ _Float128 __x, __complex__ _Float128 __y)
|
|
{ return __builtin_cpowl(__x, __y); }
|
|
#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
|
|
inline _Float128
|
|
__complex_abs(__complex__ _Float128 __z) { return __builtin_cabsf128(__z); }
|
|
|
|
inline _Float128
|
|
__complex_arg(__complex__ _Float128 __z) { return __builtin_cargf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_cos(__complex__ _Float128 __z) { return __builtin_ccosf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_cosh(__complex__ _Float128 __z) { return __builtin_ccoshf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_exp(__complex__ _Float128 __z) { return __builtin_cexpf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_log(__complex__ _Float128 __z) { return __builtin_clogf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_sin(__complex__ _Float128 __z) { return __builtin_csinf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_sinh(__complex__ _Float128 __z) { return __builtin_csinhf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_sqrt(__complex__ _Float128 __z) { return __builtin_csqrtf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_tan(__complex__ _Float128 __z) { return __builtin_ctanf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_tanh(__complex__ _Float128 __z) { return __builtin_ctanhf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_pow(__complex__ _Float128 __x, __complex__ _Float128 __y)
|
|
{ return __builtin_cpowf128(__x, __y); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline __gnu_cxx::__bfloat16_t
|
|
__complex_abs(__complex__ decltype(0.0bf16) __z)
|
|
{ return __gnu_cxx::__bfloat16_t(__builtin_cabsf(__z)); }
|
|
|
|
inline __gnu_cxx::__bfloat16_t
|
|
__complex_arg(__complex__ decltype(0.0bf16) __z)
|
|
{ return __gnu_cxx::__bfloat16_t(__builtin_cargf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_cos(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_ccosf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_cosh(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_ccoshf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_exp(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cexpf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_log(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_clogf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_sin(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_csinf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_sinh(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_csinhf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_sqrt(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_csqrtf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_tan(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_ctanf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_tanh(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_ctanhf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_pow(__complex__ decltype(0.0bf16) __x,
|
|
__complex__ decltype(0.0bf16) __y)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cpowf(__x,
|
|
__y)); }
|
|
#endif
|
|
#endif
|
|
|
|
// 26.2.7/3 abs(__z): Returns the magnitude of __z.
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
__complex_abs(const complex<_Tp>& __z)
|
|
{
|
|
_Tp __x = __z.real();
|
|
_Tp __y = __z.imag();
|
|
const _Tp __s = std::max(abs(__x), abs(__y));
|
|
if (__s == _Tp()) // well ...
|
|
return __s;
|
|
__x /= __s;
|
|
__y /= __s;
|
|
return __s * sqrt(__x * __x + __y * __y);
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline float
|
|
__complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
|
|
|
|
inline double
|
|
__complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
|
|
|
|
inline long double
|
|
__complex_abs(const __complex__ long double& __z)
|
|
{ return __builtin_cabsl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
|
|
#endif
|
|
|
|
|
|
// 26.2.7/4: arg(__z): Returns the phase angle of __z.
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
__complex_arg(const complex<_Tp>& __z)
|
|
{ return atan2(__z.imag(), __z.real()); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline float
|
|
__complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
|
|
|
|
inline double
|
|
__complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
|
|
|
|
inline long double
|
|
__complex_arg(const __complex__ long double& __z)
|
|
{ return __builtin_cargl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
|
|
#endif
|
|
|
|
// 26.2.7/5: norm(__z) returns the squared magnitude of __z.
|
|
// As defined, norm() is -not- a norm is the common mathematical
|
|
// sense used in numerics. The helper class _Norm_helper<> tries to
|
|
// distinguish between builtin floating point and the rest, so as
|
|
// to deliver an answer as close as possible to the real value.
|
|
template<bool>
|
|
struct _Norm_helper
|
|
{
|
|
template<typename _Tp>
|
|
static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return __x * __x + __y * __y;
|
|
}
|
|
};
|
|
|
|
template<>
|
|
struct _Norm_helper<true>
|
|
{
|
|
template<typename _Tp>
|
|
static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
|
|
{
|
|
//_Tp __res = std::abs(__z);
|
|
//return __res * __res;
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return __x * __x + __y * __y;
|
|
}
|
|
};
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR _Tp
|
|
norm(const complex<_Tp>& __z)
|
|
{
|
|
return _Norm_helper<__is_floating<_Tp>::__value
|
|
&& !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
polar(const _Tp& __rho, const _Tp& __theta)
|
|
{
|
|
__glibcxx_assert( __rho >= 0 );
|
|
return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
|
|
conj(const complex<_Tp>& __z)
|
|
{ return complex<_Tp>(__z.real(), -__z.imag()); }
|
|
|
|
// Transcendentals
|
|
|
|
// 26.2.8/1 cos(__z): Returns the cosine of __z.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_cos(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_cos(const __complex__ long double& __z)
|
|
{ return __builtin_ccosl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_cosh(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_cosh(const __complex__ long double& __z)
|
|
{ return __builtin_ccoshl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/3 exp(__z): Returns the complex base e exponential of x
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_exp(const complex<_Tp>& __z)
|
|
{ return std::polar<_Tp>(exp(__z.real()), __z.imag()); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_exp(const __complex__ long double& __z)
|
|
{ return __builtin_cexpl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
|
|
// The branch cut is along the negative axis.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_log(const complex<_Tp>& __z)
|
|
{ return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_log(__complex__ double __z) { return __builtin_clog(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_log(const __complex__ long double& __z)
|
|
{ return __builtin_clogl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
log(const complex<_Tp>& __z) { return __complex_log(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
log10(const complex<_Tp>& __z)
|
|
{ return std::log(__z) / log(_Tp(10.0)); }
|
|
|
|
// 26.2.8/10 sin(__z): Returns the sine of __z.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_sin(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_sin(const __complex__ long double& __z)
|
|
{ return __builtin_csinl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_sinh(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_sinh(const __complex__ long double& __z)
|
|
{ return __builtin_csinhl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
|
|
// The branch cut is on the negative axis.
|
|
template<typename _Tp>
|
|
complex<_Tp>
|
|
__complex_sqrt(const complex<_Tp>& __z)
|
|
{
|
|
_Tp __x = __z.real();
|
|
_Tp __y = __z.imag();
|
|
|
|
if (__x == _Tp())
|
|
{
|
|
_Tp __t = sqrt(abs(__y) / 2);
|
|
return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
|
|
}
|
|
else
|
|
{
|
|
_Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
|
|
_Tp __u = __t / 2;
|
|
return __x > _Tp()
|
|
? complex<_Tp>(__u, __y / __t)
|
|
: complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
|
|
}
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_sqrt(const __complex__ long double& __z)
|
|
{ return __builtin_csqrtl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/14 tan(__z): Return the complex tangent of __z.
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_tan(const complex<_Tp>& __z)
|
|
{ return std::sin(__z) / std::cos(__z); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_tan(const __complex__ long double& __z)
|
|
{ return __builtin_ctanl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
|
|
#endif
|
|
|
|
|
|
// 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_tanh(const complex<_Tp>& __z)
|
|
{ return std::sinh(__z) / std::cosh(__z); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_tanh(const __complex__ long double& __z)
|
|
{ return __builtin_ctanhl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
|
|
#endif
|
|
|
|
|
|
// 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
|
|
// raised to the __y-th power. The branch
|
|
// cut is on the negative axis.
|
|
template<typename _Tp>
|
|
complex<_Tp>
|
|
__complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
|
|
{
|
|
complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
|
|
|
|
while (__n >>= 1)
|
|
{
|
|
__x *= __x;
|
|
if (__n % 2)
|
|
__y *= __x;
|
|
}
|
|
|
|
return __y;
|
|
}
|
|
|
|
// In C++11 mode we used to implement the resolution of
|
|
// DR 844. complex pow return type is ambiguous.
|
|
// thus the following overload was disabled in that mode. However, doing
|
|
// that causes all sorts of issues, see, for example:
|
|
// http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html
|
|
// and also PR57974.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const complex<_Tp>& __z, int __n)
|
|
{
|
|
return __n < 0
|
|
? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
|
|
: std::__complex_pow_unsigned(__z, __n);
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex<_Tp>
|
|
pow(const complex<_Tp>& __x, const _Tp& __y)
|
|
{
|
|
#if ! _GLIBCXX_USE_C99_COMPLEX
|
|
if (__x == _Tp())
|
|
return _Tp();
|
|
#endif
|
|
if (__x.imag() == _Tp() && __x.real() > _Tp())
|
|
return pow(__x.real(), __y);
|
|
|
|
complex<_Tp> __t = std::log(__x);
|
|
return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_pow(__complex__ float __x, __complex__ float __y)
|
|
{ return __builtin_cpowf(__x, __y); }
|
|
|
|
inline __complex__ double
|
|
__complex_pow(__complex__ double __x, __complex__ double __y)
|
|
{ return __builtin_cpow(__x, __y); }
|
|
|
|
inline __complex__ long double
|
|
__complex_pow(const __complex__ long double& __x,
|
|
const __complex__ long double& __y)
|
|
{ return __builtin_cpowl(__x, __y); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return __complex_pow(__x.__rep(), __y.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return __complex_pow(__x, __y); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
|
|
__y.imag() * log(__x))
|
|
: std::pow(complex<_Tp>(__x), __y);
|
|
}
|
|
|
|
/// 26.2.3 complex specializations
|
|
/// complex<float> specialization
|
|
template<>
|
|
class complex<float>
|
|
{
|
|
public:
|
|
typedef float value_type;
|
|
typedef __complex__ float _ComplexT;
|
|
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
_GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
|
|
#if __cplusplus >= 201103L
|
|
: _M_value{ __r, __i } { }
|
|
#else
|
|
{
|
|
__real__ _M_value = __r;
|
|
__imag__ _M_value = __i;
|
|
}
|
|
#endif
|
|
|
|
#if __cplusplus >= 201103L
|
|
_GLIBCXX14_CONSTEXPR complex(const complex&) = default;
|
|
#endif
|
|
|
|
#if __cplusplus > 202002L
|
|
template<typename _Up>
|
|
explicit(!requires(_Up __u) { value_type{__u}; })
|
|
constexpr complex(const complex<_Up>& __z)
|
|
: _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
|
|
#else
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
|
|
#endif
|
|
|
|
#if __cplusplus >= 201103L
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr float
|
|
real() const { return __real__ _M_value; }
|
|
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr float
|
|
imag() const { return __imag__ _M_value; }
|
|
#else
|
|
float&
|
|
real() { return __real__ _M_value; }
|
|
|
|
const float&
|
|
real() const { return __real__ _M_value; }
|
|
|
|
float&
|
|
imag() { return __imag__ _M_value; }
|
|
|
|
const float&
|
|
imag() const { return __imag__ _M_value; }
|
|
#endif
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
_GLIBCXX20_CONSTEXPR void
|
|
real(float __val) { __real__ _M_value = __val; }
|
|
|
|
_GLIBCXX20_CONSTEXPR void
|
|
imag(float __val) { __imag__ _M_value = __val; }
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator=(float __f)
|
|
{
|
|
_M_value = __f;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator+=(float __f)
|
|
{
|
|
_M_value += __f;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator-=(float __f)
|
|
{
|
|
_M_value -= __f;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator*=(float __f)
|
|
{
|
|
_M_value *= __f;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator/=(float __f)
|
|
{
|
|
_M_value /= __f;
|
|
return *this;
|
|
}
|
|
|
|
// Let the compiler synthesize the copy and assignment
|
|
// operator. It always does a pretty good job.
|
|
#if __cplusplus >= 201103L
|
|
_GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value = __z.real();
|
|
__imag__ _M_value = __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator+=(const complex<_Tp>& __z)
|
|
{
|
|
_M_value += __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<class _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator-=(const complex<_Tp>& __z)
|
|
{
|
|
_M_value -= __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<class _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator*=(const complex<_Tp>& __z)
|
|
{
|
|
const _ComplexT __t = __z.__rep();
|
|
_M_value *= __t;
|
|
return *this;
|
|
}
|
|
|
|
template<class _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator/=(const complex<_Tp>& __z)
|
|
{
|
|
const _ComplexT __t = __z.__rep();
|
|
_M_value /= __t;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
|
|
|
private:
|
|
_ComplexT _M_value;
|
|
};
|
|
|
|
/// 26.2.3 complex specializations
|
|
/// complex<double> specialization
|
|
template<>
|
|
class complex<double>
|
|
{
|
|
public:
|
|
typedef double value_type;
|
|
typedef __complex__ double _ComplexT;
|
|
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
_GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
|
|
#if __cplusplus >= 201103L
|
|
: _M_value{ __r, __i } { }
|
|
#else
|
|
{
|
|
__real__ _M_value = __r;
|
|
__imag__ _M_value = __i;
|
|
}
|
|
#endif
|
|
|
|
#if __cplusplus >= 201103L
|
|
_GLIBCXX14_CONSTEXPR complex(const complex&) = default;
|
|
#endif
|
|
|
|
#if __cplusplus > 202002L
|
|
template<typename _Up>
|
|
explicit(!requires(_Up __u) { value_type{__u}; })
|
|
constexpr complex(const complex<_Up>& __z)
|
|
: _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
|
|
#else
|
|
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
|
|
#endif
|
|
|
|
#if __cplusplus >= 201103L
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr double
|
|
real() const { return __real__ _M_value; }
|
|
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr double
|
|
imag() const { return __imag__ _M_value; }
|
|
#else
|
|
double&
|
|
real() { return __real__ _M_value; }
|
|
|
|
const double&
|
|
real() const { return __real__ _M_value; }
|
|
|
|
double&
|
|
imag() { return __imag__ _M_value; }
|
|
|
|
const double&
|
|
imag() const { return __imag__ _M_value; }
|
|
#endif
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
_GLIBCXX20_CONSTEXPR void
|
|
real(double __val) { __real__ _M_value = __val; }
|
|
|
|
_GLIBCXX20_CONSTEXPR void
|
|
imag(double __val) { __imag__ _M_value = __val; }
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator=(double __d)
|
|
{
|
|
_M_value = __d;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator+=(double __d)
|
|
{
|
|
_M_value += __d;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator-=(double __d)
|
|
{
|
|
_M_value -= __d;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator*=(double __d)
|
|
{
|
|
_M_value *= __d;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator/=(double __d)
|
|
{
|
|
_M_value /= __d;
|
|
return *this;
|
|
}
|
|
|
|
// The compiler will synthesize this, efficiently.
|
|
#if __cplusplus >= 201103L
|
|
_GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator=(const complex<_Tp>& __z)
|
|
{
|
|
_M_value = __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator+=(const complex<_Tp>& __z)
|
|
{
|
|
_M_value += __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator-=(const complex<_Tp>& __z)
|
|
{
|
|
_M_value -= __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator*=(const complex<_Tp>& __z)
|
|
{
|
|
const _ComplexT __t = __z.__rep();
|
|
_M_value *= __t;
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator/=(const complex<_Tp>& __z)
|
|
{
|
|
const _ComplexT __t = __z.__rep();
|
|
_M_value /= __t;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
|
|
|
private:
|
|
_ComplexT _M_value;
|
|
};
|
|
|
|
/// 26.2.3 complex specializations
|
|
/// complex<long double> specialization
|
|
template<>
|
|
class complex<long double>
|
|
{
|
|
public:
|
|
typedef long double value_type;
|
|
typedef __complex__ long double _ComplexT;
|
|
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
_GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
|
|
long double __i = 0.0L)
|
|
#if __cplusplus >= 201103L
|
|
: _M_value{ __r, __i } { }
|
|
#else
|
|
{
|
|
__real__ _M_value = __r;
|
|
__imag__ _M_value = __i;
|
|
}
|
|
#endif
|
|
|
|
#if __cplusplus >= 201103L
|
|
_GLIBCXX14_CONSTEXPR complex(const complex&) = default;
|
|
#endif
|
|
|
|
#if __cplusplus > 202002L
|
|
template<typename _Up>
|
|
explicit(!requires(_Up __u) { value_type{__u}; })
|
|
constexpr complex(const complex<_Up>& __z)
|
|
: _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
|
|
#else
|
|
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
_GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
#endif
|
|
|
|
#if __cplusplus >= 201103L
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr long double
|
|
real() const { return __real__ _M_value; }
|
|
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr long double
|
|
imag() const { return __imag__ _M_value; }
|
|
#else
|
|
long double&
|
|
real() { return __real__ _M_value; }
|
|
|
|
const long double&
|
|
real() const { return __real__ _M_value; }
|
|
|
|
long double&
|
|
imag() { return __imag__ _M_value; }
|
|
|
|
const long double&
|
|
imag() const { return __imag__ _M_value; }
|
|
#endif
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
_GLIBCXX20_CONSTEXPR void
|
|
real(long double __val) { __real__ _M_value = __val; }
|
|
|
|
_GLIBCXX20_CONSTEXPR void
|
|
imag(long double __val) { __imag__ _M_value = __val; }
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator=(long double __r)
|
|
{
|
|
_M_value = __r;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator+=(long double __r)
|
|
{
|
|
_M_value += __r;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator-=(long double __r)
|
|
{
|
|
_M_value -= __r;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator*=(long double __r)
|
|
{
|
|
_M_value *= __r;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator/=(long double __r)
|
|
{
|
|
_M_value /= __r;
|
|
return *this;
|
|
}
|
|
|
|
// The compiler knows how to do this efficiently
|
|
#if __cplusplus >= 201103L
|
|
_GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator=(const complex<_Tp>& __z)
|
|
{
|
|
_M_value = __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator+=(const complex<_Tp>& __z)
|
|
{
|
|
_M_value += __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator-=(const complex<_Tp>& __z)
|
|
{
|
|
_M_value -= __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator*=(const complex<_Tp>& __z)
|
|
{
|
|
const _ComplexT __t = __z.__rep();
|
|
_M_value *= __t;
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR complex&
|
|
operator/=(const complex<_Tp>& __z)
|
|
{
|
|
const _ComplexT __t = __z.__rep();
|
|
_M_value /= __t;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
|
|
|
private:
|
|
_ComplexT _M_value;
|
|
};
|
|
|
|
#if __cplusplus > 202002L
|
|
template<typename _Tp>
|
|
struct __complex_type
|
|
{ };
|
|
|
|
#ifdef __STDCPP_FLOAT16_T__
|
|
template<>
|
|
struct __complex_type<_Float16>
|
|
{ typedef __complex__ _Float16 type; };
|
|
#endif
|
|
|
|
#ifdef __STDCPP_FLOAT32_T__
|
|
template<>
|
|
struct __complex_type<_Float32>
|
|
{ typedef __complex__ _Float32 type; };
|
|
#endif
|
|
|
|
#ifdef __STDCPP_FLOAT64_T__
|
|
template<>
|
|
struct __complex_type<_Float64>
|
|
{ typedef __complex__ _Float64 type; };
|
|
#endif
|
|
|
|
#ifdef __STDCPP_FLOAT128_T__
|
|
template<>
|
|
struct __complex_type<_Float128>
|
|
{ typedef __complex__ _Float128 type; };
|
|
#endif
|
|
|
|
#ifdef __STDCPP_BFLOAT16_T__
|
|
template<>
|
|
struct __complex_type<__gnu_cxx::__bfloat16_t>
|
|
{ typedef __complex__ decltype(0.0bf16) type; };
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
requires requires { typename __complex_type<_Tp>::type; }
|
|
class complex<_Tp>
|
|
{
|
|
public:
|
|
typedef _Tp value_type;
|
|
typedef typename std::__complex_type<_Tp>::type _ComplexT;
|
|
|
|
constexpr complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
constexpr complex(_Tp __r = _Tp(), _Tp __i = _Tp())
|
|
: _M_value{ __r, __i } { }
|
|
|
|
template<typename _Up>
|
|
explicit(!requires(_Up __u) { value_type{__u}; })
|
|
constexpr complex(const complex<_Up>& __z)
|
|
: _M_value{ value_type(__z.real()), value_type(__z.imag()) } { }
|
|
|
|
constexpr _Tp
|
|
real() const { return __real__ _M_value; }
|
|
|
|
constexpr _Tp
|
|
imag() const { return __imag__ _M_value; }
|
|
|
|
constexpr void
|
|
real(_Tp __val) { __real__ _M_value = __val; }
|
|
|
|
constexpr void
|
|
imag(_Tp __val) { __imag__ _M_value = __val; }
|
|
|
|
constexpr complex&
|
|
operator=(_Tp __f)
|
|
{
|
|
_M_value = __f;
|
|
return *this;
|
|
}
|
|
|
|
constexpr complex&
|
|
operator+=(_Tp __f)
|
|
{
|
|
_M_value += __f;
|
|
return *this;
|
|
}
|
|
|
|
constexpr complex&
|
|
operator-=(_Tp __f)
|
|
{
|
|
_M_value -= __f;
|
|
return *this;
|
|
}
|
|
|
|
constexpr complex&
|
|
operator*=(_Tp __f)
|
|
{
|
|
_M_value *= __f;
|
|
return *this;
|
|
}
|
|
|
|
constexpr complex&
|
|
operator/=(_Tp __f)
|
|
{
|
|
_M_value /= __f;
|
|
return *this;
|
|
}
|
|
|
|
// Let the compiler synthesize the copy and assignment
|
|
// operator. It always does a pretty good job.
|
|
constexpr complex(const complex&) = default;
|
|
constexpr complex& operator=(const complex&) = default;
|
|
|
|
template<typename _Up>
|
|
constexpr complex&
|
|
operator=(const complex<_Up>& __z)
|
|
{
|
|
__real__ _M_value = __z.real();
|
|
__imag__ _M_value = __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Up>
|
|
constexpr complex&
|
|
operator+=(const complex<_Up>& __z)
|
|
{
|
|
_M_value += __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<class _Up>
|
|
constexpr complex&
|
|
operator-=(const complex<_Up>& __z)
|
|
{
|
|
_M_value -= __z.__rep();
|
|
return *this;
|
|
}
|
|
|
|
template<class _Up>
|
|
constexpr complex&
|
|
operator*=(const complex<_Up>& __z)
|
|
{
|
|
const _ComplexT __t = __z.__rep();
|
|
_M_value *= __t;
|
|
return *this;
|
|
}
|
|
|
|
template<class _Up>
|
|
constexpr complex&
|
|
operator/=(const complex<_Up>& __z)
|
|
{
|
|
const _ComplexT __t = __z.__rep();
|
|
_M_value /= __t;
|
|
return *this;
|
|
}
|
|
|
|
constexpr _ComplexT __rep() const { return _M_value; }
|
|
|
|
private:
|
|
_ComplexT _M_value;
|
|
};
|
|
#endif
|
|
|
|
#if __cplusplus <= 202002L
|
|
// These bits have to be at the end of this file, so that the
|
|
// specializations have all been defined.
|
|
inline _GLIBCXX_CONSTEXPR
|
|
complex<float>::complex(const complex<double>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
inline _GLIBCXX_CONSTEXPR
|
|
complex<float>::complex(const complex<long double>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
inline _GLIBCXX_CONSTEXPR
|
|
complex<double>::complex(const complex<long double>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
#endif
|
|
|
|
// Inhibit implicit instantiations for required instantiations,
|
|
// which are defined via explicit instantiations elsewhere.
|
|
// NB: This syntax is a GNU extension.
|
|
#if _GLIBCXX_EXTERN_TEMPLATE
|
|
extern template istream& operator>>(istream&, complex<float>&);
|
|
extern template ostream& operator<<(ostream&, const complex<float>&);
|
|
extern template istream& operator>>(istream&, complex<double>&);
|
|
extern template ostream& operator<<(ostream&, const complex<double>&);
|
|
extern template istream& operator>>(istream&, complex<long double>&);
|
|
extern template ostream& operator<<(ostream&, const complex<long double>&);
|
|
|
|
#ifdef _GLIBCXX_USE_WCHAR_T
|
|
extern template wistream& operator>>(wistream&, complex<float>&);
|
|
extern template wostream& operator<<(wostream&, const complex<float>&);
|
|
extern template wistream& operator>>(wistream&, complex<double>&);
|
|
extern template wostream& operator<<(wostream&, const complex<double>&);
|
|
extern template wistream& operator>>(wistream&, complex<long double>&);
|
|
extern template wostream& operator<<(wostream&, const complex<long double>&);
|
|
#endif
|
|
#endif
|
|
|
|
/// @} group complex_numbers
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace
|
|
|
|
#if __cplusplus >= 201103L
|
|
|
|
namespace std _GLIBCXX_VISIBILITY(default)
|
|
{
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
|
|
|
// Forward declarations.
|
|
template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
|
|
template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
|
|
template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
|
|
|
|
template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
|
|
template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
|
|
template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
|
|
// DR 595.
|
|
template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
__complex_acos(const std::complex<_Tp>& __z)
|
|
{
|
|
const std::complex<_Tp> __t = std::asin(__z);
|
|
const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
|
|
return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_ARC
|
|
#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline __complex__ _Float16
|
|
__complex_acos(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_cacosf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_asin(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_casinf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_atan(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_catanf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_acosh(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_cacoshf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_asinh(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_casinhf(__z)); }
|
|
|
|
inline __complex__ _Float16
|
|
__complex_atanh(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_catanhf(__z)); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline __complex__ _Float32
|
|
__complex_acos(__complex__ _Float32 __z)
|
|
{ return __builtin_cacosf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_asin(__complex__ _Float32 __z)
|
|
{ return __builtin_casinf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_atan(__complex__ _Float32 __z)
|
|
{ return __builtin_catanf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_acosh(__complex__ _Float32 __z)
|
|
{ return __builtin_cacoshf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_asinh(__complex__ _Float32 __z)
|
|
{ return __builtin_casinhf(__z); }
|
|
|
|
inline __complex__ _Float32
|
|
__complex_atanh(__complex__ _Float32 __z)
|
|
{ return __builtin_catanhf(__z); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
|
|
inline __complex__ _Float64
|
|
__complex_acos(__complex__ _Float64 __z)
|
|
{ return __builtin_cacos(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_asin(__complex__ _Float64 __z)
|
|
{ return __builtin_casin(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_atan(__complex__ _Float64 __z)
|
|
{ return __builtin_catan(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_acosh(__complex__ _Float64 __z)
|
|
{ return __builtin_cacosh(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_asinh(__complex__ _Float64 __z)
|
|
{ return __builtin_casinh(__z); }
|
|
|
|
inline __complex__ _Float64
|
|
__complex_atanh(__complex__ _Float64 __z)
|
|
{ return __builtin_catanh(__z); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
|
|
inline __complex__ _Float128
|
|
__complex_acos(__complex__ _Float128 __z)
|
|
{ return __builtin_cacosl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_asin(__complex__ _Float128 __z)
|
|
{ return __builtin_casinl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_atan(__complex__ _Float128 __z)
|
|
{ return __builtin_catanl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_acosh(__complex__ _Float128 __z)
|
|
{ return __builtin_cacoshl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_asinh(__complex__ _Float128 __z)
|
|
{ return __builtin_casinhl(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_atanh(__complex__ _Float128 __z)
|
|
{ return __builtin_catanhl(__z); }
|
|
#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
|
|
inline __complex__ _Float128
|
|
__complex_acos(__complex__ _Float128 __z)
|
|
{ return __builtin_cacosf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_asin(__complex__ _Float128 __z)
|
|
{ return __builtin_casinf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_atan(__complex__ _Float128 __z)
|
|
{ return __builtin_catanf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_acosh(__complex__ _Float128 __z)
|
|
{ return __builtin_cacoshf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_asinh(__complex__ _Float128 __z)
|
|
{ return __builtin_casinhf128(__z); }
|
|
|
|
inline __complex__ _Float128
|
|
__complex_atanh(__complex__ _Float128 __z)
|
|
{ return __builtin_catanhf128(__z); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_acos(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cacosf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_asin(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_casinf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_atan(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_catanf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_acosh(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cacoshf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_asinh(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_casinhf(__z)); }
|
|
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_atanh(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_catanhf(__z)); }
|
|
#endif
|
|
#endif
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_ARC
|
|
inline __complex__ float
|
|
__complex_acos(__complex__ float __z)
|
|
{ return __builtin_cacosf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_acos(__complex__ double __z)
|
|
{ return __builtin_cacos(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_acos(const __complex__ long double& __z)
|
|
{ return __builtin_cacosl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
acos(const std::complex<_Tp>& __z)
|
|
{ return __complex_acos(__z.__rep()); }
|
|
#else
|
|
/// acos(__z) [8.1.2].
|
|
// Effects: Behaves the same as C99 function cacos, defined
|
|
// in subclause 7.3.5.1.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
acos(const std::complex<_Tp>& __z)
|
|
{ return __complex_acos(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
__complex_asin(const std::complex<_Tp>& __z)
|
|
{
|
|
std::complex<_Tp> __t(-__z.imag(), __z.real());
|
|
__t = std::asinh(__t);
|
|
return std::complex<_Tp>(__t.imag(), -__t.real());
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_ARC
|
|
inline __complex__ float
|
|
__complex_asin(__complex__ float __z)
|
|
{ return __builtin_casinf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_asin(__complex__ double __z)
|
|
{ return __builtin_casin(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_asin(const __complex__ long double& __z)
|
|
{ return __builtin_casinl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
asin(const std::complex<_Tp>& __z)
|
|
{ return __complex_asin(__z.__rep()); }
|
|
#else
|
|
/// asin(__z) [8.1.3].
|
|
// Effects: Behaves the same as C99 function casin, defined
|
|
// in subclause 7.3.5.2.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
asin(const std::complex<_Tp>& __z)
|
|
{ return __complex_asin(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_atan(const std::complex<_Tp>& __z)
|
|
{
|
|
const _Tp __r2 = __z.real() * __z.real();
|
|
const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
|
|
|
|
_Tp __num = __z.imag() + _Tp(1.0);
|
|
_Tp __den = __z.imag() - _Tp(1.0);
|
|
|
|
__num = __r2 + __num * __num;
|
|
__den = __r2 + __den * __den;
|
|
|
|
return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
|
|
_Tp(0.25) * log(__num / __den));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_ARC
|
|
inline __complex__ float
|
|
__complex_atan(__complex__ float __z)
|
|
{ return __builtin_catanf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_atan(__complex__ double __z)
|
|
{ return __builtin_catan(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_atan(const __complex__ long double& __z)
|
|
{ return __builtin_catanl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
atan(const std::complex<_Tp>& __z)
|
|
{ return __complex_atan(__z.__rep()); }
|
|
#else
|
|
/// atan(__z) [8.1.4].
|
|
// Effects: Behaves the same as C99 function catan, defined
|
|
// in subclause 7.3.5.3.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
atan(const std::complex<_Tp>& __z)
|
|
{ return __complex_atan(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_acosh(const std::complex<_Tp>& __z)
|
|
{
|
|
// Kahan's formula.
|
|
return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
|
|
+ std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_ARC
|
|
inline __complex__ float
|
|
__complex_acosh(__complex__ float __z)
|
|
{ return __builtin_cacoshf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_acosh(__complex__ double __z)
|
|
{ return __builtin_cacosh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_acosh(const __complex__ long double& __z)
|
|
{ return __builtin_cacoshl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
acosh(const std::complex<_Tp>& __z)
|
|
{ return __complex_acosh(__z.__rep()); }
|
|
#else
|
|
/// acosh(__z) [8.1.5].
|
|
// Effects: Behaves the same as C99 function cacosh, defined
|
|
// in subclause 7.3.6.1.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
acosh(const std::complex<_Tp>& __z)
|
|
{ return __complex_acosh(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_asinh(const std::complex<_Tp>& __z)
|
|
{
|
|
std::complex<_Tp> __t((__z.real() - __z.imag())
|
|
* (__z.real() + __z.imag()) + _Tp(1.0),
|
|
_Tp(2.0) * __z.real() * __z.imag());
|
|
__t = std::sqrt(__t);
|
|
|
|
return std::log(__t + __z);
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_ARC
|
|
inline __complex__ float
|
|
__complex_asinh(__complex__ float __z)
|
|
{ return __builtin_casinhf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_asinh(__complex__ double __z)
|
|
{ return __builtin_casinh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_asinh(const __complex__ long double& __z)
|
|
{ return __builtin_casinhl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
asinh(const std::complex<_Tp>& __z)
|
|
{ return __complex_asinh(__z.__rep()); }
|
|
#else
|
|
/// asinh(__z) [8.1.6].
|
|
// Effects: Behaves the same as C99 function casin, defined
|
|
// in subclause 7.3.6.2.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
asinh(const std::complex<_Tp>& __z)
|
|
{ return __complex_asinh(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_atanh(const std::complex<_Tp>& __z)
|
|
{
|
|
const _Tp __i2 = __z.imag() * __z.imag();
|
|
const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
|
|
|
|
_Tp __num = _Tp(1.0) + __z.real();
|
|
_Tp __den = _Tp(1.0) - __z.real();
|
|
|
|
__num = __i2 + __num * __num;
|
|
__den = __i2 + __den * __den;
|
|
|
|
return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
|
|
_Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_ARC
|
|
inline __complex__ float
|
|
__complex_atanh(__complex__ float __z)
|
|
{ return __builtin_catanhf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_atanh(__complex__ double __z)
|
|
{ return __builtin_catanh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_atanh(const __complex__ long double& __z)
|
|
{ return __builtin_catanhl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
atanh(const std::complex<_Tp>& __z)
|
|
{ return __complex_atanh(__z.__rep()); }
|
|
#else
|
|
/// atanh(__z) [8.1.7].
|
|
// Effects: Behaves the same as C99 function catanh, defined
|
|
// in subclause 7.3.6.3.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
atanh(const std::complex<_Tp>& __z)
|
|
{ return __complex_atanh(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
/// fabs(__z) [8.1.8].
|
|
// Effects: Behaves the same as C99 function cabs, defined
|
|
// in subclause 7.3.8.1.
|
|
fabs(const std::complex<_Tp>& __z)
|
|
{ return std::abs(__z); }
|
|
|
|
/// Additional overloads [8.1.9].
|
|
template<typename _Tp>
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
arg(_Tp __x)
|
|
{
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
|
#if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
|
|
return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
|
|
: __type();
|
|
#else
|
|
return std::arg(std::complex<__type>(__x));
|
|
#endif
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
imag(_Tp)
|
|
{ return _Tp(); }
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX20_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
norm(_Tp __x)
|
|
{
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
|
return __type(__x) * __type(__x);
|
|
}
|
|
|
|
template<typename _Tp>
|
|
_GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
real(_Tp __x)
|
|
{ return __x; }
|
|
|
|
template<typename _Tp, typename _Up>
|
|
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
|
|
pow(const std::complex<_Tp>& __x, const _Up& __y)
|
|
{
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
|
return std::pow(std::complex<__type>(__x), __type(__y));
|
|
}
|
|
|
|
template<typename _Tp, typename _Up>
|
|
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
|
|
pow(const _Tp& __x, const std::complex<_Up>& __y)
|
|
{
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
|
return std::pow(__type(__x), std::complex<__type>(__y));
|
|
}
|
|
|
|
template<typename _Tp, typename _Up>
|
|
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
|
|
pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
|
|
{
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
|
return std::pow(std::complex<__type>(__x),
|
|
std::complex<__type>(__y));
|
|
}
|
|
|
|
// Forward declarations.
|
|
// DR 781.
|
|
template<typename _Tp>
|
|
std::complex<_Tp> proj(const std::complex<_Tp>&);
|
|
|
|
// Generic implementation of std::proj, does not work for infinities.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
__complex_proj(const std::complex<_Tp>& __z)
|
|
{ return __z; }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline complex<float>
|
|
__complex_proj(const complex<float>& __z)
|
|
{ return __builtin_cprojf(__z.__rep()); }
|
|
|
|
inline complex<double>
|
|
__complex_proj(const complex<double>& __z)
|
|
{ return __builtin_cproj(__z.__rep()); }
|
|
|
|
inline complex<long double>
|
|
__complex_proj(const complex<long double>& __z)
|
|
{ return __builtin_cprojl(__z.__rep()); }
|
|
|
|
#if __cplusplus > 202002L
|
|
#if defined(__STDCPP_FLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline __complex__ _Float16
|
|
__complex_proj(__complex__ _Float16 __z)
|
|
{ return static_cast<__complex__ _Float16>(__builtin_cprojf(__z)); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT32_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline __complex__ _Float32
|
|
__complex_proj(__complex__ _Float32 __z)
|
|
{ return __builtin_cprojf(__z); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT64_T__) && defined(_GLIBCXX_DOUBLE_IS_IEEE_BINARY64)
|
|
inline __complex__ _Float64
|
|
__complex_proj(__complex__ _Float64 __z)
|
|
{ return __builtin_cproj(__z); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_LDOUBLE_IS_IEEE_BINARY128)
|
|
inline __complex__ _Float128
|
|
__complex_proj(__complex__ _Float128 __z)
|
|
{ return __builtin_cprojl(__z); }
|
|
#elif defined(__STDCPP_FLOAT128_T__) && defined(_GLIBCXX_HAVE_FLOAT128_MATH)
|
|
inline __complex__ _Float128
|
|
__complex_proj(__complex__ _Float128 __z)
|
|
{ return __builtin_cprojf128(__z); }
|
|
#endif
|
|
|
|
#if defined(__STDCPP_BFLOAT16_T__) && defined(_GLIBCXX_FLOAT_IS_IEEE_BINARY32)
|
|
inline __complex__ decltype(0.0bf16)
|
|
__complex_proj(__complex__ decltype(0.0bf16) __z)
|
|
{ return static_cast<__complex__ decltype(0.0bf16)>(__builtin_cprojf(__z)); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
requires requires { typename __complex_type<_Tp>::type; }
|
|
inline complex<_Tp>
|
|
__complex_proj(const complex<_Tp>& __z)
|
|
{ return __complex_proj(__z.__rep()); }
|
|
#endif
|
|
|
|
#elif defined _GLIBCXX_USE_C99_MATH_FUNCS
|
|
inline complex<float>
|
|
__complex_proj(const complex<float>& __z)
|
|
{
|
|
if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
|
|
return complex<float>(__builtin_inff(),
|
|
__builtin_copysignf(0.0f, __z.imag()));
|
|
return __z;
|
|
}
|
|
|
|
inline complex<double>
|
|
__complex_proj(const complex<double>& __z)
|
|
{
|
|
if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
|
|
return complex<double>(__builtin_inf(),
|
|
__builtin_copysign(0.0, __z.imag()));
|
|
return __z;
|
|
}
|
|
|
|
inline complex<long double>
|
|
__complex_proj(const complex<long double>& __z)
|
|
{
|
|
if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
|
|
return complex<long double>(__builtin_infl(),
|
|
__builtin_copysignl(0.0l, __z.imag()));
|
|
return __z;
|
|
}
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
proj(const std::complex<_Tp>& __z)
|
|
{ return __complex_proj(__z); }
|
|
|
|
// Overload for scalars
|
|
template<typename _Tp>
|
|
inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
|
|
proj(_Tp __x)
|
|
{
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
|
return std::proj(std::complex<__type>(__x));
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _GLIBCXX20_CONSTEXPR
|
|
std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
|
|
conj(_Tp __x)
|
|
{
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
|
return std::complex<__type>(__x, -__type());
|
|
}
|
|
|
|
#ifdef __cpp_lib_complex_udls // C++ >= 14
|
|
|
|
inline namespace literals {
|
|
inline namespace complex_literals {
|
|
#pragma GCC diagnostic push
|
|
#pragma GCC diagnostic ignored "-Wliteral-suffix"
|
|
|
|
constexpr std::complex<float>
|
|
operator""if(long double __num)
|
|
{ return std::complex<float>{0.0F, static_cast<float>(__num)}; }
|
|
|
|
constexpr std::complex<float>
|
|
operator""if(unsigned long long __num)
|
|
{ return std::complex<float>{0.0F, static_cast<float>(__num)}; }
|
|
|
|
constexpr std::complex<double>
|
|
operator""i(long double __num)
|
|
{ return std::complex<double>{0.0, static_cast<double>(__num)}; }
|
|
|
|
constexpr std::complex<double>
|
|
operator""i(unsigned long long __num)
|
|
{ return std::complex<double>{0.0, static_cast<double>(__num)}; }
|
|
|
|
constexpr std::complex<long double>
|
|
operator""il(long double __num)
|
|
{ return std::complex<long double>{0.0L, __num}; }
|
|
|
|
constexpr std::complex<long double>
|
|
operator""il(unsigned long long __num)
|
|
{ return std::complex<long double>{0.0L, static_cast<long double>(__num)}; }
|
|
|
|
#pragma GCC diagnostic pop
|
|
} // inline namespace complex_literals
|
|
} // inline namespace literals
|
|
|
|
#endif // __cpp_lib_complex_udls
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace
|
|
|
|
#endif // C++11
|
|
|
|
#ifdef __clang__
|
|
#pragma clang diagnostic pop
|
|
#endif
|
|
|
|
#endif /* _GLIBCXX_COMPLEX */
|