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freebsd/contrib/libc++/include/complex
T
Dimitry Andric e8948c9522 Merge clang, llvm, lld, lldb, compiler-rt and libc++ 5.0.0 release. 
MFC r309126 (by emaste):

  Correct lld llvm-tblgen dependency file name

MFC r309169:

  Get rid of separate Subversion mergeinfo properties for llvm-dwarfdump
  and llvm-lto.  The mergeinfo confuses Subversion enormously, and these
  directories will just use the mergeinfo for llvm itself.

MFC r312765:

  Pull in r276136 from upstream llvm trunk (by Wei Mi):

    Use ValueOffsetPair to enhance value reuse during SCEV expansion.

    In D12090, the ExprValueMap was added to reuse existing value during
    SCEV expansion. However, const folding and sext/zext distribution can
    make the reuse still difficult.

    A simplified case is: suppose we know S1 expands to V1 in
    ExprValueMap, and
      S1 = S2 + C_a
      S3 = S2 + C_b
    where C_a and C_b are different SCEVConstants. Then we'd like to
    expand S3 as V1 - C_a + C_b instead of expanding S2 literally. It is
    helpful when S2 is a complex SCEV expr and S2 has no entry in
    ExprValueMap, which is usually caused by the fact that S3 is
    generated from S1 after const folding.

    In order to do that, we represent ExprValueMap as a mapping from SCEV
    to ValueOffsetPair. We will save both S1->{V1, 0} and S2->{V1, C_a}
    into the ExprValueMap when we create SCEV for V1. When S3 is
    expanded, it will first expand S2 to V1 - C_a because of S2->{V1,
    C_a} in the map, then expand S3 to V1 - C_a + C_b.

    Differential Revision: https://reviews.llvm.org/D21313

  This should fix assertion failures when building OpenCV >= 3.1.

  PR:		215649

MFC r312831:

  Revert r312765 for now, since it causes assertions when building
  lang/spidermonkey24.

  Reported by:	antoine
  PR:		215649

MFC r316511 (by jhb):

  Add an implementation of __ffssi2() derived from __ffsdi2().

  Newer versions of GCC include an __ffssi2() symbol in libgcc and the
  compiler can emit calls to it in generated code.  This is true for at
  least GCC 6.2 when compiling world for mips and mips64.

  Reviewed by:	jmallett, dim
  Sponsored by:	DARPA / AFRL
  Differential Revision:	https://reviews.freebsd.org/D10086

MFC r318601 (by adrian):

  [libcompiler-rt] add bswapdi2/bswapsi2

  This is required for mips gcc 6.3 userland to build/run.

  Reviewed by:	emaste, dim
  Approved by:	emaste
  Differential Revision:	https://reviews.freebsd.org/D10838

MFC r318884 (by emaste):

  lldb: map TRAP_CAP to a trace trap

  In the absense of a more specific handler for TRAP_CAP (generated by
  ENOTCAPABLE or ECAPMODE while in capability mode) treat it as a trace
  trap.

  Example usage (testing the bug in PR219173):

  % proccontrol -m trapcap lldb usr.bin/hexdump/obj/hexdump -- -Cv -s 1 /bin/ls
  ...
  (lldb) run
  Process 12980 launching
  Process 12980 launched: '.../usr.bin/hexdump/obj/hexdump' (x86_64)
  Process 12980 stopped
  * thread #1, stop reason = trace
      frame #0: 0x0000004b80c65f1a libc.so.7`__sys_lseek + 10
  ...

  In the future we should have LLDB control the trapcap procctl itself
  (as it does with ASLR), as well as report a specific stop reason.
  This change eliminates an assertion failure from LLDB for now.

MFC r319796:

  Remove a few unneeded files from libllvm, libclang and liblldb.

MFC r319885 (by emaste):

  lld: ELF: Fix ICF crash on absolute symbol relocations.

  If two sections contained relocations to absolute symbols with the same
  value we would crash when trying to access their sections. Add a check that
  both symbols point to sections before accessing their sections, and treat
  absolute symbols as equal if their values are equal.

  Obtained from:	LLD commit r292578

MFC r319918:

  Revert r319796 for now, it can cause undefined references when linking
  in some circumstances.

  Reported by:	Shawn Webb <[email protected]>

MFC r319957 (by emaste):

  lld: Add armelf emulation mode

  Obtained from:	LLD r305375

MFC r321369:

  Upgrade our copies of clang, llvm, lld, lldb, compiler-rt and libc++ to
  5.0.0 (trunk r308421).  Upstream has branched for the 5.0.0 release,
  which should be in about a month.  Please report bugs and regressions,
  so we can get them into the release.

  Please note that from 3.5.0 onwards, clang, llvm and lldb require C++11
  support to build; see UPDATING for more information.

MFC r321420:

  Add a few more object files to liblldb, which should solve errors when
  linking the lldb executable in some cases.  In particular, when the
  -ffunction-sections -fdata-sections options are turned off, or
  ineffective.

  Reported by:	Shawn Webb, Mark Millard

MFC r321433:

  Cleanup stale Options.inc files from the previous libllvm build for
  clang 4.0.0.  Otherwise, these can get included before the two newly
  generated ones (which are different) for clang 5.0.0.

  Reported by:	Mark Millard

MFC r321439 (by bdrewery):

  Move llvm Options.inc hack from r321433 for NO_CLEAN to lib/clang/libllvm.

  The files are only ever generated to .OBJDIR, not to WORLDTMP (as a
  sysroot) and are only ever included from a compilation.  So using
  a beforebuild target here removes the file before the compilation
  tries to include it.

MFC r321664:

  Pull in r308891 from upstream llvm trunk (by Benjamin Kramer):

    [CodeGenPrepare] Cut off FindAllMemoryUses if there are too many uses.

    This avoids excessive compile time. The case I'm looking at is
    Function.cpp from an old version of LLVM that still had the giant
    memcmp string matcher in it. Before r308322 this compiled in about 2
    minutes, after it, clang takes infinite* time to compile it. With
    this patch we're at 5 min, which is still bad but this is a
    pathological case.

    The cut off at 20 uses was chosen by looking at other cut-offs in LLVM
    for user scanning. It's probably too high, but does the job and is
    very unlikely to regress anything.

    Fixes PR33900.

    * I'm impatient and aborted after 15 minutes, on the bug report it was
      killed after 2h.

  Pull in r308986 from upstream llvm trunk (by Simon Pilgrim):

    [X86][CGP] Reduce memcmp() expansion to 2 load pairs (PR33914)

    D35067/rL308322 attempted to support up to 4 load pairs for memcmp
    inlining which resulted in regressions for some optimized libc memcmp
    implementations (PR33914).

    Until we can match these more optimal cases, this patch reduces the
    memcmp expansion to a maximum of 2 load pairs (which matches what we
    do for -Os).

    This patch should be considered for the 5.0.0 release branch as well

    Differential Revision: https://reviews.llvm.org/D35830

  These fix a hang (or extremely long compile time) when building older
  LLVM ports.

  Reported by:    antoine
  PR:             219139

MFC r321719:

  Pull in r309503 from upstream clang trunk (by Richard Smith):

    PR33902: Invalidate line number cache when adding more text to
    existing buffer.

    This led to crashes as the line number cache would report a bogus
    line number for a line of code, and we'd try to find a nonexistent
    column within the line when printing diagnostics.

  This fixes an assertion when building the graphics/champlain port.

  Reported by:	antoine, kwm
  PR:		219139

MFC r321723:

  Upgrade our copies of clang, llvm, lld and lldb to r309439 from the
  upstream release_50 branch.  This is just after upstream's 5.0.0-rc1.

MFC r322320:

  Upgrade our copies of clang, llvm and libc++ to r310316 from the
  upstream release_50 branch.

MFC r322326 (by emaste):

  lldb: Make i386-*-freebsd expression work on JIT path

  * Enable i386 ABI creation for freebsd
  * Added an extra argument in ABISysV_i386::PrepareTrivialCall for mmap
    syscall
  * Unlike linux, the last argument of mmap is actually 64-bit(off_t).
    This requires us to push an additional word for the higher order bits.
  * Prior to this change, ktrace dump will show mmap failures due to
    invalid argument coming from the 6th mmap argument.

  Submitted by:	Karnajit Wangkhem
  Differential Revision:	https://reviews.llvm.org/D34776

MFC r322360 (by emaste):

  lldb: Report inferior signals as signals, not exceptions, on FreeBSD

  This is the FreeBSD equivalent of LLVM r238549.

  This serves 2 purposes:

  * LLDB should handle inferior process signals SIGSEGV/SIGILL/SIGBUS/
    SIGFPE the way it is suppose to be handled. Prior to this fix these
    signals will neither create a coredump, nor exit from the debugger
    or work for signal handling scenario.
  * eInvalidCrashReason need not report "unknown crash reason" if we have
    a valid si_signo

  llvm.org/pr23699

  Patch by Karnajit Wangkhem

  Differential Revision:  https://reviews.llvm.org/D35223

  Submitted by:	Karnajit Wangkhem
  Obtained from:	LLVM r310591

MFC r322474 (by emaste):

  lld: Add `-z muldefs` option.

  Obtained from:	LLVM r310757

MFC r322740:

  Upgrade our copies of clang, llvm, lld and libc++ to r311219 from the
  upstream release_50 branch.

MFC r322855:

  Upgrade our copies of clang, llvm, lldb and compiler-rt to r311606 from
  the upstream release_50 branch.

  As of this version, lib/msun's trig test should also work correctly
  again (see bug 220989 for more information).

  PR:		220989

MFC r323112:

  Upgrade our copies of clang, llvm, lldb and compiler-rt to r312293 from
  the upstream release_50 branch.  This corresponds to 5.0.0 rc4.

  As of this version, the cad/stepcode port should now compile in a more
  reasonable time on i386 (see bug 221836 for more information).

  PR:		221836

MFC r323245:

  Upgrade our copies of clang, llvm, lld, lldb, compiler-rt and libc++ to
  5.0.0 release (upstream r312559).

  Release notes for llvm, clang and lld will be available here soon:
  <http://releases.llvm.org/5.0.0/docs/ReleaseNotes.html>
  <http://releases.llvm.org/5.0.0/tools/clang/docs/ReleaseNotes.html>
  <http://releases.llvm.org/5.0.0/tools/lld/docs/ReleaseNotes.html>

  Relnotes:	yes
2017-09-26 19:56:36 +00:00

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// -*- C++ -*-
//===--------------------------- complex ----------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
#ifndef _LIBCPP_COMPLEX
#define _LIBCPP_COMPLEX
/*
complex synopsis
namespace std
{
template<class T>
class complex
{
public:
typedef T value_type;
complex(const T& re = T(), const T& im = T()); // constexpr in C++14
complex(const complex&); // constexpr in C++14
template<class X> complex(const complex<X>&); // constexpr in C++14
T real() const; // constexpr in C++14
T imag() const; // constexpr in C++14
void real(T);
void imag(T);
complex<T>& operator= (const T&);
complex<T>& operator+=(const T&);
complex<T>& operator-=(const T&);
complex<T>& operator*=(const T&);
complex<T>& operator/=(const T&);
complex& operator=(const complex&);
template<class X> complex<T>& operator= (const complex<X>&);
template<class X> complex<T>& operator+=(const complex<X>&);
template<class X> complex<T>& operator-=(const complex<X>&);
template<class X> complex<T>& operator*=(const complex<X>&);
template<class X> complex<T>& operator/=(const complex<X>&);
};
template<>
class complex<float>
{
public:
typedef float value_type;
constexpr complex(float re = 0.0f, float im = 0.0f);
explicit constexpr complex(const complex<double>&);
explicit constexpr complex(const complex<long double>&);
constexpr float real() const;
void real(float);
constexpr float imag() const;
void imag(float);
complex<float>& operator= (float);
complex<float>& operator+=(float);
complex<float>& operator-=(float);
complex<float>& operator*=(float);
complex<float>& operator/=(float);
complex<float>& operator=(const complex<float>&);
template<class X> complex<float>& operator= (const complex<X>&);
template<class X> complex<float>& operator+=(const complex<X>&);
template<class X> complex<float>& operator-=(const complex<X>&);
template<class X> complex<float>& operator*=(const complex<X>&);
template<class X> complex<float>& operator/=(const complex<X>&);
};
template<>
class complex<double>
{
public:
typedef double value_type;
constexpr complex(double re = 0.0, double im = 0.0);
constexpr complex(const complex<float>&);
explicit constexpr complex(const complex<long double>&);
constexpr double real() const;
void real(double);
constexpr double imag() const;
void imag(double);
complex<double>& operator= (double);
complex<double>& operator+=(double);
complex<double>& operator-=(double);
complex<double>& operator*=(double);
complex<double>& operator/=(double);
complex<double>& operator=(const complex<double>&);
template<class X> complex<double>& operator= (const complex<X>&);
template<class X> complex<double>& operator+=(const complex<X>&);
template<class X> complex<double>& operator-=(const complex<X>&);
template<class X> complex<double>& operator*=(const complex<X>&);
template<class X> complex<double>& operator/=(const complex<X>&);
};
template<>
class complex<long double>
{
public:
typedef long double value_type;
constexpr complex(long double re = 0.0L, long double im = 0.0L);
constexpr complex(const complex<float>&);
constexpr complex(const complex<double>&);
constexpr long double real() const;
void real(long double);
constexpr long double imag() const;
void imag(long double);
complex<long double>& operator=(const complex<long double>&);
complex<long double>& operator= (long double);
complex<long double>& operator+=(long double);
complex<long double>& operator-=(long double);
complex<long double>& operator*=(long double);
complex<long double>& operator/=(long double);
template<class X> complex<long double>& operator= (const complex<X>&);
template<class X> complex<long double>& operator+=(const complex<X>&);
template<class X> complex<long double>& operator-=(const complex<X>&);
template<class X> complex<long double>& operator*=(const complex<X>&);
template<class X> complex<long double>& operator/=(const complex<X>&);
};
// 26.3.6 operators:
template<class T> complex<T> operator+(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator+(const complex<T>&, const T&);
template<class T> complex<T> operator+(const T&, const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&, const T&);
template<class T> complex<T> operator-(const T&, const complex<T>&);
template<class T> complex<T> operator*(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator*(const complex<T>&, const T&);
template<class T> complex<T> operator*(const T&, const complex<T>&);
template<class T> complex<T> operator/(const complex<T>&, const complex<T>&);
template<class T> complex<T> operator/(const complex<T>&, const T&);
template<class T> complex<T> operator/(const T&, const complex<T>&);
template<class T> complex<T> operator+(const complex<T>&);
template<class T> complex<T> operator-(const complex<T>&);
template<class T> bool operator==(const complex<T>&, const complex<T>&); // constexpr in C++14
template<class T> bool operator==(const complex<T>&, const T&); // constexpr in C++14
template<class T> bool operator==(const T&, const complex<T>&); // constexpr in C++14
template<class T> bool operator!=(const complex<T>&, const complex<T>&); // constexpr in C++14
template<class T> bool operator!=(const complex<T>&, const T&); // constexpr in C++14
template<class T> bool operator!=(const T&, const complex<T>&); // constexpr in C++14
template<class T, class charT, class traits>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>&, complex<T>&);
template<class T, class charT, class traits>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>&, const complex<T>&);
// 26.3.7 values:
template<class T> T real(const complex<T>&); // constexpr in C++14
long double real(long double); // constexpr in C++14
double real(double); // constexpr in C++14
template<Integral T> double real(T); // constexpr in C++14
float real(float); // constexpr in C++14
template<class T> T imag(const complex<T>&); // constexpr in C++14
long double imag(long double); // constexpr in C++14
double imag(double); // constexpr in C++14
template<Integral T> double imag(T); // constexpr in C++14
float imag(float); // constexpr in C++14
template<class T> T abs(const complex<T>&);
template<class T> T arg(const complex<T>&);
long double arg(long double);
double arg(double);
template<Integral T> double arg(T);
float arg(float);
template<class T> T norm(const complex<T>&);
long double norm(long double);
double norm(double);
template<Integral T> double norm(T);
float norm(float);
template<class T> complex<T> conj(const complex<T>&);
complex<long double> conj(long double);
complex<double> conj(double);
template<Integral T> complex<double> conj(T);
complex<float> conj(float);
template<class T> complex<T> proj(const complex<T>&);
complex<long double> proj(long double);
complex<double> proj(double);
template<Integral T> complex<double> proj(T);
complex<float> proj(float);
template<class T> complex<T> polar(const T&, const T& = 0);
// 26.3.8 transcendentals:
template<class T> complex<T> acos(const complex<T>&);
template<class T> complex<T> asin(const complex<T>&);
template<class T> complex<T> atan(const complex<T>&);
template<class T> complex<T> acosh(const complex<T>&);
template<class T> complex<T> asinh(const complex<T>&);
template<class T> complex<T> atanh(const complex<T>&);
template<class T> complex<T> cos (const complex<T>&);
template<class T> complex<T> cosh (const complex<T>&);
template<class T> complex<T> exp (const complex<T>&);
template<class T> complex<T> log (const complex<T>&);
template<class T> complex<T> log10(const complex<T>&);
template<class T> complex<T> pow(const complex<T>&, const T&);
template<class T> complex<T> pow(const complex<T>&, const complex<T>&);
template<class T> complex<T> pow(const T&, const complex<T>&);
template<class T> complex<T> sin (const complex<T>&);
template<class T> complex<T> sinh (const complex<T>&);
template<class T> complex<T> sqrt (const complex<T>&);
template<class T> complex<T> tan (const complex<T>&);
template<class T> complex<T> tanh (const complex<T>&);
template<class T, class charT, class traits>
basic_istream<charT, traits>&
operator>>(basic_istream<charT, traits>& is, complex<T>& x);
template<class T, class charT, class traits>
basic_ostream<charT, traits>&
operator<<(basic_ostream<charT, traits>& o, const complex<T>& x);
} // std
*/
#include <__config>
#include <type_traits>
#include <stdexcept>
#include <cmath>
#include <sstream>
#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#pragma GCC system_header
#endif
_LIBCPP_BEGIN_NAMESPACE_STD
template<class _Tp> class _LIBCPP_TEMPLATE_VIS complex;
template<class _Tp> complex<_Tp> operator*(const complex<_Tp>& __z, const complex<_Tp>& __w);
template<class _Tp> complex<_Tp> operator/(const complex<_Tp>& __x, const complex<_Tp>& __y);
template<class _Tp>
class _LIBCPP_TEMPLATE_VIS complex
{
public:
typedef _Tp value_type;
private:
value_type __re_;
value_type __im_;
public:
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
complex(const value_type& __re = value_type(), const value_type& __im = value_type())
: __re_(__re), __im_(__im) {}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
complex(const complex<_Xp>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11 value_type imag() const {return __im_;}
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
_LIBCPP_INLINE_VISIBILITY complex& operator= (const value_type& __re)
{__re_ = __re; __im_ = value_type(); return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator+=(const value_type& __re) {__re_ += __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator-=(const value_type& __re) {__re_ -= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator*=(const value_type& __re) {__re_ *= __re; __im_ *= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator/=(const value_type& __re) {__re_ /= __re; __im_ /= __re; return *this;}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
{
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
{
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
{
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
{
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
};
template<> class _LIBCPP_TEMPLATE_VIS complex<double>;
template<> class _LIBCPP_TEMPLATE_VIS complex<long double>;
template<>
class _LIBCPP_TEMPLATE_VIS complex<float>
{
float __re_;
float __im_;
public:
typedef float value_type;
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(float __re = 0.0f, float __im = 0.0f)
: __re_(__re), __im_(__im) {}
_LIBCPP_INLINE_VISIBILITY
explicit _LIBCPP_CONSTEXPR complex(const complex<double>& __c);
_LIBCPP_INLINE_VISIBILITY
explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR float imag() const {return __im_;}
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
_LIBCPP_INLINE_VISIBILITY complex& operator= (float __re)
{__re_ = __re; __im_ = value_type(); return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator+=(float __re) {__re_ += __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator-=(float __re) {__re_ -= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator*=(float __re) {__re_ *= __re; __im_ *= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator/=(float __re) {__re_ /= __re; __im_ /= __re; return *this;}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
{
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
{
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
{
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
{
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
};
template<>
class _LIBCPP_TEMPLATE_VIS complex<double>
{
double __re_;
double __im_;
public:
typedef double value_type;
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(double __re = 0.0, double __im = 0.0)
: __re_(__re), __im_(__im) {}
_LIBCPP_INLINE_VISIBILITY
_LIBCPP_CONSTEXPR complex(const complex<float>& __c);
_LIBCPP_INLINE_VISIBILITY
explicit _LIBCPP_CONSTEXPR complex(const complex<long double>& __c);
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR double imag() const {return __im_;}
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
_LIBCPP_INLINE_VISIBILITY complex& operator= (double __re)
{__re_ = __re; __im_ = value_type(); return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator+=(double __re) {__re_ += __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator-=(double __re) {__re_ -= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator*=(double __re) {__re_ *= __re; __im_ *= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator/=(double __re) {__re_ /= __re; __im_ /= __re; return *this;}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
{
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
{
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
{
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
{
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
};
template<>
class _LIBCPP_TEMPLATE_VIS complex<long double>
{
long double __re_;
long double __im_;
public:
typedef long double value_type;
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR complex(long double __re = 0.0L, long double __im = 0.0L)
: __re_(__re), __im_(__im) {}
_LIBCPP_INLINE_VISIBILITY
_LIBCPP_CONSTEXPR complex(const complex<float>& __c);
_LIBCPP_INLINE_VISIBILITY
_LIBCPP_CONSTEXPR complex(const complex<double>& __c);
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double real() const {return __re_;}
_LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR long double imag() const {return __im_;}
_LIBCPP_INLINE_VISIBILITY void real(value_type __re) {__re_ = __re;}
_LIBCPP_INLINE_VISIBILITY void imag(value_type __im) {__im_ = __im;}
_LIBCPP_INLINE_VISIBILITY complex& operator= (long double __re)
{__re_ = __re; __im_ = value_type(); return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator+=(long double __re) {__re_ += __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator-=(long double __re) {__re_ -= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator*=(long double __re) {__re_ *= __re; __im_ *= __re; return *this;}
_LIBCPP_INLINE_VISIBILITY complex& operator/=(long double __re) {__re_ /= __re; __im_ /= __re; return *this;}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator= (const complex<_Xp>& __c)
{
__re_ = __c.real();
__im_ = __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator+=(const complex<_Xp>& __c)
{
__re_ += __c.real();
__im_ += __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator-=(const complex<_Xp>& __c)
{
__re_ -= __c.real();
__im_ -= __c.imag();
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator*=(const complex<_Xp>& __c)
{
*this = *this * complex(__c.real(), __c.imag());
return *this;
}
template<class _Xp> _LIBCPP_INLINE_VISIBILITY complex& operator/=(const complex<_Xp>& __c)
{
*this = *this / complex(__c.real(), __c.imag());
return *this;
}
};
inline
_LIBCPP_CONSTEXPR
complex<float>::complex(const complex<double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
inline
_LIBCPP_CONSTEXPR
complex<float>::complex(const complex<long double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
inline
_LIBCPP_CONSTEXPR
complex<double>::complex(const complex<float>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
inline
_LIBCPP_CONSTEXPR
complex<double>::complex(const complex<long double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
inline
_LIBCPP_CONSTEXPR
complex<long double>::complex(const complex<float>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
inline
_LIBCPP_CONSTEXPR
complex<long double>::complex(const complex<double>& __c)
: __re_(__c.real()), __im_(__c.imag()) {}
// 26.3.6 operators:
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__x);
__t += __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator+(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __t(__x);
__t += __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator+(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__y);
__t += __x;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__x);
__t -= __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator-(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __t(__x);
__t -= __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator-(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(-__y);
__t += __x;
return __t;
}
template<class _Tp>
complex<_Tp>
operator*(const complex<_Tp>& __z, const complex<_Tp>& __w)
{
_Tp __a = __z.real();
_Tp __b = __z.imag();
_Tp __c = __w.real();
_Tp __d = __w.imag();
_Tp __ac = __a * __c;
_Tp __bd = __b * __d;
_Tp __ad = __a * __d;
_Tp __bc = __b * __c;
_Tp __x = __ac - __bd;
_Tp __y = __ad + __bc;
if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
{
bool __recalc = false;
if (__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b))
{
__a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
__b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
if (__libcpp_isnan_or_builtin(__c))
__c = copysign(_Tp(0), __c);
if (__libcpp_isnan_or_builtin(__d))
__d = copysign(_Tp(0), __d);
__recalc = true;
}
if (__libcpp_isinf_or_builtin(__c) || __libcpp_isinf_or_builtin(__d))
{
__c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
__d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
if (__libcpp_isnan_or_builtin(__a))
__a = copysign(_Tp(0), __a);
if (__libcpp_isnan_or_builtin(__b))
__b = copysign(_Tp(0), __b);
__recalc = true;
}
if (!__recalc && (__libcpp_isinf_or_builtin(__ac) || __libcpp_isinf_or_builtin(__bd) ||
__libcpp_isinf_or_builtin(__ad) || __libcpp_isinf_or_builtin(__bc)))
{
if (__libcpp_isnan_or_builtin(__a))
__a = copysign(_Tp(0), __a);
if (__libcpp_isnan_or_builtin(__b))
__b = copysign(_Tp(0), __b);
if (__libcpp_isnan_or_builtin(__c))
__c = copysign(_Tp(0), __c);
if (__libcpp_isnan_or_builtin(__d))
__d = copysign(_Tp(0), __d);
__recalc = true;
}
if (__recalc)
{
__x = _Tp(INFINITY) * (__a * __c - __b * __d);
__y = _Tp(INFINITY) * (__a * __d + __b * __c);
}
}
return complex<_Tp>(__x, __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator*(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __t(__x);
__t *= __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator*(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__y);
__t *= __x;
return __t;
}
template<class _Tp>
complex<_Tp>
operator/(const complex<_Tp>& __z, const complex<_Tp>& __w)
{
int __ilogbw = 0;
_Tp __a = __z.real();
_Tp __b = __z.imag();
_Tp __c = __w.real();
_Tp __d = __w.imag();
_Tp __logbw = logb(fmax(fabs(__c), fabs(__d)));
if (__libcpp_isfinite_or_builtin(__logbw))
{
__ilogbw = static_cast<int>(__logbw);
__c = scalbn(__c, -__ilogbw);
__d = scalbn(__d, -__ilogbw);
}
_Tp __denom = __c * __c + __d * __d;
_Tp __x = scalbn((__a * __c + __b * __d) / __denom, -__ilogbw);
_Tp __y = scalbn((__b * __c - __a * __d) / __denom, -__ilogbw);
if (__libcpp_isnan_or_builtin(__x) && __libcpp_isnan_or_builtin(__y))
{
if ((__denom == _Tp(0)) && (!__libcpp_isnan_or_builtin(__a) || !__libcpp_isnan_or_builtin(__b)))
{
__x = copysign(_Tp(INFINITY), __c) * __a;
__y = copysign(_Tp(INFINITY), __c) * __b;
}
else if ((__libcpp_isinf_or_builtin(__a) || __libcpp_isinf_or_builtin(__b)) && __libcpp_isfinite_or_builtin(__c) && __libcpp_isfinite_or_builtin(__d))
{
__a = copysign(__libcpp_isinf_or_builtin(__a) ? _Tp(1) : _Tp(0), __a);
__b = copysign(__libcpp_isinf_or_builtin(__b) ? _Tp(1) : _Tp(0), __b);
__x = _Tp(INFINITY) * (__a * __c + __b * __d);
__y = _Tp(INFINITY) * (__b * __c - __a * __d);
}
else if (__libcpp_isinf_or_builtin(__logbw) && __logbw > _Tp(0) && __libcpp_isfinite_or_builtin(__a) && __libcpp_isfinite_or_builtin(__b))
{
__c = copysign(__libcpp_isinf_or_builtin(__c) ? _Tp(1) : _Tp(0), __c);
__d = copysign(__libcpp_isinf_or_builtin(__d) ? _Tp(1) : _Tp(0), __d);
__x = _Tp(0) * (__a * __c + __b * __d);
__y = _Tp(0) * (__b * __c - __a * __d);
}
}
return complex<_Tp>(__x, __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator/(const complex<_Tp>& __x, const _Tp& __y)
{
return complex<_Tp>(__x.real() / __y, __x.imag() / __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator/(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __t(__x);
__t /= __y;
return __t;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator+(const complex<_Tp>& __x)
{
return __x;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
operator-(const complex<_Tp>& __x)
{
return complex<_Tp>(-__x.real(), -__x.imag());
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
return __x.real() == __y.real() && __x.imag() == __y.imag();
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator==(const complex<_Tp>& __x, const _Tp& __y)
{
return __x.real() == __y && __x.imag() == 0;
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator==(const _Tp& __x, const complex<_Tp>& __y)
{
return __x == __y.real() && 0 == __y.imag();
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
return !(__x == __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator!=(const complex<_Tp>& __x, const _Tp& __y)
{
return !(__x == __y);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
bool
operator!=(const _Tp& __x, const complex<_Tp>& __y)
{
return !(__x == __y);
}
// 26.3.7 values:
template <class _Tp, bool = is_integral<_Tp>::value,
bool = is_floating_point<_Tp>::value
>
struct __libcpp_complex_overload_traits {};
// Integral Types
template <class _Tp>
struct __libcpp_complex_overload_traits<_Tp, true, false>
{
typedef double _ValueType;
typedef complex<double> _ComplexType;
};
// Floating point types
template <class _Tp>
struct __libcpp_complex_overload_traits<_Tp, false, true>
{
typedef _Tp _ValueType;
typedef complex<_Tp> _ComplexType;
};
// real
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
_Tp
real(const complex<_Tp>& __c)
{
return __c.real();
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
typename __libcpp_complex_overload_traits<_Tp>::_ValueType
real(_Tp __re)
{
return __re;
}
// imag
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
_Tp
imag(const complex<_Tp>& __c)
{
return __c.imag();
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX11
typename __libcpp_complex_overload_traits<_Tp>::_ValueType
imag(_Tp)
{
return 0;
}
// abs
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
abs(const complex<_Tp>& __c)
{
return hypot(__c.real(), __c.imag());
}
// arg
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
arg(const complex<_Tp>& __c)
{
return atan2(__c.imag(), __c.real());
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if<
is_same<_Tp, long double>::value,
long double
>::type
arg(_Tp __re)
{
return atan2l(0.L, __re);
}
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value || is_same<_Tp, double>::value,
double
>::type
arg(_Tp __re)
{
return atan2(0., __re);
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if<
is_same<_Tp, float>::value,
float
>::type
arg(_Tp __re)
{
return atan2f(0.F, __re);
}
// norm
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
_Tp
norm(const complex<_Tp>& __c)
{
if (__libcpp_isinf_or_builtin(__c.real()))
return abs(__c.real());
if (__libcpp_isinf_or_builtin(__c.imag()))
return abs(__c.imag());
return __c.real() * __c.real() + __c.imag() * __c.imag();
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename __libcpp_complex_overload_traits<_Tp>::_ValueType
norm(_Tp __re)
{
typedef typename __libcpp_complex_overload_traits<_Tp>::_ValueType _ValueType;
return static_cast<_ValueType>(__re) * __re;
}
// conj
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
conj(const complex<_Tp>& __c)
{
return complex<_Tp>(__c.real(), -__c.imag());
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
conj(_Tp __re)
{
typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
return _ComplexType(__re);
}
// proj
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
proj(const complex<_Tp>& __c)
{
std::complex<_Tp> __r = __c;
if (__libcpp_isinf_or_builtin(__c.real()) || __libcpp_isinf_or_builtin(__c.imag()))
__r = complex<_Tp>(INFINITY, copysign(_Tp(0), __c.imag()));
return __r;
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_floating_point<_Tp>::value,
typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
>::type
proj(_Tp __re)
{
if (__libcpp_isinf_or_builtin(__re))
__re = abs(__re);
return complex<_Tp>(__re);
}
template <class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_integral<_Tp>::value,
typename __libcpp_complex_overload_traits<_Tp>::_ComplexType
>::type
proj(_Tp __re)
{
typedef typename __libcpp_complex_overload_traits<_Tp>::_ComplexType _ComplexType;
return _ComplexType(__re);
}
// polar
template<class _Tp>
complex<_Tp>
polar(const _Tp& __rho, const _Tp& __theta = _Tp(0))
{
if (__libcpp_isnan_or_builtin(__rho) || signbit(__rho))
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
if (__libcpp_isnan_or_builtin(__theta))
{
if (__libcpp_isinf_or_builtin(__rho))
return complex<_Tp>(__rho, __theta);
return complex<_Tp>(__theta, __theta);
}
if (__libcpp_isinf_or_builtin(__theta))
{
if (__libcpp_isinf_or_builtin(__rho))
return complex<_Tp>(__rho, _Tp(NAN));
return complex<_Tp>(_Tp(NAN), _Tp(NAN));
}
_Tp __x = __rho * cos(__theta);
if (__libcpp_isnan_or_builtin(__x))
__x = 0;
_Tp __y = __rho * sin(__theta);
if (__libcpp_isnan_or_builtin(__y))
__y = 0;
return complex<_Tp>(__x, __y);
}
// log
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
log(const complex<_Tp>& __x)
{
return complex<_Tp>(log(abs(__x)), arg(__x));
}
// log10
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
log10(const complex<_Tp>& __x)
{
return log(__x) / log(_Tp(10));
}
// sqrt
template<class _Tp>
complex<_Tp>
sqrt(const complex<_Tp>& __x)
{
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(_Tp(INFINITY), __x.imag());
if (__libcpp_isinf_or_builtin(__x.real()))
{
if (__x.real() > _Tp(0))
return complex<_Tp>(__x.real(), __libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : copysign(_Tp(0), __x.imag()));
return complex<_Tp>(__libcpp_isnan_or_builtin(__x.imag()) ? __x.imag() : _Tp(0), copysign(__x.real(), __x.imag()));
}
return polar(sqrt(abs(__x)), arg(__x) / _Tp(2));
}
// exp
template<class _Tp>
complex<_Tp>
exp(const complex<_Tp>& __x)
{
_Tp __i = __x.imag();
if (__libcpp_isinf_or_builtin(__x.real()))
{
if (__x.real() < _Tp(0))
{
if (!__libcpp_isfinite_or_builtin(__i))
__i = _Tp(1);
}
else if (__i == 0 || !__libcpp_isfinite_or_builtin(__i))
{
if (__libcpp_isinf_or_builtin(__i))
__i = _Tp(NAN);
return complex<_Tp>(__x.real(), __i);
}
}
else if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
return __x;
_Tp __e = exp(__x.real());
return complex<_Tp>(__e * cos(__i), __e * sin(__i));
}
// pow
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
return exp(__y * log(__x));
}
template<class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY
complex<typename __promote<_Tp, _Up>::type>
pow(const complex<_Tp>& __x, const complex<_Up>& __y)
{
typedef complex<typename __promote<_Tp, _Up>::type> result_type;
return _VSTD::pow(result_type(__x), result_type(__y));
}
template<class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_arithmetic<_Up>::value,
complex<typename __promote<_Tp, _Up>::type>
>::type
pow(const complex<_Tp>& __x, const _Up& __y)
{
typedef complex<typename __promote<_Tp, _Up>::type> result_type;
return _VSTD::pow(result_type(__x), result_type(__y));
}
template<class _Tp, class _Up>
inline _LIBCPP_INLINE_VISIBILITY
typename enable_if
<
is_arithmetic<_Tp>::value,
complex<typename __promote<_Tp, _Up>::type>
>::type
pow(const _Tp& __x, const complex<_Up>& __y)
{
typedef complex<typename __promote<_Tp, _Up>::type> result_type;
return _VSTD::pow(result_type(__x), result_type(__y));
}
// asinh
template<class _Tp>
complex<_Tp>
asinh(const complex<_Tp>& __x)
{
const _Tp __pi(atan2(+0., -0.));
if (__libcpp_isinf_or_builtin(__x.real()))
{
if (__libcpp_isnan_or_builtin(__x.imag()))
return __x;
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
}
if (__libcpp_isnan_or_builtin(__x.real()))
{
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(__x.imag(), __x.real());
if (__x.imag() == 0)
return __x;
return complex<_Tp>(__x.real(), __x.real());
}
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(copysign(__x.imag(), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) + _Tp(1)));
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
}
// acosh
template<class _Tp>
complex<_Tp>
acosh(const complex<_Tp>& __x)
{
const _Tp __pi(atan2(+0., -0.));
if (__libcpp_isinf_or_builtin(__x.real()))
{
if (__libcpp_isnan_or_builtin(__x.imag()))
return complex<_Tp>(abs(__x.real()), __x.imag());
if (__libcpp_isinf_or_builtin(__x.imag()))
{
if (__x.real() > 0)
return complex<_Tp>(__x.real(), copysign(__pi * _Tp(0.25), __x.imag()));
else
return complex<_Tp>(-__x.real(), copysign(__pi * _Tp(0.75), __x.imag()));
}
if (__x.real() < 0)
return complex<_Tp>(-__x.real(), copysign(__pi, __x.imag()));
return complex<_Tp>(__x.real(), copysign(_Tp(0), __x.imag()));
}
if (__libcpp_isnan_or_builtin(__x.real()))
{
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(abs(__x.imag()), __x.real());
return complex<_Tp>(__x.real(), __x.real());
}
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(abs(__x.imag()), copysign(__pi/_Tp(2), __x.imag()));
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
return complex<_Tp>(copysign(__z.real(), _Tp(0)), copysign(__z.imag(), __x.imag()));
}
// atanh
template<class _Tp>
complex<_Tp>
atanh(const complex<_Tp>& __x)
{
const _Tp __pi(atan2(+0., -0.));
if (__libcpp_isinf_or_builtin(__x.imag()))
{
return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
}
if (__libcpp_isnan_or_builtin(__x.imag()))
{
if (__libcpp_isinf_or_builtin(__x.real()) || __x.real() == 0)
return complex<_Tp>(copysign(_Tp(0), __x.real()), __x.imag());
return complex<_Tp>(__x.imag(), __x.imag());
}
if (__libcpp_isnan_or_builtin(__x.real()))
{
return complex<_Tp>(__x.real(), __x.real());
}
if (__libcpp_isinf_or_builtin(__x.real()))
{
return complex<_Tp>(copysign(_Tp(0), __x.real()), copysign(__pi/_Tp(2), __x.imag()));
}
if (abs(__x.real()) == _Tp(1) && __x.imag() == _Tp(0))
{
return complex<_Tp>(copysign(_Tp(INFINITY), __x.real()), copysign(_Tp(0), __x.imag()));
}
complex<_Tp> __z = log((_Tp(1) + __x) / (_Tp(1) - __x)) / _Tp(2);
return complex<_Tp>(copysign(__z.real(), __x.real()), copysign(__z.imag(), __x.imag()));
}
// sinh
template<class _Tp>
complex<_Tp>
sinh(const complex<_Tp>& __x)
{
if (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
return complex<_Tp>(__x.real(), _Tp(NAN));
if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
return complex<_Tp>(__x.real(), _Tp(NAN));
if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__x.real()))
return __x;
return complex<_Tp>(sinh(__x.real()) * cos(__x.imag()), cosh(__x.real()) * sin(__x.imag()));
}
// cosh
template<class _Tp>
complex<_Tp>
cosh(const complex<_Tp>& __x)
{
if (__libcpp_isinf_or_builtin(__x.real()) && !__libcpp_isfinite_or_builtin(__x.imag()))
return complex<_Tp>(abs(__x.real()), _Tp(NAN));
if (__x.real() == 0 && !__libcpp_isfinite_or_builtin(__x.imag()))
return complex<_Tp>(_Tp(NAN), __x.real());
if (__x.real() == 0 && __x.imag() == 0)
return complex<_Tp>(_Tp(1), __x.imag());
if (__x.imag() == 0 && !__libcpp_isfinite_or_builtin(__x.real()))
return complex<_Tp>(abs(__x.real()), __x.imag());
return complex<_Tp>(cosh(__x.real()) * cos(__x.imag()), sinh(__x.real()) * sin(__x.imag()));
}
// tanh
template<class _Tp>
complex<_Tp>
tanh(const complex<_Tp>& __x)
{
if (__libcpp_isinf_or_builtin(__x.real()))
{
if (!__libcpp_isfinite_or_builtin(__x.imag()))
return complex<_Tp>(_Tp(1), _Tp(0));
return complex<_Tp>(_Tp(1), copysign(_Tp(0), sin(_Tp(2) * __x.imag())));
}
if (__libcpp_isnan_or_builtin(__x.real()) && __x.imag() == 0)
return __x;
_Tp __2r(_Tp(2) * __x.real());
_Tp __2i(_Tp(2) * __x.imag());
_Tp __d(cosh(__2r) + cos(__2i));
_Tp __2rsh(sinh(__2r));
if (__libcpp_isinf_or_builtin(__2rsh) && __libcpp_isinf_or_builtin(__d))
return complex<_Tp>(__2rsh > _Tp(0) ? _Tp(1) : _Tp(-1),
__2i > _Tp(0) ? _Tp(0) : _Tp(-0.));
return complex<_Tp>(__2rsh/__d, sin(__2i)/__d);
}
// asin
template<class _Tp>
complex<_Tp>
asin(const complex<_Tp>& __x)
{
complex<_Tp> __z = asinh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// acos
template<class _Tp>
complex<_Tp>
acos(const complex<_Tp>& __x)
{
const _Tp __pi(atan2(+0., -0.));
if (__libcpp_isinf_or_builtin(__x.real()))
{
if (__libcpp_isnan_or_builtin(__x.imag()))
return complex<_Tp>(__x.imag(), __x.real());
if (__libcpp_isinf_or_builtin(__x.imag()))
{
if (__x.real() < _Tp(0))
return complex<_Tp>(_Tp(0.75) * __pi, -__x.imag());
return complex<_Tp>(_Tp(0.25) * __pi, -__x.imag());
}
if (__x.real() < _Tp(0))
return complex<_Tp>(__pi, signbit(__x.imag()) ? -__x.real() : __x.real());
return complex<_Tp>(_Tp(0), signbit(__x.imag()) ? __x.real() : -__x.real());
}
if (__libcpp_isnan_or_builtin(__x.real()))
{
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(__x.real(), -__x.imag());
return complex<_Tp>(__x.real(), __x.real());
}
if (__libcpp_isinf_or_builtin(__x.imag()))
return complex<_Tp>(__pi/_Tp(2), -__x.imag());
if (__x.real() == 0 && (__x.imag() == 0 || isnan(__x.imag())))
return complex<_Tp>(__pi/_Tp(2), -__x.imag());
complex<_Tp> __z = log(__x + sqrt(pow(__x, _Tp(2)) - _Tp(1)));
if (signbit(__x.imag()))
return complex<_Tp>(abs(__z.imag()), abs(__z.real()));
return complex<_Tp>(abs(__z.imag()), -abs(__z.real()));
}
// atan
template<class _Tp>
complex<_Tp>
atan(const complex<_Tp>& __x)
{
complex<_Tp> __z = atanh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// sin
template<class _Tp>
complex<_Tp>
sin(const complex<_Tp>& __x)
{
complex<_Tp> __z = sinh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
// cos
template<class _Tp>
inline _LIBCPP_INLINE_VISIBILITY
complex<_Tp>
cos(const complex<_Tp>& __x)
{
return cosh(complex<_Tp>(-__x.imag(), __x.real()));
}
// tan
template<class _Tp>
complex<_Tp>
tan(const complex<_Tp>& __x)
{
complex<_Tp> __z = tanh(complex<_Tp>(-__x.imag(), __x.real()));
return complex<_Tp>(__z.imag(), -__z.real());
}
template<class _Tp, class _CharT, class _Traits>
basic_istream<_CharT, _Traits>&
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
{
if (__is.good())
{
ws(__is);
if (__is.peek() == _CharT('('))
{
__is.get();
_Tp __r;
__is >> __r;
if (!__is.fail())
{
ws(__is);
_CharT __c = __is.peek();
if (__c == _CharT(','))
{
__is.get();
_Tp __i;
__is >> __i;
if (!__is.fail())
{
ws(__is);
__c = __is.peek();
if (__c == _CharT(')'))
{
__is.get();
__x = complex<_Tp>(__r, __i);
}
else
__is.setstate(ios_base::failbit);
}
else
__is.setstate(ios_base::failbit);
}
else if (__c == _CharT(')'))
{
__is.get();
__x = complex<_Tp>(__r, _Tp(0));
}
else
__is.setstate(ios_base::failbit);
}
else
__is.setstate(ios_base::failbit);
}
else
{
_Tp __r;
__is >> __r;
if (!__is.fail())
__x = complex<_Tp>(__r, _Tp(0));
else
__is.setstate(ios_base::failbit);
}
}
else
__is.setstate(ios_base::failbit);
return __is;
}
template<class _Tp, class _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();
}
#if _LIBCPP_STD_VER > 11
// Literal suffix for complex number literals [complex.literals]
inline namespace literals
{
inline namespace complex_literals
{
constexpr complex<long double> operator""il(long double __im)
{
return { 0.0l, __im };
}
constexpr complex<long double> operator""il(unsigned long long __im)
{
return { 0.0l, static_cast<long double>(__im) };
}
constexpr complex<double> operator""i(long double __im)
{
return { 0.0, static_cast<double>(__im) };
}
constexpr complex<double> operator""i(unsigned long long __im)
{
return { 0.0, static_cast<double>(__im) };
}
constexpr complex<float> operator""if(long double __im)
{
return { 0.0f, static_cast<float>(__im) };
}
constexpr complex<float> operator""if(unsigned long long __im)
{
return { 0.0f, static_cast<float>(__im) };
}
}
}
#endif
_LIBCPP_END_NAMESPACE_STD
#endif // _LIBCPP_COMPLEX
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