891 lines
13 KiB
C++
891 lines
13 KiB
C++
// Copyright 2008-2016 Conrad Sanderson (http://conradsanderson.id.au)
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// Copyright 2008-2016 National ICT Australia (NICTA)
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// ------------------------------------------------------------------------
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//! \addtogroup arma_cmath
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//! @{
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//
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// wrappers for isfinite
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template<typename eT>
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arma_inline
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bool
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arma_isfinite(eT val)
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{
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arma_ignore(val);
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return true;
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}
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template<>
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arma_inline
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bool
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arma_isfinite(float x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::isfinite(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::isfinite(x);
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}
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#elif defined(ARMA_HAVE_ISFINITE)
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{
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return (std::isfinite(x) != 0);
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}
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#else
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{
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const float y = (std::numeric_limits<float>::max)();
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const volatile float xx = x;
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return (xx == xx) && (x >= -y) && (x <= y);
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}
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#endif
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}
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template<>
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arma_inline
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bool
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arma_isfinite(double x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::isfinite(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::isfinite(x);
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}
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#elif defined(ARMA_HAVE_ISFINITE)
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{
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return (std::isfinite(x) != 0);
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}
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#else
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{
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const double y = (std::numeric_limits<double>::max)();
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const volatile double xx = x;
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return (xx == xx) && (x >= -y) && (x <= y);
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}
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#endif
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}
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template<typename T>
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arma_inline
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bool
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arma_isfinite(const std::complex<T>& x)
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{
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if( (arma_isfinite(x.real()) == false) || (arma_isfinite(x.imag()) == false) )
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{
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return false;
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}
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else
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{
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return true;
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}
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}
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//
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// wrappers for isinf
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template<typename eT>
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arma_inline
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bool
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arma_isinf(eT val)
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{
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arma_ignore(val);
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return false;
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}
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template<>
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arma_inline
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bool
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arma_isinf(float x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::isinf(x);
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}
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#elif defined(ARMA_HAVE_ISINF)
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{
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return (std::isinf(x) != 0);
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}
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#else
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{
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const float y = (std::numeric_limits<float>::max)();
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const volatile float xx = x;
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return (xx == xx) && ((x < -y) || (x > y));
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}
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#endif
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}
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template<>
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arma_inline
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bool
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arma_isinf(double x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::isinf(x);
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}
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#elif defined(ARMA_HAVE_ISINF)
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{
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return (std::isinf(x) != 0);
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}
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#else
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{
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const double y = (std::numeric_limits<double>::max)();
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const volatile double xx = x;
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return (xx == xx) && ((x < -y) || (x > y));
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}
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#endif
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}
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template<typename T>
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arma_inline
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bool
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arma_isinf(const std::complex<T>& x)
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{
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return ( arma_isinf(x.real()) || arma_isinf(x.imag()) );
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}
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//
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// wrappers for isnan
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template<typename eT>
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arma_inline
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bool
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arma_isnan(eT val)
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{
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arma_ignore(val);
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return false;
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}
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template<>
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arma_inline
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bool
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arma_isnan(float x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::isnan(x);
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}
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#elif defined(ARMA_HAVE_ISNAN)
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{
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return (std::isnan(x) != 0);
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}
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#else
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{
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const volatile float xx = x;
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return (xx != xx);
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}
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#endif
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}
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template<>
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arma_inline
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bool
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arma_isnan(double x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::isnan(x);
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}
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#elif defined(ARMA_HAVE_ISNAN)
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{
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return (std::isnan(x) != 0);
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}
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#else
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{
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const volatile double xx = x;
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return (xx != xx);
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}
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#endif
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}
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template<typename T>
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arma_inline
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bool
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arma_isnan(const std::complex<T>& x)
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{
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return ( arma_isnan(x.real()) || arma_isnan(x.imag()) );
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}
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// rudimentary wrappers for log1p()
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arma_inline
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float
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arma_log1p(const float x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::log1p(x);
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}
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#else
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{
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if((x >= float(0)) && (x < std::numeric_limits<float>::epsilon()))
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{
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return x;
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}
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else
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if((x < float(0)) && (-x < std::numeric_limits<float>::epsilon()))
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{
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return x;
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}
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else
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{
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return std::log(float(1) + x);
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}
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}
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#endif
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}
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arma_inline
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double
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arma_log1p(const double x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::log1p(x);
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}
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#elif defined(ARMA_HAVE_LOG1P)
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{
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return log1p(x);
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}
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#else
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{
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if((x >= double(0)) && (x < std::numeric_limits<double>::epsilon()))
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{
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return x;
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}
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else
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if((x < double(0)) && (-x < std::numeric_limits<double>::epsilon()))
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{
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return x;
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}
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else
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{
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return std::log(double(1) + x);
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}
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}
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#endif
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}
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//
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// implementation of arma_sign()
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template<typename eT>
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arma_inline
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typename arma_unsigned_integral_only<eT>::result
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arma_sign(const eT x)
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{
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return (x > eT(0)) ? eT(+1) : eT(0);
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}
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template<typename eT>
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arma_inline
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typename arma_signed_integral_only<eT>::result
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arma_sign(const eT x)
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{
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return (x > eT(0)) ? eT(+1) : ( (x < eT(0)) ? eT(-1) : eT(0) );
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}
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template<typename eT>
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arma_inline
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typename arma_real_only<eT>::result
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arma_sign(const eT x)
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{
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return (x > eT(0)) ? eT(+1) : ( (x < eT(0)) ? eT(-1) : ((x == eT(0)) ? eT(0) : x) );
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}
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template<typename eT>
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arma_inline
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typename arma_cx_only<eT>::result
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arma_sign(const eT& x)
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{
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typedef typename eT::value_type T;
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const T abs_x = std::abs(x);
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return (abs_x != T(0)) ? (x / abs_x) : x;
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}
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//
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// wrappers for trigonometric functions
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//
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// wherever possible, try to use C++11 or TR1 versions of the following functions:
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//
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// complex acos
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// complex asin
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// complex atan
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//
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// real acosh
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// real asinh
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// real atanh
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//
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// complex acosh
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// complex asinh
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// complex atanh
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//
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//
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// if C++11 or TR1 are not available, we have rudimentary versions of:
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//
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// real acosh
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// real asinh
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// real atanh
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template<typename T>
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arma_inline
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std::complex<T>
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arma_acos(const std::complex<T>& x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::acos(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::acos(x);
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}
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#else
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{
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arma_ignore(x);
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arma_stop_logic_error("acos(): C++11 compiler required");
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return std::complex<T>(0);
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}
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#endif
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}
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template<typename T>
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arma_inline
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std::complex<T>
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arma_asin(const std::complex<T>& x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::asin(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::asin(x);
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}
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#else
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{
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arma_ignore(x);
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arma_stop_logic_error("asin(): C++11 compiler required");
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return std::complex<T>(0);
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}
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#endif
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}
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template<typename T>
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arma_inline
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std::complex<T>
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arma_atan(const std::complex<T>& x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::atan(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::atan(x);
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}
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#else
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{
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arma_ignore(x);
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arma_stop_logic_error("atan(): C++11 compiler required");
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return std::complex<T>(0);
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}
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#endif
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}
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template<typename eT>
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arma_inline
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eT
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arma_acosh(const eT x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::acosh(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::acosh(x);
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}
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#else
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{
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if(x >= eT(1))
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcCosh/02/
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return std::log( x + std::sqrt(x*x - eT(1)) );
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}
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else
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{
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if(std::numeric_limits<eT>::has_quiet_NaN)
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{
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return -(std::numeric_limits<eT>::quiet_NaN());
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}
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else
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{
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return eT(0);
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}
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}
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}
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#endif
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}
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template<typename eT>
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arma_inline
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eT
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arma_asinh(const eT x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::asinh(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::asinh(x);
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}
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#else
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcSinh/02/
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return std::log( x + std::sqrt(x*x + eT(1)) );
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}
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#endif
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}
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template<typename eT>
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arma_inline
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eT
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arma_atanh(const eT x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::atanh(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::atanh(x);
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}
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#else
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{
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if( (x >= eT(-1)) && (x <= eT(+1)) )
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{
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// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/02/
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return std::log( ( eT(1)+x ) / ( eT(1)-x ) ) / eT(2);
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}
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else
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{
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if(std::numeric_limits<eT>::has_quiet_NaN)
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{
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return -(std::numeric_limits<eT>::quiet_NaN());
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}
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else
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{
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return eT(0);
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}
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}
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}
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#endif
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}
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template<typename T>
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arma_inline
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std::complex<T>
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arma_acosh(const std::complex<T>& x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::acosh(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::acosh(x);
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}
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#else
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{
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arma_ignore(x);
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arma_stop_logic_error("acosh(): C++11 compiler required");
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return std::complex<T>(0);
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}
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#endif
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}
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template<typename T>
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arma_inline
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std::complex<T>
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arma_asinh(const std::complex<T>& x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::asinh(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::asinh(x);
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}
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#else
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{
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arma_ignore(x);
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arma_stop_logic_error("asinh(): C++11 compiler required");
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return std::complex<T>(0);
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}
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#endif
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}
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template<typename T>
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arma_inline
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std::complex<T>
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arma_atanh(const std::complex<T>& x)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::atanh(x);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::atanh(x);
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}
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#else
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{
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arma_ignore(x);
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arma_stop_logic_error("atanh(): C++11 compiler required");
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return std::complex<T>(0);
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}
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#endif
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}
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//
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// wrappers for hypot(x, y) = sqrt(x^2 + y^2)
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template<typename eT>
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inline
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eT
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arma_hypot_generic(const eT x, const eT y)
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{
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#if defined(ARMA_USE_CXX11)
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{
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return std::hypot(x, y);
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}
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#elif defined(ARMA_HAVE_TR1)
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{
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return std::tr1::hypot(x, y);
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}
|
|
#else
|
|
{
|
|
const eT xabs = std::abs(x);
|
|
const eT yabs = std::abs(y);
|
|
|
|
eT larger;
|
|
eT ratio;
|
|
|
|
if(xabs > yabs)
|
|
{
|
|
larger = xabs;
|
|
ratio = yabs / xabs;
|
|
}
|
|
else
|
|
{
|
|
larger = yabs;
|
|
ratio = xabs / yabs;
|
|
}
|
|
|
|
return (larger == eT(0)) ? eT(0) : (larger * std::sqrt(eT(1) + ratio * ratio));
|
|
}
|
|
#endif
|
|
}
|
|
|
|
|
|
|
|
template<typename eT>
|
|
inline
|
|
eT
|
|
arma_hypot(const eT x, const eT y)
|
|
{
|
|
arma_ignore(x);
|
|
arma_ignore(y);
|
|
|
|
arma_stop_runtime_error("arma_hypot(): not implemented for integer or complex element types");
|
|
|
|
return eT(0);
|
|
}
|
|
|
|
|
|
|
|
template<>
|
|
arma_inline
|
|
float
|
|
arma_hypot(const float x, const float y)
|
|
{
|
|
return arma_hypot_generic(x,y);
|
|
}
|
|
|
|
|
|
|
|
template<>
|
|
arma_inline
|
|
double
|
|
arma_hypot(const double x, const double y)
|
|
{
|
|
return arma_hypot_generic(x,y);
|
|
}
|
|
|
|
|
|
|
|
//
|
|
// implementation of arma_sinc()
|
|
|
|
|
|
template<typename eT>
|
|
arma_inline
|
|
eT
|
|
arma_sinc_generic(const eT x)
|
|
{
|
|
typedef typename get_pod_type<eT>::result T;
|
|
|
|
const eT tmp = Datum<T>::pi * x;
|
|
|
|
return (tmp == eT(0)) ? eT(1) : eT( std::sin(tmp) / tmp );
|
|
}
|
|
|
|
|
|
|
|
template<typename eT>
|
|
arma_inline
|
|
eT
|
|
arma_sinc(const eT x)
|
|
{
|
|
return eT( arma_sinc_generic( double(x) ) );
|
|
}
|
|
|
|
|
|
|
|
template<>
|
|
arma_inline
|
|
float
|
|
arma_sinc(const float x)
|
|
{
|
|
return arma_sinc_generic(x);
|
|
}
|
|
|
|
|
|
|
|
template<>
|
|
arma_inline
|
|
double
|
|
arma_sinc(const double x)
|
|
{
|
|
return arma_sinc_generic(x);
|
|
}
|
|
|
|
|
|
|
|
template<typename T>
|
|
arma_inline
|
|
std::complex<T>
|
|
arma_sinc(const std::complex<T>& x)
|
|
{
|
|
return arma_sinc_generic(x);
|
|
}
|
|
|
|
|
|
|
|
//
|
|
// wrappers for arg()
|
|
|
|
|
|
template<typename eT>
|
|
struct arma_arg
|
|
{
|
|
static
|
|
inline
|
|
eT
|
|
eval(const eT x)
|
|
{
|
|
#if defined(ARMA_USE_CXX11)
|
|
{
|
|
return eT( std::arg(x) );
|
|
}
|
|
#else
|
|
{
|
|
arma_ignore(x);
|
|
arma_stop_logic_error("arg(): C++11 compiler required");
|
|
|
|
return eT(0);
|
|
}
|
|
#endif
|
|
}
|
|
};
|
|
|
|
|
|
|
|
template<>
|
|
struct arma_arg<float>
|
|
{
|
|
static
|
|
arma_inline
|
|
float
|
|
eval(const float x)
|
|
{
|
|
#if defined(ARMA_USE_CXX11)
|
|
{
|
|
return std::arg(x);
|
|
}
|
|
#else
|
|
{
|
|
return std::arg( std::complex<float>( x, float(0) ) );
|
|
}
|
|
#endif
|
|
}
|
|
};
|
|
|
|
|
|
|
|
template<>
|
|
struct arma_arg<double>
|
|
{
|
|
static
|
|
arma_inline
|
|
double
|
|
eval(const double x)
|
|
{
|
|
#if defined(ARMA_USE_CXX11)
|
|
{
|
|
return std::arg(x);
|
|
}
|
|
#else
|
|
{
|
|
return std::arg( std::complex<double>( x, double(0) ) );
|
|
}
|
|
#endif
|
|
}
|
|
};
|
|
|
|
|
|
|
|
template<>
|
|
struct arma_arg< std::complex<float> >
|
|
{
|
|
static
|
|
arma_inline
|
|
float
|
|
eval(const std::complex<float>& x)
|
|
{
|
|
return std::arg(x);
|
|
}
|
|
};
|
|
|
|
|
|
|
|
template<>
|
|
struct arma_arg< std::complex<double> >
|
|
{
|
|
static
|
|
arma_inline
|
|
double
|
|
eval(const std::complex<double>& x)
|
|
{
|
|
return std::arg(x);
|
|
}
|
|
};
|
|
|
|
|
|
|
|
//! @}
|