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2018-06-09 21:48:32 +01:00
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boost/math/complex/acos.hpp
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// (C) Copyright John Maddock 2005.
// Distributed under the Boost Software License, Version 1.0. (See accompanying
// file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_COMPLEX_ACOS_INCLUDED
#define BOOST_MATH_COMPLEX_ACOS_INCLUDED
#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
# include <boost/math/complex/details.hpp>
#endif
#ifndef BOOST_MATH_LOG1P_INCLUDED
# include <boost/math/special_functions/log1p.hpp>
#endif
#include <boost/assert.hpp>
#ifdef BOOST_NO_STDC_NAMESPACE
namespace std{ using ::sqrt; using ::fabs; using ::acos; using ::asin; using ::atan; using ::atan2; }
#endif
namespace boost{ namespace math{
template<class T>
std::complex<T> acos(const std::complex<T>& z)
{
//
// This implementation is a transcription of the pseudo-code in:
//
// "Implementing the Complex Arcsine and Arccosine Functions using Exception Handling."
// T E Hull, Thomas F Fairgrieve and Ping Tak Peter Tang.
// ACM Transactions on Mathematical Software, Vol 23, No 3, Sept 1997.
//
//
// These static constants should really be in a maths constants library,
// note that we have tweaked a_crossover as per: https://svn.boost.org/trac/boost/ticket/7290
//
static const T one = static_cast<T>(1);
//static const T two = static_cast<T>(2);
static const T half = static_cast<T>(0.5L);
static const T a_crossover = static_cast<T>(10);
static const T b_crossover = static_cast<T>(0.6417L);
static const T s_pi = boost::math::constants::pi<T>();
static const T half_pi = s_pi / 2;
static const T log_two = boost::math::constants::ln_two<T>();
static const T quarter_pi = s_pi / 4;
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4127)
#endif
//
// Get real and imaginary parts, discard the signs as we can
// figure out the sign of the result later:
//
T x = std::fabs(z.real());
T y = std::fabs(z.imag());
T real, imag; // these hold our result
//
// Handle special cases specified by the C99 standard,
// many of these special cases aren't really needed here,
// but doing it this way prevents overflow/underflow arithmetic
// in the main body of the logic, which may trip up some machines:
//
if((boost::math::isinf)(x))
{
if((boost::math::isinf)(y))
{
real = quarter_pi;
imag = std::numeric_limits<T>::infinity();
}
else if((boost::math::isnan)(y))
{
return std::complex<T>(y, -std::numeric_limits<T>::infinity());
}
else
{
// y is not infinity or nan:
real = 0;
imag = std::numeric_limits<T>::infinity();
}
}
else if((boost::math::isnan)(x))
{
if((boost::math::isinf)(y))
return std::complex<T>(x, ((boost::math::signbit)(z.imag())) ? std::numeric_limits<T>::infinity() : -std::numeric_limits<T>::infinity());
return std::complex<T>(x, x);
}
else if((boost::math::isinf)(y))
{
real = half_pi;
imag = std::numeric_limits<T>::infinity();
}
else if((boost::math::isnan)(y))
{
return std::complex<T>((x == 0) ? half_pi : y, y);
}
else
{
//
// What follows is the regular Hull et al code,
// begin with the special case for real numbers:
//
if((y == 0) && (x <= one))
return std::complex<T>((x == 0) ? half_pi : std::acos(z.real()), (boost::math::changesign)(z.imag()));
//
// Figure out if our input is within the "safe area" identified by Hull et al.
// This would be more efficient with portable floating point exception handling;
// fortunately the quantities M and u identified by Hull et al (figure 3),
// match with the max and min methods of numeric_limits<T>.
//
T safe_max = detail::safe_max(static_cast<T>(8));
T safe_min = detail::safe_min(static_cast<T>(4));
T xp1 = one + x;
T xm1 = x - one;
if((x < safe_max) && (x > safe_min) && (y < safe_max) && (y > safe_min))
{
T yy = y * y;
T r = std::sqrt(xp1*xp1 + yy);
T s = std::sqrt(xm1*xm1 + yy);
T a = half * (r + s);
T b = x / a;
if(b <= b_crossover)
{
real = std::acos(b);
}
else
{
T apx = a + x;
if(x <= one)
{
real = std::atan(std::sqrt(half * apx * (yy /(r + xp1) + (s-xm1)))/x);
}
else
{
real = std::atan((y * std::sqrt(half * (apx/(r + xp1) + apx/(s+xm1))))/x);
}
}
if(a <= a_crossover)
{
T am1;
if(x < one)
{
am1 = half * (yy/(r + xp1) + yy/(s - xm1));
}
else
{
am1 = half * (yy/(r + xp1) + (s + xm1));
}
imag = boost::math::log1p(am1 + std::sqrt(am1 * (a + one)));
}
else
{
imag = std::log(a + std::sqrt(a*a - one));
}
}
else
{
//
// This is the Hull et al exception handling code from Fig 6 of their paper:
//
if(y <= (std::numeric_limits<T>::epsilon() * std::fabs(xm1)))
{
if(x < one)
{
real = std::acos(x);
imag = y / std::sqrt(xp1*(one-x));
}
else
{
// This deviates from Hull et al's paper as per https://svn.boost.org/trac/boost/ticket/7290
if(((std::numeric_limits<T>::max)() / xp1) > xm1)
{
// xp1 * xm1 won't overflow:
real = y / std::sqrt(xm1*xp1);
imag = boost::math::log1p(xm1 + std::sqrt(xp1*xm1));
}
else
{
real = y / x;
imag = log_two + std::log(x);
}
}
}
else if(y <= safe_min)
{
// There is an assumption in Hull et al's analysis that
// if we get here then x == 1. This is true for all "good"
// machines where :
//
// E^2 > 8*sqrt(u); with:
//
// E = std::numeric_limits<T>::epsilon()
// u = (std::numeric_limits<T>::min)()
//
// Hull et al provide alternative code for "bad" machines
// but we have no way to test that here, so for now just assert
// on the assumption:
//
BOOST_ASSERT(x == 1);
real = std::sqrt(y);
imag = std::sqrt(y);
}
else if(std::numeric_limits<T>::epsilon() * y - one >= x)
{
real = half_pi;
imag = log_two + std::log(y);
}
else if(x > one)
{
real = std::atan(y/x);
T xoy = x/y;
imag = log_two + std::log(y) + half * boost::math::log1p(xoy*xoy);
}
else
{
real = half_pi;
T a = std::sqrt(one + y*y);
imag = half * boost::math::log1p(static_cast<T>(2)*y*(y+a));
}
}
}
//
// Finish off by working out the sign of the result:
//
if((boost::math::signbit)(z.real()))
real = s_pi - real;
if(!(boost::math::signbit)(z.imag()))
imag = (boost::math::changesign)(imag);
return std::complex<T>(real, imag);
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
}
} } // namespaces
#endif // BOOST_MATH_COMPLEX_ACOS_INCLUDED
boost/math/complex/acosh.hpp
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// (C) Copyright John Maddock 2005.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_COMPLEX_ACOSH_INCLUDED
#define BOOST_MATH_COMPLEX_ACOSH_INCLUDED
#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
# include <boost/math/complex/details.hpp>
#endif
#ifndef BOOST_MATH_COMPLEX_ATANH_INCLUDED
# include <boost/math/complex/acos.hpp>
#endif
namespace boost{ namespace math{
template<class T>
inline std::complex<T> acosh(const std::complex<T>& z)
{
//
// We use the relation acosh(z) = +-i acos(z)
// Choosing the sign of multiplier to give real(acosh(z)) >= 0
// as well as compatibility with C99.
//
std::complex<T> result = boost::math::acos(z);
if(!(boost::math::isnan)(result.imag()) && signbit(result.imag()))
return detail::mult_i(result);
return detail::mult_minus_i(result);
}
} } // namespaces
#endif // BOOST_MATH_COMPLEX_ACOSH_INCLUDED
boost/math/complex/asin.hpp
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// (C) Copyright John Maddock 2005.
// Distributed under the Boost Software License, Version 1.0. (See accompanying
// file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_COMPLEX_ASIN_INCLUDED
#define BOOST_MATH_COMPLEX_ASIN_INCLUDED
#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
# include <boost/math/complex/details.hpp>
#endif
#ifndef BOOST_MATH_LOG1P_INCLUDED
# include <boost/math/special_functions/log1p.hpp>
#endif
#include <boost/assert.hpp>
#ifdef BOOST_NO_STDC_NAMESPACE
namespace std{ using ::sqrt; using ::fabs; using ::acos; using ::asin; using ::atan; using ::atan2; }
#endif
namespace boost{ namespace math{
template<class T>
inline std::complex<T> asin(const std::complex<T>& z)
{
//
// This implementation is a transcription of the pseudo-code in:
//
// "Implementing the complex Arcsine and Arccosine Functions using Exception Handling."
// T E Hull, Thomas F Fairgrieve and Ping Tak Peter Tang.
// ACM Transactions on Mathematical Software, Vol 23, No 3, Sept 1997.
//
//
// These static constants should really be in a maths constants library,
// note that we have tweaked the value of a_crossover as per https://svn.boost.org/trac/boost/ticket/7290:
//
static const T one = static_cast<T>(1);
//static const T two = static_cast<T>(2);
static const T half = static_cast<T>(0.5L);
static const T a_crossover = static_cast<T>(10);
static const T b_crossover = static_cast<T>(0.6417L);
static const T s_pi = boost::math::constants::pi<T>();
static const T half_pi = s_pi / 2;
static const T log_two = boost::math::constants::ln_two<T>();
static const T quarter_pi = s_pi / 4;
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4127)
#endif
//
// Get real and imaginary parts, discard the signs as we can
// figure out the sign of the result later:
//
T x = std::fabs(z.real());
T y = std::fabs(z.imag());
T real, imag; // our results
//
// Begin by handling the special cases for infinities and nan's
// specified in C99, most of this is handled by the regular logic
// below, but handling it as a special case prevents overflow/underflow
// arithmetic which may trip up some machines:
//
if((boost::math::isnan)(x))
{
if((boost::math::isnan)(y))
return std::complex<T>(x, x);
if((boost::math::isinf)(y))
{
real = x;
imag = std::numeric_limits<T>::infinity();
}
else
return std::complex<T>(x, x);
}
else if((boost::math::isnan)(y))
{
if(x == 0)
{
real = 0;
imag = y;
}
else if((boost::math::isinf)(x))
{
real = y;
imag = std::numeric_limits<T>::infinity();
}
else
return std::complex<T>(y, y);
}
else if((boost::math::isinf)(x))
{
if((boost::math::isinf)(y))
{
real = quarter_pi;
imag = std::numeric_limits<T>::infinity();
}
else
{
real = half_pi;
imag = std::numeric_limits<T>::infinity();
}
}
else if((boost::math::isinf)(y))
{
real = 0;
imag = std::numeric_limits<T>::infinity();
}
else
{
//
// special case for real numbers:
//
if((y == 0) && (x <= one))
return std::complex<T>(std::asin(z.real()), z.imag());
//
// Figure out if our input is within the "safe area" identified by Hull et al.
// This would be more efficient with portable floating point exception handling;
// fortunately the quantities M and u identified by Hull et al (figure 3),
// match with the max and min methods of numeric_limits<T>.
//
T safe_max = detail::safe_max(static_cast<T>(8));
T safe_min = detail::safe_min(static_cast<T>(4));
T xp1 = one + x;
T xm1 = x - one;
if((x < safe_max) && (x > safe_min) && (y < safe_max) && (y > safe_min))
{
T yy = y * y;
T r = std::sqrt(xp1*xp1 + yy);
T s = std::sqrt(xm1*xm1 + yy);
T a = half * (r + s);
T b = x / a;
if(b <= b_crossover)
{
real = std::asin(b);
}
else
{
T apx = a + x;
if(x <= one)
{
real = std::atan(x/std::sqrt(half * apx * (yy /(r + xp1) + (s-xm1))));
}
else
{
real = std::atan(x/(y * std::sqrt(half * (apx/(r + xp1) + apx/(s+xm1)))));
}
}
if(a <= a_crossover)
{
T am1;
if(x < one)
{
am1 = half * (yy/(r + xp1) + yy/(s - xm1));
}
else
{
am1 = half * (yy/(r + xp1) + (s + xm1));
}
imag = boost::math::log1p(am1 + std::sqrt(am1 * (a + one)));
}
else
{
imag = std::log(a + std::sqrt(a*a - one));
}
}
else
{
//
// This is the Hull et al exception handling code from Fig 3 of their paper:
//
if(y <= (std::numeric_limits<T>::epsilon() * std::fabs(xm1)))
{
if(x < one)
{
real = std::asin(x);
imag = y / std::sqrt(-xp1*xm1);
}
else
{
real = half_pi;
if(((std::numeric_limits<T>::max)() / xp1) > xm1)
{
// xp1 * xm1 won't overflow:
imag = boost::math::log1p(xm1 + std::sqrt(xp1*xm1));
}
else
{
imag = log_two + std::log(x);
}
}
}
else if(y <= safe_min)
{
// There is an assumption in Hull et al's analysis that
// if we get here then x == 1. This is true for all "good"
// machines where :
//
// E^2 > 8*sqrt(u); with:
//
// E = std::numeric_limits<T>::epsilon()
// u = (std::numeric_limits<T>::min)()
//
// Hull et al provide alternative code for "bad" machines
// but we have no way to test that here, so for now just assert
// on the assumption:
//
BOOST_ASSERT(x == 1);
real = half_pi - std::sqrt(y);
imag = std::sqrt(y);
}
else if(std::numeric_limits<T>::epsilon() * y - one >= x)
{
real = x/y; // This can underflow!
imag = log_two + std::log(y);
}
else if(x > one)
{
real = std::atan(x/y);
T xoy = x/y;
imag = log_two + std::log(y) + half * boost::math::log1p(xoy*xoy);
}
else
{
T a = std::sqrt(one + y*y);
real = x/a; // This can underflow!
imag = half * boost::math::log1p(static_cast<T>(2)*y*(y+a));
}
}
}
//
// Finish off by working out the sign of the result:
//
if((boost::math::signbit)(z.real()))
real = (boost::math::changesign)(real);
if((boost::math::signbit)(z.imag()))
imag = (boost::math::changesign)(imag);
return std::complex<T>(real, imag);
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
}
} } // namespaces
#endif // BOOST_MATH_COMPLEX_ASIN_INCLUDED
boost/math/complex/asinh.hpp
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// (C) Copyright John Maddock 2005.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_COMPLEX_ASINH_INCLUDED
#define BOOST_MATH_COMPLEX_ASINH_INCLUDED
#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
# include <boost/math/complex/details.hpp>
#endif
#ifndef BOOST_MATH_COMPLEX_ASIN_INCLUDED
# include <boost/math/complex/asin.hpp>
#endif
namespace boost{ namespace math{
template<class T>
inline std::complex<T> asinh(const std::complex<T>& x)
{
//
// We use asinh(z) = i asin(-i z);
// Note that C99 defines this the other way around (which is
// to say asin is specified in terms of asinh), this is consistent
// with C99 though:
//
return ::boost::math::detail::mult_i(::boost::math::asin(::boost::math::detail::mult_minus_i(x)));
}
} } // namespaces
#endif // BOOST_MATH_COMPLEX_ASINH_INCLUDED
boost/math/complex/atan.hpp
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// (C) Copyright John Maddock 2005.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_COMPLEX_ATAN_INCLUDED
#define BOOST_MATH_COMPLEX_ATAN_INCLUDED
#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
# include <boost/math/complex/details.hpp>
#endif
#ifndef BOOST_MATH_COMPLEX_ATANH_INCLUDED
# include <boost/math/complex/atanh.hpp>
#endif
namespace boost{ namespace math{
template<class T>
std::complex<T> atan(const std::complex<T>& x)
{
//
// We're using the C99 definition here; atan(z) = -i atanh(iz):
//
if(x.real() == 0)
{
if(x.imag() == 1)
return std::complex<T>(0, std::numeric_limits<T>::has_infinity ? std::numeric_limits<T>::infinity() : static_cast<T>(HUGE_VAL));
if(x.imag() == -1)
return std::complex<T>(0, std::numeric_limits<T>::has_infinity ? -std::numeric_limits<T>::infinity() : -static_cast<T>(HUGE_VAL));
}
return ::boost::math::detail::mult_minus_i(::boost::math::atanh(::boost::math::detail::mult_i(x)));
}
} } // namespaces
#endif // BOOST_MATH_COMPLEX_ATAN_INCLUDED
boost/math/complex/atanh.hpp
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// (C) Copyright John Maddock 2005.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_COMPLEX_ATANH_INCLUDED
#define BOOST_MATH_COMPLEX_ATANH_INCLUDED
#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
# include <boost/math/complex/details.hpp>
#endif
#ifndef BOOST_MATH_LOG1P_INCLUDED
# include <boost/math/special_functions/log1p.hpp>
#endif
#include <boost/assert.hpp>
#ifdef BOOST_NO_STDC_NAMESPACE
namespace std{ using ::sqrt; using ::fabs; using ::acos; using ::asin; using ::atan; using ::atan2; }
#endif
namespace boost{ namespace math{
template<class T>
std::complex<T> atanh(const std::complex<T>& z)
{
//
// References:
//
// Eric W. Weisstein. "Inverse Hyperbolic Tangent."
// From MathWorld--A Wolfram Web Resource.
// http://mathworld.wolfram.com/InverseHyperbolicTangent.html
//
// Also: The Wolfram Functions Site,
// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/
//
// Also "Abramowitz and Stegun. Handbook of Mathematical Functions."
// at : http://jove.prohosting.com/~skripty/toc.htm
//
// See also: https://svn.boost.org/trac/boost/ticket/7291
//
static const T pi = boost::math::constants::pi<T>();
static const T half_pi = pi / 2;
static const T one = static_cast<T>(1.0L);
static const T two = static_cast<T>(2.0L);
static const T four = static_cast<T>(4.0L);
static const T zero = static_cast<T>(0);
static const T log_two = boost::math::constants::ln_two<T>();
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4127)
#endif
T x = std::fabs(z.real());
T y = std::fabs(z.imag());
T real, imag; // our results
T safe_upper = detail::safe_max(two);
T safe_lower = detail::safe_min(static_cast<T>(2));
//
// Begin by handling the special cases specified in C99:
//
if((boost::math::isnan)(x))
{
if((boost::math::isnan)(y))
return std::complex<T>(x, x);
else if((boost::math::isinf)(y))
return std::complex<T>(0, ((boost::math::signbit)(z.imag()) ? -half_pi : half_pi));
else
return std::complex<T>(x, x);
}
else if((boost::math::isnan)(y))
{
if(x == 0)
return std::complex<T>(x, y);
if((boost::math::isinf)(x))
return std::complex<T>(0, y);
else
return std::complex<T>(y, y);
}
else if((x > safe_lower) && (x < safe_upper) && (y > safe_lower) && (y < safe_upper))
{
T yy = y*y;
T mxm1 = one - x;
///
// The real part is given by:
//
// real(atanh(z)) == log1p(4*x / ((x-1)*(x-1) + y^2))
//
real = boost::math::log1p(four * x / (mxm1*mxm1 + yy));
real /= four;
if((boost::math::signbit)(z.real()))
real = (boost::math::changesign)(real);
imag = std::atan2((y * two), (mxm1*(one+x) - yy));
imag /= two;
if(z.imag() < 0)
imag = (boost::math::changesign)(imag);
}
else
{
//
// This section handles exception cases that would normally cause
// underflow or overflow in the main formulas.
//
// Begin by working out the real part, we need to approximate
// real = boost::math::log1p(4x / ((x-1)^2 + y^2))
// without either overflow or underflow in the squared terms.
//
T mxm1 = one - x;
if(x >= safe_upper)
{
// x-1 = x to machine precision:
if((boost::math::isinf)(x) || (boost::math::isinf)(y))
{
real = 0;
}
else if(y >= safe_upper)
{
// Big x and y: divide through by x*y:
real = boost::math::log1p((four/y) / (x/y + y/x));
}
else if(y > one)
{
// Big x: divide through by x:
real = boost::math::log1p(four / (x + y*y/x));
}
else
{
// Big x small y, as above but neglect y^2/x:
real = boost::math::log1p(four/x);
}
}
else if(y >= safe_upper)
{
if(x > one)
{
// Big y, medium x, divide through by y:
real = boost::math::log1p((four*x/y) / (y + mxm1*mxm1/y));
}
else
{
// Small or medium x, large y:
real = four*x/y/y;
}
}
else if (x != one)
{
// y is small, calculate divisor carefully:
T div = mxm1*mxm1;
if(y > safe_lower)
div += y*y;
real = boost::math::log1p(four*x/div);
}
else
real = boost::math::changesign(two * (std::log(y) - log_two));
real /= four;
if((boost::math::signbit)(z.real()))
real = (boost::math::changesign)(real);
//
// Now handle imaginary part, this is much easier,
// if x or y are large, then the formula:
// atan2(2y, (1-x)*(1+x) - y^2)
// evaluates to +-(PI - theta) where theta is negligible compared to PI.
//
if((x >= safe_upper) || (y >= safe_upper))
{
imag = pi;
}
else if(x <= safe_lower)
{
//
// If both x and y are small then atan(2y),
// otherwise just x^2 is negligible in the divisor:
//
if(y <= safe_lower)
imag = std::atan2(two*y, one);
else
{
if((y == zero) && (x == zero))
imag = 0;
else
imag = std::atan2(two*y, one - y*y);
}
}
else
{
//
// y^2 is negligible:
//
if((y == zero) && (x == one))
imag = 0;
else
imag = std::atan2(two*y, mxm1*(one+x));
}
imag /= two;
if((boost::math::signbit)(z.imag()))
imag = (boost::math::changesign)(imag);
}
return std::complex<T>(real, imag);
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
}
} } // namespaces
#endif // BOOST_MATH_COMPLEX_ATANH_INCLUDED
boost/math/complex/details.hpp
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// (C) Copyright John Maddock 2005.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
#define BOOST_MATH_COMPLEX_DETAILS_INCLUDED
//
// This header contains all the support code that is common to the
// inverse trig complex functions, it also contains all the includes
// that we need to implement all these functions.
//
#include <boost/config.hpp>
#include <boost/detail/workaround.hpp>
#include <boost/config/no_tr1/complex.hpp>
#include <boost/limits.hpp>
#include <math.h> // isnan where available
#include <boost/config/no_tr1/cmath.hpp>
#include <boost/math/special_functions/sign.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
#include <boost/math/special_functions/sign.hpp>
#include <boost/math/constants/constants.hpp>
#ifdef BOOST_NO_STDC_NAMESPACE
namespace std{ using ::sqrt; }
#endif
namespace boost{ namespace math{ namespace detail{
template <class T>
inline T mult_minus_one(const T& t)
{
return (boost::math::isnan)(t) ? t : (boost::math::changesign)(t);
}
template <class T>
inline std::complex<T> mult_i(const std::complex<T>& t)
{
return std::complex<T>(mult_minus_one(t.imag()), t.real());
}
template <class T>
inline std::complex<T> mult_minus_i(const std::complex<T>& t)
{
return std::complex<T>(t.imag(), mult_minus_one(t.real()));
}
template <class T>
inline T safe_max(T t)
{
return std::sqrt((std::numeric_limits<T>::max)()) / t;
}
inline long double safe_max(long double t)
{
// long double sqrt often returns infinity due to
// insufficient internal precision:
return std::sqrt((std::numeric_limits<double>::max)()) / t;
}
#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
// workaround for type deduction bug:
inline float safe_max(float t)
{
return std::sqrt((std::numeric_limits<float>::max)()) / t;
}
inline double safe_max(double t)
{
return std::sqrt((std::numeric_limits<double>::max)()) / t;
}
#endif
template <class T>
inline T safe_min(T t)
{
return std::sqrt((std::numeric_limits<T>::min)()) * t;
}
inline long double safe_min(long double t)
{
// long double sqrt often returns zero due to
// insufficient internal precision:
return std::sqrt((std::numeric_limits<double>::min)()) * t;
}
#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x564))
// type deduction workaround:
inline double safe_min(double t)
{
return std::sqrt((std::numeric_limits<double>::min)()) * t;
}
inline float safe_min(float t)
{
return std::sqrt((std::numeric_limits<float>::min)()) * t;
}
#endif
} } } // namespaces
#endif // BOOST_MATH_COMPLEX_DETAILS_INCLUDED
boost/math/complex/fabs.hpp
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// (C) Copyright John Maddock 2005.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_COMPLEX_FABS_INCLUDED
#define BOOST_MATH_COMPLEX_FABS_INCLUDED
#ifndef BOOST_MATH_HYPOT_INCLUDED
# include <boost/math/special_functions/hypot.hpp>
#endif
namespace boost{ namespace math{
template<class T>
inline T fabs(const std::complex<T>& z)
{
return ::boost::math::hypot(z.real(), z.imag());
}
} } // namespaces
#endif // BOOST_MATH_COMPLEX_FABS_INCLUDED