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Diff: tvmet/NumericTraits.h
- Revision:
- 15:9c5aaeda36dc
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/tvmet/NumericTraits.h Sat Apr 06 20:57:54 2013 +0000
@@ -0,0 +1,1363 @@
+/*
+ * Tiny Vector Matrix Library
+ * Dense Vector Matrix Libary of Tiny size using Expression Templates
+ *
+ * Copyright (C) 2001 - 2007 Olaf Petzold <opetzold@users.sourceforge.net>
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ *
+ * $Id: NumericTraits.h,v 1.16 2007-06-23 15:58:58 opetzold Exp $
+ */
+
+#ifndef TVMET_NUMERIC_TRAITS_H
+#define TVMET_NUMERIC_TRAITS_H
+
+#if defined(TVMET_HAVE_COMPLEX)
+# include <complex>
+#endif
+#include <cmath>
+#include <limits>
+
+#include <tvmet/CompileTimeError.h>
+
+
+namespace tvmet {
+
+
+/**
+ * \class NumericTraits NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits for integral types for operations.
+ *
+ * For each type we have to specialize this traits.
+ *
+ * \note Keep in mind that the long types long long and long double doesn't
+ * have traits. This is due to the sum_type. We can't give a guarantee
+ * that there is a type of holding the sum. Therefore using this traits
+ * is only safe if you have long long resp. long double types by
+ * working on long ints and doubles. Otherwise you will get not expected
+ * result for some circumstances. Anyway, you can use big integer/float
+ * libraries and specialize the traits by your own.
+ *
+ * \todo The abs function of complex<non_float_type> can have an
+ * overrun due to numeric computation. Solve it (someone
+ * using value_type=long here?)
+ */
+template<class T>
+struct NumericTraits {
+ typedef T base_type;
+ typedef T value_type;
+ typedef value_type sum_type;
+ typedef value_type diff_type;
+ typedef value_type float_type;
+ typedef value_type signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef const value_type& argument_type;
+
+ static inline
+ base_type real(argument_type x);
+
+ static inline
+ base_type imag(argument_type x);
+
+ static inline
+ value_type conj(argument_type x);
+
+ static inline
+ base_type abs(argument_type x);
+
+ static inline
+ value_type sqrt(argument_type x);
+
+ static inline
+ base_type norm_1(argument_type x) {
+ return NumericTraits<base_type>::abs(traits_type::real(x))
+ + NumericTraits<base_type>::abs(traits_type::imag(x));
+ }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) {
+ return std::max(NumericTraits<base_type>::abs(traits_type::real(x)),
+ NumericTraits<base_type>::abs(traits_type::imag(x)));
+ }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ static base_type sqrt_epsilon(
+ NumericTraits<base_type>::sqrt(
+ std::numeric_limits<base_type>::epsilon()));
+
+ return traits_type::norm_inf(lhs - rhs) < sqrt_epsilon *
+ std::max(std::max(traits_type::norm_inf(lhs),
+ traits_type::norm_inf(rhs)),
+ std::numeric_limits<base_type>::min());
+ }
+};
+
+
+/*
+ * numeric traits for standard types
+ */
+
+
+/**
+ * \class NumericTraits<char> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for char.
+ */
+template<>
+struct NumericTraits<char> {
+ typedef char value_type;
+ typedef value_type base_type;
+ typedef long sum_type;
+ typedef int diff_type;
+ typedef float float_type;
+ typedef char signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ value_type conj(argument_type x) { return x; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) {
+ return static_cast<value_type>(std::sqrt(static_cast<float_type>(x)));
+ }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) { return lhs == rhs; }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<unsigned char> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for unsigned char.
+ *
+ * \note Normally it doesn't make sense to call <tt>conj</tt>
+ * for an unsigned type! An unary minus operator
+ * applied to unsigned type will result unsigned. Therefore
+ * this function is missing here.
+ */
+template<>
+struct NumericTraits<unsigned char> {
+ typedef unsigned char value_type;
+ typedef value_type base_type;
+ typedef unsigned long sum_type;
+ typedef int diff_type;
+ typedef float float_type;
+ typedef int signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) {
+ return static_cast<value_type>(std::sqrt(static_cast<float_type>(x)));
+ }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) { return lhs == rhs; }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<short int> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for short int.
+ */
+template<>
+struct NumericTraits<short int> {
+ typedef short int value_type;
+ typedef value_type base_type;
+#if defined(TVMET_HAVE_LONG_LONG)
+ typedef long long sum_type;
+#else
+ typedef long sum_type;
+#endif
+ typedef int diff_type;
+ typedef float float_type;
+ typedef short int signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ value_type conj(argument_type x) { return x; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) {
+ return static_cast<value_type>(std::sqrt(static_cast<float_type>(x)));
+ }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) { return lhs == rhs; }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<short unsigned int> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for short unsigned int.
+ *
+ * \note Normally it doesn't make sense to call <tt>conj</tt>
+ * for an unsigned type! An unary minus operator
+ * applied to unsigned type will result unsigned. Therefore
+ * this function is missing here.
+ */
+template<>
+struct NumericTraits<short unsigned int> {
+ typedef short unsigned int value_type;
+ typedef value_type base_type;
+#if defined(TVMET_HAVE_LONG_LONG)
+ typedef unsigned long long sum_type;
+#else
+ typedef unsigned long sum_type;
+#endif
+ typedef int diff_type;
+ typedef float float_type;
+ typedef int signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) {
+ return static_cast<value_type>(std::sqrt(static_cast<float_type>(x)));
+ }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) { return lhs == rhs; }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<int> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for int.
+ */
+template<>
+struct NumericTraits<int> {
+ typedef int value_type;
+ typedef value_type base_type;
+#if defined(TVMET_HAVE_LONG_LONG)
+ typedef long long sum_type;
+#else
+ typedef long sum_type;
+#endif
+ typedef int diff_type;
+ typedef double float_type;
+ typedef int signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ value_type conj(argument_type x) { return x; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) {
+ return static_cast<value_type>(std::sqrt(static_cast<float_type>(x)));
+ }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) { return lhs == rhs; }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<unsigned int> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for unsigned int.
+ *
+ * \note Normally it doesn't make sense to call <tt>conj</tt>
+ * for an unsigned type! An unary minus operator
+ * applied to unsigned type will result unsigned. Therefore
+ * this function is missing here.
+ */
+template<>
+struct NumericTraits<unsigned int> {
+ typedef unsigned int value_type;
+ typedef value_type base_type;
+#if defined(TVMET_HAVE_LONG_LONG)
+ typedef unsigned long long sum_type;
+#else
+ typedef unsigned long sum_type;
+#endif
+ typedef int diff_type;
+ typedef double float_type;
+ typedef long signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ base_type abs(argument_type x) { return x; }
+
+ static inline
+ value_type sqrt(argument_type x) {
+ return static_cast<value_type>(std::sqrt(static_cast<float_type>(x)));
+ }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) { return lhs == rhs; }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<long> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for long.
+ */
+template<>
+struct NumericTraits<long> {
+ typedef long value_type;
+ typedef value_type base_type;
+#if defined(TVMET_HAVE_LONG_LONG)
+ typedef long long sum_type;
+#else
+ typedef long sum_type;
+#endif
+ typedef long diff_type;
+ typedef double float_type;
+ typedef long signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ value_type conj(argument_type x) { return x; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) {
+ return static_cast<value_type>(std::sqrt(static_cast<float_type>(x)));
+ }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) { return lhs == rhs; }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<unsigned long> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for unsigned long.
+ *
+ * \note Normally it doesn't make sense to call <tt>conj</tt>
+ * for an unsigned type! An unary minus operator
+ * applied to unsigned type will result unsigned. Therefore
+ * this function is missing here.
+ */
+template<>
+struct NumericTraits<unsigned long> {
+ typedef unsigned long value_type;
+ typedef value_type base_type;
+#if defined(TVMET_HAVE_LONG_LONG)
+ typedef unsigned long long sum_type;
+#else
+ typedef unsigned long sum_type;
+#endif
+ typedef unsigned long diff_type;
+ typedef double float_type;
+ typedef long signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ base_type abs(argument_type x) { return x; }
+
+ static inline
+ value_type sqrt(argument_type x) {
+ return static_cast<value_type>(std::sqrt(static_cast<float_type>(x)));
+ }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) { return lhs == rhs; }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<float> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for float.
+ */
+template<>
+struct NumericTraits<float> {
+ typedef float value_type;
+ typedef value_type base_type;
+ typedef double sum_type;
+ typedef float diff_type;
+ typedef float float_type;
+ typedef float signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ value_type conj(argument_type x) { return x; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) { return std::sqrt(x); }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ static base_type sqrt_epsilon(
+ NumericTraits<base_type>::sqrt(
+ std::numeric_limits<base_type>::epsilon()));
+
+ return traits_type::norm_inf(lhs - rhs) < sqrt_epsilon *
+ std::max(std::max(traits_type::norm_inf(lhs),
+ traits_type::norm_inf(rhs)),
+ std::numeric_limits<base_type>::min());
+ }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits<double> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for double.
+ */
+template<>
+struct NumericTraits<double> {
+ typedef double value_type;
+ typedef value_type base_type;
+#if defined(TVMET_HAVE_LONG_DOUBLE)
+ typedef long double sum_type;
+#else
+ typedef double sum_type;
+#endif
+ typedef double diff_type;
+ typedef double float_type;
+ typedef double signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ value_type conj(argument_type x) { return x; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) { return std::sqrt(x); }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ static base_type sqrt_epsilon(
+ NumericTraits<base_type>::sqrt(
+ std::numeric_limits<base_type>::epsilon()));
+
+ return traits_type::norm_inf(lhs - rhs) < sqrt_epsilon *
+ std::max(std::max(traits_type::norm_inf(lhs),
+ traits_type::norm_inf(rhs)),
+ std::numeric_limits<base_type>::min());
+ }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+
+
+#if defined(TVMET_HAVE_LONG_DOUBLE)
+/**
+ * \class NumericTraits<long double> NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for long double.
+ */
+template<>
+struct NumericTraits<long double> {
+ typedef long double value_type;
+ typedef value_type base_type;
+ typedef long double sum_type;
+ typedef long double diff_type;
+ typedef long double float_type;
+ typedef long double signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef value_type argument_type;
+
+ static inline
+ base_type real(argument_type x) { return x; }
+
+ static inline
+ base_type imag(argument_type) { return 0; }
+
+ static inline
+ value_type conj(argument_type x) { return x; }
+
+ static inline
+ base_type abs(argument_type x) { return std::abs(x); }
+
+ static inline
+ value_type sqrt(argument_type x) { return std::sqrt(x); }
+
+ static inline
+ base_type norm_1(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_2(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ base_type norm_inf(argument_type x) { return traits_type::abs(x); }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ static base_type sqrt_epsilon(
+ NumericTraits<base_type>::sqrt(
+ std::numeric_limits<base_type>::epsilon()));
+
+ return traits_type::norm_inf(lhs - rhs) < sqrt_epsilon *
+ std::max(std::max(traits_type::norm_inf(lhs),
+ traits_type::norm_inf(rhs)),
+ std::numeric_limits<base_type>::min());
+ }
+
+ enum { is_complex = false };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 1, /**< Complexity on plus/minus ops. */
+ ops_muls = 1 /**< Complexity on multiplications. */
+ };
+};
+#endif // TVMET_HAVE_LONG_DOUBLE
+
+
+/*
+ * numeric traits for complex types
+ */
+#if defined(TVMET_HAVE_COMPLEX)
+
+/**
+ * \class NumericTraits< std::complex<int> > NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for std::complex<int>.
+ */
+template<>
+struct NumericTraits< std::complex<int> > {
+ typedef int base_type;
+ typedef std::complex<int> value_type;
+ typedef std::complex<long> sum_type;
+ typedef std::complex<int> diff_type;
+ typedef std::complex<float> float_type;
+ typedef std::complex<int> signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef const value_type& argument_type;
+
+ static inline
+ base_type real(argument_type z) { return std::real(z); }
+
+ static inline
+ base_type imag(argument_type z) { return std::imag(z); }
+
+ static inline
+ value_type conj(argument_type z) { return std::conj(z); }
+
+ static inline
+ base_type abs(argument_type z) {
+ base_type x = z.real();
+ base_type y = z.imag();
+
+ // XXX probably case of overrun; header complex uses scaling
+ return static_cast<base_type>(NumericTraits<base_type>::sqrt(x * x + y * y));
+ }
+
+ static /* inline */
+ value_type sqrt(argument_type z) {
+ // borrowed and adapted from header complex
+ base_type x = z.real();
+ base_type y = z.imag();
+
+ if(x == base_type()) {
+ base_type t = NumericTraits<base_type>::sqrt(
+ NumericTraits<base_type>::abs(y) / 2);
+ return value_type(t, y < base_type() ? -t : t);
+ }
+ else {
+ base_type t = NumericTraits<base_type>::sqrt(
+ 2 * (traits_type::abs(z)
+ + NumericTraits<base_type>::abs(x)));
+ base_type u = t / 2;
+ return x > base_type()
+ ? value_type(u, y / t)
+ : value_type(NumericTraits<base_type>::abs(y) / t, y < base_type() ? -u : u);
+ }
+ }
+
+ static inline
+ base_type norm_1(argument_type z) {
+ return NumericTraits<base_type>::abs((traits_type::real(z)))
+ + NumericTraits<base_type>::abs((traits_type::imag(z)));
+ }
+
+ static inline
+ base_type norm_2(argument_type z) { return traits_type::abs(z); }
+
+ static inline
+ base_type norm_inf(argument_type z) {
+ return std::max(NumericTraits<base_type>::abs(traits_type::real(z)),
+ NumericTraits<base_type>::abs(traits_type::imag(z)));
+ }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ return (traits_type::real(lhs) == traits_type::real(rhs))
+ && (traits_type::imag(lhs) == traits_type::imag(rhs));
+ }
+
+ enum { is_complex = true };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 2, /**< Complexity on plus/minus ops. */
+ ops_muls = 6 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits< std::complex<unsigned int> > NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for std::complex<unsigned int>.
+ *
+ * \note Normally it doesn't make sense to call <tt>conj</tt>
+ * for an unsigned type! An unary minus operator
+ * applied to unsigned type will result unsigned. Therefore
+ * this function is missing here.
+ */
+template<>
+struct NumericTraits< std::complex<unsigned int> > {
+ typedef unsigned int base_type;
+ typedef std::complex<unsigned int> value_type;
+ typedef std::complex<unsigned long> sum_type;
+ typedef std::complex<int> diff_type;
+ typedef std::complex<float> float_type;
+ typedef std::complex<int> signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef const value_type& argument_type;
+
+ static inline
+ base_type real(argument_type z) { return std::real(z); }
+
+ static inline
+ base_type imag(argument_type z) { return std::imag(z); }
+
+ static inline
+ base_type abs(argument_type z) {
+ base_type x = z.real();
+ base_type y = z.imag();
+
+ // XXX probably case of overrun; header complex uses scaling
+ return static_cast<base_type>(NumericTraits<base_type>::sqrt(x * x + y * y));
+ }
+
+ static /* inline */
+ value_type sqrt(argument_type z) {
+ // borrowed and adapted from header complex
+ base_type x = z.real();
+ base_type y = z.imag();
+
+ if(x == base_type()) {
+ base_type t = NumericTraits<base_type>::sqrt(
+ NumericTraits<base_type>::abs(y) / 2);
+ return value_type(t, t);
+ }
+ else {
+ base_type t = NumericTraits<base_type>::sqrt(
+ 2 * (traits_type::abs(z)
+ + NumericTraits<base_type>::abs(x)));
+ return value_type(t / 2, y / t);
+ }
+ }
+
+ static inline
+ base_type norm_1(argument_type z) {
+ return NumericTraits<base_type>::abs((traits_type::real(z)))
+ + NumericTraits<base_type>::abs((traits_type::imag(z)));
+ }
+
+ static inline
+ base_type norm_2(argument_type z) { return traits_type::abs(z); }
+
+ static inline
+ base_type norm_inf(argument_type z) {
+ return std::max(NumericTraits<base_type>::abs(traits_type::real(z)),
+ NumericTraits<base_type>::abs(traits_type::imag(z)));
+ }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ return (traits_type::real(lhs) == traits_type::real(rhs))
+ && (traits_type::imag(lhs) == traits_type::imag(rhs));
+ }
+
+ enum { is_complex = true };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 2, /**< Complexity on plus/minus ops. */
+ ops_muls = 6 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits< std::complex<long> > NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for std::complex<long>.
+ */
+template<>
+struct NumericTraits< std::complex<long> > {
+ typedef long base_type;
+ typedef std::complex<long> value_type;
+#if defined(TVMET_HAVE_LONG_LONG)
+ typedef std::complex<long long> sum_type;
+#else
+ typedef std::complex<long> sum_type;
+#endif
+ typedef std::complex<int> diff_type;
+ typedef std::complex<float> float_type;
+ typedef std::complex<int> signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef const value_type& argument_type;
+
+ static inline
+ base_type real(argument_type z) { return std::real(z); }
+
+ static inline
+ base_type imag(argument_type z) { return std::imag(z); }
+
+ static inline
+ value_type conj(argument_type z) { return std::conj(z); }
+
+ static inline
+ base_type abs(argument_type z) {
+ base_type x = z.real();
+ base_type y = z.imag();
+
+ // XXX probably case of overrun; header complex uses scaling
+ return static_cast<base_type>(NumericTraits<base_type>::sqrt(x * x + y * y));
+ }
+
+ static /* inline */
+ value_type sqrt(argument_type z) {
+ // borrowed and adapted from header complex
+ base_type x = z.real();
+ base_type y = z.imag();
+
+ if(x == base_type()) {
+ base_type t = NumericTraits<base_type>::sqrt(
+ NumericTraits<base_type>::abs(y) / 2);
+ return value_type(t, y < base_type() ? -t : t);
+ }
+ else {
+ base_type t = NumericTraits<base_type>::sqrt(
+ 2 * (traits_type::abs(z)
+ + NumericTraits<base_type>::abs(x)));
+ base_type u = t / 2;
+ return x > base_type()
+ ? value_type(u, y / t)
+ : value_type(NumericTraits<base_type>::abs(y) / t, y < base_type() ? -u : u);
+ }
+ }
+
+ static inline
+ base_type norm_1(argument_type z) {
+ return NumericTraits<base_type>::abs((traits_type::real(z)))
+ + NumericTraits<base_type>::abs((traits_type::imag(z)));
+ }
+
+ static inline
+ base_type norm_2(argument_type z) { return traits_type::abs(z); }
+
+ static inline
+ base_type norm_inf(argument_type z) {
+ return std::max(NumericTraits<base_type>::abs(traits_type::real(z)),
+ NumericTraits<base_type>::abs(traits_type::imag(z)));
+ }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ return (traits_type::real(lhs) == traits_type::real(rhs))
+ && (traits_type::imag(lhs) == traits_type::imag(rhs));
+ }
+
+ enum { is_complex = true };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 2, /**< Complexity on plus/minus ops. */
+ ops_muls = 6 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits< std::complex<unsigned long> > NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for std::complex<unsigned long>.
+ *
+ * \note Normally it doesn't make sense to call <tt>conj</tt>
+ * for an unsigned type! An unary minus operator
+ * applied to unsigned type will result unsigned. Therefore
+ * this function is missing here.
+ */
+template<>
+struct NumericTraits< std::complex<unsigned long> > {
+ typedef unsigned long base_type;
+ typedef std::complex<unsigned long> value_type;
+#if defined(TVMET_HAVE_LONG_LONG)
+ typedef std::complex<unsigned long long> sum_type;
+#else
+ typedef std::complex<unsigned long> sum_type;
+#endif
+ typedef std::complex<long> diff_type;
+ typedef std::complex<float> float_type;
+ typedef std::complex<long> signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef const value_type& argument_type;
+
+ static inline
+ base_type real(argument_type z) { return std::real(z); }
+
+ static inline
+ base_type imag(argument_type z) { return std::imag(z); }
+
+ static inline
+ base_type abs(argument_type z) {
+ base_type x = z.real();
+ base_type y = z.imag();
+
+ // XXX probably case of overrun; header complex uses scaling
+ return static_cast<base_type>(NumericTraits<base_type>::sqrt(x * x + y * y));
+ }
+
+ static /* inline */
+ value_type sqrt(argument_type z) {
+ // borrowed and adapted from header complex
+ base_type x = z.real();
+ base_type y = z.imag();
+
+ if(x == base_type()) {
+ base_type t = NumericTraits<base_type>::sqrt(
+ NumericTraits<base_type>::abs(y) / 2);
+ return value_type(t, t);
+ }
+ else {
+ base_type t = NumericTraits<base_type>::sqrt(
+ 2 * (traits_type::abs(z)
+ + NumericTraits<base_type>::abs(x)));
+ return value_type(t / 2, y / t);
+ }
+ }
+
+ static inline
+ base_type norm_1(argument_type z) {
+ return NumericTraits<base_type>::abs((traits_type::real(z)))
+ + NumericTraits<base_type>::abs((traits_type::imag(z)));
+ }
+
+ static inline
+ base_type norm_2(argument_type z) { return traits_type::abs(z); }
+
+ static inline
+ base_type norm_inf(argument_type z) {
+ return std::max(NumericTraits<base_type>::abs(traits_type::real(z)),
+ NumericTraits<base_type>::abs(traits_type::imag(z)));
+ }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ return (traits_type::real(lhs) == traits_type::real(rhs))
+ && (traits_type::imag(lhs) == traits_type::imag(rhs));
+ }
+
+ enum { is_complex = true };
+
+ /** Complexity on operations.*/
+ enum {
+ ops_plus = 2, /**< Complexity on plus/minus ops. */
+ ops_muls = 6 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits< std::complex<float> > NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for std::complex<float>.
+ */
+template<>
+struct NumericTraits< std::complex<float> > {
+ typedef float base_type;
+ typedef std::complex<float> value_type;
+ typedef std::complex<double> sum_type;
+ typedef std::complex<float> diff_type;
+ typedef std::complex<float> float_type;
+ typedef std::complex<float> signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef const value_type& argument_type;
+
+ static inline
+ base_type real(argument_type z) { return std::real(z); }
+
+ static inline
+ base_type imag(argument_type z) { return std::imag(z); }
+
+ static inline
+ value_type conj(argument_type z) { return std::conj(z); }
+
+ static inline
+ base_type abs(argument_type z) { return std::abs(z); }
+
+ static inline
+ value_type sqrt(argument_type z) { return std::sqrt(z); }
+
+ static inline
+ base_type norm_1(argument_type z) {
+ return NumericTraits<base_type>::abs((traits_type::real(z)))
+ + NumericTraits<base_type>::abs((traits_type::imag(z)));
+ }
+
+ static inline
+ base_type norm_2(argument_type z) { return traits_type::abs(z); }
+
+ static inline
+ base_type norm_inf(argument_type z) {
+ return std::max(NumericTraits<base_type>::abs(traits_type::real(z)),
+ NumericTraits<base_type>::abs(traits_type::imag(z)));
+ }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ static base_type sqrt_epsilon(
+ NumericTraits<base_type>::sqrt(
+ std::numeric_limits<base_type>::epsilon()));
+
+ return traits_type::norm_inf(lhs - rhs) < sqrt_epsilon *
+ std::max(std::max(traits_type::norm_inf(lhs),
+ traits_type::norm_inf(rhs)),
+ std::numeric_limits<base_type>::min());
+ }
+
+ enum { is_complex = true };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 2, /**< Complexity on plus/minus ops. */
+ ops_muls = 6 /**< Complexity on multiplications. */
+ };
+};
+
+
+/**
+ * \class NumericTraits< std::complex<double> > NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for std::complex<double>.
+ */
+template<>
+struct NumericTraits< std::complex<double> > {
+ typedef double base_type;
+ typedef std::complex<double> value_type;
+#if defined(TVMET_HAVE_LONG_DOUBLE)
+ typedef std::complex<long double> sum_type;
+#else
+ typedef std::complex<double> sum_type;
+#endif
+ typedef std::complex<double> diff_type;
+ typedef std::complex<double> float_type;
+ typedef std::complex<double> signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef const value_type& argument_type;
+
+ static inline
+ base_type real(argument_type z) { return std::real(z); }
+
+ static inline
+ base_type imag(argument_type z) { return std::imag(z); }
+
+ static inline
+ value_type conj(argument_type z) { return std::conj(z); }
+
+ static inline
+ base_type abs(argument_type z) { return std::abs(z); }
+
+ static inline
+ value_type sqrt(argument_type z) { return std::sqrt(z); }
+
+ static inline
+ base_type norm_1(argument_type z) {
+ return NumericTraits<base_type>::abs((traits_type::real(z)))
+ + NumericTraits<base_type>::abs((traits_type::imag(z)));
+ }
+
+ static inline
+ base_type norm_2(argument_type z) { return traits_type::abs(z); }
+
+ static inline
+ base_type norm_inf(argument_type z) {
+ return std::max(NumericTraits<base_type>::abs(traits_type::real(z)),
+ NumericTraits<base_type>::abs(traits_type::imag(z)));
+ }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ static base_type sqrt_epsilon(
+ NumericTraits<base_type>::sqrt(
+ std::numeric_limits<base_type>::epsilon()));
+
+ return traits_type::norm_inf(lhs - rhs) < sqrt_epsilon *
+ std::max(std::max(traits_type::norm_inf(lhs),
+ traits_type::norm_inf(rhs)),
+ std::numeric_limits<base_type>::min());
+ }
+
+ enum { is_complex = true };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 2, /**< Complexity on plus/minus ops. */
+ ops_muls = 6 /**< Complexity on multiplications. */
+ };
+};
+
+
+#if defined(TVMET_HAVE_LONG_DOUBLE)
+/**
+ * \class NumericTraits< std::complex<long double> > NumericTraits.h "tvmet/NumericTraits.h"
+ * \brief Traits specialized for std::complex<double>.
+ */
+template<>
+struct NumericTraits< std::complex<long double> > {
+ typedef long double base_type;
+ typedef std::complex<long double> value_type;
+ typedef std::complex<long double> sum_type;
+ typedef std::complex<long double> diff_type;
+ typedef std::complex<long double> float_type;
+ typedef std::complex<long double> signed_type;
+
+ typedef NumericTraits<value_type> traits_type;
+ typedef const value_type& argument_type;
+
+ static inline
+ base_type real(argument_type z) { return std::real(z); }
+
+ static inline
+ base_type imag(argument_type z) { return std::imag(z); }
+
+ static inline
+ value_type conj(argument_type z) { return std::conj(z); }
+
+ static inline
+ base_type abs(argument_type z) { return std::abs(z); }
+
+ static inline
+ value_type sqrt(argument_type z) { return std::sqrt(z); }
+
+ static inline
+ base_type norm_1(argument_type z) {
+ return NumericTraits<base_type>::abs((traits_type::real(z)))
+ + NumericTraits<base_type>::abs((traits_type::imag(z)));
+ }
+
+ static inline
+ base_type norm_2(argument_type z) { return traits_type::abs(z); }
+
+ static inline
+ base_type norm_inf(argument_type z) {
+ return std::max(NumericTraits<base_type>::abs(traits_type::real(z)),
+ NumericTraits<base_type>::abs(traits_type::imag(z)));
+ }
+
+ static inline
+ bool equals(argument_type lhs, argument_type rhs) {
+ static base_type sqrt_epsilon(
+ NumericTraits<base_type>::sqrt(
+ std::numeric_limits<base_type>::epsilon()));
+
+ return traits_type::norm_inf(lhs - rhs) < sqrt_epsilon *
+ std::max(std::max(traits_type::norm_inf(lhs),
+ traits_type::norm_inf(rhs)),
+ std::numeric_limits<base_type>::min());
+ }
+
+ enum { is_complex = true };
+
+ /** Complexity on operations. */
+ enum {
+ ops_plus = 2, /**< Complexity on plus/minus ops. */
+ ops_muls = 6 /**< Complexity on multiplications. */
+ };
+};
+#endif // defined(TVMET_HAVE_LONG_DOUBLE)
+
+
+#endif // defined(TVMET_HAVE_COMPLEX)
+
+
+} // namespace tvmet
+
+
+#endif // TVMET_NUMERIC_TRAITS_H
+
+
+// Local Variables:
+// mode:C++
+// tab-width:8
+// End: