mark more methods as const. also rename, Numeric.h->NumTraits.h

src/Core/NumTraits.h

@@ -0,0 +1,177 @@
+
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2006-2007 Benoit Jacob <jacob@math.jussieu.fr>
+//
+// Eigen is free software; you can redistribute it and/or modify it under the
+// terms of the GNU General Public License as published by the Free Software
+// Foundation; either version 2 or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+// details.
+//
+// You should have received a copy of the GNU General Public License along
+// with Eigen; if not, write to the Free Software Foundation, Inc., 51
+// Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
+//
+// As a special exception, if other files instantiate templates or use macros
+// or functions from this file, or you compile this file and link it
+// with other works to produce a work based on this file, this file does not
+// by itself cause the resulting work to be covered by the GNU General Public
+// License. This exception does not invalidate any other reasons why a work
+// based on this file might be covered by the GNU General Public License.
+
+#ifndef EI_NUMERIC_H
+#define EI_NUMERIC_H
+
+template<typename T> struct NumTraits;
+
+template<> struct NumTraits<int>
+{
+  typedef int Real;
+  typedef double FloatingPoint;
+  typedef double RealFloatingPoint;
+  
+  static const bool IsComplex = false;
+  static const bool HasFloatingPoint = false;
+  
+  static int precision() { return 0; }
+  static int real(const int& x) { return x; }
+  static int imag(const int& x) { EI_UNUSED(x); return 0; }
+  static int conj(const int& x) { return x; }
+  static double sqrt(const int& x) { return std::sqrt(static_cast<double>(x)); }
+  static int abs(const int& x) { return std::abs(x); }
+  static int abs2(const int& x) { return x*x; }
+  static int random()
+  {
+    // "random() % n" is bad, they say, because the low-order bits are not random enough.
+    // However here, 21 is odd, so random() % 21 uses the high-order bits
+    // as well, so there's no problem.
+    return (std::rand() % 21) - 10;
+  }
+  static bool isMuchSmallerThan(const int& a, const int& b, const int& prec = precision())
+  {
+    EI_UNUSED(b);
+    EI_UNUSED(prec);
+    return a == 0;
+  }
+  static bool isApprox(const int& a, const int& b, const int& prec = precision())
+  {
+    EI_UNUSED(prec);
+    return a == b;
+  }
+  static bool isApproxOrLessThan(const int& a, const int& b, const int& prec = precision())
+  {
+    EI_UNUSED(prec);
+    return a <= b;
+  }
+};
+
+template<> struct NumTraits<float>
+{
+  typedef float Real;
+  typedef float FloatingPoint;
+  typedef float RealFloatingPoint;
+  
+  static const bool IsComplex = false;
+  static const bool HasFloatingPoint = true;
+  
+  static float precision() { return 1e-5f; }
+  static float real(const float& x) { return x; }
+  static float imag(const float& x) { EI_UNUSED(x); return 0; }
+  static float conj(const float& x) { return x; }
+  static float sqrt(const float& x) { return std::sqrt(x); }
+  static float abs(const float& x) { return std::abs(x); }
+  static float abs2(const float& x) { return x*x; }
+  static float random()
+  {
+    return std::rand() / (RAND_MAX/20.0f) - 10.0f;
+  }
+  static bool isMuchSmallerThan(const float& a, const float& b, const float& prec = precision())
+  {
+    return abs(a) <= abs(b) * prec;
+  }
+  static bool isApprox(const float& a, const float& b, const float& prec = precision())
+  {
+    return abs(a - b) <= std::min(abs(a), abs(b)) * prec;
+  }
+  static bool isApproxOrLessThan(const float& a, const float& b, const float& prec = precision())
+  {
+    return a <= b || isApprox(a, b, prec);
+  }
+};
+
+template<> struct NumTraits<double>
+{
+  typedef double Real;
+  typedef double FloatingPoint;
+  typedef double RealFloatingPoint;
+  
+  static const bool IsComplex = false;
+  static const bool HasFloatingPoint = true;
+  
+  static double precision() { return 1e-11; }
+  static double real(const double& x) { return x; }
+  static double imag(const double& x) { EI_UNUSED(x); return 0; }
+  static double conj(const double& x) { return x; }
+  static double sqrt(const double& x) { return std::sqrt(x); }
+  static double abs(const double& x) { return std::abs(x); }
+  static double abs2(const double& x) { return x*x; }
+  static double random()
+  {
+    return std::rand() / (RAND_MAX/20.0) - 10.0;
+  }
+  static bool isMuchSmallerThan(const double& a, const double& b, const double& prec = precision())
+  {
+    return abs(a) <= abs(b) * prec;
+  }
+  static bool isApprox(const double& a, const double& b, const double& prec = precision())
+  {
+    return abs(a - b) <= std::min(abs(a), abs(b)) * prec;
+  }
+  static bool isApproxOrLessThan(const double& a, const double& b, const double& prec = precision())
+  {
+    return a <= b || isApprox(a, b, prec);
+  }
+};
+
+template<typename _Real> struct NumTraits<std::complex<_Real> >
+{
+  typedef _Real Real;
+  typedef std::complex<Real> Complex;
+  typedef std::complex<double> FloatingPoint;
+  typedef typename NumTraits<Real>::FloatingPoint RealFloatingPoint;
+  
+  static const bool IsComplex = true;
+  static const bool HasFloatingPoint = NumTraits<Real>::HasFloatingPoint;
+  
+  static Real precision() { return NumTraits<Real>::precision(); }
+  static Real real(const Complex& x) { return std::real(x); }
+  static Real imag(const Complex& x) { return std::imag(x); }
+  static Complex conj(const Complex& x) { return std::conj(x); }
+  static FloatingPoint sqrt(const Complex& x)
+  { return std::sqrt(static_cast<FloatingPoint>(x)); }
+  static RealFloatingPoint abs(const Complex& x)
+  { return std::abs(static_cast<FloatingPoint>(x)); }
+  static Real abs2(const Complex& x)
+  { return std::real(x) * std::real(x) + std::imag(x) * std::imag(x); }
+  static Complex random()
+  {
+    return Complex(NumTraits<Real>::random(), NumTraits<Real>::random());
+  }
+  static bool isMuchSmallerThan(const Complex& a, const Complex& b, const Real& prec = precision())
+  {
+    return abs2(a) <= abs2(b) * prec * prec;
+  }
+  static bool isApprox(const Complex& a, const Complex& b, const Real& prec = precision())
+  {
+    return NumTraits<Real>::isApprox(std::real(a), std::real(b), prec)
+        && NumTraits<Real>::isApprox(std::imag(a), std::imag(b), prec);
+  }
+  // isApproxOrLessThan wouldn't make sense for complex numbers
+};
+
+#endif // EI_NUMERIC_H