TMathBase.h

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// @(#)root/base:
// Authors: Rene Brun, Fons Rademakers   29/07/95
 
/*************************************************************************
 * Copyright (C) 1995-2004, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
#ifndef ROOT_TMathBase
#define ROOT_TMathBase
 
 
//////////////////////////////////////////////////////////////////////////
//                                                                      //
// TMath Base functions                                                 //
//                                                                      //
// Define the functions Min, Max, Abs, Sign, Range for all types.       //
// NB: These functions are unfortunately not available in a portable    //
// way in std::.                                                        //
//                                                                      //
// More functions are defined in TMath.h. TMathBase.h is designed to be //
// a stable file and used in place of TMath.h in the ROOT miniCore.     //
//                                                                      //
//////////////////////////////////////////////////////////////////////////
 
#include "RtypesCore.h"
 
#include <cstdlib>
#include <cmath>
#include <algorithm>
 
namespace TMath {
 
   // Abs
   inline Short_t  Abs(Short_t d);
   inline Int_t    Abs(Int_t d);
   inline Long_t   Abs(Long_t d);
   inline Long64_t Abs(Long64_t d);
   inline Float_t  Abs(Float_t d);
   inline Double_t Abs(Double_t d);
   inline LongDouble_t Abs(LongDouble_t d);
 
   // Even/Odd
   inline Bool_t   Even(Long_t a);
   inline Bool_t   Odd(Long_t a);
 
   // SignBit
   template<typename Integer>
   inline Bool_t SignBit(Integer a);
   inline Bool_t SignBit(Float_t a);
   inline Bool_t SignBit(Double_t a);
   inline Bool_t SignBit(LongDouble_t a);
 
   // Sign
   template<typename T1, typename T2>
   inline T1 Sign( T1 a, T2 b);
   inline Float_t  Sign(Float_t a, Float_t b);
   inline Double_t Sign(Double_t a, Double_t b);
   inline LongDouble_t Sign(LongDouble_t a, LongDouble_t b);
 
   // Min, Max of two scalars
   inline Short_t   Min(Short_t a, Short_t b);
   inline UShort_t  Min(UShort_t a, UShort_t b);
   inline Int_t     Min(Int_t a, Int_t b);
   inline UInt_t    Min(UInt_t a, UInt_t b);
   inline Long_t    Min(Long_t a, Long_t b);
   inline ULong_t   Min(ULong_t a, ULong_t b);
   inline Long64_t  Min(Long64_t a, Long64_t b);
   inline ULong64_t Min(ULong64_t a, ULong64_t b);
   inline Float_t   Min(Float_t a, Float_t b);
   inline Double_t  Min(Double_t a, Double_t b);
 
   inline Short_t   Max(Short_t a, Short_t b);
   inline UShort_t  Max(UShort_t a, UShort_t b);
   inline Int_t     Max(Int_t a, Int_t b);
   inline UInt_t    Max(UInt_t a, UInt_t b);
   inline Long_t    Max(Long_t a, Long_t b);
   inline ULong_t   Max(ULong_t a, ULong_t b);
   inline Long64_t  Max(Long64_t a, Long64_t b);
   inline ULong64_t Max(ULong64_t a, ULong64_t b);
   inline Float_t   Max(Float_t a, Float_t b);
   inline Double_t  Max(Double_t a, Double_t b);
 
   // Range
   inline Short_t   Range(Short_t lb, Short_t ub, Short_t x);
   inline Int_t     Range(Int_t lb, Int_t ub, Int_t x);
   inline Long_t    Range(Long_t lb, Long_t ub, Long_t x);
   inline ULong_t   Range(ULong_t lb, ULong_t ub, ULong_t x);
   inline Double_t  Range(Double_t lb, Double_t ub, Double_t x);
 
   //NextPrime is used by the Core classes.
   Long_t   NextPrime(Long_t x);   // Least prime number greater than x
 
   // Binary search
   template <typename T> Long64_t BinarySearch(Long64_t n, const T  *array, T value);
   template <typename T> Long64_t BinarySearch(Long64_t n, const T **array, T value);
   template <typename Iterator, typename Element> Iterator BinarySearch(Iterator first, Iterator last, Element value)
       R__DEPRECATED(6,40, "Undefined behavior in case \"value\" is smaller than the first element. Use STL algorithms instead, e.g. std::lower_bound(v.rbegin(), v.rend(), value, std::greater{}).");
 
   // Sorting
   template <typename Element, typename Index>
   void Sort(Index n, const Element* a, Index* index, Bool_t down=kTRUE);
   template <typename Iterator, typename IndexIterator>
   void SortItr(Iterator first, Iterator last, IndexIterator index, Bool_t down=kTRUE);
}
 
 
//---- Even/odd ----------------------------------------------------------------
 
/// Returns `true` if `a` is even.
inline Bool_t TMath::Even(Long_t a)
   { return ! (a & 1); }
 
/// Returns `true` if `a` is odd.
inline Bool_t TMath::Odd(Long_t a)
   { return (a & 1); }
 
//---- Abs ---------------------------------------------------------------------
 
/// Returns the absolute value of parameter `Short_t d`.
inline Short_t TMath::Abs(Short_t d)
{ return (d >= 0) ? d : Short_t(-d);  }
 
/// Returns the absolute value of parameter `Int_t d`.
inline Int_t TMath::Abs(Int_t d)
{ return std::abs(d); }
 
/// Returns the absolute value of parameter `Long_t d`.
inline Long_t TMath::Abs(Long_t d)
{ return std::labs(d); }
 
/// Returns the absolute value of parameter `Long64_t d`.
inline Long64_t TMath::Abs(Long64_t d)
{ return std::llabs(d); }
 
/// Returns the absolute value of parameter `Float_t d`.
inline Float_t TMath::Abs(Float_t d)
{ return std::abs(d); }
 
/// Returns the absolute value of parameter `Double_t d`.
inline Double_t TMath::Abs(Double_t d)
{ return std::abs(d); }
 
/// Returns the absolute value of parameter `LongDouble_t d`.
inline LongDouble_t TMath::Abs(LongDouble_t d)
{ return std::abs(d); }
 
 
//---- Sign Bit--------------------------------------------------------------------
 
/// Returns whether the sign of `Integer a` is negative.
template<typename Integer>
inline Bool_t TMath::SignBit( Integer a)
   { return (a < 0); }
 
/// Returns whether the sign of `Float_t a` is negative.
inline Bool_t TMath::SignBit(Float_t a)
   { return std::signbit(a);  }
 
/// Returns whether the sign of `Double_t a` is negative.
inline Bool_t TMath::SignBit(Double_t a)
   { return std::signbit(a);  }
 
/// Returns whether the sign of `LongDouble_t a` is negative.
inline Bool_t TMath::SignBit(LongDouble_t a)
   { return std::signbit(a);  }
 
 
//---- Sign --------------------------------------------------------------------
 
/// Returns a value with the magnitude of `a` and the sign of `b`.
template<typename T1, typename T2>
inline T1 TMath::Sign( T1 a, T2 b)
   { return (SignBit(b)) ? - Abs(a) : Abs(a); }
 
/// Returns a value with the magnitude of `a` and the sign of `b`.
/// `a`and `b` are `Short_t`.
inline Float_t TMath::Sign(Float_t a, Float_t b)
   { return std::copysign(a,b);  }
 
/// Returns a value with the magnitude of `a` and the sign of `b`.
/// `a`and `b` are `Double_t`.
inline Double_t TMath::Sign(Double_t a, Double_t b)
   { return std::copysign(a,b);  }
 
/// Returns a value with the magnitude of `a` and the sign of `b`.
/// `a`and `b` are `LongDouble_t`.
inline LongDouble_t TMath::Sign(LongDouble_t a, LongDouble_t b)
   { return std::copysign(a,b);  }
 
 
//---- Min ---------------------------------------------------------------------
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Short_t`.
inline Short_t TMath::Min(Short_t a, Short_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `UShort_t`.
inline UShort_t TMath::Min(UShort_t a, UShort_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Int_t`.
inline Int_t TMath::Min(Int_t a, Int_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Short_t`.
inline UInt_t TMath::Min(UInt_t a, UInt_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Long_t`.
inline Long_t TMath::Min(Long_t a, Long_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `ULong_t`.
inline ULong_t TMath::Min(ULong_t a, ULong_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Long64_t`.
inline Long64_t TMath::Min(Long64_t a, Long64_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `ULong64_t`.
inline ULong64_t TMath::Min(ULong64_t a, ULong64_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Float_t`.
inline Float_t TMath::Min(Float_t a, Float_t b)
   { return a <= b ? a : b; }
 
/// Returns the smallest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Double_t`.
inline Double_t TMath::Min(Double_t a, Double_t b)
   { return a <= b ? a : b; }
 
//---- Max ---------------------------------------------------------------------
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Short_t`.
inline Short_t TMath::Max(Short_t a, Short_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `UShort_t`.
inline UShort_t TMath::Max(UShort_t a, UShort_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Int_t`.
inline Int_t TMath::Max(Int_t a, Int_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `UInt_t`.
inline UInt_t TMath::Max(UInt_t a, UInt_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Long_t`.
inline Long_t TMath::Max(Long_t a, Long_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `ULong_t`.
inline ULong_t TMath::Max(ULong_t a, ULong_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Long64_t`.
inline Long64_t TMath::Max(Long64_t a, Long64_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `ULong64_t`.
inline ULong64_t TMath::Max(ULong64_t a, ULong64_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Float_t`.
inline Float_t TMath::Max(Float_t a, Float_t b)
   { return a >= b ? a : b; }
 
/// Returns the largest of `a` and `b`. If both are equivalent, `a` is returned.
/// `a`and `b` are `Double_t`.
inline Double_t TMath::Max(Double_t a, Double_t b)
   { return a >= b ? a : b; }
 
//---- Range -------------------------------------------------------------------
 
/// Returns `x` if `lb < x < up`, `lb` if `x < lb` and `ub` if `x > ub`.
/// `lb`, `ub` and `x` are `Short_t`.
inline Short_t TMath::Range(Short_t lb, Short_t ub, Short_t x)
   { return x < lb ? lb : (x > ub ? ub : x); }
 
/// Returns `x` if `lb < x < up`, `lb` if `x < lb` and `ub` if `x > ub`.
/// `lb`, `ub` and `x` are `Int_t`.
inline Int_t TMath::Range(Int_t lb, Int_t ub, Int_t x)
   { return x < lb ? lb : (x > ub ? ub : x); }
 
/// Returns `x` if `lb < x < up`, `lb` if `x < lb` and `ub` if `x > ub`.
/// `lb`, `ub` and `x` are `Long_t`.
inline Long_t TMath::Range(Long_t lb, Long_t ub, Long_t x)
   { return x < lb ? lb : (x > ub ? ub : x); }
 
/// Returns `x` if `lb < x < up`, `lb` if `x < lb` and `ub` if `x > ub`.
/// `lb`, `ub` and `x` are `ULong_t`.
inline ULong_t TMath::Range(ULong_t lb, ULong_t ub, ULong_t x)
   { return x < lb ? lb : (x > ub ? ub : x); }
 
/// Returns `x` if `lb < x < up`, `lb` if `x < lb` and `ub` if `x > ub`.
/// `lb`, `ub` and `x` are `Double_t`.
inline Double_t TMath::Range(Double_t lb, Double_t ub, Double_t x)
   { return x < lb ? lb : (x > ub ? ub : x); }
 
/// Binary search in an array defined by its iterators.
///
/// The values in the iterators range are supposed to be sorted
/// prior to this call.  If match is found, function returns
/// position of element.  If no match found, function gives nearest
/// element smaller than value.
template <typename Iterator, typename Element>
Iterator TMath::BinarySearch(Iterator first, Iterator last, Element value)
{
   Iterator pind;
   pind = std::lower_bound(first, last, value);
   if ( (pind != last) && (*pind == value) )
      return pind;
   else
      return ( pind - 1);
}
 
/// Binary search in an array of n values to locate value.
///
/// Array is supposed  to be sorted prior to this call.
/// If match is found, function returns position of element.
/// If no match found, function gives nearest element smaller than value.
template <typename T> Long64_t TMath::BinarySearch(Long64_t n, const T  *array, T value)
{
   const T* pind;
   pind = std::lower_bound(array, array + n, value);
   if ( (pind != array + n) && (*pind == value) )
      return (pind - array);
   else
      return ( pind - array - 1);
}
 
/// Binary search in an array of n values to locate value.
///
/// Array is supposed  to be sorted prior to this call.
/// If match is found, function returns position of element.
/// If no match found, function gives nearest element smaller than value.
template <typename T> Long64_t TMath::BinarySearch(Long64_t n, const T **array, T value)
{
   const T* pind;
   pind = std::lower_bound(*array, *array + n, value);
   if ( (pind != *array + n) && (*pind == value) )
      return (pind - *array);
   else
      return ( pind - *array - 1);
}
 
template<typename T>
struct CompareDesc {
 
   CompareDesc(T d) : fData(d) {}
 
   template<typename Index>
   bool operator()(Index i1, Index i2) {
      return *(fData + i1) > *(fData + i2);
   }
 
   T fData;
};
 
template<typename T>
struct CompareAsc {
 
   CompareAsc(T d) : fData(d) {}
 
   template<typename Index>
   bool operator()(Index i1, Index i2) {
      return *(fData + i1) < *(fData + i2);
   }
 
   T fData;
};
 
/// Sort the n1 elements of the Short_t array defined by its
/// iterators.  In output the array index contains the indices of
/// the sorted array.  If down is false sort in increasing order
/// (default is decreasing order).
///
/// NOTE that the array index must be created with a length bigger
/// or equal than the main array before calling this function.
template <typename Iterator, typename IndexIterator>
void TMath::SortItr(Iterator first, Iterator last, IndexIterator index, Bool_t down)
{
   int i = 0;
 
   IndexIterator cindex = index;
   for ( Iterator cfirst = first; cfirst != last; ++cfirst )
   {
      *cindex = i++;
      ++cindex;
   }
 
   if ( down )
      std::sort(index, cindex, CompareDesc<Iterator>(first) );
   else
      std::sort(index, cindex, CompareAsc<Iterator>(first) );
}
 
/// Sort the n elements of the  array a of generic templated type Element.
/// In output the array index of type Index contains the indices of the sorted array.
/// If down is false sort in increasing order (default is decreasing order).
///
/// NOTE that the array index must be created with a length >= n
/// before calling this function.
/// NOTE also that the size type for n must be the same type used for the index array
/// (templated type Index)
template <typename Element, typename Index> void TMath::Sort(Index n, const Element* a, Index* index, Bool_t down)
{
   for(Index i = 0; i < n; i++) { index[i] = i; }
   if ( down )
      std::sort(index, index + n, CompareDesc<const Element*>(a) );
   else
      std::sort(index, index + n, CompareAsc<const Element*>(a) );
}
 
#endif