1 files changed, 383 insertions, 383 deletions
diff --git a/zen/basic_math.h b/zen/basic_math.h
index eed23477..7836ae81 100644..100755
--- a/zen/basic_math.h
+++ b/zen/basic_math.h
@@ -1,383 +1,383 @@
-// *****************************************************************************
-// * This file is part of the FreeFileSync project. It is distributed under    *
-// * GNU General Public License: http://www.gnu.org/licenses/gpl-3.0           *
-// * Copyright (C) Zenju (zenju AT freefilesync DOT org) - All Rights Reserved *
-// *****************************************************************************
-
-#ifndef BASIC_MATH_H_3472639843265675
-#define BASIC_MATH_H_3472639843265675
-
-#include <algorithm>
-#include <iterator>
-#include <limits>
-#include <cmath>
-#include <functional>
-#include <cassert>
-
-
-namespace numeric
-{
-template <class T> T abs(T value);
-template <class T> auto dist(T a, T b);
-template <class T> int sign(T value); //returns one of {-1, 0, 1}
-template <class T> T min(T a, T b, T c);
-template <class T> T max(T a, T b, T c);
-template <class T> bool isNull(T value);
-
-template <class T>
-void clamp(T& val, T minVal, T maxVal); //make sure minVal <= val && val <= maxVal
-template <class T>
-T clampCpy(T val, T minVal, T maxVal);
-
-template <class T, class InputIterator> //precondition: range must be sorted!
-auto nearMatch(const T& val, InputIterator first, InputIterator last);
-
-int round(double d); //"little rounding function"
-
-template <class N, class D>
-auto integerDivideRoundUp(N numerator, D denominator);
-
-template <size_t N, class T>
-T power(T value);
-
-double radToDeg(double rad);    //convert unit [rad] into [°]
-double degToRad(double degree); //convert unit [°] into [rad]
-
-template <class InputIterator>
-double arithmeticMean(InputIterator first, InputIterator last);
-
-template <class RandomAccessIterator>
-double median(RandomAccessIterator first, RandomAccessIterator last); //note: invalidates input range!
-
-template <class InputIterator>
-double stdDeviation(InputIterator first, InputIterator last, double* mean = nullptr); //estimate standard deviation (and thereby arithmetic mean)
-
-//median absolute deviation: "mad / 0.6745" is a robust measure for standard deviation of a normal distribution
-template <class RandomAccessIterator>
-double mad(RandomAccessIterator first, RandomAccessIterator last); //note: invalidates input range!
-
-template <class InputIterator>
-double norm2(InputIterator first, InputIterator last);
-
-//constants
-const double pi    = 3.14159265358979323846;
-const double e     = 2.71828182845904523536;
-const double sqrt2 = 1.41421356237309504880;
-const double ln2   = 0.693147180559945309417;
-//----------------------------------------------------------------------------------
-
-
-
-
-
-
-
-
-
-
-
-
-
-//################# inline implementation #########################
-template <class T> inline
-T abs(T value)
-{
-    //static_assert(std::is_signed<T>::value, "");
-    if (value < 0)
-        return -value; //operator "?:" caveat: may be different type than "value"
-    else
-        return value;
-}
-
-template <class T> inline
-auto dist(T a, T b) //return type might be different than T, e.g. std::chrono::duration instead of std::chrono::time_point
-{
-    return a > b ? a - b : b - a;
-}
-
-
-template <class T> inline
-int sign(T value) //returns one of {-1, 0, 1}
-{
-    static_assert(std::is_signed<T>::value, "");
-    return value < 0 ? -1 : (value > 0 ? 1 : 0);
-}
-
-
-template <class T> inline
-T min(T a, T b, T c) //don't follow std::min's "const T&(const T&, const T&)" API
-{
-    if (a < b)
-        return a < c ? a : c;
-    else
-        return b < c ? b : c;
-    //return std::min(std::min(a, b), c);
-}
-
-
-template <class T> inline
-T max(T a, T b, T c)
-{
-    if (a > b)
-        return a > c ? a : c;
-    else
-        return b > c ? b : c;
-    //return std::max(std::max(a, b), c);
-}
-
-
-template <class T> inline
-T clampCpy(T val, T minVal, T maxVal)
-{
-    assert(minVal <= maxVal);
-    if (val < minVal)
-        return minVal;
-    else if (val > maxVal)
-        return maxVal;
-    return val;
-}
-
-template <class T> inline
-void clamp(T& val, T minVal, T maxVal)
-{
-    assert(minVal <= maxVal);
-    if (val < minVal)
-        val = minVal;
-    else if (val > maxVal)
-        val = maxVal;
-}
-
-
-/*
-part of C++11 now!
-template <class InputIterator, class Compare> inline
-std::pair<InputIterator, InputIterator> minMaxElement(InputIterator first, InputIterator last, Compare compLess)
-{
-    //by factor 1.5 to 3 faster than boost::minmax_element (=two-step algorithm) for built-in types!
-
-    InputIterator lowest  = first;
-    InputIterator largest = first;
-
-    if (first != last)
-    {
-        auto minVal = *lowest;  //nice speedup on 64 bit!
-        auto maxVal = *largest; //
-        for (;;)
-        {
-            ++first;
-            if (first == last)
-                break;
-            const auto val = *first;
-
-            if (compLess(maxVal, val))
-            {
-                largest = first;
-                maxVal  = val;
-            }
-            else if (compLess(val, minVal))
-            {
-                lowest = first;
-                minVal = val;
-            }
-        }
-    }
-    return std::make_pair(lowest, largest);
-}
-
-
-template <class InputIterator> inline
-std::pair<InputIterator, InputIterator> minMaxElement(InputIterator first, InputIterator last)
-{
-    return minMaxElement(first, last, std::less<typename std::iterator_traits<InputIterator>::value_type>());
-}
-*/
-
-template <class T, class InputIterator> inline
-auto nearMatch(const T& val, InputIterator first, InputIterator last)
-{
-    if (first == last)
-        return static_cast<decltype(*first)>(0);
-
-    assert(std::is_sorted(first, last));
-    InputIterator it = std::lower_bound(first, last, val);
-    if (it == last)
-        return *--last;
-    if (it == first)
-        return *first;
-
-    const auto nextVal = *it;
-    const auto prevVal = *--it;
-    return val - prevVal < nextVal - val ? prevVal : nextVal;
-}
-
-
-template <class T> inline
-bool isNull(T value)
-{
-    return abs(value) <= std::numeric_limits<T>::epsilon(); //epsilon is 0 für integral types => less-equal
-}
-
-
-inline
-int round(double d)
-{
-    assert(d - 0.5 >= std::numeric_limits<int>::min() && //if double is larger than what int can represent:
-           d + 0.5 <= std::numeric_limits<int>::max());  //=> undefined behavior!
-    return static_cast<int>(d < 0 ? d - 0.5 : d + 0.5);
-}
-
-
-template <class N, class D> inline
-auto integerDivideRoundUp(N numerator, D denominator)
-{
-    static_assert(std::is_integral<N>::value && std::is_unsigned<N>::value, "");
-    static_assert(std::is_integral<D>::value && std::is_unsigned<D>::value, "");
-    assert(denominator > 0);
-    return (numerator + denominator - 1) / denominator;
-}
-
-
-namespace
-{
-template <size_t N, class T> struct PowerImpl;
-/*
-    template <size_t N, class T> -> let's use non-recursive specializations to help the compiler
-    struct PowerImpl { static T result(const T& value) { return PowerImpl<N - 1, T>::result(value) * value; } };
-*/
-template <class T> struct PowerImpl<2, T> { static T result(T value) { return value * value; } };
-template <class T> struct PowerImpl<3, T> { static T result(T value) { return value * value * value; } };
-}
-
-template <size_t n, class T> inline
-T power(T value)
-{
-    return PowerImpl<n, T>::result(value);
-}
-
-
-inline
-double radToDeg(double rad)
-{
-    return rad * 180.0 / numeric::pi;
-}
-
-
-inline
-double degToRad(double degree)
-{
-    return degree * numeric::pi / 180.0;
-}
-
-
-template <class InputIterator> inline
-double arithmeticMean(InputIterator first, InputIterator last)
-{
-    size_t n      = 0; //avoid random-access requirement for iterator!
-    double sum_xi = 0;
-
-    for (; first != last; ++first, ++n)
-        sum_xi += *first;
-
-    return n == 0 ? 0 : sum_xi / n;
-}
-
-
-template <class RandomAccessIterator> inline
-double median(RandomAccessIterator first, RandomAccessIterator last) //note: invalidates input range!
-{
-    const size_t n = last - first;
-    if (n > 0)
-    {
-        std::nth_element(first, first + n / 2, last); //complexity: O(n)
-        const double midVal = *(first + n / 2);
-
-        if (n % 2 != 0)
-            return midVal;
-        else //n is even and >= 2 in this context: return mean of two middle values
-            return 0.5 * (*std::max_element(first, first + n / 2) + midVal); //this operation is the reason why median() CANNOT support a comparison predicate!!!
-    }
-    return 0;
-}
-
-
-template <class RandomAccessIterator> inline
-double mad(RandomAccessIterator first, RandomAccessIterator last) //note: invalidates input range!
-{
-    //http://en.wikipedia.org/wiki/Median_absolute_deviation
-
-    const size_t n = last - first;
-    if (n > 0)
-    {
-        const double m = median(first, last);
-
-        //the second median needs to operate on absolute residuals => avoid transforming input range which may have less than double precision!
-
-        auto lessMedAbs = [m](double lhs, double rhs) { return abs(lhs - m) < abs(rhs - m); };
-
-        std::nth_element(first, first + n / 2, last, lessMedAbs); //complexity: O(n)
-        const double midVal = abs(*(first + n / 2) - m);
-
-        if (n % 2 != 0)
-            return midVal;
-        else //n is even and >= 2 in this context: return mean of two middle values
-            return 0.5 * (abs(*std::max_element(first, first + n / 2, lessMedAbs) - m) + midVal);
-    }
-    return 0;
-}
-
-
-template <class InputIterator> inline
-double stdDeviation(InputIterator first, InputIterator last, double* arithMean)
-{
-    //implementation minimizing rounding errors, see: http://en.wikipedia.org/wiki/Standard_deviation
-    //combined with techinque avoiding overflow, see: http://www.netlib.org/blas/dnrm2.f -> only 10% performance degradation
-
-    size_t n     = 0;
-    double mean  = 0;
-    double q     = 0;
-    double scale = 1;
-
-    for (; first != last; ++first)
-    {
-        ++n;
-        const double val = *first - mean;
-
-        if (abs(val) > scale)
-        {
-            q = (n - 1.0) / n + q * power<2>(scale / val);
-            scale = abs(val);
-        }
-        else
-            q += (n - 1.0) * power<2>(val / scale) / n;
-
-        mean += val / n;
-    }
-
-    if (arithMean)
-        *arithMean = mean;
-
-    return n <= 1 ? 0 : std::sqrt(q / (n - 1)) * scale;
-}
-
-
-template <class InputIterator> inline
-double norm2(InputIterator first, InputIterator last)
-{
-    double result = 0;
-    double scale  = 1;
-    for (; first != last; ++first)
-    {
-        const double tmp = abs(*first);
-        if (tmp > scale)
-        {
-            result = 1 + result * power<2>(scale / tmp);
-            scale = tmp;
-        }
-        else
-            result += power<2>(tmp / scale);
-    }
-    return std::sqrt(result) * scale;
-}
-}
-
-#endif //BASIC_MATH_H_3472639843265675
+// *****************************************************************************
+// * This file is part of the FreeFileSync project. It is distributed under    *
+// * GNU General Public License: http://www.gnu.org/licenses/gpl-3.0           *
+// * Copyright (C) Zenju (zenju AT freefilesync DOT org) - All Rights Reserved *
+// *****************************************************************************
+
+#ifndef BASIC_MATH_H_3472639843265675
+#define BASIC_MATH_H_3472639843265675
+
+#include <algorithm>
+#include <iterator>
+#include <limits>
+#include <cmath>
+#include <functional>
+#include <cassert>
+
+
+namespace numeric
+{
+template <class T> T abs(T value);
+template <class T> auto dist(T a, T b);
+template <class T> int sign(T value); //returns one of {-1, 0, 1}
+template <class T> T min(T a, T b, T c);
+template <class T> T max(T a, T b, T c);
+template <class T> bool isNull(T value);
+
+template <class T>
+void clamp(T& val, T minVal, T maxVal); //make sure minVal <= val && val <= maxVal
+template <class T>
+T clampCpy(T val, T minVal, T maxVal);
+
+template <class T, class InputIterator> //precondition: range must be sorted!
+auto nearMatch(const T& val, InputIterator first, InputIterator last);
+
+int round(double d); //"little rounding function"
+
+template <class N, class D>
+auto integerDivideRoundUp(N numerator, D denominator);
+
+template <size_t N, class T>
+T power(T value);
+
+double radToDeg(double rad);    //convert unit [rad] into [°]
+double degToRad(double degree); //convert unit [°] into [rad]
+
+template <class InputIterator>
+double arithmeticMean(InputIterator first, InputIterator last);
+
+template <class RandomAccessIterator>
+double median(RandomAccessIterator first, RandomAccessIterator last); //note: invalidates input range!
+
+template <class InputIterator>
+double stdDeviation(InputIterator first, InputIterator last, double* mean = nullptr); //estimate standard deviation (and thereby arithmetic mean)
+
+//median absolute deviation: "mad / 0.6745" is a robust measure for standard deviation of a normal distribution
+template <class RandomAccessIterator>
+double mad(RandomAccessIterator first, RandomAccessIterator last); //note: invalidates input range!
+
+template <class InputIterator>
+double norm2(InputIterator first, InputIterator last);
+
+//constants
+const double pi    = 3.14159265358979323846;
+const double e     = 2.71828182845904523536;
+const double sqrt2 = 1.41421356237309504880;
+const double ln2   = 0.693147180559945309417;
+//----------------------------------------------------------------------------------
+
+
+
+
+
+
+
+
+
+
+
+
+
+//################# inline implementation #########################
+template <class T> inline
+T abs(T value)
+{
+    //static_assert(std::is_signed<T>::value, "");
+    if (value < 0)
+        return -value; //operator "?:" caveat: may be different type than "value"
+    else
+        return value;
+}
+
+template <class T> inline
+auto dist(T a, T b) //return type might be different than T, e.g. std::chrono::duration instead of std::chrono::time_point
+{
+    return a > b ? a - b : b - a;
+}
+
+
+template <class T> inline
+int sign(T value) //returns one of {-1, 0, 1}
+{
+    static_assert(std::is_signed<T>::value, "");
+    return value < 0 ? -1 : (value > 0 ? 1 : 0);
+}
+
+
+template <class T> inline
+T min(T a, T b, T c) //don't follow std::min's "const T&(const T&, const T&)" API
+{
+    if (a < b)
+        return a < c ? a : c;
+    else
+        return b < c ? b : c;
+    //return std::min(std::min(a, b), c);
+}
+
+
+template <class T> inline
+T max(T a, T b, T c)
+{
+    if (a > b)
+        return a > c ? a : c;
+    else
+        return b > c ? b : c;
+    //return std::max(std::max(a, b), c);
+}
+
+
+template <class T> inline
+T clampCpy(T val, T minVal, T maxVal)
+{
+    assert(minVal <= maxVal);
+    if (val < minVal)
+        return minVal;
+    else if (val > maxVal)
+        return maxVal;
+    return val;
+}
+
+template <class T> inline
+void clamp(T& val, T minVal, T maxVal)
+{
+    assert(minVal <= maxVal);
+    if (val < minVal)
+        val = minVal;
+    else if (val > maxVal)
+        val = maxVal;
+}
+
+
+/*
+part of C++11 now!
+template <class InputIterator, class Compare> inline
+std::pair<InputIterator, InputIterator> minMaxElement(InputIterator first, InputIterator last, Compare compLess)
+{
+    //by factor 1.5 to 3 faster than boost::minmax_element (=two-step algorithm) for built-in types!
+
+    InputIterator lowest  = first;
+    InputIterator largest = first;
+
+    if (first != last)
+    {
+        auto minVal = *lowest;  //nice speedup on 64 bit!
+        auto maxVal = *largest; //
+        for (;;)
+        {
+            ++first;
+            if (first == last)
+                break;
+            const auto val = *first;
+
+            if (compLess(maxVal, val))
+            {
+                largest = first;
+                maxVal  = val;
+            }
+            else if (compLess(val, minVal))
+            {
+                lowest = first;
+                minVal = val;
+            }
+        }
+    }
+    return std::make_pair(lowest, largest);
+}
+
+
+template <class InputIterator> inline
+std::pair<InputIterator, InputIterator> minMaxElement(InputIterator first, InputIterator last)
+{
+    return minMaxElement(first, last, std::less<typename std::iterator_traits<InputIterator>::value_type>());
+}
+*/
+
+template <class T, class InputIterator> inline
+auto nearMatch(const T& val, InputIterator first, InputIterator last)
+{
+    if (first == last)
+        return static_cast<decltype(*first)>(0);
+
+    assert(std::is_sorted(first, last));
+    InputIterator it = std::lower_bound(first, last, val);
+    if (it == last)
+        return *--last;
+    if (it == first)
+        return *first;
+
+    const auto nextVal = *it;
+    const auto prevVal = *--it;
+    return val - prevVal < nextVal - val ? prevVal : nextVal;
+}
+
+
+template <class T> inline
+bool isNull(T value)
+{
+    return abs(value) <= std::numeric_limits<T>::epsilon(); //epsilon is 0 für integral types => less-equal
+}
+
+
+inline
+int round(double d)
+{
+    assert(d - 0.5 >= std::numeric_limits<int>::min() && //if double is larger than what int can represent:
+           d + 0.5 <= std::numeric_limits<int>::max());  //=> undefined behavior!
+    return static_cast<int>(d < 0 ? d - 0.5 : d + 0.5);
+}
+
+
+template <class N, class D> inline
+auto integerDivideRoundUp(N numerator, D denominator)
+{
+    static_assert(std::is_integral<N>::value && std::is_unsigned<N>::value, "");
+    static_assert(std::is_integral<D>::value && std::is_unsigned<D>::value, "");
+    assert(denominator > 0);
+    return (numerator + denominator - 1) / denominator;
+}
+
+
+namespace
+{
+template <size_t N, class T> struct PowerImpl;
+/*
+    template <size_t N, class T> -> let's use non-recursive specializations to help the compiler
+    struct PowerImpl { static T result(const T& value) { return PowerImpl<N - 1, T>::result(value) * value; } };
+*/
+template <class T> struct PowerImpl<2, T> { static T result(T value) { return value * value; } };
+template <class T> struct PowerImpl<3, T> { static T result(T value) { return value * value * value; } };
+}
+
+template <size_t n, class T> inline
+T power(T value)
+{
+    return PowerImpl<n, T>::result(value);
+}
+
+
+inline
+double radToDeg(double rad)
+{
+    return rad * 180.0 / numeric::pi;
+}
+
+
+inline
+double degToRad(double degree)
+{
+    return degree * numeric::pi / 180.0;
+}
+
+
+template <class InputIterator> inline
+double arithmeticMean(InputIterator first, InputIterator last)
+{
+    size_t n      = 0; //avoid random-access requirement for iterator!
+    double sum_xi = 0;
+
+    for (; first != last; ++first, ++n)
+        sum_xi += *first;
+
+    return n == 0 ? 0 : sum_xi / n;
+}
+
+
+template <class RandomAccessIterator> inline
+double median(RandomAccessIterator first, RandomAccessIterator last) //note: invalidates input range!
+{
+    const size_t n = last - first;
+    if (n > 0)
+    {
+        std::nth_element(first, first + n / 2, last); //complexity: O(n)
+        const double midVal = *(first + n / 2);
+
+        if (n % 2 != 0)
+            return midVal;
+        else //n is even and >= 2 in this context: return mean of two middle values
+            return 0.5 * (*std::max_element(first, first + n / 2) + midVal); //this operation is the reason why median() CANNOT support a comparison predicate!!!
+    }
+    return 0;
+}
+
+
+template <class RandomAccessIterator> inline
+double mad(RandomAccessIterator first, RandomAccessIterator last) //note: invalidates input range!
+{
+    //http://en.wikipedia.org/wiki/Median_absolute_deviation
+
+    const size_t n = last - first;
+    if (n > 0)
+    {
+        const double m = median(first, last);
+
+        //the second median needs to operate on absolute residuals => avoid transforming input range which may have less than double precision!
+
+        auto lessMedAbs = [m](double lhs, double rhs) { return abs(lhs - m) < abs(rhs - m); };
+
+        std::nth_element(first, first + n / 2, last, lessMedAbs); //complexity: O(n)
+        const double midVal = abs(*(first + n / 2) - m);
+
+        if (n % 2 != 0)
+            return midVal;
+        else //n is even and >= 2 in this context: return mean of two middle values
+            return 0.5 * (abs(*std::max_element(first, first + n / 2, lessMedAbs) - m) + midVal);
+    }
+    return 0;
+}
+
+
+template <class InputIterator> inline
+double stdDeviation(InputIterator first, InputIterator last, double* arithMean)
+{
+    //implementation minimizing rounding errors, see: http://en.wikipedia.org/wiki/Standard_deviation
+    //combined with technique avoiding overflow, see: http://www.netlib.org/blas/dnrm2.f -> only 10% performance degradation
+
+    size_t n     = 0;
+    double mean  = 0;
+    double q     = 0;
+    double scale = 1;
+
+    for (; first != last; ++first)
+    {
+        ++n;
+        const double val = *first - mean;
+
+        if (abs(val) > scale)
+        {
+            q = (n - 1.0) / n + q * power<2>(scale / val);
+            scale = abs(val);
+        }
+        else
+            q += (n - 1.0) * power<2>(val / scale) / n;
+
+        mean += val / n;
+    }
+
+    if (arithMean)
+        *arithMean = mean;
+
+    return n <= 1 ? 0 : std::sqrt(q / (n - 1)) * scale;
+}
+
+
+template <class InputIterator> inline
+double norm2(InputIterator first, InputIterator last)
+{
+    double result = 0;
+    double scale  = 1;
+    for (; first != last; ++first)
+    {
+        const double tmp = abs(*first);
+        if (tmp > scale)
+        {
+            result = 1 + result * power<2>(scale / tmp);
+            scale = tmp;
+        }
+        else
+            result += power<2>(tmp / scale);
+    }
+    return std::sqrt(result) * scale;
+}
+}
+
+#endif //BASIC_MATH_H_3472639843265675