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authorDaniel Wilhelm <shieldwed@outlook.com>2017-04-20 16:55:28 -0600
committerDaniel Wilhelm <shieldwed@outlook.com>2017-04-20 16:59:56 -0600
commit823740e1ffa2b3bd39f8dea8062f5c5a0d9c741b (patch)
tree63222010af3b90a36f29c1c9c360116973cdff38 /zen/basic_math.h
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normalize most lineendings
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-rwxr-xr-xzen/basic_math.h766
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diff --git a/zen/basic_math.h b/zen/basic_math.h
index 7836ae81..722722a5 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 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
+// *****************************************************************************
+// * 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
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