/* NUM.cpp
 *
 * Copyright (C) 1992-2021,2023,2024 Paul Boersma
 *
 * This code 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 of the License, or (at
 * your option) any later version.
 *
 * This code 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 this work. If not, see <http://www.gnu.org/licenses/>.
 */

#include "melder.h"

/*
	Local functions.
*/

static longdouble NUMsum_longdouble (constVECVU const& vec) {
	/*
		This function started to crash on October 27, 2020.
		The cause was that if `vec.firstCell == nullptr`,
		`& vec [1]` is a "null reference" (see the definition of constvectorview::operator[]).
		This causes "undefined behaviour", even if `p` is never read from that address
		(which it isn't, because if `vec.firstCell == nullptr`, then `vec.size` must be 0).
		What precisely happened was that although `vec.size` was null,
		the processor would branch-predict into the `if (_n & 1)` branch of PAIRWISE_SUM,
		thereby pre-fetching `p` from the address `& vec [1]`,
		which would lead to a Bad Access exception.

		A possible repair is to use a pointer instead of a reference.
	*/
	if (vec.stride == 1) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			//const double *p = & vec [1],   // valid C++ only if vec is well-defined
			const double *p = & vec. firstCell [1 - 1],   // null *pointers* are fine
			longdouble (*p),
			p += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			//const double *p = & vec [1],   // valid C++ only if vec is well-defined
			const double *p = & vec. firstCell [1 - 1],   // null *pointers* are fine
			longdouble (*p),
			p += vec.stride
		)
		return sum;
	}
}
static longdouble NUMsum_longdouble (constMATVU const& mat) {
	if (mat.nrow <= mat.ncol) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, mat.nrow,
			integer irow = 1,
			NUMsum_longdouble (mat [irow]),
			irow += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, mat.ncol,
			integer icol = 1,
			NUMsum_longdouble (mat.column (icol)),
			icol += 1
		)
		return sum;
	}
}
static longdouble NUMsumOfSquaredDifferences_longdouble (constVECVU const& vec, const double mean) {
	if (vec.stride == 1) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			const double *p = vec. firstCell,
			longdouble (*p - mean) * longdouble (*p - mean),
			p += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			const double *p = vec. firstCell,
			longdouble (*p - mean) * longdouble (*p - mean),
			p += vec.stride
		)
		return sum;
	}
}
static longdouble NUMsum2_longdouble (constVECVU const& vec) {
	if (vec.stride == 1) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			const double *p = vec. firstCell,
			longdouble (*p) * longdouble (*p),
			p += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			const double *p = vec. firstCell,
			longdouble (*p) * longdouble (*p),
			p += vec.stride
		)
		return sum;
	}
}
static longdouble NUMsum2_longdouble (constMATVU const& mat) {
	if (mat.nrow <= mat.ncol) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, mat.nrow,
			integer irow = 1,
			NUMsum2_longdouble (mat [irow]),
			irow += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, mat.ncol,
			integer icol = 1,
			NUMsum2_longdouble (mat.column (icol)),
			icol += 1
		)
		return sum;
	}
}
static longdouble NUMsumAbs_longdouble (constVECVU const& vec) {
	if (vec.stride == 1) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			const double *p = vec. firstCell,
			longdouble (fabs (*p)),
			p += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			const double *p = vec. firstCell,
			longdouble (fabs (*p)),
			p += vec.stride
		)
		return sum;
	}
}
static longdouble NUMsumAbs_longdouble (constMATVU const& mat) {
	if (mat.nrow <= mat.ncol) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, mat.nrow,
			integer irow = 1,
			NUMsumAbs_longdouble (mat [irow]),
			irow += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, mat.ncol,
			integer icol = 1,
			NUMsumAbs_longdouble (mat.column (icol)),
			icol += 1
		)
		return sum;
	}
}
static longdouble NUMsumPower_longdouble (constVECVU const& vec, const longdouble power) {
	if (vec.stride == 1) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			const double *p = vec. firstCell,
			powl (longdouble (fabs (*p)), power),
			p += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, vec.size,
			const double *p = vec. firstCell,
			powl (longdouble (fabs (*p)), power),
			p += vec.stride
		)
		return sum;
	}
}
static longdouble NUMsumPower_longdouble (constMATVU const& mat, const longdouble power) {
	if (mat.nrow <= mat.ncol) {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, mat.nrow,
			integer irow = 1,
			NUMsumPower_longdouble (mat [irow], power),
			irow += 1
		)
		return sum;
	} else {
		PAIRWISE_SUM (
			longdouble, sum,
			integer, mat.ncol,
			integer icol = 1,
			NUMsumPower_longdouble (mat.column (icol), power),
			icol += 1
		)
		return sum;
	}
}

struct MelderMeanSumsq_longdouble {
	longdouble mean, sumsq;
};

static MelderMeanSumsq_longdouble NUMmeanSumsq (constVECVU const& vec) noexcept {
	MelderMeanSumsq_longdouble result;
	result.mean = NUMsum_longdouble (vec) / vec.size;
	const double mean = double (result.mean);
	if (vec.stride == 1) {
		PAIRWISE_SUM (longdouble, sumsq, integer, vec.size,
			const double *p = vec. firstCell,
			longdouble (*p - mean) * longdouble (*p - mean),
			p += 1
		)
		result.sumsq = sumsq;
	} else {
		PAIRWISE_SUM (longdouble, sumsq, integer, vec.size,
			const double *p = vec. firstCell,
			longdouble (*p - mean) * longdouble (*p - mean),
			p += vec.stride
		)
		result.sumsq = sumsq;
	}
	return result;
}
static MelderMeanSumsq_longdouble NUMmeanSumsq (constMATVU const& mat) noexcept {
	MelderMeanSumsq_longdouble result;
	result.mean = NUMsum_longdouble (mat) / (mat.nrow * mat.ncol);
	const double mean = double (result.mean);
	if (mat.nrow <= mat.ncol) {
		PAIRWISE_SUM (longdouble, sumsq, integer, mat.nrow,
			integer irow = 1,
			NUMsumOfSquaredDifferences_longdouble (mat [irow], mean),
			irow += 1
		)
		result.sumsq = sumsq;
	} else {
		PAIRWISE_SUM (longdouble, sumsq, integer, mat.ncol,
			integer icol = 1,
			NUMsumOfSquaredDifferences_longdouble (mat.column (icol), mean),
			icol += 1
		)
		result.sumsq = sumsq;
	}
	return result;
}

/*
	Global functions in alphabetic order.
*/

double NUMcenterOfGravity (constVECVU const& x) noexcept {
	longdouble weightedSumOfIndexes = 0.0, sumOfWeights = 0.0;
	for (integer i = 1; i <= x.size; i ++) {
		weightedSumOfIndexes += i * x [i];
		sumOfWeights += x [i];
	}
	return double (weightedSumOfIndexes / sumOfWeights);
}

double NUMinner (constVECVU const& x, constVECVU const& y) noexcept {
	if (x.stride == 1) {
		if (y.stride == 1) {
			PAIRWISE_SUM (longdouble, sum, integer, x.size,
				const double *px = x. firstCell;
				const double *py = y. firstCell,
				longdouble (*px) * longdouble (*py),
				(px += 1, py += 1)
			)
			return double (sum);
		} else {
			PAIRWISE_SUM (longdouble, sum, integer, x.size,
				const double *px = x. firstCell;
				const double *py = y. firstCell,
				longdouble (*px) * longdouble (*py),
				(px += 1, py += y.stride)
			)
			return double (sum);
		}
	} else if (y.stride == 1) {
		PAIRWISE_SUM (longdouble, sum, integer, x.size,
			const double *px = x. firstCell;
			const double *py = y. firstCell,
			longdouble (*px) * longdouble (*py),
			(px += x.stride, py += 1)
		)
		return double (sum);
	} else {
		PAIRWISE_SUM (longdouble, sum, integer, x.size,
			const double *px = x. firstCell;
			const double *py = y. firstCell,
			longdouble (*px) * longdouble (*py),
			(px += x.stride, py += y.stride)
		)
		return double (sum);
	}
}

static longdouble NUMinnerMinusMean_longdouble (constVECVU const& x, const longdouble meanX, constVECVU const& y, const longdouble meanY) noexcept {
	if (x.stride == 1) {
		if (y.stride == 1) {
			PAIRWISE_SUM (longdouble, sum, integer, x.size,
				const double *px = x. firstCell;
				const double *py = y. firstCell,
				(longdouble (*px) - meanX) * (longdouble (*py) - meanY),
				(px += 1, py += 1)
			)
			return sum;
		} else {
			PAIRWISE_SUM (longdouble, sum, integer, x.size,
				const double *px = x. firstCell;
				const double *py = y. firstCell,
				(longdouble (*px) - meanX) * (longdouble (*py) - meanY),
				(px += 1, py += y.stride)
			)
			return sum;
		}
	} else if (y.stride == 1) {
		PAIRWISE_SUM (longdouble, sum, integer, x.size,
			const double *px = x. firstCell;
			const double *py = y. firstCell,
			(longdouble (*px) - meanX) * (longdouble (*py) - meanY),
			(px += x.stride, py += 1)
		)
		return sum;
	} else {
		PAIRWISE_SUM (longdouble, sum, integer, x.size,
			const double *px = x. firstCell;
			const double *py = y. firstCell,
			(longdouble (*px) - meanX) * (longdouble (*py) - meanY),
			(px += x.stride, py += y.stride)
		)
		return sum;
	}
}

double NUMmean (constVECVU const& vec) noexcept {
	if (NUMisEmpty (vec))
		return undefined;
	const longdouble sum = NUMsum_longdouble (vec);
	return double (sum / vec.size);
}
double NUMmean (constMATVU const& mat) noexcept {
	if (NUMisEmpty (mat))
		return undefined;
	const longdouble sum = NUMsum_longdouble (mat);
	return double (sum / (mat.nrow * mat.ncol));
}

MelderGaussianStats NUMmeanStdev (constVECVU const& vec) noexcept {
	MelderGaussianStats result;
	MelderMeanSumsq_longdouble stats = NUMmeanSumsq (vec);
	result.mean = double (stats.mean);   // SHOULD be undefined if vec.size < 1
	const integer df = vec.size - 1;
	result.stdev = ( df <= 0 ? undefined : sqrt (double (stats.sumsq) / df) );
	return result;
}

MelderGaussianStats NUMmeanStdev (constMATVU const& mat) noexcept {
	MelderGaussianStats result;
	MelderMeanSumsq_longdouble stats = NUMmeanSumsq (mat);
	result.mean = double (stats.mean);   // SHOULD be undefined if mat.nrow * mat.ncol < 1
	const integer df = mat.nrow * mat.ncol - 1;
	result.stdev = ( df <= 0 ? undefined : sqrt (double (stats.sumsq / df)) );
	return result;
}

template <bool canError>
double NUMmin (constVECVU const& vec) {   // propagate NaNs (including -inf and +inf)
	if (NUMisEmpty (vec))
		if constexpr (canError)
			Melder_throw (U"min_e: cannot determine the minimum of an empty vector.");
		else
			return undefined;
	/*
		The following procedure is the simplest, and possibly the best.

		We also tried a "smart" version, which had fewer `isundef` calls,
		namely by rewriting the test as `if (! (value >= minimum)`.
		This captured cases where `minimum` is NaN, so that the condition
		`if (isundef (value))` could be moved into the then-part of `if (! (value >= minimum))`.
		This saved a lot of `isundef`s and handled NaN and -inf;
		however, it didn't handle +inf.
		The version below does handle all infinities, and guess what?: the procedure is
		not more than 2 percent slower than without the `isundef` test!
		(last checked 2023-02-07 for the Mac)
		Hence: DON'T OPTIMIZE.
	 */
	double minimum = + std::numeric_limits<double>::infinity();
	for (integer i = 1; i <= vec.size; i ++) {
		const double value = vec [i];
		if (isundef (value))
			if constexpr (canError)
				Melder_throw (U"min_e: cannot determine the minimum of a vector: element ", i, U" is undefined.");
			else
				return undefined;
		if (value < minimum)
			minimum = value;
	}
	return minimum;
}
double NUMmin_e (constVECVU const& vec) {
	return NUMmin <true> (vec);
}
double NUMmin_u (constVECVU const& vec) noexcept {
	return NUMmin <false> (vec);
}

template <bool canError>
double NUMmin_removeUndefined (constVECVU const& vec) {
	double minimum = + std::numeric_limits<double>::infinity();
	for (integer i = 1; i <= vec.size; i ++) {
		const double value = vec [i];
		if (value < minimum)   // NaN-safe, because false if value is undefined
			minimum = value;
	}
	/*
		We have been ignoring undefineds, but this is inappropriate if *all* elements are undefined.
		This includes the case of a zero-sized vector.
	*/
	if (isundef (minimum))   // including the original infinity
		if constexpr (canError)
			if (NUMisEmpty (vec))
				Melder_throw (U"min_e: cannot determine the minimum of an empty vector.");
			else
				Melder_throw (U"min_e: cannot determine the minimum of a vector with only undefined elements.");
		else
			return undefined;
	return minimum;
}
double NUMmin_removeUndefined_e (constVECVU const& vec) {
	return NUMmin_removeUndefined <true> (vec);
}
double NUMmin_removeUndefined_u (constVECVU const& vec) noexcept {
	return NUMmin_removeUndefined <false> (vec);
}

template <bool canError>
integer NUMmin (constINTVECVU const& vec) {
	if (NUMisEmpty (vec))
		if constexpr (canError)
			Melder_throw (U"min_e: cannot determine the minimum of an empty integer vector.");
		else
			return INTEGER_MAX;
	integer minimum = vec [1];
	for (integer i = 2; i <= vec.size; i ++) {
		const integer value = vec [i];
		if (value < minimum)
			minimum = value;
	}
	return minimum;
}
integer NUMmin_e (constINTVECVU const& vec) {
	return NUMmin <true> (vec);
}
integer NUMmin_u (constINTVECVU const& vec) noexcept {
	return NUMmin <false> (vec);
}

template <bool canError>
double NUMmin (constMATVU const& mat) {   // propagate NaNs (including -inf and +inf)
	if (NUMisEmpty (mat))
		if constexpr (canError)
			Melder_throw (U"min_e: cannot determine the minimum of an empty matrix.");
		else
			return undefined;
	double minimum = + std::numeric_limits<double>::infinity();
	for (integer irow = 1; irow <= mat.nrow; irow ++) {
		for (integer icol = 1; icol <= mat.ncol; icol ++) {
			const double value = mat [irow] [icol];
			if (isundef (value))
				if (canError)
					Melder_throw (U"min_e: cannot determine the minimum of a matrix: element [", irow, U", ", icol, U"] is undefined.");
				else
					return undefined;
			if (value < minimum)
				minimum = value;
		}
	}
	return minimum;
}
double NUMmin_e (constMATVU const& mat) {
	return NUMmin <true> (mat);
}
double NUMmin_u (constMATVU const& mat) noexcept {
	return NUMmin <false> (mat);
}

template <bool canError>
double NUMmin_removeUndefined (constMATVU const& mat) {
	double minimum = + std::numeric_limits<double>::infinity();
	for (integer irow = 1; irow <= mat.nrow; irow ++) {
		for (integer icol = 1; icol <= mat.ncol; icol ++) {
			const double value = mat [irow] [icol];
			if (value < minimum)   // NaN-correct, because false if value is undefined
				minimum = value;
		}
	}
	if (isundef (minimum))   // including the original infinity
		if constexpr (canError)
			if (NUMisEmpty (mat))
				Melder_throw (U"min_removeUndefined_e: cannot determine the minimum of an empty matrix.");
			else
				Melder_throw (U"min_removeUndefined_e: cannot determine the minimum of a matrix with only undefined cells.");
		else
			return undefined;
	return minimum;
}
double NUMmin_removeUndefined_e (constMATVU const& mat) {
	return NUMmin_removeUndefined <true> (mat);
}
double NUMmin_removeUndefined_u (constMATVU const& mat) noexcept {
	return NUMmin_removeUndefined <false> (mat);
}

template <bool canError>
double NUMmax (constVECVU const& vec) {   // propagate NaNs (including -inf and +inf)
	if (NUMisEmpty (vec))
		if constexpr (canError)
			Melder_throw (U"max_e: cannot determine the maximum of an empty vector.");
		else
			return undefined;
	double maximum = - std::numeric_limits<double>::infinity();
	for (integer i = 1; i <= vec.size; i ++) {
		const double value = vec [i];
		if (isundef (value))
			if constexpr (canError)
				Melder_throw (U"max_e: cannot determine the maximum of a vector: element ", i, U" is undefined.");
			else
				return undefined;
		if (value > maximum)
			maximum = value;
	}
	return maximum;
}
double NUMmax_e (constVECVU const& vec) {
	return NUMmax <true> (vec);
}
double NUMmax_u (constVECVU const& vec) noexcept {
	return NUMmax <false> (vec);
}

template <bool canError>
double NUMmax_removeUndefined (constVECVU const& vec) {
	double maximum = - std::numeric_limits<double>::infinity();
	for (integer i = 1; i <= vec.size; i ++) {
		const double value = vec [i];
		if (value > maximum)   // NaN-safe, because false if value is undefined
			maximum = value;
	}
	if (isundef (maximum))   // including the original -infinity
		if constexpr (canError)
			if (NUMisEmpty (vec))
				Melder_throw (U"max_removeUndefined_e: cannot determine the maximum of an empty vector.");
			else
				Melder_throw (U"max_removeUndefined_e: cannot determine the maximum of a vector with only undefined elements.");
		else
			return undefined;
	return maximum;
}
double NUMmax_removeUndefined_e (constVECVU const& vec) {
	return NUMmax_removeUndefined <true> (vec);
}
double NUMmax_removeUndefined_u (constVECVU const& vec) noexcept {
	return NUMmax_removeUndefined <false> (vec);
}

template <bool canError>
integer NUMmax (constINTVECVU const& vec) {
	if (NUMisEmpty (vec))
		if constexpr (canError)
			Melder_throw (U"max_e: cannot determine the maximum of an empty integer vector.");
		else
			return INTEGER_MIN;
	integer maximum = vec [1];
	for (integer i = 2; i <= vec.size; i ++) {
		const integer value = vec [i];
		if (value > maximum)
			maximum = value;
	}
	return maximum;
}
integer NUMmax_e (constINTVECVU const& vec) {
	return NUMmax <true> (vec);
}
integer NUMmax_u (constINTVECVU const& vec) noexcept {
	return NUMmax <false> (vec);
}

template <bool canError>
double NUMmax (constMATVU const& mat) {   // propagate NaNs (including -inf and +inf)
	if (NUMisEmpty (mat))
		if constexpr (canError)
			Melder_throw (U"max_e: cannot determine the maximum of an empty matrix.");
		else
			return undefined;
	double maximum = - std::numeric_limits<double>::infinity();
	for (integer irow = 1; irow <= mat.nrow; irow ++) {
		for (integer icol = 1; icol <= mat.ncol; icol ++) {
			const double value = mat [irow] [icol];
			if (isundef (value))
				if constexpr (canError)
					Melder_throw (U"max_e: cannot determine the maximum of a matrix: element [", irow, U", ", icol, U"] is undefined.");
				else
					return undefined;
			if (value > maximum)
				maximum = value;
		}
	}
	return maximum;
}
double NUMmax_e (constMATVU const& mat) {
	return NUMmax <true> (mat);
}
double NUMmax_u (constMATVU const& mat) noexcept {   // propagate NaNs (including -inf and +inf)
	return NUMmax <false> (mat);
}

template <bool canError>
double NUMmax_removeUndefined (constMATVU const& mat) {
	double maximum = - std::numeric_limits<double>::infinity();
	for (integer irow = 1; irow <= mat.nrow; irow ++) {
		for (integer icol = 1; icol <= mat.ncol; icol ++) {
			const double value = mat [irow] [icol];
			if (value > maximum)   // NaN-safe, because false if value is undefined
				maximum = value;
		}
	}
	if (isundef (maximum))   // including the original -infinity
		if constexpr (canError)
			if (NUMisEmpty (mat))
				Melder_throw (U"max_removeUndefined_e: cannot determine the maximum of an empty matrix.");
			else
				Melder_throw (U"max_removeUndefined_e: cannot determine the maximum of a matrix with only undefined cells.");
		else
			return undefined;
	return maximum;
}
double NUMmax_removeUndefined_e (constMATVU const& mat) {
	return NUMmax_removeUndefined <true> (mat);
}
double NUMmax_removeUndefined_u (constMATVU const& mat) noexcept {
	return NUMmax_removeUndefined <false> (mat);
}

template <bool canError>
MelderRealRange NUMextrema (constVECVU const& vec) {
	if (NUMisEmpty (vec))
		if constexpr (canError)
			Melder_throw (U"extrema_e: cannot compute the extrema of an empty vector.");
		else
			return { undefined, undefined };
	double minimum = + std::numeric_limits<double>::infinity();
	double maximum = - std::numeric_limits<double>::infinity();
	for (integer i = 1; i <= vec.size; i ++) {
		const double value = vec [i];
		if (isundef (value))
			if constexpr (canError)
				Melder_throw (U"extrema_e: cannot compute the extrema of a vector: element ", i, U" is undefined.");
			else
				return { undefined, undefined };
		if (value < minimum)
			minimum = value;
		if (value > maximum)
			maximum = value;
	}
	return { minimum, maximum };
}
MelderRealRange NUMextrema_e (constVECVU const& vec) {
	return NUMextrema <true> (vec);
}
MelderRealRange NUMextrema_u (constVECVU const& vec) noexcept {
	return NUMextrema <false> (vec);
}

template <bool canError>
MelderRealRange NUMextrema (constMATVU const& mat) {
	if (NUMisEmpty (mat))
		if constexpr (canError)
			Melder_throw (U"extrema_e: cannot compute the extrema of an empty matrix.");
		else
			return { undefined, undefined };
	double minimum = + std::numeric_limits<double>::infinity();
	double maximum = - std::numeric_limits<double>::infinity();
	for (integer irow = 1; irow <= mat.nrow; irow ++) {
		for (integer icol = 1; icol <= mat.ncol; icol ++) {
			const double value = mat [irow] [icol];
			if (isundef (value))
				if constexpr (canError)
					Melder_throw (U"extrema_e: cannot the compute extrema of a matrix: element [", irow, U", ", icol, U"] is undefined.");
				else
					return { undefined, undefined };
			if (value < minimum)
				minimum = value;
			if (value > maximum)
				maximum = value;
		}
	}
	return { minimum, maximum };
}
MelderRealRange NUMextrema_e (constMATVU const& mat) {
	return NUMextrema <true> (mat);
}
MelderRealRange NUMextrema_u (constMATVU const& mat) noexcept {
	return NUMextrema <false> (mat);
}

template <bool canError>
MelderIntegerRange NUMextrema (constINTVECVU const& vec) {
	if (NUMisEmpty (vec))
		if constexpr (canError)
			Melder_throw (U"extrema_e: cannot compute the extrema of an empty integer vector.");
		else
			return { INTEGER_MIN, INTEGER_MAX };
	integer minimum = vec [1], maximum = minimum;
	for (integer i = 2; i <= vec.size; i ++) {
		const integer value = vec [i];
		if (value < minimum)
			minimum = value;
		if (value > maximum)
			maximum = value;
	}
	return { minimum, maximum };
}
MelderIntegerRange NUMextrema_e (constINTVECVU const& vec) {
	return NUMextrema <true> (vec);
}
MelderIntegerRange NUMextrema_u (constINTVECVU const& vec) noexcept {
	return NUMextrema <false> (vec);
}

double NUMminimumLength (constSTRVEC const& x) noexcept {
	if (NUMisEmpty (x))
		return undefined;
	double result = NUMlength (x [1]);
	for (integer i = 2; i <= x.size; i ++) {
		const double length = NUMlength (x [i]);
		if (length < result)
			result = length;
	}
	return result;
}
double NUMmaximumLength (constSTRVEC const& x) noexcept {
	if (NUMisEmpty (x))
		return undefined;
	double result = NUMlength (x [1]);
	for (integer i = 2; i <= x.size; i ++) {
		const double length = NUMlength (x [i]);
		if (length > result)
			result = length;
	}
	return result;
}

double NUMnorm (constVECVU const& vec, const double power) noexcept {
	if (power < 0.0)
		return undefined;
	if (power == 2.0) {
		const double sum2 = double (NUMsum2_longdouble (vec));
		return sqrt (sum2);
	} else if (power == 1.0) {
		const double sumAbs = double (NUMsumAbs_longdouble (vec));
		return sumAbs;
	} else {
		const longdouble sumPower = NUMsumPower_longdouble (vec, power);
		return double (powl (sumPower, longdouble (1.0) / power));
	}
}
double NUMnorm (constMATVU const& mat, const double power) noexcept {
	if (power < 0.0)
		return undefined;
	if (power == 2.0) {
		const double sum2 = double (NUMsum2_longdouble (mat));
		return sqrt (sum2);
	} else if (power == 1.0) {
		const double sumAbs = double (NUMsumAbs_longdouble (mat));
		return sumAbs;
	} else {
		const longdouble sumPower = NUMsumPower_longdouble (mat, power);
		return double (powl (sumPower, longdouble (1.0) / power));
	}
}

integer NUMnumberOfTokens (const conststring32 string) noexcept {
	integer numberOfTokens = 0;
	const char32 *p = & string [0];
	for (;;) {
		Melder_skipHorizontalOrVerticalSpace (& p);
		if (*p == U'\0')
			break;
		numberOfTokens ++;
		p ++;   // step over first nonspace
		p = Melder_findEndOfInk (p);
	}
	return numberOfTokens;
}

double NUMstdev (constVECVU const& vec) noexcept {
	const integer df = vec.size - 1;
	if (df <= 0)
		return undefined;
	MelderMeanSumsq_longdouble stats = NUMmeanSumsq (vec);
	const longdouble variance = stats.sumsq / df;
	const double stdev = sqrt (double (variance));
	return stdev;
}
double NUMstdev (constMATVU const& mat) noexcept {
	const integer df = mat.nrow * mat.ncol - 1;
	if (df <= 0)
		return undefined;
	MelderMeanSumsq_longdouble stats = NUMmeanSumsq (mat);
	const longdouble variance = stats.sumsq / df;
	const double stdev = sqrt (double (variance));
	return stdev;
}

double NUMsum (constVECVU const& vec) noexcept {
	const longdouble sum = NUMsum_longdouble (vec);
	return double (sum);
}
double NUMsum (constMATVU const& mat) noexcept {
	const longdouble sum = NUMsum_longdouble (mat);
	return double (sum);
}

double NUMsum2 (constVECVU const& vec) {
	return double (NUMsum2_longdouble (vec));
}
double NUMsum2 (constMATVU const& mat) {
	return double (NUMsum2_longdouble (mat));
}

double NUMsumOfSquaredDifferences (constVECVU const& vec, const double mean) {
	return double (NUMsumOfSquaredDifferences_longdouble (vec, mean));
}

double NUMcorrelation (constVECVU const& vec1, constVECVU const& vec2) {
	if (vec1.size != vec2.size)
		return undefined;
	if (vec1.size < 2)
		return undefined;
	const MelderMeanSumsq_longdouble meanSumsq1 = NUMmeanSumsq (vec1);
	const MelderMeanSumsq_longdouble meanSumsq2 = NUMmeanSumsq (vec2);
	const longdouble inner = NUMinnerMinusMean_longdouble (vec1, meanSumsq1.mean, vec2, meanSumsq2.mean);
	return double (inner) / sqrt (double (meanSumsq1.sumsq * meanSumsq2.sumsq));
}

double NUMtotalLength (constSTRVEC const& x) {
	double totalLength = 0.0;
	for (integer i = 1; i <= x.size; i ++)
		totalLength += NUMlength (x [i]);
	return double (totalLength);
}

double NUMvariance (constVECVU const& vec) noexcept {
	MelderMeanSumsq_longdouble stats = NUMmeanSumsq (vec);
	const longdouble variance = stats.sumsq / (vec.size - 1);
	return double (variance);
}
double NUMvariance (constMATVU const& mat) noexcept {
	MelderMeanSumsq_longdouble stats = NUMmeanSumsq (mat);
	const longdouble variance = stats.sumsq / (mat.nrow * mat.ncol - 1);
	return double (variance);
}

/* End of file NUM.cpp */
