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+/*****************************************************************************
+
+Copyright (c) 1994, 2015, Oracle and/or its affiliates. All Rights Reserved.
+
+This program 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; version 2 of the License.
+
+This program 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 program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1335 USA
+
+*****************************************************************************/
+
+/**************************************************************//**
+@file include/ut0ut.ic
+Various utilities
+
+Created 5/30/1994 Heikki Tuuri
+*******************************************************************/
+
+#include <algorithm>
+
+/** Calculate the minimum of two pairs.
+@param[out]	min_hi	MSB of the minimum pair
+@param[out]	min_lo	LSB of the minimum pair
+@param[in]	a_hi	MSB of the first pair
+@param[in]	a_lo	LSB of the first pair
+@param[in]	b_hi	MSB of the second pair
+@param[in]	b_lo	LSB of the second pair */
+UNIV_INLINE
+void
+ut_pair_min(
+	ulint*	min_hi,
+	ulint*	min_lo,
+	ulint	a_hi,
+	ulint	a_lo,
+	ulint	b_hi,
+	ulint	b_lo)
+{
+	if (a_hi == b_hi) {
+		*min_hi = a_hi;
+		*min_lo = std::min(a_lo, b_lo);
+	} else if (a_hi < b_hi) {
+		*min_hi = a_hi;
+		*min_lo = a_lo;
+	} else {
+		*min_hi = b_hi;
+		*min_lo = b_lo;
+	}
+}
+
+/******************************************************//**
+Compares two ulints.
+@return 1 if a > b, 0 if a == b, -1 if a < b */
+UNIV_INLINE
+int
+ut_ulint_cmp(
+/*=========*/
+	ulint	a,	/*!< in: ulint */
+	ulint	b)	/*!< in: ulint */
+{
+	if (a < b) {
+		return(-1);
+	} else if (a == b) {
+		return(0);
+	} else {
+		return(1);
+	}
+}
+
+/** Compare two pairs of integers.
+@param[in]	a_h	more significant part of first pair
+@param[in]	a_l	less significant part of first pair
+@param[in]	b_h	more significant part of second pair
+@param[in]	b_l	less significant part of second pair
+@return comparison result of (a_h,a_l) and (b_h,b_l)
+@retval -1 if (a_h,a_l) is less than (b_h,b_l)
+@retval 0 if (a_h,a_l) is equal to (b_h,b_l)
+@retval 1 if (a_h,a_l) is greater than (b_h,b_l) */
+UNIV_INLINE
+int
+ut_pair_cmp(
+	ulint	a_h,
+	ulint	a_l,
+	ulint	b_h,
+	ulint	b_l)
+{
+	if (a_h < b_h) {
+		return(-1);
+	}
+	if (a_h > b_h) {
+		return(1);
+	}
+	return(ut_ulint_cmp(a_l, b_l));
+}
+
+/*************************************************************//**
+Calculates fast the 2-logarithm of a number, rounded upward to an
+integer.
+@return logarithm in the base 2, rounded upward */
+UNIV_INLINE
+ulint
+ut_2_log(
+/*=====*/
+	ulint	n)	/*!< in: number != 0 */
+{
+	ulint	res;
+
+	res = 0;
+
+	ut_ad(n > 0);
+
+	n = n - 1;
+
+	for (;;) {
+		n = n / 2;
+
+		if (n == 0) {
+			break;
+		}
+
+		res++;
+	}
+
+	return(res + 1);
+}
+
+/*************************************************************//**
+Calculates 2 to power n.
+@return 2 to power n */
+UNIV_INLINE
+ulint
+ut_2_exp(
+/*=====*/
+	ulint	n)	/*!< in: number */
+{
+	return((ulint) 1 << n);
+}