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// Copyright 2016 The Draco Authors.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
#ifndef DRACO_CORE_MATH_UTILS_H_
#define DRACO_CORE_MATH_UTILS_H_
#include <inttypes.h>
#include "draco/core/vector_d.h"
#define DRACO_INCREMENT_MOD(I, M) (((I) == ((M)-1)) ? 0 : ((I) + 1))
// Returns floor(sqrt(x)) where x is an integer number. The main intend of this
// function is to provide a cross platform and deterministic implementation of
// square root for integer numbers. This function is not intended to be a
// replacement for std::sqrt() for general cases. IntSqrt is in fact about 3X
// slower compared to most implementation of std::sqrt().
inline uint64_t IntSqrt(uint64_t number) {
if (number == 0)
return 0;
// First estimate good initial value of the square root as log2(number).
uint64_t act_number = number;
uint64_t square_root = 1;
while (act_number >= 2) {
// Double the square root until |square_root * square_root > number|.
square_root *= 2;
act_number /= 4;
}
// Perform Newton's (or Babylonian) method to find the true floor(sqrt()).
do {
// New |square_root| estimate is computed as the average between
// |square_root| and |number / square_root|.
square_root = (square_root + number / square_root) / 2;
// Note that after the first iteration, the estimate is always going to be
// larger or equal to the true square root value. Therefore to check
// convergence, we can simply detect condition when the square of the
// estimated square root is larger than the input.
} while (square_root * square_root > number);
return square_root;
}
#endif // DRACO_CORE_MATH_UTILS_H_
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