/* Copyright 2015 The TensorFlow Authors. All Rights Reserved.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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==============================================================================*/
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#ifndef TENSORFLOW_STREAM_EXECUTOR_LIB_MATHUTIL_H_
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#define TENSORFLOW_STREAM_EXECUTOR_LIB_MATHUTIL_H_
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#include <algorithm>
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#include <cmath>
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#include <limits>
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#include <type_traits>
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#include <vector>
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#include "tensorflow/stream_executor/platform/logging.h"
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#include "tensorflow/stream_executor/platform/port.h"
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namespace stream_executor {
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namespace port {
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class MathUtil {
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public:
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template <typename IntegralType>
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static IntegralType CeilOfRatio(IntegralType numerator,
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IntegralType denominator) {
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return CeilOrFloorOfRatio<IntegralType, true>(numerator, denominator);
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}
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template <typename IntegralType>
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static IntegralType FloorOfRatio(IntegralType numerator,
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IntegralType denominator) {
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return CeilOrFloorOfRatio<IntegralType, false>(numerator, denominator);
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}
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template <typename IntegralType, bool ceil>
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static IntegralType CeilOrFloorOfRatio(IntegralType numerator,
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IntegralType denominator);
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};
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// ---- CeilOrFloorOfRatio ----
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// This is a branching-free, cast-to-double-free implementation.
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//
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// Casting to double is in general incorrect because of loss of precision
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// when casting an int64 into a double.
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//
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// There's a bunch of 'recipes' to compute a integer ceil (or floor) on the web,
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// and most of them are incorrect.
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template<typename IntegralType, bool ceil>
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IntegralType MathUtil::CeilOrFloorOfRatio(IntegralType numerator,
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IntegralType denominator) {
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static_assert(std::is_integral<IntegralType>::value,
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"CeilOfRatio_is_only_defined_for_integral_types");
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assert(denominator != 0);
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// Dividing the smallest signed integer by -1 is not supported: it would
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// SIGFPE
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assert(!std::is_signed<IntegralType>::value ||
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numerator != std::numeric_limits<IntegralType>::min() ||
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denominator != -1);
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const IntegralType rounded_toward_zero = numerator / denominator;
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const IntegralType intermediate_product = rounded_toward_zero * denominator;
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if (ceil) { // Compile-time condition: not an actual branching
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// When rounded_toward_zero is negative, then an adjustment is never needed:
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// the real ratio is negative, and so rounded toward zero is the ceil.
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// When rounded_toward_zero is non-negative, an adjustment is needed if the
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// sign of the difference numerator - intermediate_product is the same as
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// the sign of the denominator.
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//
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// Using a bool and then a static_cast to IntegralType is not strictly
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// necessary, but it makes the code clear, and anyway the compiler should
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// get rid of it.
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const bool needs_adjustment = (rounded_toward_zero >= 0) &&
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((denominator > 0 && numerator > intermediate_product) ||
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(denominator < 0 && numerator < intermediate_product));
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const IntegralType adjustment = static_cast<IntegralType>(needs_adjustment);
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const IntegralType ceil_of_ratio = rounded_toward_zero + adjustment;
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return ceil_of_ratio;
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} else {
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// Floor case: symmetrical to the previous one
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const bool needs_adjustment = (rounded_toward_zero <= 0) &&
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((denominator > 0 && numerator < intermediate_product) ||
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(denominator < 0 && numerator > intermediate_product));
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const IntegralType adjustment = static_cast<IntegralType>(needs_adjustment);
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const IntegralType floor_of_ratio = rounded_toward_zero - adjustment;
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return floor_of_ratio;
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}
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}
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} // namespace port
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} // namespace stream_executor
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#endif // TENSORFLOW_STREAM_EXECUTOR_LIB_MATHUTIL_H_
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