1 /* Copyright 2015 The TensorFlow Authors. All Rights Reserved.
2
3 Licensed under the Apache License, Version 2.0 (the "License");
4 you may not use this file except in compliance with the License.
5 You may obtain a copy of the License at
6
7 http://www.apache.org/licenses/LICENSE-2.0
8
9 Unless required by applicable law or agreed to in writing, software
10 distributed under the License is distributed on an "AS IS" BASIS,
11 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 See the License for the specific language governing permissions and
13 limitations under the License.
14 ==============================================================================*/
15
16 #ifndef TENSORFLOW_STREAM_EXECUTOR_LIB_MATHUTIL_H_
17 #define TENSORFLOW_STREAM_EXECUTOR_LIB_MATHUTIL_H_
18
19 #include <algorithm>
20 #include <cmath>
21 #include <limits>
22 #include <type_traits>
23 #include <vector>
24
25 #include "tensorflow/stream_executor/platform/logging.h"
26 #include "tensorflow/stream_executor/platform/port.h"
27
28 namespace perftools {
29 namespace gputools {
30 namespace port {
31
32 class MathUtil {
33 public:
34 template <typename IntegralType>
CeilOfRatio(IntegralType numerator,IntegralType denominator)35 static IntegralType CeilOfRatio(IntegralType numerator,
36 IntegralType denominator) {
37 return CeilOrFloorOfRatio<IntegralType, true>(numerator, denominator);
38 }
39 template <typename IntegralType>
FloorOfRatio(IntegralType numerator,IntegralType denominator)40 static IntegralType FloorOfRatio(IntegralType numerator,
41 IntegralType denominator) {
42 return CeilOrFloorOfRatio<IntegralType, false>(numerator, denominator);
43 }
44 template <typename IntegralType, bool ceil>
45 static IntegralType CeilOrFloorOfRatio(IntegralType numerator,
46 IntegralType denominator);
47 };
48
49 // ---- CeilOrFloorOfRatio ----
50 // This is a branching-free, cast-to-double-free implementation.
51 //
52 // Casting to double is in general incorrect because of loss of precision
53 // when casting an int64 into a double.
54 //
55 // There's a bunch of 'recipes' to compute a integer ceil (or floor) on the web,
56 // and most of them are incorrect.
57 template<typename IntegralType, bool ceil>
CeilOrFloorOfRatio(IntegralType numerator,IntegralType denominator)58 IntegralType MathUtil::CeilOrFloorOfRatio(IntegralType numerator,
59 IntegralType denominator) {
60 static_assert(std::is_integral<IntegralType>::value,
61 "CeilOfRatio_is_only_defined_for_integral_types");
62 assert(denominator != 0);
63 // Dividing the smallest signed integer by -1 is not supported: it would
64 // SIGFPE
65 assert(!std::is_signed<IntegralType>::value ||
66 numerator != std::numeric_limits<IntegralType>::min() ||
67 denominator != -1);
68
69 const IntegralType rounded_toward_zero = numerator / denominator;
70 const IntegralType intermediate_product = rounded_toward_zero * denominator;
71
72 if (ceil) { // Compile-time condition: not an actual branching
73 // When rounded_toward_zero is negative, then an adjustment is never needed:
74 // the real ratio is negative, and so rounded toward zero is the ceil.
75 // When rounded_toward_zero is non-negative, an adjustment is needed if the
76 // sign of the difference numerator - intermediate_product is the same as
77 // the sign of the denominator.
78 //
79 // Using a bool and then a static_cast to IntegralType is not strictly
80 // necessary, but it makes the code clear, and anyway the compiler should
81 // get rid of it.
82 const bool needs_adjustment = (rounded_toward_zero >= 0) &&
83 ((denominator > 0 && numerator > intermediate_product) ||
84 (denominator < 0 && numerator < intermediate_product));
85 const IntegralType adjustment = static_cast<IntegralType>(needs_adjustment);
86 const IntegralType ceil_of_ratio = rounded_toward_zero + adjustment;
87 return ceil_of_ratio;
88 } else {
89 // Floor case: symmetrical to the previous one
90 const bool needs_adjustment = (rounded_toward_zero <= 0) &&
91 ((denominator > 0 && numerator < intermediate_product) ||
92 (denominator < 0 && numerator > intermediate_product));
93 const IntegralType adjustment = static_cast<IntegralType>(needs_adjustment);
94 const IntegralType floor_of_ratio = rounded_toward_zero - adjustment;
95 return floor_of_ratio;
96 }
97 }
98
99 } // namespace port
100 } // namespace gputools
101 } // namespace perftools
102
103 #endif // TENSORFLOW_STREAM_EXECUTOR_LIB_MATHUTIL_H_
104