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fast_math.h
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1 /***************************************************************************************************
2 * Copyright (c) 2017-2019, NVIDIA CORPORATION. All rights reserved.
3 *
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5 * provided that the following conditions are met:
6 * * Redistributions of source code must retain the above copyright notice, this list of
7 * conditions and the following disclaimer.
8 * * Redistributions in binary form must reproduce the above copyright notice, this list of
9 * conditions and the following disclaimer in the documentation and/or other materials
10 * provided with the distribution.
11 * * Neither the name of the NVIDIA CORPORATION nor the names of its contributors may be used
12 * to endorse or promote products derived from this software without specific prior written
13 * permission.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR
16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
17 * FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL NVIDIA CORPORATION BE LIABLE
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19 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
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22 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
23 *
24 **************************************************************************************************/
25
26 #pragma once
27
28 #include <cstdint>
29 #include "cutlass/cutlass.h"
30
36 namespace cutlass {
37
38 /******************************************************************************
39 * Static math utilities
40 ******************************************************************************/
41
45 template <int N>
46 struct is_pow2 {
47 static bool const value = ((N & (N - 1)) == 0);
48 };
49
53 template <int N, int CurrentVal = N, int Count = 0>
54 struct log2_down {
56 enum { value = log2_down<N, (CurrentVal >> 1), Count + 1>::value };
57 };
58
59 // Base case
60 template <int N, int Count>
61 struct log2_down<N, 1, Count> {
62 enum { value = Count };
63 };
64
68 template <int N, int CurrentVal = N, int Count = 0>
69 struct log2_up {
71 enum { value = log2_up<N, (CurrentVal >> 1), Count + 1>::value };
72 };
73
74 // Base case
75 template <int N, int Count>
76 struct log2_up<N, 1, Count> {
77 enum { value = ((1 << Count) < N) ? Count + 1 : Count };
78 };
79
83 template <int N>
84 struct sqrt_est {
85 enum { value = 1 << (log2_up<N>::value / 2) };
86 };
87
92 template <int Dividend, int Divisor>
93 struct divide_assert {
94 enum { value = Dividend / Divisor };
95
96 static_assert((Dividend % Divisor == 0), "Not an even multiple");
97 };
98
99 /******************************************************************************
100 * Rounding
101 ******************************************************************************/
102
106 template <typename dividend_t, typename divisor_t>
107 CUTLASS_HOST_DEVICE dividend_t round_nearest(dividend_t dividend, divisor_t divisor) {
108 return ((dividend + divisor - 1) / divisor) * divisor;
109 }
110
114 template <typename value_t>
115 CUTLASS_HOST_DEVICE value_t gcd(value_t a, value_t b) {
116 for (;;) {
117 if (a == 0) return b;
118 b %= a;
119 if (b == 0) return a;
120 a %= b;
121 }
122 }
123
127 template <typename value_t>
128 CUTLASS_HOST_DEVICE value_t lcm(value_t a, value_t b) {
129 value_t temp = gcd(a, b);
130
131 return temp ? (a / temp * b) : 0;
132 }
133
139 template <typename value_t>
140 CUTLASS_HOST_DEVICE value_t clz(value_t x) {
141 for (int i = 31; i >= 0; --i) {
142 if ((1 << i) & x) return 31 - i;
143 }
144 return 32;
145 }
146
147 template <typename value_t>
148 CUTLASS_HOST_DEVICE value_t find_log2(value_t x) {
149 int a = int(31 - clz(x));
150 a += (x & (x - 1)) != 0; // Round up, add 1 if not a power of 2.
151 return a;
152 }
153
154
158 CUTLASS_HOST_DEVICE
159 void find_divisor(unsigned int& mul, unsigned int& shr, unsigned int denom) {
160 if (denom == 1) {
161 mul = 0;
162 shr = 0;
163 } else {
164 unsigned int p = 31 + find_log2(denom);
165 unsigned m = unsigned(((1ull << p) + unsigned(denom) - 1) / unsigned(denom));
166
167 mul = m;
168 shr = p - 32;
169 }
170 }
171
175 CUTLASS_HOST_DEVICE
176 void fast_divmod(int& quo, int& rem, int src, int div, unsigned int mul, unsigned int shr) {
177
178 #if defined(__CUDA_ARCH__)
179 // Use IMUL.HI if div != 1, else simply copy the source.
180 quo = (div != 1) ? __umulhi(src, mul) >> shr : src;
181 #else
182 quo = int((div != 1) ? int(src * mul) >> shr : src);
183 #endif
184
185 // The remainder.
186 rem = src - (quo * div);
187
188 }
189
190 // For long int input
191 CUTLASS_HOST_DEVICE
192 void fast_divmod(int& quo, int64_t& rem, int64_t src, int div, unsigned int mul, unsigned int shr) {
193
194 #if defined(__CUDA_ARCH__)
195 // Use IMUL.HI if div != 1, else simply copy the source.
196 quo = (div != 1) ? __umulhi(src, mul) >> shr : src;
197 #else
198 quo = int((div != 1) ? (src * mul) >> shr : src);
199 #endif
200 // The remainder.
201 rem = src - (quo * div);
202 }
203
204 /******************************************************************************
205 * Min/Max
206 ******************************************************************************/
207
208 template <int A, int B>
209 struct Min {
210 static int const kValue = (A < B) ? A : B;
211 };
212
213 template <int A, int B>
214 struct Max {
215 static int const kValue = (A > B) ? A : B;
216 };
217
218 CUTLASS_HOST_DEVICE
219 constexpr int const_min(int a, int b) {
220 return (b < a ? b : a);
221 }
222
223 CUTLASS_HOST_DEVICE
224 constexpr int const_max(int a, int b) {
225 return (b > a ? b : a);
226 }
227
228 } // namespace cutlass
cutlass
Definition: aligned_buffer.h:35
constexpr
#define constexpr
Definition: platform.h:137
cutlass::fast_divmod
CUTLASS_HOST_DEVICE void fast_divmod(int &quo, int &rem, int src, int div, unsigned int mul, unsigned int shr)
Definition: fast_math.h:176
cutlass::find_log2
CUTLASS_HOST_DEVICE value_t find_log2(value_t x)
Definition: fast_math.h:148
cutlass::log2_down
Definition: fast_math.h:54
cutlass::Min
Definition: fast_math.h:209
cutlass::const_max
CUTLASS_HOST_DEVICE constexpr int const_max(int a, int b)
Definition: fast_math.h:224
cutlass::is_pow2::value
static bool const value
Definition: fast_math.h:47
cutlass::lcm
CUTLASS_HOST_DEVICE value_t lcm(value_t a, value_t b)
Definition: fast_math.h:128
cutlass::round_nearest
CUTLASS_HOST_DEVICE dividend_t round_nearest(dividend_t dividend, divisor_t divisor)
Definition: fast_math.h:107
CUTLASS_HOST_DEVICE
#define CUTLASS_HOST_DEVICE
Definition: cutlass.h:89
static_assert
#define static_assert(__e, __m)
Definition: platform.h:153
cutlass::Max
Definition: fast_math.h:214
cutlass::find_divisor
CUTLASS_HOST_DEVICE void find_divisor(unsigned int &mul, unsigned int &shr, unsigned int denom)
Definition: fast_math.h:159
cutlass::gcd
CUTLASS_HOST_DEVICE value_t gcd(value_t a, value_t b)
Definition: fast_math.h:115
cutlass::divide_assert
Definition: fast_math.h:93
cutlass::log2_up
Definition: fast_math.h:69
cutlass::clz
CUTLASS_HOST_DEVICE value_t clz(value_t x)
Definition: fast_math.h:140
cutlass::is_pow2
Definition: fast_math.h:46
cutlass::const_min
CUTLASS_HOST_DEVICE constexpr int const_min(int a, int b)
Definition: fast_math.h:219
cutlass.h
Basic include for CUTLASS.
cutlass::sqrt_est
Definition: fast_math.h:84