CUDA/Complex.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
5 // Copyright (C) 2021 C. Antonio Sanchez <cantonios@google.com>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 #ifndef EIGEN_COMPLEX_CUDA_H
12 #define EIGEN_COMPLEX_CUDA_H
13 
14 // clang-format off
15 // Many std::complex methods such as operator+, operator-, operator* and
16 // operator/ are not constexpr. Due to this, GCC and older versions of clang do
17 // not treat them as device functions and thus Eigen functors making use of
18 // these operators fail to compile. Here, we manually specialize these
19 // operators and functors for complex types when building for CUDA to enable
20 // their use on-device.
21 
22 #if defined(EIGEN_CUDACC) && defined(EIGEN_GPU_COMPILE_PHASE)
23 
24 // ICC already specializes std::complex<float> and std::complex<double>
25 // operators, preventing us from making them device functions here.
26 // This will lead to silent runtime errors if the operators are used on device.
27 //
28 // To allow std::complex operator use on device, define _OVERRIDE_COMPLEX_SPECIALIZATION_
29 // prior to first inclusion of <complex>. This prevents ICC from adding
30 // its own specializations, so our custom ones below can be used instead.
31 #if !(defined(EIGEN_COMP_ICC) && defined(_USE_COMPLEX_SPECIALIZATION_))
32 
33 // Import Eigen's internal operator specializations.
34 #define EIGEN_USING_STD_COMPLEX_OPERATORS \
35  using Eigen::complex_operator_detail::operator+; \
36  using Eigen::complex_operator_detail::operator-; \
37  using Eigen::complex_operator_detail::operator*; \
38  using Eigen::complex_operator_detail::operator/; \
39  using Eigen::complex_operator_detail::operator+=; \
40  using Eigen::complex_operator_detail::operator-=; \
41  using Eigen::complex_operator_detail::operator*=; \
42  using Eigen::complex_operator_detail::operator/=; \
43  using Eigen::complex_operator_detail::operator==; \
44  using Eigen::complex_operator_detail::operator!=;
45 
46 namespace Eigen {
47 
48 // Specialized std::complex overloads.
49 namespace complex_operator_detail {
50 
51 template<typename T>
52 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
53 std::complex<T> complex_multiply(const std::complex<T>& a, const std::complex<T>& b) {
54  const T a_real = numext::real(a);
55  const T a_imag = numext::imag(a);
56  const T b_real = numext::real(b);
57  const T b_imag = numext::imag(b);
58  return std::complex<T>(
59  a_real * b_real - a_imag * b_imag,
60  a_imag * b_real + a_real * b_imag);
61 }
62 
63 template<typename T>
64 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
65 std::complex<T> complex_divide_fast(const std::complex<T>& a, const std::complex<T>& b) {
66  const T a_real = numext::real(a);
67  const T a_imag = numext::imag(a);
68  const T b_real = numext::real(b);
69  const T b_imag = numext::imag(b);
70  const T norm = (b_real * b_real + b_imag * b_imag);
71  return std::complex<T>((a_real * b_real + a_imag * b_imag) / norm,
72  (a_imag * b_real - a_real * b_imag) / norm);
73 }
74 
75 template<typename T>
76 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
77 std::complex<T> complex_divide_stable(const std::complex<T>& a, const std::complex<T>& b) {
78  const T a_real = numext::real(a);
79  const T a_imag = numext::imag(a);
80  const T b_real = numext::real(b);
81  const T b_imag = numext::imag(b);
82  // Smith's complex division (https://arxiv.org/pdf/1210.4539.pdf),
83  // guards against over/under-flow.
84  const bool scale_imag = numext::abs(b_imag) <= numext::abs(b_real);
85  const T rscale = scale_imag ? T(1) : b_real / b_imag;
86  const T iscale = scale_imag ? b_imag / b_real : T(1);
87  const T denominator = b_real * rscale + b_imag * iscale;
88  return std::complex<T>((a_real * rscale + a_imag * iscale) / denominator,
89  (a_imag * rscale - a_real * iscale) / denominator);
90 }
91 
92 template<typename T>
93 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
94 std::complex<T> complex_divide(const std::complex<T>& a, const std::complex<T>& b) {
95 #if EIGEN_FAST_MATH
96  return complex_divide_fast(a, b);
97 #else
98  return complex_divide_stable(a, b);
99 #endif
100 }
101 
102 // NOTE: We cannot specialize compound assignment operators with Scalar T,
103 // (i.e. operator@=(const T&), for @=+,-,*,/)
104 // since they are already specialized for float/double/long double within
105 // the standard <complex> header. We also do not specialize the stream
106 // operators.
107 #define EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(T) \
108  \
109 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
110 std::complex<T> operator+(const std::complex<T>& a) { return a; } \
111  \
112 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
113 std::complex<T> operator-(const std::complex<T>& a) { \
114  return std::complex<T>(-numext::real(a), -numext::imag(a)); \
115 } \
116  \
117 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
118 std::complex<T> operator+(const std::complex<T>& a, const std::complex<T>& b) { \
119  return std::complex<T>(numext::real(a) + numext::real(b), numext::imag(a) + numext::imag(b)); \
120 } \
121  \
122 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
123 std::complex<T> operator+(const std::complex<T>& a, const T& b) { \
124  return std::complex<T>(numext::real(a) + b, numext::imag(a)); \
125 } \
126  \
127 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
128 std::complex<T> operator+(const T& a, const std::complex<T>& b) { \
129  return std::complex<T>(a + numext::real(b), numext::imag(b)); \
130 } \
131  \
132 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
133 std::complex<T> operator-(const std::complex<T>& a, const std::complex<T>& b) { \
134  return std::complex<T>(numext::real(a) - numext::real(b), numext::imag(a) - numext::imag(b)); \
135 } \
136  \
137 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
138 std::complex<T> operator-(const std::complex<T>& a, const T& b) { \
139  return std::complex<T>(numext::real(a) - b, numext::imag(a)); \
140 } \
141  \
142 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
143 std::complex<T> operator-(const T& a, const std::complex<T>& b) { \
144  return std::complex<T>(a - numext::real(b), -numext::imag(b)); \
145 } \
146  \
147 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
148 std::complex<T> operator*(const std::complex<T>& a, const std::complex<T>& b) { \
149  return complex_multiply(a, b); \
150 } \
151  \
152 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
153 std::complex<T> operator*(const std::complex<T>& a, const T& b) { \
154  return std::complex<T>(numext::real(a) * b, numext::imag(a) * b); \
155 } \
156  \
157 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
158 std::complex<T> operator*(const T& a, const std::complex<T>& b) { \
159  return std::complex<T>(a * numext::real(b), a * numext::imag(b)); \
160 } \
161  \
162 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
163 std::complex<T> operator/(const std::complex<T>& a, const std::complex<T>& b) { \
164  return complex_divide(a, b); \
165 } \
166  \
167 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
168 std::complex<T> operator/(const std::complex<T>& a, const T& b) { \
169  return std::complex<T>(numext::real(a) / b, numext::imag(a) / b); \
170 } \
171  \
172 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
173 std::complex<T> operator/(const T& a, const std::complex<T>& b) { \
174  return complex_divide(std::complex<T>(a, 0), b); \
175 } \
176  \
177 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
178 std::complex<T>& operator+=(std::complex<T>& a, const std::complex<T>& b) { \
179  numext::real_ref(a) += numext::real(b); \
180  numext::imag_ref(a) += numext::imag(b); \
181  return a; \
182 } \
183  \
184 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
185 std::complex<T>& operator-=(std::complex<T>& a, const std::complex<T>& b) { \
186  numext::real_ref(a) -= numext::real(b); \
187  numext::imag_ref(a) -= numext::imag(b); \
188  return a; \
189 } \
190  \
191 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
192 std::complex<T>& operator*=(std::complex<T>& a, const std::complex<T>& b) { \
193  a = complex_multiply(a, b); \
194  return a; \
195 } \
196  \
197 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
198 std::complex<T>& operator/=(std::complex<T>& a, const std::complex<T>& b) { \
199  a = complex_divide(a, b); \
200  return a; \
201 } \
202  \
203 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
204 bool operator==(const std::complex<T>& a, const std::complex<T>& b) { \
205  return numext::real(a) == numext::real(b) && numext::imag(a) == numext::imag(b); \
206 } \
207  \
208 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
209 bool operator==(const std::complex<T>& a, const T& b) { \
210  return numext::real(a) == b && numext::imag(a) == 0; \
211 } \
212  \
213 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
214 bool operator==(const T& a, const std::complex<T>& b) { \
215  return a == numext::real(b) && 0 == numext::imag(b); \
216 } \
217  \
218 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
219 bool operator!=(const std::complex<T>& a, const std::complex<T>& b) { \
220  return !(a == b); \
221 } \
222  \
223 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
224 bool operator!=(const std::complex<T>& a, const T& b) { \
225  return !(a == b); \
226 } \
227  \
228 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
229 bool operator!=(const T& a, const std::complex<T>& b) { \
230  return !(a == b); \
231 }
232 
233 // Do not specialize for long double, since that reduces to double on device.
234 EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(float)
235 EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS(double)
236 
237 #undef EIGEN_CREATE_STD_COMPLEX_OPERATOR_SPECIALIZATIONS
238 
239 
240 } // namespace complex_operator_detail
241 
242 EIGEN_USING_STD_COMPLEX_OPERATORS
243 
244 namespace numext {
245 EIGEN_USING_STD_COMPLEX_OPERATORS
246 } // namespace numext
247 
248 namespace internal {
249 EIGEN_USING_STD_COMPLEX_OPERATORS
250 
251 } // namespace internal
252 } // namespace Eigen
253 
254 #endif // !(EIGEN_COMP_ICC && _USE_COMPLEX_SPECIALIZATION_)
255 
256 #endif // EIGEN_CUDACC && EIGEN_GPU_COMPILE_PHASE
257 
258 #endif // EIGEN_COMPLEX_CUDA_H
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#define EIGEN_DEVICE_FUNC
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