Block-Structured AMR Software Framework
AMReX_Math.H
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1 #ifndef AMREX_MATH_H_
2 #define AMREX_MATH_H_
3 #include <AMReX_Config.H>
4 
5 #include <AMReX_GpuQualifiers.H>
6 #include <AMReX_Extension.H>
7 #include <AMReX_INT.H>
8 #include <AMReX_REAL.H>
9 #include <cmath>
10 #include <cstdlib>
11 #include <type_traits>
12 #include <utility>
13 
14 #ifdef AMREX_USE_SYCL
15 # include <sycl/sycl.hpp>
16 #endif
17 
18 namespace amrex { inline namespace disabled {
19  // If it is inside namespace amrex, or amrex namespace is imported with using namespace amrex or
20  // amrex::disabled, unqualified abs functions are disabled with a compile time error such as,
21  // call of overload abs(int&) is ambiguous, or a link time error such as, undefined reference to
22  // `amrex::disabled::abs(double)'. To fix it, one can use `std::abs` or `amrex::Math::abs`.
23  // The latter works in both host and device functions, whereas `std::abs` does not currently
24  // work on device with HIP and SYCL.
25  AMREX_GPU_HOST_DEVICE double abs (double);
26  AMREX_GPU_HOST_DEVICE float abs (float);
27  AMREX_GPU_HOST_DEVICE long double abs (long double);
30  AMREX_GPU_HOST_DEVICE long long abs (long long);
31 }}
32 
33 namespace amrex::Math {
34 
35 // Since Intel's SYCL compiler now supports the following std functions on device,
36 // one no longer needs to use amrex::Math::abs, etc. They are kept here for
37 // backward compatibility.
38 
39 using std::abs;
40 using std::ceil;
41 using std::copysign;
42 using std::floor;
43 using std::round;
44 
45 // However, since Intel's SYCL compiler is very aggressive with fast floating
46 // point optimisations, the following must be kept, as using the std functions
47 // always evaluates to false (even at -O1).
48 
49 #ifdef AMREX_USE_SYCL
50 
51 using sycl::isfinite;
52 using sycl::isinf;
53 
54 #else
55 
56 using std::isfinite;
57 using std::isinf;
58 
59 #endif
60 
61 template <typename T>
62 constexpr std::enable_if_t<std::is_floating_point_v<T>,T> pi ()
63 {
64  return T(3.1415926535897932384626433832795029L);
65 }
66 
69 double cospi (double x)
70 {
71 #if defined(AMREX_USE_SYCL)
72  return sycl::cospi(x);
73 #else
75  AMREX_IF_ON_HOST(( return std::cos(pi<double>()*x); ))
76 #endif
77 }
78 
81 float cospi (float x)
82 {
83 #if defined(AMREX_USE_SYCL)
84  return sycl::cospi(x);
85 #else
86  AMREX_IF_ON_DEVICE(( return ::cospif(x); ))
87  AMREX_IF_ON_HOST(( return std::cos(pi<float>()*x); ))
88 #endif
89 }
90 
93 double sinpi (double x)
94 {
95 #if defined(AMREX_USE_SYCL)
96  return sycl::sinpi(x);
97 #else
99  AMREX_IF_ON_HOST(( return std::sin(pi<double>()*x); ))
100 #endif
101 }
102 
105 float sinpi (float x)
106 {
107 #if defined(AMREX_USE_SYCL)
108  return sycl::sinpi(x);
109 #else
110  AMREX_IF_ON_DEVICE(( return ::sinpif(x); ))
111  AMREX_IF_ON_HOST(( return std::sin(pi<float>()*x); ))
112 #endif
113 }
114 
115 namespace detail {
116  AMREX_FORCE_INLINE void sincos (double x, double* sinx, double* cosx) {
117 #if defined(_GNU_SOURCE) && !defined(__APPLE__)
118  ::sincos(x, sinx, cosx);
119 #else
120  *sinx = std::sin(x);
121  *cosx = std::cos(x);
122 #endif
123  }
124 
125  AMREX_FORCE_INLINE void sincosf (float x, float* sinx, float* cosx) {
126 #if defined(_GNU_SOURCE) && !defined(__APPLE__)
127  ::sincosf(x, sinx, cosx);
128 #else
129  *sinx = std::sin(x);
130  *cosx = std::cos(x);
131 #endif
132  }
133 }
134 
137 std::pair<double,double> sincos (double x)
138 {
139  std::pair<double,double> r;
140 #if defined(AMREX_USE_SYCL)
141  r.first = sycl::sincos(x, sycl::private_ptr<double>(&r.second));
142 #else
143  AMREX_IF_ON_DEVICE(( ::sincos(x, &r.first, &r.second); ))
144  AMREX_IF_ON_HOST(( detail::sincos(x, &r.first, &r.second); ))
145 #endif
146  return r;
147 }
148 
151 std::pair<float,float> sincos (float x)
152 {
153  std::pair<float,float> r;
154 #if defined(AMREX_USE_SYCL)
155  r.first = sycl::sincos(x, sycl::private_ptr<float>(&r.second));
156 #else
157  AMREX_IF_ON_DEVICE(( ::sincosf(x, &r.first, &r.second); ))
158  AMREX_IF_ON_HOST(( detail::sincosf(x, &r.first, &r.second); ))
159 #endif
160  return r;
161 }
162 
165 std::pair<double,double> sincospi (double x)
166 {
167  std::pair<double,double> r;
168 #if defined(AMREX_USE_SYCL)
169  r = sincos(pi<double>()*x);
170 #else
171  AMREX_IF_ON_DEVICE(( ::sincospi(x, &r.first, &r.second); ))
172  AMREX_IF_ON_HOST(( r = sincos(pi<double>()*x); ))
173 #endif
174  return r;
175 }
176 
179 std::pair<float,float> sincospi (float x)
180 {
181  std::pair<float,float> r;
182 #if defined(AMREX_USE_SYCL)
183  r = sincos(pi<float>()*x);
184 #else
185  AMREX_IF_ON_DEVICE(( ::sincospif(x, &r.first, &r.second); ))
186  AMREX_IF_ON_HOST(( r = sincos(pi<float>()*x); ))
187 #endif
188  return r;
189 }
190 
192 template <int Power, typename T,
193  typename = std::enable_if_t<!std::is_integral<T>() || Power>=0>>
195 constexpr T powi (T x) noexcept
196 {
197  if constexpr (Power < 0) {
198  return T(1)/powi<-Power>(x);
199  } else if constexpr (Power == 0) {
200  //note: 0^0 is implementation-defined, but most compilers return 1
201  return T(1);
202  } else if constexpr (Power == 1) {
203  return x;
204  } else if constexpr (Power == 2) {
205  return x*x;
206  } else if constexpr (Power%2 == 0) {
207  return powi<2>(powi<Power/2>(x));
208  } else {
209  return x*powi<Power-1>(x);
210  }
211 }
212 
213 #if defined(AMREX_INT128_SUPPORTED)
215 std::uint64_t umulhi (std::uint64_t a, std::uint64_t b)
216 {
217 #if defined(AMREX_USE_SYCL)
218  return sycl::mul_hi(a,b);
219 #else
220  AMREX_IF_ON_DEVICE(( return __umul64hi(a, b); ))
222  auto tmp = amrex::UInt128_t(a) * amrex::UInt128_t(b);
223  return std::uint64_t(tmp >> 64);
224  ))
225 #endif
226 }
227 #endif
228 
229 template <typename T>
232 {
233  // Computing K based on DLMF
234  // https://dlmf.nist.gov/19.8
235  T tol = std::numeric_limits<T>::epsilon();
236 
237  T a0 = 1.0;
238  T g0 = std::sqrt(1.0 - k*k);
239  T a = a0;
240  T g = g0;
241 
242  // Find Arithmetic Geometric mean
243  while(std::abs(a0 - g0) > tol) {
244  a = 0.5*(a0 + g0);
245  g = std::sqrt(a0 * g0);
246 
247  a0 = a;
248  g0 = g;
249  }
250 
251  return 0.5*pi<T>()/a;
252 }
253 
254 template <typename T>
257 {
258  // Computing E based on DLMF
259  // https://dlmf.nist.gov/19.8
260  T Kcomp = amrex::Math::comp_ellint_1<T>(k);
261  T tol = std::numeric_limits<T>::epsilon();
262 
263  // Step Zero
264  T a0 = 1.0;
265  T g0 = std::sqrt(1.0 - k*k);
266  T cn = std::sqrt(a0*a0 - g0*g0);
267 
268  // Step 1
269  int n = 1;
270  T a = 0.5 * (a0 + g0);
271  T g = std::sqrt(a0*g0);
272  cn = 0.25*cn*cn/a;
273 
274  T sum_val = a*a;
275  a0 = a;
276  g0 = g;
277 
278  while(std::abs(cn*cn) > tol) {
279  // Compute coefficients for this iteration
280  a = 0.5 * (a0 + g0);
281  g = std::sqrt(a0*g0);
282  cn = 0.25*cn*cn/a;
283 
284  n++;
285  sum_val -= std::pow(2,n-1)*cn*cn;
286 
287  // Save a and g for next iteration
288  a0 = a;
289  g0 = g;
290  }
291 
292  return Kcomp*sum_val;
293 }
294 
295 /***************************************************************************************************
296  * Copyright (c) 2017 - 2024 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
297  * SPDX-License-Identifier: BSD-3-Clause
298  *
299  * Redistribution and use in source and binary forms, with or without
300  * modification, are permitted provided that the following conditions are met:
301  *
302  * 1. Redistributions of source code must retain the above copyright notice, this
303  * list of conditions and the following disclaimer.
304  *
305  * 2. Redistributions in binary form must reproduce the above copyright notice,
306  * this list of conditions and the following disclaimer in the documentation
307  * and/or other materials provided with the distribution.
308  *
309  * 3. Neither the name of the copyright holder nor the names of its
310  * contributors may be used to endorse or promote products derived from
311  * this software without specific prior written permission.
312  *
313  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
314  * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
315  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
316  * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
317  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
318  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
319  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
320  * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
321  * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
322  * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
323  *
324  **************************************************************************************************/
325 
327 
343 {
344  std::uint64_t divisor = 0;
345 
346 #ifdef AMREX_INT128_SUPPORTED
347  std::uint64_t multiplier = 1U;
348  unsigned int shift_right = 0;
349  unsigned int round_up = 0;
350 
351  //
352  // Static methods
353  //
354 
356  static std::uint32_t integer_log2 (std::uint64_t x)
357  {
358  std::uint32_t n = 0;
359  while (x >>= 1) {
360  ++n;
361  }
362  return n;
363  }
364 
368  FastDivmodU64 (std::uint64_t divisor_)
369  : divisor(divisor_)
370  {
371  if (divisor) {
372  shift_right = integer_log2(divisor);
373 
374  if ((divisor & (divisor - 1)) == 0) {
375  multiplier = 0;
376  }
377  else {
378  std::uint64_t power_of_two = (std::uint64_t(1) << shift_right);
379  auto n = amrex::UInt128_t(power_of_two) << 64;
380  std::uint64_t multiplier_lo = n / divisor;
381  n += power_of_two;
382  multiplier = n / divisor;
383  round_up = (multiplier_lo == multiplier ? 1 : 0);
384  }
385  }
386  }
387 
388 #else
389 
390  FastDivmodU64 (std::uint64_t divisor_) : divisor(divisor_) {}
391 
392 #endif
393 
395  FastDivmodU64 () = default;
396 
398  [[nodiscard]] AMREX_GPU_HOST_DEVICE
399  std::uint64_t divide (std::uint64_t dividend) const
400  {
401 #if defined(AMREX_INT128_SUPPORTED)
402  auto x = dividend;
403  if (multiplier) {
404  x = amrex::Math::umulhi(dividend + round_up, multiplier);
405  }
406  return (x >> shift_right);
407 #else
408  return dividend / divisor;
409 #endif
410  }
411 
413  [[nodiscard]] AMREX_GPU_HOST_DEVICE
414  std::uint64_t modulus (std::uint64_t quotient, std::uint64_t dividend) const
415  {
416  return dividend - quotient * divisor;
417  }
418 
420  [[nodiscard]] AMREX_GPU_HOST_DEVICE
421  std::uint64_t divmod (std::uint64_t &remainder, std::uint64_t dividend) const
422  {
423  auto quotient = divide(dividend);
424  remainder = modulus(quotient, dividend);
425  return quotient;
426  }
427 
431  void operator() (std::uint64_t &quotient, std::uint64_t &remainder, std::uint64_t dividend) const
432  {
433  quotient = divmod(remainder, dividend);
434  }
435 };
436 
437 }
438 
439 #endif
#define AMREX_FORCE_INLINE
Definition: AMReX_Extension.H:119
#define AMREX_IF_ON_DEVICE(CODE)
Definition: AMReX_GpuQualifiers.H:56
#define AMREX_IF_ON_HOST(CODE)
Definition: AMReX_GpuQualifiers.H:58
#define AMREX_GPU_HOST_DEVICE
Definition: AMReX_GpuQualifiers.H:20
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE bool isinf(T m) noexcept
Definition: AMReX_GpuUtility.H:161
AMREX_FORCE_INLINE void sincos(double x, double *sinx, double *cosx)
Definition: AMReX_Math.H:116
AMREX_FORCE_INLINE void sincosf(float x, float *sinx, float *cosx)
Definition: AMReX_Math.H:125
Definition: AMReX_Math.H:33
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE T comp_ellint_1(T k)
Definition: AMReX_Math.H:231
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE double sinpi(double x)
Return sin(x*pi) given x.
Definition: AMReX_Math.H:93
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE std::pair< float, float > sincos(float x)
Return sine and cosine of given number.
Definition: AMReX_Math.H:151
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE float sinpi(float x)
Return sin(x*pi) given x.
Definition: AMReX_Math.H:105
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE T comp_ellint_2(T k)
Definition: AMReX_Math.H:256
constexpr AMREX_FORCE_INLINE T powi(T x) noexcept
Return pow(x, Power), where Power is an integer known at compile time.
Definition: AMReX_Math.H:195
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE std::pair< double, double > sincos(double x)
Return sine and cosine of given number.
Definition: AMReX_Math.H:137
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE double cospi(double x)
Return cos(x*pi) given x.
Definition: AMReX_Math.H:69
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE float cospi(float x)
Return cos(x*pi) given x.
Definition: AMReX_Math.H:81
constexpr std::enable_if_t< std::is_floating_point_v< T >, T > pi()
Definition: AMReX_Math.H:62
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE std::pair< double, double > sincospi(double x)
Return sin(pi*x) and cos(pi*x) given x.
Definition: AMReX_Math.H:165
AMREX_GPU_HOST_DEVICE long long abs(long long)
AMREX_GPU_HOST_DEVICE double abs(double)
Definition: AMReX_Amr.cpp:49
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE GpuComplex< T > pow(const GpuComplex< T > &a_z, const T &a_y) noexcept
Raise a complex number to a (real) power.
Definition: AMReX_GpuComplex.H:418
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE GpuComplex< T > sqrt(const GpuComplex< T > &a_z) noexcept
Return the square root of a complex number.
Definition: AMReX_GpuComplex.H:373
Definition: AMReX_FabArrayCommI.H:896
Definition: AMReX_Math.H:343
AMREX_GPU_HOST_DEVICE std::uint64_t divmod(std::uint64_t &remainder, std::uint64_t dividend) const
Returns the quotient of floor(dividend / divisor) and computes the remainder.
Definition: AMReX_Math.H:421
AMREX_GPU_HOST_DEVICE std::uint64_t modulus(std::uint64_t quotient, std::uint64_t dividend) const
Computes the remainder given a computed quotient and dividend.
Definition: AMReX_Math.H:414
std::uint64_t divisor
Definition: AMReX_Math.H:344
AMREX_GPU_HOST_DEVICE void operator()(std::uint64_t &quotient, std::uint64_t &remainder, std::uint64_t dividend) const
Definition: AMReX_Math.H:431
AMREX_GPU_HOST_DEVICE std::uint64_t divide(std::uint64_t dividend) const
Returns the quotient of floor(dividend / divisor)
Definition: AMReX_Math.H:399
FastDivmodU64(std::uint64_t divisor_)
Definition: AMReX_Math.H:390
FastDivmodU64()=default
Default construct an invalid&#160;FastDivmodU64.