xref: /petsc/include/petscmath.h (revision 8a351411900e2f006ce81ef96982413e6caeb851)
1 /*
2 
3       PETSc mathematics include file. Defines certain basic mathematical
4     constants and functions for working with single, double, and quad precision
5     floating point numbers as well as complex single and double.
6 
7     This file is included by petscsys.h and should not be used directly.
8 
9 */
10 
11 #if !defined(__PETSCMATH_H)
12 #define __PETSCMATH_H
13 #include <math.h>
14 
15 /*
16 
17      Defines operations that are different for complex and real numbers;
18    note that one cannot mix the use of complex and real in the same
19    PETSc program. All PETSc objects in one program are built around the object
20    PetscScalar which is either always a real or a complex.
21 
22 */
23 
24 #if defined(PETSC_USE_REAL_SINGLE)
25 #define MPIU_REAL   MPI_FLOAT
26 typedef float PetscReal;
27 #define PetscSqrtReal(a)    sqrt(a)
28 #define PetscExpReal(a)     exp(a)
29 #define PetscLogReal(a)     log(a)
30 #define PetscLog10Real(a)   log10(a)
31 #ifdef PETSC_HAVE_LOG2
32 #define PetscLog2Real(a)    log2(a)
33 #endif
34 #define PetscSinReal(a)     sin(a)
35 #define PetscCosReal(a)     cos(a)
36 #define PetscTanReal(a)     tan(a)
37 #define PetscAsinReal(a)    asin(a)
38 #define PetscAcosReal(a)    acos(a)
39 #define PetscAtanReal(a)    atan(a)
40 #define PetscAtan2Real(a,b) atan2(a,b)
41 #define PetscSinhReal(a)    sinh(a)
42 #define PetscCoshReal(a)    cosh(a)
43 #define PetscTanhReal(a)    tanh(a)
44 #define PetscPowReal(a,b)   pow(a,b)
45 #define PetscCeilReal(a)    ceil(a)
46 #define PetscFloorReal(a)   floor(a)
47 #define PetscFmodReal(a,b)  fmod(a,b)
48 #define PetscTGamma(a)      tgammaf(a)
49 #elif defined(PETSC_USE_REAL_DOUBLE)
50 #define MPIU_REAL   MPI_DOUBLE
51 typedef double PetscReal;
52 #define PetscSqrtReal(a)    sqrt(a)
53 #define PetscExpReal(a)     exp(a)
54 #define PetscLogReal(a)     log(a)
55 #define PetscLog10Real(a)   log10(a)
56 #ifdef PETSC_HAVE_LOG2
57 #define PetscLog2Real(a)    log2(a)
58 #endif
59 #define PetscSinReal(a)     sin(a)
60 #define PetscCosReal(a)     cos(a)
61 #define PetscTanReal(a)     tan(a)
62 #define PetscAsinReal(a)    asin(a)
63 #define PetscAcosReal(a)    acos(a)
64 #define PetscAtanReal(a)    atan(a)
65 #define PetscAtan2Real(a,b) atan2(a,b)
66 #define PetscSinhReal(a)    sinh(a)
67 #define PetscCoshReal(a)    cosh(a)
68 #define PetscTanhReal(a)    tanh(a)
69 #define PetscPowReal(a,b)   pow(a,b)
70 #define PetscCeilReal(a)    ceil(a)
71 #define PetscFloorReal(a)   floor(a)
72 #define PetscFmodReal(a,b)  fmod(a,b)
73 #define PetscTGamma(a)      tgamma(a)
74 #elif defined(PETSC_USE_REAL___FLOAT128)
75 #if defined(__cplusplus)
76 extern "C" {
77 #endif
78 #include <quadmath.h>
79 #if defined(__cplusplus)
80 }
81 #endif
82 PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
83 #define MPIU_REAL MPIU___FLOAT128
84 typedef __float128 PetscReal;
85 #define PetscSqrtReal(a)    sqrtq(a)
86 #define PetscExpReal(a)     expq(a)
87 #define PetscLogReal(a)     logq(a)
88 #define PetscLog10Real(a)   log10q(a)
89 #ifdef PETSC_HAVE_LOG2
90 #define PetscLog2Real(a)    log2q(a)
91 #endif
92 #define PetscSinReal(a)     sinq(a)
93 #define PetscCosReal(a)     cosq(a)
94 #define PetscTanReal(a)     tanq(a)
95 #define PetscAsinReal(a)    asinq(a)
96 #define PetscAcosReal(a)    acosq(a)
97 #define PetscAtanReal(a)    atanq(a)
98 #define PetscAtan2Real(a,b) atan2q(a,b)
99 #define PetscSinhReal(a)    sinhq(a)
100 #define PetscCoshReal(a)    coshq(a)
101 #define PetscTanhReal(a)    tanhq(a)
102 #define PetscPowReal(a,b)   powq(a,b)
103 #define PetscCeilReal(a)    ceilq(a)
104 #define PetscFloorReal(a)   floorq(a)
105 #define PetscFmodReal(a,b)  fmodq(a,b)
106 #define PetscTGamma(a)      tgammaq(a)
107 #elif defined(PETSC_USE_REAL___FP16)
108 PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
109 #define MPIU_REAL MPIU___FP16
110 typedef __fp16 PetscReal;
111 #define PetscSqrtReal(a)    sqrtf(a)
112 #define PetscExpReal(a)     expf(a)
113 #define PetscLogReal(a)     logf(a)
114 #define PetscLog10Real(a)   log10f(a)
115 #ifdef PETSC_HAVE_LOG2
116 #define PetscLog2Real(a)    log2f(a)
117 #endif
118 #define PetscSinReal(a)     sinf(a)
119 #define PetscCosReal(a)     cosf(a)
120 #define PetscTanReal(a)     tanf(a)
121 #define PetscAsinReal(a)    asinf(a)
122 #define PetscAcosReal(a)    acosf(a)
123 #define PetscAtanReal(a)    atanf(a)
124 #define PetscAtan2Real(a,b) atan2f(a,b)
125 #define PetscSinhReal(a)    sinhf(a)
126 #define PetscCoshReal(a)    coshf(a)
127 #define PetscTanhReal(a)    tanhf(a)
128 #define PetscPowReal(a,b)   powf(a,b)
129 #define PetscCeilReal(a)    ceilf(a)
130 #define PetscFloorReal(a)   floorf(a)
131 #define PetscFmodReal(a,b)  fmodf(a,b)
132 #define PetscTGamma(a)      tgammaf(a)
133 #endif /* PETSC_USE_REAL_* */
134 
135 /*
136     Complex number definitions
137  */
138 #if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
139 #if !defined(PETSC_SKIP_COMPLEX)
140 #define PETSC_HAVE_COMPLEX 1
141 /* C++ support of complex number */
142 #if defined(PETSC_HAVE_CUSP)
143 #define complexlib cusp
144 #include <cusp/complex.h>
145 #elif defined(PETSC_HAVE_VECCUDA) && __CUDACC_VER_MAJOR__ > 6
146 /* complex headers in thrust only available in CUDA 7.0 and above */
147 #define complexlib thrust
148 #include <thrust/complex.h>
149 #else
150 #define complexlib std
151 #include <complex>
152 #endif
153 
154 #define PetscRealPartComplex(a)      (a).real()
155 #define PetscImaginaryPartComplex(a) (a).imag()
156 #define PetscAbsComplex(a)           complexlib::abs(a)
157 #define PetscConjComplex(a)          complexlib::conj(a)
158 #define PetscSqrtComplex(a)          complexlib::sqrt(a)
159 #define PetscPowComplex(a,b)         complexlib::pow(a,b)
160 #define PetscExpComplex(a)           complexlib::exp(a)
161 #define PetscLogComplex(a)           complexlib::log(a)
162 #define PetscSinComplex(a)           complexlib::sin(a)
163 #define PetscCosComplex(a)           complexlib::cos(a)
164 #define PetscAsinComplex(a)          complexlib::asin(a)
165 #define PetscAcosComplex(a)          complexlib::acos(a)
166 #if defined(PETSC_HAVE_TANCOMPLEX)
167 #define PetscTanComplex(a)           complexlib::tan(a)
168 #else
169 #define PetscTanComplex(a)           PetscSinComplex(a)/PetscCosComplex(a)
170 #endif
171 #define PetscSinhComplex(a)          complexlib::sinh(a)
172 #define PetscCoshComplex(a)          complexlib::cosh(a)
173 #if defined(PETSC_HAVE_TANHCOMPLEX)
174 #define PetscTanhComplex(a)          complexlib::tanh(a)
175 #else
176 #define PetscTanhComplex(a)          PetscSinhComplex(a)/PetscCoshComplex(a)
177 #endif
178 
179 #if defined(PETSC_USE_REAL_SINGLE)
180 typedef complexlib::complex<float> PetscComplex;
181 #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND)
182 static inline PetscComplex operator+(const PetscComplex& lhs, const double& rhs) { return lhs + float(rhs); }
183 static inline PetscComplex operator+(const double& lhs, const PetscComplex& rhs) { return float(lhs) + rhs; }
184 static inline PetscComplex operator-(const PetscComplex& lhs, const double& rhs) { return lhs - float(rhs); }
185 static inline PetscComplex operator-(const double& lhs, const PetscComplex& rhs) { return float(lhs) - rhs; }
186 static inline PetscComplex operator*(const PetscComplex& lhs, const double& rhs) { return lhs * float(rhs); }
187 static inline PetscComplex operator*(const double& lhs, const PetscComplex& rhs) { return float(lhs) * rhs; }
188 static inline PetscComplex operator/(const PetscComplex& lhs, const double& rhs) { return lhs / float(rhs); }
189 static inline PetscComplex operator/(const double& lhs, const PetscComplex& rhs) { return float(lhs) / rhs; }
190 static inline bool operator==(const PetscComplex& lhs, const double& rhs) { return lhs.imag() == float(0) && lhs.real() == float(rhs); }
191 static inline bool operator==(const double& lhs, const PetscComplex& rhs) { return rhs.imag() == float(0) && rhs.real() == float(lhs); }
192 static inline bool operator!=(const PetscComplex& lhs, const double& rhs) { return lhs.imag() != float(0) || lhs.real() != float(rhs); }
193 static inline bool operator!=(const double& lhs, const PetscComplex& rhs) { return rhs.imag() != float(0) || rhs.real() != float(lhs); }
194 #endif  /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */
195 #elif defined(PETSC_USE_REAL_DOUBLE)
196 typedef complexlib::complex<double> PetscComplex;
197 #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND)
198 static inline PetscComplex operator+(const PetscComplex& lhs, const PetscInt& rhs) { return lhs + double(rhs); }
199 static inline PetscComplex operator+(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) + rhs; }
200 static inline PetscComplex operator-(const PetscComplex& lhs, const PetscInt& rhs) { return lhs - double(rhs); }
201 static inline PetscComplex operator-(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) - rhs; }
202 static inline PetscComplex operator*(const PetscComplex& lhs, const PetscInt& rhs) { return lhs * double(rhs); }
203 static inline PetscComplex operator*(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) * rhs; }
204 static inline PetscComplex operator/(const PetscComplex& lhs, const PetscInt& rhs) { return lhs / double(rhs); }
205 static inline PetscComplex operator/(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) / rhs; }
206 static inline bool operator==(const PetscComplex& lhs, const PetscInt& rhs) { return lhs.imag() == double(0) && lhs.real() == double(rhs); }
207 static inline bool operator==(const PetscInt& lhs, const PetscComplex& rhs) { return rhs.imag() == double(0) && rhs.real() == double(lhs); }
208 static inline bool operator!=(const PetscComplex& lhs, const PetscInt& rhs) { return lhs.imag() != double(0) || lhs.real() != double(rhs); }
209 static inline bool operator!=(const PetscInt& lhs, const PetscComplex& rhs) { return rhs.imag() != double(0) || rhs.real() != double(lhs); }
210 #endif  /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */
211 #elif defined(PETSC_USE_REAL___FLOAT128)
212 typedef complexlib::complex<__float128> PetscComplex; /* Notstandard and not expected to work, use __complex128 */
213 PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128;
214 #endif  /* PETSC_USE_REAL_ */
215 #endif  /* ! PETSC_SKIP_COMPLEX */
216 
217 #elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX) && !defined(PETSC_USE_REAL___FP16)
218 #if !defined(PETSC_SKIP_COMPLEX)
219 #define PETSC_HAVE_COMPLEX 1
220 #include <complex.h>
221 
222 #if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
223 typedef float _Complex PetscComplex;
224 
225 #define PetscRealPartComplex(a)      crealf(a)
226 #define PetscImaginaryPartComplex(a) cimagf(a)
227 #define PetscAbsComplex(a)           cabsf(a)
228 #define PetscConjComplex(a)          conjf(a)
229 #define PetscSqrtComplex(a)          csqrtf(a)
230 #define PetscPowComplex(a,b)         cpowf(a,b)
231 #define PetscExpComplex(a)           cexpf(a)
232 #define PetscLogComplex(a)           clogf(a)
233 #define PetscSinComplex(a)           csinf(a)
234 #define PetscCosComplex(a)           ccosf(a)
235 #define PetscAsinComplex(a)          casinf(a)
236 #define PetscAcosComplex(a)          cacosf(a)
237 #define PetscTanComplex(a)           ctanf(a)
238 #define PetscSinhComplex(a)          csinhf(a)
239 #define PetscCoshComplex(a)          ccoshf(a)
240 #define PetscTanhComplex(a)          ctanhf(a)
241 
242 #elif defined(PETSC_USE_REAL_DOUBLE)
243 typedef double _Complex PetscComplex;
244 
245 #define PetscRealPartComplex(a)      creal(a)
246 #define PetscImaginaryPartComplex(a) cimag(a)
247 #define PetscAbsComplex(a)           cabs(a)
248 #define PetscConjComplex(a)          conj(a)
249 #define PetscSqrtComplex(a)          csqrt(a)
250 #define PetscPowComplex(a,b)         cpow(a,b)
251 #define PetscExpComplex(a)           cexp(a)
252 #define PetscLogComplex(a)           clog(a)
253 #define PetscSinComplex(a)           csin(a)
254 #define PetscCosComplex(a)           ccos(a)
255 #define PetscAsinComplex(a)          casin(a)
256 #define PetscAcosComplex(a)          cacos(a)
257 #define PetscTanComplex(a)           ctan(a)
258 #define PetscSinhComplex(a)          csinh(a)
259 #define PetscCoshComplex(a)          ccosh(a)
260 #define PetscTanhComplex(a)          ctanh(a)
261 
262 #elif defined(PETSC_USE_REAL___FLOAT128)
263 typedef __complex128 PetscComplex;
264 PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
265 
266 #define PetscRealPartComplex(a)      crealq(a)
267 #define PetscImaginaryPartComplex(a) cimagq(a)
268 #define PetscAbsComplex(a)           cabsq(a)
269 #define PetscConjComplex(a)          conjq(a)
270 #define PetscSqrtComplex(a)          csqrtq(a)
271 #define PetscPowComplex(a,b)         cpowq(a,b)
272 #define PetscExpComplex(a)           cexpq(a)
273 #define PetscLogComplex(a)           clogq(a)
274 #define PetscSinComplex(a)           csinq(a)
275 #define PetscCosComplex(a)           ccosq(a)
276 #define PetscAsinComplex(a)          casinq(a)
277 #define PetscAcosComplex(a)          cacosq(a)
278 #define PetscTanComplex(a)           ctanq(a)
279 #define PetscSinhComplex(a)          csinhq(a)
280 #define PetscCoshComplex(a)          ccoshq(a)
281 #define PetscTanhComplex(a)          ctanhq(a)
282 
283 #endif /* PETSC_USE_REAL_* */
284 #elif (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
285 #error "PETSc was configured --with-scalar-type=complex, but a language-appropriate complex library is not available"
286 #endif /* !PETSC_SKIP_COMPLEX */
287 #endif /* (__cplusplus && PETSC_HAVE_CXX_COMPLEX) else-if (!__cplusplus && PETSC_HAVE_C99_COMPLEX) */
288 
289 #if defined(PETSC_HAVE_COMPLEX)
290 #if defined(PETSC_HAVE_MPI_C_DOUBLE_COMPLEX)
291 #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX
292 #define MPIU_C_COMPLEX MPI_C_COMPLEX
293 #else
294 # if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX)
295   typedef complexlib::complex<double> petsc_mpiu_c_double_complex;
296   typedef complexlib::complex<float> petsc_mpiu_c_complex;
297 # elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
298   typedef double _Complex petsc_mpiu_c_double_complex;
299   typedef float _Complex petsc_mpiu_c_complex;
300 # else
301   typedef struct {double real,imag;} petsc_mpiu_c_double_complex;
302   typedef struct {float real,imag;} petsc_mpiu_c_complex;
303 # endif
304 PETSC_EXTERN MPI_Datatype MPIU_C_DOUBLE_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_double_complex);
305 PETSC_EXTERN MPI_Datatype MPIU_C_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_complex);
306 #endif /* PETSC_HAVE_MPI_C_DOUBLE_COMPLEX */
307 #endif /* PETSC_HAVE_COMPLEX */
308 
309 #if defined(PETSC_HAVE_COMPLEX)
310 #  if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
311 #    define MPIU_COMPLEX MPIU_C_COMPLEX
312 #  elif defined(PETSC_USE_REAL_DOUBLE)
313 #    define MPIU_COMPLEX MPIU_C_DOUBLE_COMPLEX
314 #  elif defined(PETSC_USE_REAL___FLOAT128)
315 #    define MPIU_COMPLEX MPIU___COMPLEX128
316 #  endif /* PETSC_USE_REAL_* */
317 #endif
318 
319 #if (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
320 typedef PetscComplex PetscScalar;
321 #define PetscRealPart(a)      PetscRealPartComplex(a)
322 #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)
323 #define PetscAbsScalar(a)     PetscAbsComplex(a)
324 #define PetscConj(a)          PetscConjComplex(a)
325 #define PetscSqrtScalar(a)    PetscSqrtComplex(a)
326 #define PetscPowScalar(a,b)   PetscPowComplex(a,b)
327 #define PetscExpScalar(a)     PetscExpComplex(a)
328 #define PetscLogScalar(a)     PetscLogComplex(a)
329 #define PetscSinScalar(a)     PetscSinComplex(a)
330 #define PetscCosScalar(a)     PetscCosComplex(a)
331 #define PetscAsinScalar(a)    PetscAsinComplex(a)
332 #define PetscAcosScalar(a)    PetscAcosComplex(a)
333 #define PetscTanScalar(a)     PetscTanComplex(a)
334 #define PetscSinhScalar(a)    PetscSinhComplex(a)
335 #define PetscCoshScalar(a)    PetscCoshComplex(a)
336 #define PetscTanhScalar(a)    PetscTanhComplex(a)
337 #define MPIU_SCALAR MPIU_COMPLEX
338 
339 /*
340     real number definitions
341  */
342 #else /* PETSC_USE_COMPLEX */
343 typedef PetscReal PetscScalar;
344 #define MPIU_SCALAR MPIU_REAL
345 
346 #define PetscRealPart(a)      (a)
347 #define PetscImaginaryPart(a) ((PetscReal)0.)
348 PETSC_STATIC_INLINE PetscReal PetscAbsScalar(PetscScalar a) {return a < 0.0 ? -a : a;}
349 #define PetscConj(a)          (a)
350 #if !defined(PETSC_USE_REAL___FLOAT128)  && !defined(PETSC_USE_REAL___FP16)
351 #define PetscSqrtScalar(a)    sqrt(a)
352 #define PetscPowScalar(a,b)   pow(a,b)
353 #define PetscExpScalar(a)     exp(a)
354 #define PetscLogScalar(a)     log(a)
355 #define PetscSinScalar(a)     sin(a)
356 #define PetscCosScalar(a)     cos(a)
357 #define PetscAsinScalar(a)    asin(a)
358 #define PetscAcosScalar(a)    acos(a)
359 #define PetscTanScalar(a)     tan(a)
360 #define PetscSinhScalar(a)    sinh(a)
361 #define PetscCoshScalar(a)    cosh(a)
362 #define PetscTanhScalar(a)    tanh(a)
363 #elif defined(PETSC_USE_REAL___FP16)
364 #define PetscSqrtScalar(a)    sqrtf(a)
365 #define PetscPowScalar(a,b)   powf(a,b)
366 #define PetscExpScalar(a)     expf(a)
367 #define PetscLogScalar(a)     logf(a)
368 #define PetscSinScalar(a)     sinf(a)
369 #define PetscCosScalar(a)     cosf(a)
370 #define PetscAsinScalar(a)    asinf(a)
371 #define PetscAcosScalar(a)    acosf(a)
372 #define PetscTanScalar(a)     tanf(a)
373 #define PetscSinhScalar(a)    sinhf(a)
374 #define PetscCoshScalar(a)    coshf(a)
375 #define PetscTanhScalar(a)    tanhf(a)
376 #else /* PETSC_USE_REAL___FLOAT128 */
377 #define PetscSqrtScalar(a)    sqrtq(a)
378 #define PetscPowScalar(a,b)   powq(a,b)
379 #define PetscExpScalar(a)     expq(a)
380 #define PetscLogScalar(a)     logq(a)
381 #define PetscSinScalar(a)     sinq(a)
382 #define PetscCosScalar(a)     cosq(a)
383 #define PetscAsinScalar(a)    asinq(a)
384 #define PetscAcosScalar(a)    acosq(a)
385 #define PetscTanScalar(a)     tanq(a)
386 #define PetscSinhScalar(a)    sinhq(a)
387 #define PetscCoshScalar(a)    coshq(a)
388 #define PetscTanhScalar(a)    tanhq(a)
389 #endif /* PETSC_USE_REAL___FLOAT128 */
390 
391 #endif /* PETSC_USE_COMPLEX */
392 
393 #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)
394 #define PetscSignReal(a) (((a) >= 0.0) ? ((a) == 0.0 ? 0.0 : 1.0) : -1.0)
395 #define PetscAbs(a)  (((a) >= 0) ? (a) : -(a))
396 
397 /* --------------------------------------------------------------------------*/
398 
399 /*
400    Certain objects may be created using either single or double precision.
401    This is currently not used.
402 */
403 typedef enum { PETSC_SCALAR_DOUBLE,PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;
404 
405 #if defined(PETSC_HAVE_COMPLEX)
406 /* PETSC_i is the imaginary number, i */
407 PETSC_EXTERN PetscComplex PETSC_i;
408 
409 /* Try to do the right thing for complex number construction: see
410 
411   http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
412 
413   for details
414 */
415 static inline PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
416 {
417 #if   defined(__cplusplus)
418   return PetscComplex(x,y);
419 #elif defined(_Imaginary_I)
420   return x + y * _Imaginary_I;
421 #else
422 #if   defined(PETSC_USE_REAL_SINGLE) && defined(CMPLXF)
423   return CMPLXF(x,y);
424   PETSC_REAL
425 #elif defined(PETSC_USE_REAL_DOUBLE) && defined(CMPLX)
426   return CMPLX(x,y);
427 #else
428   return x + y * PETSC_i;
429 #endif
430 #endif
431 }
432 #endif
433 
434 
435 /*MC
436    PetscMin - Returns minimum of two numbers
437 
438    Synopsis:
439    #include <petscmath.h>
440    type PetscMin(type v1,type v2)
441 
442    Not Collective
443 
444    Input Parameter:
445 +  v1 - first value to find minimum of
446 -  v2 - second value to find minimum of
447 
448    Notes: type can be integer or floating point value
449 
450    Level: beginner
451 
452 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
453 
454 M*/
455 #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))
456 
457 /*MC
458    PetscMax - Returns maxium of two numbers
459 
460    Synopsis:
461    #include <petscmath.h>
462    type max PetscMax(type v1,type v2)
463 
464    Not Collective
465 
466    Input Parameter:
467 +  v1 - first value to find maximum of
468 -  v2 - second value to find maximum of
469 
470    Notes: type can be integer or floating point value
471 
472    Level: beginner
473 
474 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
475 
476 M*/
477 #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))
478 
479 /*MC
480    PetscClipInterval - Returns a number clipped to be within an interval
481 
482    Synopsis:
483    #include <petscmath.h>
484    type clip PetscClipInterval(type x,type a,type b)
485 
486    Not Collective
487 
488    Input Parameter:
489 +  x - value to use if within interval (a,b)
490 .  a - lower end of interval
491 -  b - upper end of interval
492 
493    Notes: type can be integer or floating point value
494 
495    Level: beginner
496 
497 .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
498 
499 M*/
500 #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))
501 
502 /*MC
503    PetscAbsInt - Returns the absolute value of an integer
504 
505    Synopsis:
506    #include <petscmath.h>
507    int abs PetscAbsInt(int v1)
508 
509    Not Collective
510 
511    Input Parameter:
512 .   v1 - the integer
513 
514    Level: beginner
515 
516 .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()
517 
518 M*/
519 #define PetscAbsInt(a)  (((a)<0)   ? -(a) : (a))
520 
521 /*MC
522    PetscAbsReal - Returns the absolute value of an real number
523 
524    Synopsis:
525    #include <petscmath.h>
526    Real abs PetscAbsReal(PetscReal v1)
527 
528    Not Collective
529 
530    Input Parameter:
531 .   v1 - the double
532 
533 
534    Level: beginner
535 
536 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()
537 
538 M*/
539 #define PetscAbsReal(a) (((a)<0)   ? -(a) : (a))
540 
541 /*MC
542    PetscSqr - Returns the square of a number
543 
544    Synopsis:
545    #include <petscmath.h>
546    type sqr PetscSqr(type v1)
547 
548    Not Collective
549 
550    Input Parameter:
551 .   v1 - the value
552 
553    Notes: type can be integer or floating point value
554 
555    Level: beginner
556 
557 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()
558 
559 M*/
560 #define PetscSqr(a)     ((a)*(a))
561 
562 /* ----------------------------------------------------------------------------*/
563 /*
564      Basic constants
565 */
566 #if defined(PETSC_USE_REAL___FLOAT128)
567 #define PETSC_PI                 M_PIq
568 #elif defined(M_PI)
569 #define PETSC_PI                 M_PI
570 #else
571 #define PETSC_PI                 3.14159265358979323846264338327950288419716939937510582
572 #endif
573 
574 #if !defined(PETSC_USE_64BIT_INDICES)
575 #define PETSC_MAX_INT            2147483647
576 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
577 #else
578 #define PETSC_MAX_INT            9223372036854775807L
579 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
580 #endif
581 
582 #if defined(PETSC_USE_REAL_SINGLE)
583 #  define PETSC_MAX_REAL                3.40282346638528860e+38F
584 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
585 #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
586 #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
587 #  define PETSC_SMALL                   1.e-5
588 #elif defined(PETSC_USE_REAL_DOUBLE)
589 #  define PETSC_MAX_REAL                1.7976931348623157e+308
590 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
591 #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
592 #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
593 #  define PETSC_SMALL                   1.e-10
594 #elif defined(PETSC_USE_REAL___FLOAT128)
595 #  define PETSC_MAX_REAL                FLT128_MAX
596 #  define PETSC_MIN_REAL                -FLT128_MAX
597 #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
598 #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078e-17q
599 #  define PETSC_SMALL                   1.e-20q
600 #elif defined(PETSC_USE_REAL___FP16)  /* maybe should use single precision values for these? */
601 #  define PETSC_MAX_REAL                65504.
602 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
603 #  define PETSC_MACHINE_EPSILON         .00097656
604 #  define PETSC_SQRT_MACHINE_EPSILON    .0312
605 #  define PETSC_SMALL                   5.e-3
606 #endif
607 
608 #define PETSC_INFINITY                PETSC_MAX_REAL/4.0
609 #define PETSC_NINFINITY              -PETSC_INFINITY
610 
611 PETSC_EXTERN PetscErrorCode PetscIsInfOrNanReal(PetscReal);
612 PETSC_EXTERN PetscErrorCode PetscIsNanReal(PetscReal);
613 PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
614 PETSC_STATIC_INLINE PetscErrorCode PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
615 PETSC_STATIC_INLINE PetscErrorCode PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
616 PETSC_STATIC_INLINE PetscErrorCode PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}
617 
618 /*
619     These macros are currently hardwired to match the regular data types, so there is no support for a different
620     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
621  */
622 #define MPIU_MATSCALAR MPIU_SCALAR
623 typedef PetscScalar MatScalar;
624 typedef PetscReal MatReal;
625 
626 struct petsc_mpiu_2scalar {PetscScalar a,b;};
627 PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
628 #if defined(PETSC_USE_64BIT_INDICES) || !defined(MPI_2INT)
629 struct petsc_mpiu_2int {PetscInt a,b;};
630 PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
631 #else
632 #define MPIU_2INT MPI_2INT
633 #endif
634 
635 PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
636 {
637   PetscInt result = 1;
638   while (power) {
639     if (power & 1) result *= base;
640     power >>= 1;
641     base *= base;
642   }
643   return result;
644 }
645 
646 PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
647 {
648   PetscReal result = 1;
649   if (power < 0) {
650     power = -power;
651     base  = ((PetscReal)1)/base;
652   }
653   while (power) {
654     if (power & 1) result *= base;
655     power >>= 1;
656     base *= base;
657   }
658   return result;
659 }
660 
661 PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
662 {
663   PetscScalar result = 1;
664   if (power < 0) {
665     power = -power;
666     base  = ((PetscReal)1)/base;
667   }
668   while (power) {
669     if (power & 1) result *= base;
670     power >>= 1;
671     base *= base;
672   }
673   return result;
674 }
675 
676 PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
677 {
678   PetscScalar cpower = power;
679   return PetscPowScalar(base,cpower);
680 }
681 
682 #ifndef PETSC_HAVE_LOG2
683 PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal n)
684 {
685   return PetscLogReal(n)/PetscLogReal(2.0);
686 }
687 #endif
688 #endif
689