xref: /petsc/include/petscmath.h (revision e6d0a238963c2a97dd04845ea512b529992c7cdb)
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 PETSC_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 #elif defined(PETSC_USE_REAL_DOUBLE) && defined(CMPLX)
425   return CMPLX(x,y);
426 #else
427   { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),
428 
429        "For each floating type there is a corresponding real type, which is always a real floating
430        type. For real floating types, it is the same type. For complex types, it is the type given
431        by deleting the keyword _Complex from the type name."
432 
433        So type punning should be portable. */
434     union { PetscComplex z; PetscReal f[2]; } uz;
435 
436     uz.f[0] = x;
437     uz.f[1] = y;
438     return uz.z;
439   }
440 #endif
441 #endif
442 }
443 #endif
444 
445 
446 /*MC
447    PetscMin - Returns minimum of two numbers
448 
449    Synopsis:
450    #include <petscmath.h>
451    type PetscMin(type v1,type v2)
452 
453    Not Collective
454 
455    Input Parameter:
456 +  v1 - first value to find minimum of
457 -  v2 - second value to find minimum of
458 
459    Notes: type can be integer or floating point value
460 
461    Level: beginner
462 
463 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
464 
465 M*/
466 #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))
467 
468 /*MC
469    PetscMax - Returns maxium of two numbers
470 
471    Synopsis:
472    #include <petscmath.h>
473    type max PetscMax(type v1,type v2)
474 
475    Not Collective
476 
477    Input Parameter:
478 +  v1 - first value to find maximum of
479 -  v2 - second value to find maximum of
480 
481    Notes: type can be integer or floating point value
482 
483    Level: beginner
484 
485 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
486 
487 M*/
488 #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))
489 
490 /*MC
491    PetscClipInterval - Returns a number clipped to be within an interval
492 
493    Synopsis:
494    #include <petscmath.h>
495    type clip PetscClipInterval(type x,type a,type b)
496 
497    Not Collective
498 
499    Input Parameter:
500 +  x - value to use if within interval (a,b)
501 .  a - lower end of interval
502 -  b - upper end of interval
503 
504    Notes: type can be integer or floating point value
505 
506    Level: beginner
507 
508 .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
509 
510 M*/
511 #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))
512 
513 /*MC
514    PetscAbsInt - Returns the absolute value of an integer
515 
516    Synopsis:
517    #include <petscmath.h>
518    int abs PetscAbsInt(int v1)
519 
520    Not Collective
521 
522    Input Parameter:
523 .   v1 - the integer
524 
525    Level: beginner
526 
527 .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()
528 
529 M*/
530 #define PetscAbsInt(a)  (((a)<0)   ? -(a) : (a))
531 
532 /*MC
533    PetscAbsReal - Returns the absolute value of an real number
534 
535    Synopsis:
536    #include <petscmath.h>
537    Real abs PetscAbsReal(PetscReal v1)
538 
539    Not Collective
540 
541    Input Parameter:
542 .   v1 - the double
543 
544 
545    Level: beginner
546 
547 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()
548 
549 M*/
550 #define PetscAbsReal(a) (((a)<0)   ? -(a) : (a))
551 
552 /*MC
553    PetscSqr - Returns the square of a number
554 
555    Synopsis:
556    #include <petscmath.h>
557    type sqr PetscSqr(type v1)
558 
559    Not Collective
560 
561    Input Parameter:
562 .   v1 - the value
563 
564    Notes: type can be integer or floating point value
565 
566    Level: beginner
567 
568 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()
569 
570 M*/
571 #define PetscSqr(a)     ((a)*(a))
572 
573 /* ----------------------------------------------------------------------------*/
574 /*
575      Basic constants
576 */
577 #if defined(PETSC_USE_REAL___FLOAT128)
578 #define PETSC_PI                 M_PIq
579 #elif defined(M_PI)
580 #define PETSC_PI                 M_PI
581 #else
582 #define PETSC_PI                 3.14159265358979323846264338327950288419716939937510582
583 #endif
584 
585 #if !defined(PETSC_USE_64BIT_INDICES)
586 #define PETSC_MAX_INT            2147483647
587 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
588 #else
589 #define PETSC_MAX_INT            9223372036854775807L
590 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
591 #endif
592 
593 #if defined(PETSC_USE_REAL_SINGLE)
594 #  define PETSC_MAX_REAL                3.40282346638528860e+38F
595 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
596 #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
597 #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
598 #  define PETSC_SMALL                   1.e-5
599 #elif defined(PETSC_USE_REAL_DOUBLE)
600 #  define PETSC_MAX_REAL                1.7976931348623157e+308
601 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
602 #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
603 #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
604 #  define PETSC_SMALL                   1.e-10
605 #elif defined(PETSC_USE_REAL___FLOAT128)
606 #  define PETSC_MAX_REAL                FLT128_MAX
607 #  define PETSC_MIN_REAL                -FLT128_MAX
608 #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
609 #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078e-17q
610 #  define PETSC_SMALL                   1.e-20q
611 #elif defined(PETSC_USE_REAL___FP16)  /* maybe should use single precision values for these? */
612 #  define PETSC_MAX_REAL                65504.
613 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
614 #  define PETSC_MACHINE_EPSILON         .00097656
615 #  define PETSC_SQRT_MACHINE_EPSILON    .0312
616 #  define PETSC_SMALL                   5.e-3
617 #endif
618 
619 #define PETSC_INFINITY                PETSC_MAX_REAL/4.0
620 #define PETSC_NINFINITY              -PETSC_INFINITY
621 
622 PETSC_EXTERN PetscErrorCode PetscIsInfOrNanReal(PetscReal);
623 PETSC_EXTERN PetscErrorCode PetscIsNanReal(PetscReal);
624 PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
625 PETSC_STATIC_INLINE PetscErrorCode PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
626 PETSC_STATIC_INLINE PetscErrorCode PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
627 PETSC_STATIC_INLINE PetscErrorCode PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}
628 
629 /*
630     These macros are currently hardwired to match the regular data types, so there is no support for a different
631     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
632  */
633 #define MPIU_MATSCALAR MPIU_SCALAR
634 typedef PetscScalar MatScalar;
635 typedef PetscReal MatReal;
636 
637 struct petsc_mpiu_2scalar {PetscScalar a,b;};
638 PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
639 #if defined(PETSC_USE_64BIT_INDICES) || !defined(MPI_2INT)
640 struct petsc_mpiu_2int {PetscInt a,b;};
641 PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
642 #else
643 #define MPIU_2INT MPI_2INT
644 #endif
645 
646 PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
647 {
648   PetscInt result = 1;
649   while (power) {
650     if (power & 1) result *= base;
651     power >>= 1;
652     base *= base;
653   }
654   return result;
655 }
656 
657 PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
658 {
659   PetscReal result = 1;
660   if (power < 0) {
661     power = -power;
662     base  = ((PetscReal)1)/base;
663   }
664   while (power) {
665     if (power & 1) result *= base;
666     power >>= 1;
667     base *= base;
668   }
669   return result;
670 }
671 
672 PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
673 {
674   PetscScalar result = 1;
675   if (power < 0) {
676     power = -power;
677     base  = ((PetscReal)1)/base;
678   }
679   while (power) {
680     if (power & 1) result *= base;
681     power >>= 1;
682     base *= base;
683   }
684   return result;
685 }
686 
687 PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
688 {
689   PetscScalar cpower = power;
690   return PetscPowScalar(base,cpower);
691 }
692 
693 #ifndef PETSC_HAVE_LOG2
694 PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal n)
695 {
696   return PetscLogReal(n)/PetscLogReal(2.0);
697 }
698 #endif
699 #endif
700