xref: /petsc/include/petscmath.h (revision 390e1bf27627d887df99a9f4d0d0ad68037f55ec)
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 #endif
409 
410 /*MC
411    PetscMin - Returns minimum of two numbers
412 
413    Synopsis:
414    #include <petscmath.h>
415    type PetscMin(type v1,type v2)
416 
417    Not Collective
418 
419    Input Parameter:
420 +  v1 - first value to find minimum of
421 -  v2 - second value to find minimum of
422 
423    Notes: type can be integer or floating point value
424 
425    Level: beginner
426 
427 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
428 
429 M*/
430 #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))
431 
432 /*MC
433    PetscMax - Returns maxium of two numbers
434 
435    Synopsis:
436    #include <petscmath.h>
437    type max PetscMax(type v1,type v2)
438 
439    Not Collective
440 
441    Input Parameter:
442 +  v1 - first value to find maximum of
443 -  v2 - second value to find maximum of
444 
445    Notes: type can be integer or floating point value
446 
447    Level: beginner
448 
449 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
450 
451 M*/
452 #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))
453 
454 /*MC
455    PetscClipInterval - Returns a number clipped to be within an interval
456 
457    Synopsis:
458    #include <petscmath.h>
459    type clip PetscClipInterval(type x,type a,type b)
460 
461    Not Collective
462 
463    Input Parameter:
464 +  x - value to use if within interval (a,b)
465 .  a - lower end of interval
466 -  b - upper end of interval
467 
468    Notes: type can be integer or floating point value
469 
470    Level: beginner
471 
472 .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
473 
474 M*/
475 #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))
476 
477 /*MC
478    PetscAbsInt - Returns the absolute value of an integer
479 
480    Synopsis:
481    #include <petscmath.h>
482    int abs PetscAbsInt(int v1)
483 
484    Not Collective
485 
486    Input Parameter:
487 .   v1 - the integer
488 
489    Level: beginner
490 
491 .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()
492 
493 M*/
494 #define PetscAbsInt(a)  (((a)<0)   ? -(a) : (a))
495 
496 /*MC
497    PetscAbsReal - Returns the absolute value of an real number
498 
499    Synopsis:
500    #include <petscmath.h>
501    Real abs PetscAbsReal(PetscReal v1)
502 
503    Not Collective
504 
505    Input Parameter:
506 .   v1 - the double
507 
508 
509    Level: beginner
510 
511 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()
512 
513 M*/
514 #define PetscAbsReal(a) (((a)<0)   ? -(a) : (a))
515 
516 /*MC
517    PetscSqr - Returns the square of a number
518 
519    Synopsis:
520    #include <petscmath.h>
521    type sqr PetscSqr(type v1)
522 
523    Not Collective
524 
525    Input Parameter:
526 .   v1 - the value
527 
528    Notes: type can be integer or floating point value
529 
530    Level: beginner
531 
532 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()
533 
534 M*/
535 #define PetscSqr(a)     ((a)*(a))
536 
537 /* ----------------------------------------------------------------------------*/
538 /*
539      Basic constants
540 */
541 #if defined(PETSC_USE_REAL___FLOAT128)
542 #define PETSC_PI                 M_PIq
543 #elif defined(M_PI)
544 #define PETSC_PI                 M_PI
545 #else
546 #define PETSC_PI                 3.14159265358979323846264338327950288419716939937510582
547 #endif
548 
549 #if !defined(PETSC_USE_64BIT_INDICES)
550 #define PETSC_MAX_INT            2147483647
551 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
552 #else
553 #define PETSC_MAX_INT            9223372036854775807L
554 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
555 #endif
556 
557 #if defined(PETSC_USE_REAL_SINGLE)
558 #  define PETSC_MAX_REAL                3.40282346638528860e+38F
559 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
560 #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
561 #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
562 #  define PETSC_SMALL                   1.e-5
563 #elif defined(PETSC_USE_REAL_DOUBLE)
564 #  define PETSC_MAX_REAL                1.7976931348623157e+308
565 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
566 #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
567 #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
568 #  define PETSC_SMALL                   1.e-10
569 #elif defined(PETSC_USE_REAL___FLOAT128)
570 #  define PETSC_MAX_REAL                FLT128_MAX
571 #  define PETSC_MIN_REAL                -FLT128_MAX
572 #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
573 #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078e-17q
574 #  define PETSC_SMALL                   1.e-20q
575 #elif defined(PETSC_USE_REAL___FP16)  /* maybe should use single precision values for these? */
576 #  define PETSC_MAX_REAL                65504.
577 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
578 #  define PETSC_MACHINE_EPSILON         .00097656
579 #  define PETSC_SQRT_MACHINE_EPSILON    .0312
580 #  define PETSC_SMALL                   5.e-3
581 #endif
582 
583 #define PETSC_INFINITY                PETSC_MAX_REAL/4.0
584 #define PETSC_NINFINITY              -PETSC_INFINITY
585 
586 PETSC_EXTERN PetscErrorCode PetscIsInfOrNanReal(PetscReal);
587 PETSC_EXTERN PetscErrorCode PetscIsNanReal(PetscReal);
588 PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
589 PETSC_STATIC_INLINE PetscErrorCode PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
590 PETSC_STATIC_INLINE PetscErrorCode PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
591 PETSC_STATIC_INLINE PetscErrorCode PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}
592 
593 /*
594     These macros are currently hardwired to match the regular data types, so there is no support for a different
595     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
596  */
597 #define MPIU_MATSCALAR MPIU_SCALAR
598 typedef PetscScalar MatScalar;
599 typedef PetscReal MatReal;
600 
601 struct petsc_mpiu_2scalar {PetscScalar a,b;};
602 PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
603 #if defined(PETSC_USE_64BIT_INDICES) || !defined(MPI_2INT)
604 struct petsc_mpiu_2int {PetscInt a,b;};
605 PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
606 #else
607 #define MPIU_2INT MPI_2INT
608 #endif
609 
610 PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
611 {
612   PetscInt result = 1;
613   while (power) {
614     if (power & 1) result *= base;
615     power >>= 1;
616     base *= base;
617   }
618   return result;
619 }
620 
621 PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
622 {
623   PetscReal result = 1;
624   if (power < 0) {
625     power = -power;
626     base  = ((PetscReal)1)/base;
627   }
628   while (power) {
629     if (power & 1) result *= base;
630     power >>= 1;
631     base *= base;
632   }
633   return result;
634 }
635 
636 PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
637 {
638   PetscScalar result = 1;
639   if (power < 0) {
640     power = -power;
641     base  = ((PetscReal)1)/base;
642   }
643   while (power) {
644     if (power & 1) result *= base;
645     power >>= 1;
646     base *= base;
647   }
648   return result;
649 }
650 
651 PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
652 {
653   PetscScalar cpower = power;
654   return PetscPowScalar(base,cpower);
655 }
656 
657 #ifndef PETSC_HAVE_LOG2
658 PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal n)
659 {
660   return PetscLogReal(n)/PetscLogReal(2.0);
661 }
662 #endif
663 #endif
664