xref: /petsc/include/petscmath.h (revision fecfb7146cb415f81e8cc7ef8d4ae968f3ac4b11)
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 #endif /* PETSC_USE_REAL_* */
108 
109 /*
110     Complex number definitions
111  */
112 #if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
113 #if !defined(PETSC_SKIP_COMPLEX)
114 #define PETSC_HAVE_COMPLEX 1
115 /* C++ support of complex number */
116 #if defined(PETSC_HAVE_CUSP)
117 #define complexlib cusp
118 #include <cusp/complex.h>
119 #elif defined(PETSC_HAVE_VECCUDA) && __CUDACC_VER_MAJOR__ > 6
120 /* complex headers in thrust only available in CUDA 7.0 and above */
121 #define complexlib thrust
122 #include <thrust/complex.h>
123 #else
124 #define complexlib std
125 #include <complex>
126 #endif
127 
128 #define PetscRealPartComplex(a)      (a).real()
129 #define PetscImaginaryPartComplex(a) (a).imag()
130 #define PetscAbsComplex(a)           complexlib::abs(a)
131 #define PetscConjComplex(a)          complexlib::conj(a)
132 #define PetscSqrtComplex(a)          complexlib::sqrt(a)
133 #define PetscPowComplex(a,b)         complexlib::pow(a,b)
134 #define PetscExpComplex(a)           complexlib::exp(a)
135 #define PetscLogComplex(a)           complexlib::log(a)
136 #define PetscSinComplex(a)           complexlib::sin(a)
137 #define PetscCosComplex(a)           complexlib::cos(a)
138 #define PetscAsinComplex(a)          complexlib::asin(a)
139 #define PetscAcosComplex(a)          complexlib::acos(a)
140 #if defined(PETSC_HAVE_TANCOMPLEX)
141 #define PetscTanComplex(a)           complexlib::tan(a)
142 #else
143 #define PetscTanComplex(a)           PetscSinComplex(a)/PetscCosComplex(a)
144 #endif
145 #define PetscSinhComplex(a)          complexlib::sinh(a)
146 #define PetscCoshComplex(a)          complexlib::cosh(a)
147 #if defined(PETSC_HAVE_TANHCOMPLEX)
148 #define PetscTanhComplex(a)          complexlib::tanh(a)
149 #else
150 #define PetscTanhComplex(a)          PetscSinhComplex(a)/PetscCoshComplex(a)
151 #endif
152 
153 #if defined(PETSC_USE_REAL_SINGLE)
154 typedef complexlib::complex<float> PetscComplex;
155 #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND)
156 static inline PetscComplex operator+(const PetscComplex& lhs, const double& rhs) { return lhs + float(rhs); }
157 static inline PetscComplex operator+(const double& lhs, const PetscComplex& rhs) { return float(lhs) + rhs; }
158 static inline PetscComplex operator-(const PetscComplex& lhs, const double& rhs) { return lhs - float(rhs); }
159 static inline PetscComplex operator-(const double& lhs, const PetscComplex& rhs) { return float(lhs) - rhs; }
160 static inline PetscComplex operator*(const PetscComplex& lhs, const double& rhs) { return lhs * float(rhs); }
161 static inline PetscComplex operator*(const double& lhs, const PetscComplex& rhs) { return float(lhs) * rhs; }
162 static inline PetscComplex operator/(const PetscComplex& lhs, const double& rhs) { return lhs / float(rhs); }
163 static inline PetscComplex operator/(const double& lhs, const PetscComplex& rhs) { return float(lhs) / rhs; }
164 static inline bool operator==(const PetscComplex& lhs, const double& rhs) { return lhs.imag() == float(0) && lhs.real() == float(rhs); }
165 static inline bool operator==(const double& lhs, const PetscComplex& rhs) { return rhs.imag() == float(0) && rhs.real() == float(lhs); }
166 static inline bool operator!=(const PetscComplex& lhs, const double& rhs) { return lhs.imag() != float(0) || lhs.real() != float(rhs); }
167 static inline bool operator!=(const double& lhs, const PetscComplex& rhs) { return rhs.imag() != float(0) || rhs.real() != float(lhs); }
168 #endif  /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */
169 #elif defined(PETSC_USE_REAL_DOUBLE)
170 typedef complexlib::complex<double> PetscComplex;
171 #elif defined(PETSC_USE_REAL___FLOAT128)
172 typedef complexlib::complex<__float128> PetscComplex; /* Notstandard and not expected to work, use __complex128 */
173 PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128;
174 #endif  /* PETSC_USE_REAL_ */
175 #endif  /* ! PETSC_SKIP_COMPLEX */
176 
177 #elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
178 #if !defined(PETSC_SKIP_COMPLEX)
179 #define PETSC_HAVE_COMPLEX 1
180 #include <complex.h>
181 
182 #if defined(PETSC_USE_REAL_SINGLE)
183 typedef float _Complex PetscComplex;
184 
185 #define PetscRealPartComplex(a)      crealf(a)
186 #define PetscImaginaryPartComplex(a) cimagf(a)
187 #define PetscAbsComplex(a)           cabsf(a)
188 #define PetscConjComplex(a)          conjf(a)
189 #define PetscSqrtComplex(a)          csqrtf(a)
190 #define PetscPowComplex(a,b)         cpowf(a,b)
191 #define PetscExpComplex(a)           cexpf(a)
192 #define PetscLogComplex(a)           clogf(a)
193 #define PetscSinComplex(a)           csinf(a)
194 #define PetscCosComplex(a)           ccosf(a)
195 #define PetscAsinComplex(a)          casinf(a)
196 #define PetscAcosComplex(a)          cacosf(a)
197 #define PetscTanComplex(a)           ctanf(a)
198 #define PetscSinhComplex(a)          csinhf(a)
199 #define PetscCoshComplex(a)          ccoshf(a)
200 #define PetscTanhComplex(a)          ctanhf(a)
201 
202 #elif defined(PETSC_USE_REAL_DOUBLE)
203 typedef double _Complex PetscComplex;
204 
205 #define PetscRealPartComplex(a)      creal(a)
206 #define PetscImaginaryPartComplex(a) cimag(a)
207 #define PetscAbsComplex(a)           cabs(a)
208 #define PetscConjComplex(a)          conj(a)
209 #define PetscSqrtComplex(a)          csqrt(a)
210 #define PetscPowComplex(a,b)         cpow(a,b)
211 #define PetscExpComplex(a)           cexp(a)
212 #define PetscLogComplex(a)           clog(a)
213 #define PetscSinComplex(a)           csin(a)
214 #define PetscCosComplex(a)           ccos(a)
215 #define PetscAsinComplex(a)          casin(a)
216 #define PetscAcosComplex(a)          cacos(a)
217 #define PetscTanComplex(a)           ctan(a)
218 #define PetscSinhComplex(a)          csinh(a)
219 #define PetscCoshComplex(a)          ccosh(a)
220 #define PetscTanhComplex(a)          ctanh(a)
221 
222 #elif defined(PETSC_USE_REAL___FLOAT128)
223 typedef __complex128 PetscComplex;
224 PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
225 
226 #define PetscRealPartComplex(a)      crealq(a)
227 #define PetscImaginaryPartComplex(a) cimagq(a)
228 #define PetscAbsComplex(a)           cabsq(a)
229 #define PetscConjComplex(a)          conjq(a)
230 #define PetscSqrtComplex(a)          csqrtq(a)
231 #define PetscPowComplex(a,b)         cpowq(a,b)
232 #define PetscExpComplex(a)           cexpq(a)
233 #define PetscLogComplex(a)           clogq(a)
234 #define PetscSinComplex(a)           csinq(a)
235 #define PetscCosComplex(a)           ccosq(a)
236 #define PetscAsinComplex(a)          casinq(a)
237 #define PetscAcosComplex(a)          cacosq(a)
238 #define PetscTanComplex(a)           ctanq(a)
239 #define PetscSinhComplex(a)          csinhq(a)
240 #define PetscCoshComplex(a)          ccoshq(a)
241 #define PetscTanhComplex(a)          ctanhq(a)
242 
243 #endif /* PETSC_USE_REAL_* */
244 #elif (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
245 #error "PETSc was configured --with-scalar-type=complex, but a language-appropriate complex library is not available"
246 #endif /* !PETSC_SKIP_COMPLEX */
247 #endif /* (__cplusplus && PETSC_HAVE_CXX_COMPLEX) else-if (!__cplusplus && PETSC_HAVE_C99_COMPLEX) */
248 
249 #if defined(PETSC_HAVE_COMPLEX)
250 #if defined(PETSC_HAVE_MPI_C_DOUBLE_COMPLEX)
251 #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX
252 #define MPIU_C_COMPLEX MPI_C_COMPLEX
253 #else
254 # if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX)
255   typedef complexlib::complex<double> petsc_mpiu_c_double_complex;
256   typedef complexlib::complex<float> petsc_mpiu_c_complex;
257 # elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
258   typedef double _Complex petsc_mpiu_c_double_complex;
259   typedef float _Complex petsc_mpiu_c_complex;
260 # else
261   typedef struct {double real,imag;} petsc_mpiu_c_double_complex;
262   typedef struct {float real,imag;} petsc_mpiu_c_complex;
263 # endif
264 PETSC_EXTERN MPI_Datatype MPIU_C_DOUBLE_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_double_complex);
265 PETSC_EXTERN MPI_Datatype MPIU_C_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_complex);
266 #endif /* PETSC_HAVE_MPI_C_DOUBLE_COMPLEX */
267 #endif /* PETSC_HAVE_COMPLEX */
268 
269 #if defined(PETSC_HAVE_COMPLEX)
270 #  if defined(PETSC_USE_REAL_SINGLE)
271 #    define MPIU_COMPLEX MPIU_C_COMPLEX
272 #  elif defined(PETSC_USE_REAL_DOUBLE)
273 #    define MPIU_COMPLEX MPIU_C_DOUBLE_COMPLEX
274 #  elif defined(PETSC_USE_REAL___FLOAT128)
275 #    define MPIU_COMPLEX MPIU___COMPLEX128
276 #  endif /* PETSC_USE_REAL_* */
277 #endif
278 
279 #if (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
280 typedef PetscComplex PetscScalar;
281 #define PetscRealPart(a)      PetscRealPartComplex(a)
282 #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)
283 #define PetscAbsScalar(a)     PetscAbsComplex(a)
284 #define PetscConj(a)          PetscConjComplex(a)
285 #define PetscSqrtScalar(a)    PetscSqrtComplex(a)
286 #define PetscPowScalar(a,b)   PetscPowComplex(a,b)
287 #define PetscExpScalar(a)     PetscExpComplex(a)
288 #define PetscLogScalar(a)     PetscLogComplex(a)
289 #define PetscSinScalar(a)     PetscSinComplex(a)
290 #define PetscCosScalar(a)     PetscCosComplex(a)
291 #define PetscAsinScalar(a)    PetscAsinComplex(a)
292 #define PetscAcosScalar(a)    PetscAcosComplex(a)
293 #define PetscTanScalar(a)     PetscTanComplex(a)
294 #define PetscSinhScalar(a)    PetscSinhComplex(a)
295 #define PetscCoshScalar(a)    PetscCoshComplex(a)
296 #define PetscTanhScalar(a)    PetscTanhComplex(a)
297 #define MPIU_SCALAR MPIU_COMPLEX
298 
299 /*
300     real number definitions
301  */
302 #else /* PETSC_USE_COMPLEX */
303 typedef PetscReal PetscScalar;
304 #define MPIU_SCALAR MPIU_REAL
305 
306 #define PetscRealPart(a)      (a)
307 #define PetscImaginaryPart(a) ((PetscReal)0.)
308 PETSC_STATIC_INLINE PetscReal PetscAbsScalar(PetscScalar a) {return a < 0.0 ? -a : a;}
309 #define PetscConj(a)          (a)
310 #if !defined(PETSC_USE_REAL___FLOAT128)
311 #define PetscSqrtScalar(a)    sqrt(a)
312 #define PetscPowScalar(a,b)   pow(a,b)
313 #define PetscExpScalar(a)     exp(a)
314 #define PetscLogScalar(a)     log(a)
315 #define PetscSinScalar(a)     sin(a)
316 #define PetscCosScalar(a)     cos(a)
317 #define PetscAsinScalar(a)    asin(a)
318 #define PetscAcosScalar(a)    acos(a)
319 #define PetscTanScalar(a)     tan(a)
320 #define PetscSinhScalar(a)    sinh(a)
321 #define PetscCoshScalar(a)    cosh(a)
322 #define PetscTanhScalar(a)    tanh(a)
323 #else /* PETSC_USE_REAL___FLOAT128 */
324 #define PetscSqrtScalar(a)    sqrtq(a)
325 #define PetscPowScalar(a,b)   powq(a,b)
326 #define PetscExpScalar(a)     expq(a)
327 #define PetscLogScalar(a)     logq(a)
328 #define PetscSinScalar(a)     sinq(a)
329 #define PetscCosScalar(a)     cosq(a)
330 #define PetscAsinScalar(a)    asinq(a)
331 #define PetscAcosScalar(a)    acosq(a)
332 #define PetscTanScalar(a)     tanq(a)
333 #define PetscSinhScalar(a)    sinhq(a)
334 #define PetscCoshScalar(a)    coshq(a)
335 #define PetscTanhScalar(a)    tanhq(a)
336 #endif /* PETSC_USE_REAL___FLOAT128 */
337 
338 #endif /* PETSC_USE_COMPLEX */
339 
340 #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)
341 #define PetscAbs(a)  (((a) >= 0) ? (a) : -(a))
342 
343 /* --------------------------------------------------------------------------*/
344 
345 /*
346    Certain objects may be created using either single or double precision.
347    This is currently not used.
348 */
349 typedef enum { PETSC_SCALAR_DOUBLE,PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE } PetscScalarPrecision;
350 
351 #if defined(PETSC_HAVE_COMPLEX)
352 /* PETSC_i is the imaginary number, i */
353 PETSC_EXTERN PetscComplex PETSC_i;
354 #endif
355 
356 /*MC
357    PetscMin - Returns minimum of two numbers
358 
359    Synopsis:
360    #include <petscmath.h>
361    type PetscMin(type v1,type v2)
362 
363    Not Collective
364 
365    Input Parameter:
366 +  v1 - first value to find minimum of
367 -  v2 - second value to find minimum of
368 
369    Notes: type can be integer or floating point value
370 
371    Level: beginner
372 
373 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
374 
375 M*/
376 #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))
377 
378 /*MC
379    PetscMax - Returns maxium of two numbers
380 
381    Synopsis:
382    #include <petscmath.h>
383    type max PetscMax(type v1,type v2)
384 
385    Not Collective
386 
387    Input Parameter:
388 +  v1 - first value to find maximum of
389 -  v2 - second value to find maximum of
390 
391    Notes: type can be integer or floating point value
392 
393    Level: beginner
394 
395 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
396 
397 M*/
398 #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))
399 
400 /*MC
401    PetscClipInterval - Returns a number clipped to be within an interval
402 
403    Synopsis:
404    #include <petscmath.h>
405    type clip PetscClipInterval(type x,type a,type b)
406 
407    Not Collective
408 
409    Input Parameter:
410 +  x - value to use if within interval (a,b)
411 .  a - lower end of interval
412 -  b - upper end of interval
413 
414    Notes: type can be integer or floating point value
415 
416    Level: beginner
417 
418 .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
419 
420 M*/
421 #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))
422 
423 /*MC
424    PetscAbsInt - Returns the absolute value of an integer
425 
426    Synopsis:
427    #include <petscmath.h>
428    int abs PetscAbsInt(int v1)
429 
430    Not Collective
431 
432    Input Parameter:
433 .   v1 - the integer
434 
435    Level: beginner
436 
437 .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()
438 
439 M*/
440 #define PetscAbsInt(a)  (((a)<0)   ? -(a) : (a))
441 
442 /*MC
443    PetscAbsReal - Returns the absolute value of an real number
444 
445    Synopsis:
446    #include <petscmath.h>
447    Real abs PetscAbsReal(PetscReal v1)
448 
449    Not Collective
450 
451    Input Parameter:
452 .   v1 - the double
453 
454 
455    Level: beginner
456 
457 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()
458 
459 M*/
460 #define PetscAbsReal(a) (((a)<0)   ? -(a) : (a))
461 
462 /*MC
463    PetscSqr - Returns the square of a number
464 
465    Synopsis:
466    #include <petscmath.h>
467    type sqr PetscSqr(type v1)
468 
469    Not Collective
470 
471    Input Parameter:
472 .   v1 - the value
473 
474    Notes: type can be integer or floating point value
475 
476    Level: beginner
477 
478 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()
479 
480 M*/
481 #define PetscSqr(a)     ((a)*(a))
482 
483 /* ----------------------------------------------------------------------------*/
484 /*
485      Basic constants
486 */
487 #if defined(PETSC_USE_REAL___FLOAT128)
488 #define PETSC_PI                 M_PIq
489 #elif defined(M_PI)
490 #define PETSC_PI                 M_PI
491 #else
492 #define PETSC_PI                 3.14159265358979323846264338327950288419716939937510582
493 #endif
494 
495 #if !defined(PETSC_USE_64BIT_INDICES)
496 #define PETSC_MAX_INT            2147483647
497 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
498 #else
499 #define PETSC_MAX_INT            9223372036854775807L
500 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
501 #endif
502 
503 #if defined(PETSC_USE_REAL_SINGLE)
504 #  define PETSC_MAX_REAL                3.40282346638528860e+38F
505 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
506 #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
507 #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
508 #  define PETSC_SMALL                   1.e-5
509 #elif defined(PETSC_USE_REAL_DOUBLE)
510 #  define PETSC_MAX_REAL                1.7976931348623157e+308
511 #  define PETSC_MIN_REAL                -PETSC_MAX_REAL
512 #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
513 #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
514 #  define PETSC_SMALL                   1.e-10
515 #elif defined(PETSC_USE_REAL___FLOAT128)
516 #  define PETSC_MAX_REAL                FLT128_MAX
517 #  define PETSC_MIN_REAL                -FLT128_MAX
518 #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
519 #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078e-17q
520 #  define PETSC_SMALL                   1.e-20q
521 #endif
522 
523 #define PETSC_INFINITY                PETSC_MAX_REAL/4.0
524 #define PETSC_NINFINITY              -PETSC_INFINITY
525 
526 PETSC_EXTERN PetscErrorCode PetscIsInfOrNanReal(PetscReal);
527 PETSC_EXTERN PetscErrorCode PetscIsNanReal(PetscReal);
528 PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
529 PETSC_STATIC_INLINE PetscErrorCode PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
530 PETSC_STATIC_INLINE PetscErrorCode PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
531 PETSC_STATIC_INLINE PetscErrorCode PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}
532 
533 /*
534     These macros are currently hardwired to match the regular data types, so there is no support for a different
535     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
536  */
537 #define MPIU_MATSCALAR MPIU_SCALAR
538 typedef PetscScalar MatScalar;
539 typedef PetscReal MatReal;
540 
541 struct petsc_mpiu_2scalar {PetscScalar a,b;};
542 PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
543 #if defined(PETSC_USE_64BIT_INDICES) || !defined(MPI_2INT)
544 struct petsc_mpiu_2int {PetscInt a,b;};
545 PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
546 #else
547 #define MPIU_2INT MPI_2INT
548 #endif
549 
550 PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
551 {
552   PetscInt result = 1;
553   while (power) {
554     if (power & 1) result *= base;
555     power >>= 1;
556     base *= base;
557   }
558   return result;
559 }
560 
561 PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
562 {
563   PetscReal result = 1;
564   if (power < 0) {
565     power = -power;
566     base  = ((PetscReal)1)/base;
567   }
568   while (power) {
569     if (power & 1) result *= base;
570     power >>= 1;
571     base *= base;
572   }
573   return result;
574 }
575 
576 PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
577 {
578   PetscScalar result = 1;
579   if (power < 0) {
580     power = -power;
581     base  = ((PetscReal)1)/base;
582   }
583   while (power) {
584     if (power & 1) result *= base;
585     power >>= 1;
586     base *= base;
587   }
588   return result;
589 }
590 
591 PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
592 {
593   PetscScalar cpower = power;
594   return PetscPowScalar(base,cpower);
595 }
596 
597 #ifndef PETSC_HAVE_LOG2
598 PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal n)
599 {
600   return PetscLogReal(n)/PetscLogReal(2.0);
601 }
602 #endif
603 #endif
604