xref: /petsc/include/petscmath.h (revision b724ec41a692ea93fcd25473f3bd97088e04f9b6)
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 #include <petscsystypes.h>
15 
16 /*
17 
18    Defines operations that are different for complex and real numbers.
19    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 /*
25     Real number definitions
26  */
27 #if defined(PETSC_USE_REAL_SINGLE)
28 #define PetscSqrtReal(a)    sqrtf(a)
29 #define PetscCbrtReal(a)    cbrtf(a)
30 #define PetscHypotReal(a,b) hypotf(a,b)
31 #define PetscAtan2Real(a,b) atan2f(a,b)
32 #define PetscPowReal(a,b)   powf(a,b)
33 #define PetscExpReal(a)     expf(a)
34 #define PetscLogReal(a)     logf(a)
35 #define PetscLog10Real(a)   log10f(a)
36 #define PetscLog2Real(a)    log2f(a)
37 #define PetscSinReal(a)     sinf(a)
38 #define PetscCosReal(a)     cosf(a)
39 #define PetscTanReal(a)     tanf(a)
40 #define PetscAsinReal(a)    asinf(a)
41 #define PetscAcosReal(a)    acosf(a)
42 #define PetscAtanReal(a)    atanf(a)
43 #define PetscSinhReal(a)    sinhf(a)
44 #define PetscCoshReal(a)    coshf(a)
45 #define PetscTanhReal(a)    tanhf(a)
46 #define PetscAsinhReal(a)   asinhf(a)
47 #define PetscAcoshReal(a)   acoshf(a)
48 #define PetscAtanhReal(a)   atanhf(a)
49 #define PetscCeilReal(a)    ceilf(a)
50 #define PetscFloorReal(a)   floorf(a)
51 #define PetscFmodReal(a,b)  fmodf(a,b)
52 #define PetscTGamma(a)      tgammaf(a)
53 #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
54 #define PetscLGamma(a)      gammaf(a)
55 #else
56 #define PetscLGamma(a)      lgammaf(a)
57 #endif
58 
59 #elif defined(PETSC_USE_REAL_DOUBLE)
60 #define PetscSqrtReal(a)    sqrt(a)
61 #define PetscCbrtReal(a)    cbrt(a)
62 #define PetscHypotReal(a,b) hypot(a,b)
63 #define PetscAtan2Real(a,b) atan2(a,b)
64 #define PetscPowReal(a,b)   pow(a,b)
65 #define PetscExpReal(a)     exp(a)
66 #define PetscLogReal(a)     log(a)
67 #define PetscLog10Real(a)   log10(a)
68 #define PetscLog2Real(a)    log2(a)
69 #define PetscSinReal(a)     sin(a)
70 #define PetscCosReal(a)     cos(a)
71 #define PetscTanReal(a)     tan(a)
72 #define PetscAsinReal(a)    asin(a)
73 #define PetscAcosReal(a)    acos(a)
74 #define PetscAtanReal(a)    atan(a)
75 #define PetscSinhReal(a)    sinh(a)
76 #define PetscCoshReal(a)    cosh(a)
77 #define PetscTanhReal(a)    tanh(a)
78 #define PetscAsinhReal(a)   asinh(a)
79 #define PetscAcoshReal(a)   acosh(a)
80 #define PetscAtanhReal(a)   atanh(a)
81 #define PetscCeilReal(a)    ceil(a)
82 #define PetscFloorReal(a)   floor(a)
83 #define PetscFmodReal(a,b)  fmod(a,b)
84 #define PetscTGamma(a)      tgamma(a)
85 #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
86 #define PetscLGamma(a)      gamma(a)
87 #else
88 #define PetscLGamma(a)      lgamma(a)
89 #endif
90 
91 #elif defined(PETSC_USE_REAL___FLOAT128)
92 #define PetscSqrtReal(a)    sqrtq(a)
93 #define PetscCbrtReal(a)    cbrtq(a)
94 #define PetscHypotReal(a,b) hypotq(a,b)
95 #define PetscAtan2Real(a,b) atan2q(a,b)
96 #define PetscPowReal(a,b)   powq(a,b)
97 #define PetscExpReal(a)     expq(a)
98 #define PetscLogReal(a)     logq(a)
99 #define PetscLog10Real(a)   log10q(a)
100 #define PetscLog2Real(a)    log2q(a)
101 #define PetscSinReal(a)     sinq(a)
102 #define PetscCosReal(a)     cosq(a)
103 #define PetscTanReal(a)     tanq(a)
104 #define PetscAsinReal(a)    asinq(a)
105 #define PetscAcosReal(a)    acosq(a)
106 #define PetscAtanReal(a)    atanq(a)
107 #define PetscSinhReal(a)    sinhq(a)
108 #define PetscCoshReal(a)    coshq(a)
109 #define PetscTanhReal(a)    tanhq(a)
110 #define PetscAsinhReal(a)   asinhq(a)
111 #define PetscAcoshReal(a)   acoshq(a)
112 #define PetscAtanhReal(a)   atanhq(a)
113 #define PetscCeilReal(a)    ceilq(a)
114 #define PetscFloorReal(a)   floorq(a)
115 #define PetscFmodReal(a,b)  fmodq(a,b)
116 #define PetscTGamma(a)      tgammaq(a)
117 #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
118 #define PetscLGamma(a)      gammaq(a)
119 #else
120 #define PetscLGamma(a)      lgammaq(a)
121 #endif
122 
123 #elif defined(PETSC_USE_REAL___FP16)
124 #define PetscSqrtReal(a)    sqrtf(a)
125 #define PetscCbrtReal(a)    cbrtf(a)
126 #define PetscHypotReal(a,b) hypotf(a,b)
127 #define PetscAtan2Real(a,b) atan2f(a,b)
128 #define PetscPowReal(a,b)   powf(a,b)
129 #define PetscExpReal(a)     expf(a)
130 #define PetscLogReal(a)     logf(a)
131 #define PetscLog10Real(a)   log10f(a)
132 #define PetscLog2Real(a)    log2f(a)
133 #define PetscSinReal(a)     sinf(a)
134 #define PetscCosReal(a)     cosf(a)
135 #define PetscTanReal(a)     tanf(a)
136 #define PetscAsinReal(a)    asinf(a)
137 #define PetscAcosReal(a)    acosf(a)
138 #define PetscAtanReal(a)    atanf(a)
139 #define PetscSinhReal(a)    sinhf(a)
140 #define PetscCoshReal(a)    coshf(a)
141 #define PetscTanhReal(a)    tanhf(a)
142 #define PetscAsinhReal(a)   asinhf(a)
143 #define PetscAcoshReal(a)   acoshf(a)
144 #define PetscAtanhReal(a)   atanhf(a)
145 #define PetscCeilReal(a)    ceilf(a)
146 #define PetscFloorReal(a)   floorf(a)
147 #define PetscFmodReal(a,b)  fmodf(a,b)
148 #define PetscTGamma(a)      tgammaf(a)
149 #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
150 #define PetscLGamma(a)      gammaf(a)
151 #else
152 #define PetscLGamma(a)      lgammaf(a)
153 #endif
154 
155 #endif /* PETSC_USE_REAL_* */
156 
157 PETSC_STATIC_INLINE PetscReal PetscSignReal(PetscReal a)
158 {
159   return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0));
160 }
161 
162 #if !defined(PETSC_HAVE_LOG2)
163 #undef PetscLog2Real
164 PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal a)
165 {
166   return PetscLogReal(a)/PetscLogReal((PetscReal)2);
167 }
168 #endif
169 
170 #if defined(PETSC_USE_REAL___FLOAT128)
171 PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
172 #endif
173 #if defined(PETSC_USE_REAL___FP16)
174 PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
175 #endif
176 
177 /*MC
178    MPIU_REAL - MPI datatype corresponding to PetscReal
179 
180    Notes:
181    In MPI calls that require an MPI datatype that matches a PetscReal or array of PetscReal values, pass this value.
182 
183    Level: beginner
184 
185 .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT
186 M*/
187 #if defined(PETSC_USE_REAL_SINGLE)
188 #  define MPIU_REAL MPI_FLOAT
189 #elif defined(PETSC_USE_REAL_DOUBLE)
190 #  define MPIU_REAL MPI_DOUBLE
191 #elif defined(PETSC_USE_REAL___FLOAT128)
192 #  define MPIU_REAL MPIU___FLOAT128
193 #elif defined(PETSC_USE_REAL___FP16)
194 #  define MPIU_REAL MPIU___FP16
195 #endif /* PETSC_USE_REAL_* */
196 
197 /*
198     Complex number definitions
199  */
200 #if defined(PETSC_HAVE_COMPLEX)
201 #if defined(__cplusplus)
202 /* C++ support of complex number */
203 
204 #define PetscRealPartComplex(a)      (a).real()
205 #define PetscImaginaryPartComplex(a) (a).imag()
206 #define PetscAbsComplex(a)           petsccomplexlib::abs(a)
207 #define PetscArgComplex(a)           petsccomplexlib::arg(a)
208 #define PetscConjComplex(a)          petsccomplexlib::conj(a)
209 #define PetscSqrtComplex(a)          petsccomplexlib::sqrt(a)
210 #define PetscPowComplex(a,b)         petsccomplexlib::pow(a,b)
211 #define PetscExpComplex(a)           petsccomplexlib::exp(a)
212 #define PetscLogComplex(a)           petsccomplexlib::log(a)
213 #define PetscSinComplex(a)           petsccomplexlib::sin(a)
214 #define PetscCosComplex(a)           petsccomplexlib::cos(a)
215 #define PetscTanComplex(a)           petsccomplexlib::tan(a)
216 #define PetscAsinComplex(a)          petsccomplexlib::asin(a)
217 #define PetscAcosComplex(a)          petsccomplexlib::acos(a)
218 #define PetscAtanComplex(a)          petsccomplexlib::atan(a)
219 #define PetscSinhComplex(a)          petsccomplexlib::sinh(a)
220 #define PetscCoshComplex(a)          petsccomplexlib::cosh(a)
221 #define PetscTanhComplex(a)          petsccomplexlib::tanh(a)
222 #define PetscAsinhComplex(a)         petsccomplexlib::asinh(a)
223 #define PetscAcoshComplex(a)         petsccomplexlib::acosh(a)
224 #define PetscAtanhComplex(a)         petsccomplexlib::atanh(a)
225 
226 /* TODO: Add configure tests
227 
228 #if !defined(PETSC_HAVE_CXX_TAN_COMPLEX)
229 #undef PetscTanComplex
230 PETSC_STATIC_INLINE PetscComplex PetscTanComplex(PetscComplex z)
231 {
232   return PetscSinComplex(z)/PetscCosComplex(z);
233 }
234 #endif
235 
236 #if !defined(PETSC_HAVE_CXX_TANH_COMPLEX)
237 #undef PetscTanhComplex
238 PETSC_STATIC_INLINE PetscComplex PetscTanhComplex(PetscComplex z)
239 {
240   return PetscSinhComplex(z)/PetscCoshComplex(z);
241 }
242 #endif
243 
244 #if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX)
245 #undef PetscAsinComplex
246 PETSC_STATIC_INLINE PetscComplex PetscAsinComplex(PetscComplex z)
247 {
248   const PetscComplex j(0,1);
249   return -j*PetscLogComplex(j*z+PetscSqrtComplex(1.0f-z*z));
250 }
251 #endif
252 
253 #if !defined(PETSC_HAVE_CXX_ACOS_COMPLEX)
254 #undef PetscAcosComplex
255 PETSC_STATIC_INLINE PetscComplex PetscAcosComplex(PetscComplex z)
256 {
257   const PetscComplex j(0,1);
258   return j*PetscLogComplex(z-j*PetscSqrtComplex(1.0f-z*z));
259 }
260 #endif
261 
262 #if !defined(PETSC_HAVE_CXX_ATAN_COMPLEX)
263 #undef PetscAtanComplex
264 PETSC_STATIC_INLINE PetscComplex PetscAtanComplex(PetscComplex z)
265 {
266   const PetscComplex j(0,1);
267   return 0.5f*j*PetscLogComplex((1.0f-j*z)/(1.0f+j*z));
268 }
269 #endif
270 
271 #if !defined(PETSC_HAVE_CXX_ASINH_COMPLEX)
272 #undef PetscAsinhComplex
273 PETSC_STATIC_INLINE PetscComplex PetscAsinhComplex(PetscComplex z)
274 {
275   return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f));
276 }
277 #endif
278 
279 #if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX)
280 #undef PetscAcoshComplex
281 PETSC_STATIC_INLINE PetscComplex PetscAcoshComplex(PetscComplex z)
282 {
283   return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f));
284 }
285 #endif
286 
287 #if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX)
288 #undef PetscAtanhComplex
289 PETSC_STATIC_INLINE PetscComplex PetscAtanhComplex(PetscComplex z)
290 {
291   return 0.5f*PetscLogComplex((1.0f+z)/(1.0f-z));
292 }
293 #endif
294 
295 */
296 
297 #else /* C99 support of complex number */
298 
299 #if defined(PETSC_USE_REAL_SINGLE)
300 #define PetscRealPartComplex(a)      crealf(a)
301 #define PetscImaginaryPartComplex(a) cimagf(a)
302 #define PetscAbsComplex(a)           cabsf(a)
303 #define PetscArgComplex(a)           cargf(a)
304 #define PetscConjComplex(a)          conjf(a)
305 #define PetscSqrtComplex(a)          csqrtf(a)
306 #define PetscPowComplex(a,b)         cpowf(a,b)
307 #define PetscExpComplex(a)           cexpf(a)
308 #define PetscLogComplex(a)           clogf(a)
309 #define PetscSinComplex(a)           csinf(a)
310 #define PetscCosComplex(a)           ccosf(a)
311 #define PetscTanComplex(a)           ctanf(a)
312 #define PetscAsinComplex(a)          casinf(a)
313 #define PetscAcosComplex(a)          cacosf(a)
314 #define PetscAtanComplex(a)          catanf(a)
315 #define PetscSinhComplex(a)          csinhf(a)
316 #define PetscCoshComplex(a)          ccoshf(a)
317 #define PetscTanhComplex(a)          ctanhf(a)
318 #define PetscAsinhComplex(a)         casinhf(a)
319 #define PetscAcoshComplex(a)         cacoshf(a)
320 #define PetscAtanhComplex(a)         catanhf(a)
321 
322 #elif defined(PETSC_USE_REAL_DOUBLE)
323 #define PetscRealPartComplex(a)      creal(a)
324 #define PetscImaginaryPartComplex(a) cimag(a)
325 #define PetscAbsComplex(a)           cabs(a)
326 #define PetscArgComplex(a)           carg(a)
327 #define PetscConjComplex(a)          conj(a)
328 #define PetscSqrtComplex(a)          csqrt(a)
329 #define PetscPowComplex(a,b)         cpow(a,b)
330 #define PetscExpComplex(a)           cexp(a)
331 #define PetscLogComplex(a)           clog(a)
332 #define PetscSinComplex(a)           csin(a)
333 #define PetscCosComplex(a)           ccos(a)
334 #define PetscTanComplex(a)           ctan(a)
335 #define PetscAsinComplex(a)          casin(a)
336 #define PetscAcosComplex(a)          cacos(a)
337 #define PetscAtanComplex(a)          catan(a)
338 #define PetscSinhComplex(a)          csinh(a)
339 #define PetscCoshComplex(a)          ccosh(a)
340 #define PetscTanhComplex(a)          ctanh(a)
341 #define PetscAsinhComplex(a)         casinh(a)
342 #define PetscAcoshComplex(a)         cacosh(a)
343 #define PetscAtanhComplex(a)         catanh(a)
344 
345 #elif defined(PETSC_USE_REAL___FLOAT128)
346 #define PetscRealPartComplex(a)      crealq(a)
347 #define PetscImaginaryPartComplex(a) cimagq(a)
348 #define PetscAbsComplex(a)           cabsq(a)
349 #define PetscArgComplex(a)           cargq(a)
350 #define PetscConjComplex(a)          conjq(a)
351 #define PetscSqrtComplex(a)          csqrtq(a)
352 #define PetscPowComplex(a,b)         cpowq(a,b)
353 #define PetscExpComplex(a)           cexpq(a)
354 #define PetscLogComplex(a)           clogq(a)
355 #define PetscSinComplex(a)           csinq(a)
356 #define PetscCosComplex(a)           ccosq(a)
357 #define PetscTanComplex(a)           ctanq(a)
358 #define PetscAsinComplex(a)          casinq(a)
359 #define PetscAcosComplex(a)          cacosq(a)
360 #define PetscAtanComplex(a)          catanq(a)
361 #define PetscSinhComplex(a)          csinhq(a)
362 #define PetscCoshComplex(a)          ccoshq(a)
363 #define PetscTanhComplex(a)          ctanhq(a)
364 #define PetscAsinhComplex(a)         casinhq(a)
365 #define PetscAcoshComplex(a)         cacoshq(a)
366 #define PetscAtanhComplex(a)         catanhq(a)
367 
368 #endif /* PETSC_USE_REAL_* */
369 #endif /* (__cplusplus) */
370 
371 /*
372    PETSC_i is the imaginary number, i
373 */
374 PETSC_EXTERN PetscComplex PETSC_i;
375 
376 /*
377    Try to do the right thing for complex number construction: see
378    http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
379    for details
380 */
381 PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
382 {
383 #if defined(__cplusplus)
384   return PetscComplex(x,y);
385 #elif defined(_Imaginary_I)
386   return x + y * _Imaginary_I;
387 #else
388   { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),
389 
390        "For each floating type there is a corresponding real type, which is always a real floating
391        type. For real floating types, it is the same type. For complex types, it is the type given
392        by deleting the keyword _Complex from the type name."
393 
394        So type punning should be portable. */
395     union { PetscComplex z; PetscReal f[2]; } uz;
396 
397     uz.f[0] = x;
398     uz.f[1] = y;
399     return uz.z;
400   }
401 #endif
402 }
403 
404 #define MPIU_C_COMPLEX MPI_C_COMPLEX PETSC_DEPRECATED_MACRO("GCC warning \"MPIU_C_COMPLEX macro is deprecated use MPI_C_COMPLEX (since version 3.15)\"")
405 #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX PETSC_DEPRECATED_MACRO("GCC warning \"MPIU_C_DOUBLE_COMPLEX macro is deprecated use MPI_C_DOUBLE_COMPLEX (since version 3.15)\"")
406 
407 #if defined(PETSC_USE_REAL___FLOAT128)
408 PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
409 #endif /* PETSC_USE_REAL___FLOAT128 */
410 
411 /*MC
412    MPIU_COMPLEX - MPI datatype corresponding to PetscComplex
413 
414    Notes:
415    In MPI calls that require an MPI datatype that matches a PetscComplex or array of PetscComplex values, pass this value.
416 
417    Level: beginner
418 
419 .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT, PETSC_i
420 M*/
421 #if defined(PETSC_USE_REAL_SINGLE)
422 #  define MPIU_COMPLEX MPI_C_COMPLEX
423 #elif defined(PETSC_USE_REAL_DOUBLE)
424 #  define MPIU_COMPLEX MPI_C_DOUBLE_COMPLEX
425 #elif defined(PETSC_USE_REAL___FLOAT128)
426 #  define MPIU_COMPLEX MPIU___COMPLEX128
427 #elif defined(PETSC_USE_REAL___FP16)
428 #  define MPIU_COMPLEX MPI_C_COMPLEX
429 #endif /* PETSC_USE_REAL_* */
430 
431 #endif /* PETSC_HAVE_COMPLEX */
432 
433 /*
434     Scalar number definitions
435  */
436 #if defined(PETSC_USE_COMPLEX) && defined(PETSC_HAVE_COMPLEX)
437 /*MC
438    MPIU_SCALAR - MPI datatype corresponding to PetscScalar
439 
440    Notes:
441    In MPI calls that require an MPI datatype that matches a PetscScalar or array of PetscScalar values, pass this value.
442 
443    Level: beginner
444 
445 .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_COMPLEX, MPIU_INT
446 M*/
447 #define MPIU_SCALAR MPIU_COMPLEX
448 
449 /*MC
450    PetscRealPart - Returns the real part of a PetscScalar
451 
452    Synopsis:
453    #include <petscmath.h>
454    PetscReal PetscRealPart(PetscScalar v)
455 
456    Not Collective
457 
458    Input Parameter:
459 .  v - value to find the real part of
460 
461    Level: beginner
462 
463 .seealso: PetscScalar, PetscImaginaryPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
464 
465 M*/
466 #define PetscRealPart(a)      PetscRealPartComplex(a)
467 
468 /*MC
469    PetscImaginaryPart - Returns the imaginary part of a PetscScalar
470 
471    Synopsis:
472    #include <petscmath.h>
473    PetscReal PetscImaginaryPart(PetscScalar v)
474 
475    Not Collective
476 
477    Input Parameter:
478 .  v - value to find the imaginary part of
479 
480    Level: beginner
481 
482    Notes:
483        If PETSc was configured for real numbers then this always returns the value 0
484 
485 .seealso: PetscScalar, PetscRealPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
486 
487 M*/
488 #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)
489 
490 #define PetscAbsScalar(a)     PetscAbsComplex(a)
491 #define PetscArgScalar(a)     PetscArgComplex(a)
492 #define PetscConj(a)          PetscConjComplex(a)
493 #define PetscSqrtScalar(a)    PetscSqrtComplex(a)
494 #define PetscPowScalar(a,b)   PetscPowComplex(a,b)
495 #define PetscExpScalar(a)     PetscExpComplex(a)
496 #define PetscLogScalar(a)     PetscLogComplex(a)
497 #define PetscSinScalar(a)     PetscSinComplex(a)
498 #define PetscCosScalar(a)     PetscCosComplex(a)
499 #define PetscTanScalar(a)     PetscTanComplex(a)
500 #define PetscAsinScalar(a)    PetscAsinComplex(a)
501 #define PetscAcosScalar(a)    PetscAcosComplex(a)
502 #define PetscAtanScalar(a)    PetscAtanComplex(a)
503 #define PetscSinhScalar(a)    PetscSinhComplex(a)
504 #define PetscCoshScalar(a)    PetscCoshComplex(a)
505 #define PetscTanhScalar(a)    PetscTanhComplex(a)
506 #define PetscAsinhScalar(a)   PetscAsinhComplex(a)
507 #define PetscAcoshScalar(a)   PetscAcoshComplex(a)
508 #define PetscAtanhScalar(a)   PetscAtanhComplex(a)
509 
510 #else /* PETSC_USE_COMPLEX */
511 #define MPIU_SCALAR MPIU_REAL
512 #define PetscRealPart(a)      (a)
513 #define PetscImaginaryPart(a) ((PetscReal)0)
514 #define PetscAbsScalar(a)     PetscAbsReal(a)
515 #define PetscArgScalar(a)     (((a) < (PetscReal)0) ? PETSC_PI : (PetscReal)0)
516 #define PetscConj(a)          (a)
517 #define PetscSqrtScalar(a)    PetscSqrtReal(a)
518 #define PetscPowScalar(a,b)   PetscPowReal(a,b)
519 #define PetscExpScalar(a)     PetscExpReal(a)
520 #define PetscLogScalar(a)     PetscLogReal(a)
521 #define PetscSinScalar(a)     PetscSinReal(a)
522 #define PetscCosScalar(a)     PetscCosReal(a)
523 #define PetscTanScalar(a)     PetscTanReal(a)
524 #define PetscAsinScalar(a)    PetscAsinReal(a)
525 #define PetscAcosScalar(a)    PetscAcosReal(a)
526 #define PetscAtanScalar(a)    PetscAtanReal(a)
527 #define PetscSinhScalar(a)    PetscSinhReal(a)
528 #define PetscCoshScalar(a)    PetscCoshReal(a)
529 #define PetscTanhScalar(a)    PetscTanhReal(a)
530 #define PetscAsinhScalar(a)   PetscAsinhReal(a)
531 #define PetscAcoshScalar(a)   PetscAcoshReal(a)
532 #define PetscAtanhScalar(a)   PetscAtanhReal(a)
533 
534 #endif /* PETSC_USE_COMPLEX */
535 
536 /*
537    Certain objects may be created using either single or double precision.
538    This is currently not used.
539 */
540 typedef enum { PETSC_SCALAR_DOUBLE, PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;
541 
542 /* --------------------------------------------------------------------------*/
543 
544 /*MC
545    PetscAbs - Returns the absolute value of a number
546 
547    Synopsis:
548    #include <petscmath.h>
549    type PetscAbs(type v)
550 
551    Not Collective
552 
553    Input Parameter:
554 .  v - the number
555 
556    Notes:
557     type can be integer or real floating point value
558 
559    Level: beginner
560 
561 .seealso: PetscAbsInt(), PetscAbsReal(), PetscAbsScalar()
562 
563 M*/
564 #define PetscAbs(a)  (((a) >= 0) ? (a) : (-(a)))
565 
566 /*MC
567    PetscSign - Returns the sign of a number as an integer
568 
569    Synopsis:
570    #include <petscmath.h>
571    int PetscSign(type v)
572 
573    Not Collective
574 
575    Input Parameter:
576 .  v - the number
577 
578    Notes:
579     type can be integer or real floating point value
580 
581    Level: beginner
582 
583 M*/
584 #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)
585 
586 /*MC
587    PetscMin - Returns minimum of two numbers
588 
589    Synopsis:
590    #include <petscmath.h>
591    type PetscMin(type v1,type v2)
592 
593    Not Collective
594 
595    Input Parameter:
596 +  v1 - first value to find minimum of
597 -  v2 - second value to find minimum of
598 
599    Notes:
600     type can be integer or floating point value
601 
602    Level: beginner
603 
604 .seealso: PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
605 
606 M*/
607 #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))
608 
609 /*MC
610    PetscMax - Returns maxium of two numbers
611 
612    Synopsis:
613    #include <petscmath.h>
614    type max PetscMax(type v1,type v2)
615 
616    Not Collective
617 
618    Input Parameter:
619 +  v1 - first value to find maximum of
620 -  v2 - second value to find maximum of
621 
622    Notes:
623     type can be integer or floating point value
624 
625    Level: beginner
626 
627 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
628 
629 M*/
630 #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))
631 
632 /*MC
633    PetscClipInterval - Returns a number clipped to be within an interval
634 
635    Synopsis:
636    #include <petscmath.h>
637    type clip PetscClipInterval(type x,type a,type b)
638 
639    Not Collective
640 
641    Input Parameter:
642 +  x - value to use if within interval [a,b]
643 .  a - lower end of interval
644 -  b - upper end of interval
645 
646    Notes:
647     type can be integer or floating point value
648 
649    Level: beginner
650 
651 .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
652 
653 M*/
654 #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))
655 
656 /*MC
657    PetscAbsInt - Returns the absolute value of an integer
658 
659    Synopsis:
660    #include <petscmath.h>
661    int abs PetscAbsInt(int v1)
662 
663    Not Collective
664 
665    Input Parameter:
666 .   v1 - the integer
667 
668    Level: beginner
669 
670 .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()
671 
672 M*/
673 #define PetscAbsInt(a)  (((a)<0)   ? (-(a)) : (a))
674 
675 /*MC
676    PetscAbsReal - Returns the absolute value of an real number
677 
678    Synopsis:
679    #include <petscmath.h>
680    Real abs PetscAbsReal(PetscReal v1)
681 
682    Not Collective
683 
684    Input Parameter:
685 .   v1 - the double
686 
687 
688    Level: beginner
689 
690 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()
691 
692 M*/
693 #if defined(PETSC_USE_REAL_SINGLE)
694 #define PetscAbsReal(a) fabsf(a)
695 #elif defined(PETSC_USE_REAL_DOUBLE)
696 #define PetscAbsReal(a) fabs(a)
697 #elif defined(PETSC_USE_REAL___FLOAT128)
698 #define PetscAbsReal(a) fabsq(a)
699 #elif defined(PETSC_USE_REAL___FP16)
700 #define PetscAbsReal(a) fabsf(a)
701 #endif
702 
703 /*MC
704    PetscSqr - Returns the square of a number
705 
706    Synopsis:
707    #include <petscmath.h>
708    type sqr PetscSqr(type v1)
709 
710    Not Collective
711 
712    Input Parameter:
713 .   v1 - the value
714 
715    Notes:
716     type can be integer or floating point value
717 
718    Level: beginner
719 
720 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()
721 
722 M*/
723 #define PetscSqr(a)     ((a)*(a))
724 
725 /* ----------------------------------------------------------------------------*/
726 
727 #if defined(PETSC_USE_REAL_SINGLE)
728 #define PetscRealConstant(constant) constant##F
729 #elif defined(PETSC_USE_REAL_DOUBLE)
730 #define PetscRealConstant(constant) constant
731 #elif defined(PETSC_USE_REAL___FLOAT128)
732 #define PetscRealConstant(constant) constant##Q
733 #elif defined(PETSC_USE_REAL___FP16)
734 #define PetscRealConstant(constant) constant##F
735 #endif
736 
737 /*
738      Basic constants
739 */
740 #define PETSC_PI    PetscRealConstant(3.1415926535897932384626433832795029)
741 #define PETSC_PHI   PetscRealConstant(1.6180339887498948482045868343656381)
742 #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)
743 
744 #if !defined(PETSC_USE_64BIT_INDICES)
745 #define PETSC_MAX_INT            2147483647
746 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
747 #else
748 #define PETSC_MAX_INT            9223372036854775807L
749 #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
750 #endif
751 #define PETSC_MAX_UINT16         65535
752 
753 #if defined(PETSC_USE_REAL_SINGLE)
754 #  define PETSC_MAX_REAL                3.40282346638528860e+38F
755 #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
756 #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
757 #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
758 #  define PETSC_SMALL                   1.e-5F
759 #elif defined(PETSC_USE_REAL_DOUBLE)
760 #  define PETSC_MAX_REAL                1.7976931348623157e+308
761 #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
762 #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
763 #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
764 #  define PETSC_SMALL                   1.e-10
765 #elif defined(PETSC_USE_REAL___FLOAT128)
766 #  define PETSC_MAX_REAL                FLT128_MAX
767 #  define PETSC_MIN_REAL                (-FLT128_MAX)
768 #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
769 #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078144567552953958511352539e-17Q
770 #  define PETSC_SMALL                   1.e-20Q
771 #elif defined(PETSC_USE_REAL___FP16)
772 #  define PETSC_MAX_REAL                65504.0F
773 #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
774 #  define PETSC_MACHINE_EPSILON         .0009765625F
775 #  define PETSC_SQRT_MACHINE_EPSILON    .03125F
776 #  define PETSC_SMALL                   5.e-3F
777 #endif
778 
779 #define PETSC_INFINITY               (PETSC_MAX_REAL/4)
780 #define PETSC_NINFINITY              (-PETSC_INFINITY)
781 
782 PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal);
783 PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal);
784 PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
785 PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;}
786 PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));}
787 PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
788 PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
789 PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}
790 
791 PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal,PetscReal,PetscReal,PetscReal);
792 PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
793 PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);
794 
795 /*
796     These macros are currently hardwired to match the regular data types, so there is no support for a different
797     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
798  */
799 #define MPIU_MATSCALAR MPIU_SCALAR
800 typedef PetscScalar MatScalar;
801 typedef PetscReal MatReal;
802 
803 struct petsc_mpiu_2scalar {PetscScalar a,b;};
804 PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
805 
806 #if defined(PETSC_USE_64BIT_INDICES)
807 struct petsc_mpiu_2int {PetscInt a,b;};
808 PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
809 #else
810 #define MPIU_2INT MPI_2INT
811 #endif
812 
813 PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
814 {
815   PetscInt result = 1;
816   while (power) {
817     if (power & 1) result *= base;
818     power >>= 1;
819     base *= base;
820   }
821   return result;
822 }
823 
824 PETSC_STATIC_INLINE PetscInt64 PetscPowInt64(PetscInt base,PetscInt power)
825 {
826   PetscInt64 result = 1;
827   while (power) {
828     if (power & 1) result *= base;
829     power >>= 1;
830     base *= base;
831   }
832   return result;
833 }
834 
835 PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
836 {
837   PetscReal result = 1;
838   if (power < 0) {
839     power = -power;
840     base  = ((PetscReal)1)/base;
841   }
842   while (power) {
843     if (power & 1) result *= base;
844     power >>= 1;
845     base *= base;
846   }
847   return result;
848 }
849 
850 PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
851 {
852   PetscScalar result = (PetscReal)1;
853   if (power < 0) {
854     power = -power;
855     base  = ((PetscReal)1)/base;
856   }
857   while (power) {
858     if (power & 1) result *= base;
859     power >>= 1;
860     base *= base;
861   }
862   return result;
863 }
864 
865 PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
866 {
867   PetscScalar cpower = power;
868   return PetscPowScalar(base,cpower);
869 }
870 
871 PETSC_EXTERN PetscErrorCode PetscLinearRegression(PetscInt,const PetscReal[],const PetscReal[],PetscReal*,PetscReal*);
872 #endif
873