Actual source code: petscmath.h

petsc-master 2019-07-20
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  1: /*

  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.

  7:     This file is included by petscsys.h and should not be used directly.

  9: */

 11: #if !defined(PETSCMATH_H)
 12: #define PETSCMATH_H
 13: #include <math.h>
 14:  #include <petscsystypes.h>

 16: /*MC
 17:    MPIU_REAL - MPI datatype corresponding to PetscReal

 19:    Notes:
 20:    In MPI calls that require an MPI datatype that matches a PetscReal or array of PetscReal values, pass this value.

 22:    Level: beginner

 24: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT
 25: M*/

 27: /*

 29:      Defines operations that are different for complex and real numbers;
 30:    note that one cannot mix the use of complex and real in the same
 31:    PETSc program. All PETSc objects in one program are built around the object
 32:    PetscScalar which is either always a real or a complex.

 34: */

 36: #if defined(PETSC_USE_REAL_SINGLE)
 37: #define MPIU_REAL   MPI_FLOAT
 38: #define PetscRoundReal(a)   roundf(a)
 39: #define PetscSqrtReal(a)    sqrtf(a)
 40: #define PetscExpReal(a)     expf(a)
 41: #define PetscLogReal(a)     logf(a)
 42: #define PetscLog10Real(a)   log10f(a)
 43: #ifdef PETSC_HAVE_LOG2
 44: #define PetscLog2Real(a)    log2f(a)
 45: #endif
 46: #define PetscSinReal(a)     sinf(a)
 47: #define PetscCosReal(a)     cosf(a)
 48: #define PetscTanReal(a)     tanf(a)
 49: #define PetscAsinReal(a)    asinf(a)
 50: #define PetscAcosReal(a)    acosf(a)
 51: #define PetscAtanReal(a)    atanf(a)
 52: #define PetscAtan2Real(a,b) atan2f(a,b)
 53: #define PetscSinhReal(a)    sinhf(a)
 54: #define PetscCoshReal(a)    coshf(a)
 55: #define PetscTanhReal(a)    tanhf(a)
 56: #define PetscPowReal(a,b)   powf(a,b)
 57: #define PetscCeilReal(a)    ceilf(a)
 58: #define PetscFloorReal(a)   floorf(a)
 59: #define PetscFmodReal(a,b)  fmodf(a,b)
 60: #define PetscTGamma(a)      tgammaf(a)
 61: #elif defined(PETSC_USE_REAL_DOUBLE)
 62: #define MPIU_REAL   MPI_DOUBLE
 63: #define PetscRoundReal(a)   round(a)
 64: #define PetscSqrtReal(a)    sqrt(a)
 65: #define PetscExpReal(a)     exp(a)
 66: #define PetscLogReal(a)     log(a)
 67: #define PetscLog10Real(a)   log10(a)
 68: #ifdef PETSC_HAVE_LOG2
 69: #define PetscLog2Real(a)    log2(a)
 70: #endif
 71: #define PetscSinReal(a)     sin(a)
 72: #define PetscCosReal(a)     cos(a)
 73: #define PetscTanReal(a)     tan(a)
 74: #define PetscAsinReal(a)    asin(a)
 75: #define PetscAcosReal(a)    acos(a)
 76: #define PetscAtanReal(a)    atan(a)
 77: #define PetscAtan2Real(a,b) atan2(a,b)
 78: #define PetscSinhReal(a)    sinh(a)
 79: #define PetscCoshReal(a)    cosh(a)
 80: #define PetscTanhReal(a)    tanh(a)
 81: #define PetscPowReal(a,b)   pow(a,b)
 82: #define PetscCeilReal(a)    ceil(a)
 83: #define PetscFloorReal(a)   floor(a)
 84: #define PetscFmodReal(a,b)  fmod(a,b)
 85: #define PetscTGamma(a)      tgamma(a)
 86: #elif defined(PETSC_USE_REAL___FLOAT128)
 87: #if defined(__cplusplus)
 88: extern "C" {
 89: #endif
 90: #include <quadmath.h>
 91: #if defined(__cplusplus)
 92: }
 93: #endif
 94: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
 95: #define MPIU_REAL MPIU___FLOAT128
 96: #define PetscRoundReal(a)   roundq(a)
 97: #define PetscSqrtReal(a)    sqrtq(a)
 98: #define PetscExpReal(a)     expq(a)
 99: #define PetscLogReal(a)     logq(a)
100: #define PetscLog10Real(a)   log10q(a)
101: #ifdef PETSC_HAVE_LOG2
102: #define PetscLog2Real(a)    log2q(a)
103: #endif
104: #define PetscSinReal(a)     sinq(a)
105: #define PetscCosReal(a)     cosq(a)
106: #define PetscTanReal(a)     tanq(a)
107: #define PetscAsinReal(a)    asinq(a)
108: #define PetscAcosReal(a)    acosq(a)
109: #define PetscAtanReal(a)    atanq(a)
110: #define PetscAtan2Real(a,b) atan2q(a,b)
111: #define PetscSinhReal(a)    sinhq(a)
112: #define PetscCoshReal(a)    coshq(a)
113: #define PetscTanhReal(a)    tanhq(a)
114: #define PetscPowReal(a,b)   powq(a,b)
115: #define PetscCeilReal(a)    ceilq(a)
116: #define PetscFloorReal(a)   floorq(a)
117: #define PetscFmodReal(a,b)  fmodq(a,b)
118: #define PetscTGamma(a)      tgammaq(a)
119: #elif defined(PETSC_USE_REAL___FP16)
120: PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
121: #define MPIU_REAL MPIU___FP16
122: #define PetscRoundReal(a)   roundf(a)
123: #define PetscSqrtReal(a)    sqrtf(a)
124: #define PetscExpReal(a)     expf(a)
125: #define PetscLogReal(a)     logf(a)
126: #define PetscLog10Real(a)   log10f(a)
127: #ifdef PETSC_HAVE_LOG2
128: #define PetscLog2Real(a)    log2f(a)
129: #endif
130: #define PetscSinReal(a)     sinf(a)
131: #define PetscCosReal(a)     cosf(a)
132: #define PetscTanReal(a)     tanf(a)
133: #define PetscAsinReal(a)    asinf(a)
134: #define PetscAcosReal(a)    acosf(a)
135: #define PetscAtanReal(a)    atanf(a)
136: #define PetscAtan2Real(a,b) atan2f(a,b)
137: #define PetscSinhReal(a)    sinhf(a)
138: #define PetscCoshReal(a)    coshf(a)
139: #define PetscTanhReal(a)    tanhf(a)
140: #define PetscPowReal(a,b)   powf(a,b)
141: #define PetscCeilReal(a)    ceilf(a)
142: #define PetscFloorReal(a)   floorf(a)
143: #define PetscFmodReal(a,b)  fmodf(a,b)
144: #define PetscTGamma(a)      tgammaf(a)
145: #endif /* PETSC_USE_REAL_* */

147: /*MC
148:    MPIU_COMPLEX - MPI datatype corresponding to PetscComplex

150:    Notes:
151:    In MPI calls that require an MPI datatype that matches a PetscComplex or array of PetscComplex values, pass this value.

153:    Level: beginner

155: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT, PETSC_i
156: M*/

158: /*
159:     Complex number definitions
160:  */
161: #if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
162: #if defined(PETSC_HAVE_COMPLEX)
163: /* C++ support of complex number */

165: #define PetscRealPartComplex(a)      (a).real()
166: #define PetscImaginaryPartComplex(a) (a).imag()
167: #define PetscAbsComplex(a)           petsccomplexlib::abs(a)
168: #define PetscConjComplex(a)          petsccomplexlib::conj(a)
169: #define PetscSqrtComplex(a)          petsccomplexlib::sqrt(a)
170: #define PetscPowComplex(a,b)         petsccomplexlib::pow(a,b)
171: #define PetscExpComplex(a)           petsccomplexlib::exp(a)
172: #define PetscLogComplex(a)           petsccomplexlib::log(a)
173: #define PetscSinComplex(a)           petsccomplexlib::sin(a)
174: #define PetscCosComplex(a)           petsccomplexlib::cos(a)
175: #define PetscAsinComplex(a)          petsccomplexlib::asin(a)
176: #define PetscAcosComplex(a)          petsccomplexlib::acos(a)
177: #if defined(PETSC_HAVE_TANCOMPLEX)
178: #define PetscTanComplex(a)           petsccomplexlib::tan(a)
179: #else
180: #define PetscTanComplex(a)           PetscSinComplex(a)/PetscCosComplex(a)
181: #endif
182: #define PetscSinhComplex(a)          petsccomplexlib::sinh(a)
183: #define PetscCoshComplex(a)          petsccomplexlib::cosh(a)
184: #if defined(PETSC_HAVE_TANHCOMPLEX)
185: #define PetscTanhComplex(a)          petsccomplexlib::tanh(a)
186: #else
187: #define PetscTanhComplex(a)          PetscSinhComplex(a)/PetscCoshComplex(a)
188: #endif

190: #if defined(PETSC_USE_REAL_SINGLE)
191: #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND)
192: static inline PetscComplex operator+(const PetscComplex& lhs, const double& rhs) { return lhs + float(rhs); }
193: static inline PetscComplex operator+(const double& lhs, const PetscComplex& rhs) { return float(lhs) + rhs; }
194: static inline PetscComplex operator-(const PetscComplex& lhs, const double& rhs) { return lhs - float(rhs); }
195: static inline PetscComplex operator-(const double& lhs, const PetscComplex& rhs) { return float(lhs) - rhs; }
196: static inline PetscComplex operator*(const PetscComplex& lhs, const double& rhs) { return lhs * float(rhs); }
197: static inline PetscComplex operator*(const double& lhs, const PetscComplex& rhs) { return float(lhs) * rhs; }
198: static inline PetscComplex operator/(const PetscComplex& lhs, const double& rhs) { return lhs / float(rhs); }
199: static inline PetscComplex operator/(const double& lhs, const PetscComplex& rhs) { return float(lhs) / rhs; }
200: static inline bool operator==(const PetscComplex& lhs, const double& rhs) { return lhs.imag() == float(0) && lhs.real() == float(rhs); }
201: static inline bool operator==(const double& lhs, const PetscComplex& rhs) { return rhs.imag() == float(0) && rhs.real() == float(lhs); }
202: static inline bool operator!=(const PetscComplex& lhs, const double& rhs) { return lhs.imag() != float(0) || lhs.real() != float(rhs); }
203: static inline bool operator!=(const double& lhs, const PetscComplex& rhs) { return rhs.imag() != float(0) || rhs.real() != float(lhs); }
204: #endif  /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */
205: #elif defined(PETSC_USE_REAL_DOUBLE)
206: #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND)
207: static inline PetscComplex operator+(const PetscComplex& lhs, const PetscInt& rhs) { return lhs + double(rhs); }
208: static inline PetscComplex operator+(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) + rhs; }
209: static inline PetscComplex operator-(const PetscComplex& lhs, const PetscInt& rhs) { return lhs - double(rhs); }
210: static inline PetscComplex operator-(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) - rhs; }
211: static inline PetscComplex operator*(const PetscComplex& lhs, const PetscInt& rhs) { return lhs * double(rhs); }
212: static inline PetscComplex operator*(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) * rhs; }
213: static inline PetscComplex operator/(const PetscComplex& lhs, const PetscInt& rhs) { return lhs / double(rhs); }
214: static inline PetscComplex operator/(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) / rhs; }
215: static inline bool operator==(const PetscComplex& lhs, const PetscInt& rhs) { return lhs.imag() == double(0) && lhs.real() == double(rhs); }
216: static inline bool operator==(const PetscInt& lhs, const PetscComplex& rhs) { return rhs.imag() == double(0) && rhs.real() == double(lhs); }
217: static inline bool operator!=(const PetscComplex& lhs, const PetscInt& rhs) { return lhs.imag() != double(0) || lhs.real() != double(rhs); }
218: static inline bool operator!=(const PetscInt& lhs, const PetscComplex& rhs) { return rhs.imag() != double(0) || rhs.real() != double(lhs); }
219: #endif  /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */
220: #elif defined(PETSC_USE_REAL___FLOAT128)
221: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128;
222: #endif
223: #endif  /* PETSC_HAVE_COMPLEX */

225: #elif defined(PETSC_HAVE_C99_COMPLEX) && !defined(PETSC_USE_REAL___FP16)
226: #if defined(PETSC_HAVE_COMPLEX)

228: #if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
229: #define PetscRealPartComplex(a)      crealf(a)
230: #define PetscImaginaryPartComplex(a) cimagf(a)
231: #define PetscAbsComplex(a)           cabsf(a)
232: #define PetscConjComplex(a)          conjf(a)
233: #define PetscSqrtComplex(a)          csqrtf(a)
234: #define PetscPowComplex(a,b)         cpowf(a,b)
235: #define PetscExpComplex(a)           cexpf(a)
236: #define PetscLogComplex(a)           clogf(a)
237: #define PetscSinComplex(a)           csinf(a)
238: #define PetscCosComplex(a)           ccosf(a)
239: #define PetscAsinComplex(a)          casinf(a)
240: #define PetscAcosComplex(a)          cacosf(a)
241: #define PetscTanComplex(a)           ctanf(a)
242: #define PetscSinhComplex(a)          csinhf(a)
243: #define PetscCoshComplex(a)          ccoshf(a)
244: #define PetscTanhComplex(a)          ctanhf(a)

246: #elif defined(PETSC_USE_REAL_DOUBLE)
247: #define PetscRealPartComplex(a)      creal(a)
248: #define PetscImaginaryPartComplex(a) cimag(a)
249: #define PetscAbsComplex(a)           cabs(a)
250: #define PetscConjComplex(a)          conj(a)
251: #define PetscSqrtComplex(a)          csqrt(a)
252: #define PetscPowComplex(a,b)         cpow(a,b)
253: #define PetscExpComplex(a)           cexp(a)
254: #define PetscLogComplex(a)           clog(a)
255: #define PetscSinComplex(a)           csin(a)
256: #define PetscCosComplex(a)           ccos(a)
257: #define PetscAsinComplex(a)          casin(a)
258: #define PetscAcosComplex(a)          cacos(a)
259: #define PetscTanComplex(a)           ctan(a)
260: #define PetscSinhComplex(a)          csinh(a)
261: #define PetscCoshComplex(a)          ccosh(a)
262: #define PetscTanhComplex(a)          ctanh(a)

264: #elif defined(PETSC_USE_REAL___FLOAT128)
265: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);

267: #define PetscRealPartComplex(a)      crealq(a)
268: #define PetscImaginaryPartComplex(a) cimagq(a)
269: #define PetscAbsComplex(a)           cabsq(a)
270: #define PetscConjComplex(a)          conjq(a)
271: #define PetscSqrtComplex(a)          csqrtq(a)
272: #define PetscPowComplex(a,b)         cpowq(a,b)
273: #define PetscExpComplex(a)           cexpq(a)
274: #define PetscLogComplex(a)           clogq(a)
275: #define PetscSinComplex(a)           csinq(a)
276: #define PetscCosComplex(a)           ccosq(a)
277: #define PetscAsinComplex(a)          casinq(a)
278: #define PetscAcosComplex(a)          cacosq(a)
279: #define PetscTanComplex(a)           ctanq(a)
280: #define PetscSinhComplex(a)          csinhq(a)
281: #define PetscCoshComplex(a)          ccoshq(a)
282: #define PetscTanhComplex(a)          ctanhq(a)

284: #endif /* PETSC_USE_REAL_* */
285: #endif /* PETSC_HAVE_COMPLEX */
286: #endif /* (__cplusplus && PETSC_HAVE_CXX_COMPLEX) else-if (!__cplusplus && PETSC_HAVE_C99_COMPLEX) */

288: #if defined(PETSC_HAVE_COMPLEX)
289: #if defined(PETSC_HAVE_MPI_C_DOUBLE_COMPLEX)
290: #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX
291: #define MPIU_C_COMPLEX MPI_C_COMPLEX
292: #else
293: # if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
294:   typedef petsccomplexlib::complex<double> petsc_mpiu_c_double_complex;
295:   typedef petsccomplexlib::complex<float> petsc_mpiu_c_complex;
296: # elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
297:   typedef double _Complex petsc_mpiu_c_double_complex;
298:   typedef float _Complex petsc_mpiu_c_complex;
299: # else
300:   typedef struct {double real,imag;} petsc_mpiu_c_double_complex;
301:   typedef struct {float real,imag;} petsc_mpiu_c_complex;
302: # endif
303: PETSC_EXTERN MPI_Datatype MPIU_C_DOUBLE_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_double_complex);
304: PETSC_EXTERN MPI_Datatype MPIU_C_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_complex);
305: #endif /* PETSC_HAVE_MPI_C_DOUBLE_COMPLEX */
306: #endif /* PETSC_HAVE_COMPLEX */

308: #if defined(PETSC_HAVE_COMPLEX)
309: #  if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
310: #    define MPIU_COMPLEX MPIU_C_COMPLEX
311: #  elif defined(PETSC_USE_REAL_DOUBLE)
312: #    define MPIU_COMPLEX MPIU_C_DOUBLE_COMPLEX
313: #  elif defined(PETSC_USE_REAL___FLOAT128)
314: #    define MPIU_COMPLEX MPIU___COMPLEX128
315: #  endif /* PETSC_USE_REAL_* */
316: #endif

318: /*MC
319:    MPIU_SCALAR - MPI datatype corresponding to PetscScalar

321:    Notes:
322:    In MPI calls that require an MPI datatype that matches a PetscScalar or array of PetscScalar values, pass this value.

324:    Level: beginner

326: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_COMPLEX, MPIU_INT
327: M*/

329: #if (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))

331: /*MC
332:    PetscRealPart - Returns the real part of a PetscScalar

334:    Synopsis:
335:    #include <petscmath.h>
336:    PetscScalar PetscRealPart(PetscScalar v)

338:    Not Collective

340:    Input Parameter:
341: .  v - value to find the real part of

343:    Level: beginner

345: .seealso: PetscScalar, PetscImaginaryPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()

347: M*/
348: #define PetscRealPart(a)      PetscRealPartComplex(a)

350: /*MC
351:    PetscImaginaryPart - Returns the imaginary part of a PetscScalar

353:    Synopsis:
354:    #include <petscmath.h>
355:    PetscScalar PetscImaginaryPart(PetscScalar v)

357:    Not Collective

359:    Input Parameter:
360: .  v - value to find the imaginary part of

362:    Level: beginner

364:    Notes:
365:        If PETSc was configured for real numbers then this always returns the value 0

367: .seealso: PetscScalar, PetscRealPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()

369: M*/
370: #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)

372: #define PetscAbsScalar(a)     PetscAbsComplex(a)
373: #define PetscConj(a)          PetscConjComplex(a)
374: #define PetscSqrtScalar(a)    PetscSqrtComplex(a)
375: #define PetscPowScalar(a,b)   PetscPowComplex(a,b)
376: #define PetscExpScalar(a)     PetscExpComplex(a)
377: #define PetscLogScalar(a)     PetscLogComplex(a)
378: #define PetscSinScalar(a)     PetscSinComplex(a)
379: #define PetscCosScalar(a)     PetscCosComplex(a)
380: #define PetscAsinScalar(a)    PetscAsinComplex(a)
381: #define PetscAcosScalar(a)    PetscAcosComplex(a)
382: #define PetscTanScalar(a)     PetscTanComplex(a)
383: #define PetscSinhScalar(a)    PetscSinhComplex(a)
384: #define PetscCoshScalar(a)    PetscCoshComplex(a)
385: #define PetscTanhScalar(a)    PetscTanhComplex(a)
386: #define MPIU_SCALAR MPIU_COMPLEX

388: /*
389:     real number definitions
390:  */
391: #else /* PETSC_USE_COMPLEX */
392: #define MPIU_SCALAR MPIU_REAL

394: #define PetscRealPart(a)      (a)
395: #define PetscImaginaryPart(a) ((PetscReal)0.)
396: PETSC_STATIC_INLINE PetscReal PetscAbsScalar(PetscScalar a) {return a < 0.0 ? -a : a;}
397: #define PetscConj(a)          (a)
398: #if !defined(PETSC_USE_REAL___FLOAT128)  && !defined(PETSC_USE_REAL___FP16)
399: #define PetscSqrtScalar(a)    sqrt(a)
400: #define PetscPowScalar(a,b)   pow(a,b)
401: #define PetscExpScalar(a)     exp(a)
402: #define PetscLogScalar(a)     log(a)
403: #define PetscSinScalar(a)     sin(a)
404: #define PetscCosScalar(a)     cos(a)
405: #define PetscAsinScalar(a)    asin(a)
406: #define PetscAcosScalar(a)    acos(a)
407: #define PetscTanScalar(a)     tan(a)
408: #define PetscSinhScalar(a)    sinh(a)
409: #define PetscCoshScalar(a)    cosh(a)
410: #define PetscTanhScalar(a)    tanh(a)
411: #elif defined(PETSC_USE_REAL___FP16)
412: #define PetscSqrtScalar(a)    sqrtf(a)
413: #define PetscPowScalar(a,b)   powf(a,b)
414: #define PetscExpScalar(a)     expf(a)
415: #define PetscLogScalar(a)     logf(a)
416: #define PetscSinScalar(a)     sinf(a)
417: #define PetscCosScalar(a)     cosf(a)
418: #define PetscAsinScalar(a)    asinf(a)
419: #define PetscAcosScalar(a)    acosf(a)
420: #define PetscTanScalar(a)     tanf(a)
421: #define PetscSinhScalar(a)    sinhf(a)
422: #define PetscCoshScalar(a)    coshf(a)
423: #define PetscTanhScalar(a)    tanhf(a)
424: #else /* PETSC_USE_REAL___FLOAT128 */
425: #define PetscSqrtScalar(a)    sqrtq(a)
426: #define PetscPowScalar(a,b)   powq(a,b)
427: #define PetscExpScalar(a)     expq(a)
428: #define PetscLogScalar(a)     logq(a)
429: #define PetscSinScalar(a)     sinq(a)
430: #define PetscCosScalar(a)     cosq(a)
431: #define PetscAsinScalar(a)    asinq(a)
432: #define PetscAcosScalar(a)    acosq(a)
433: #define PetscTanScalar(a)     tanq(a)
434: #define PetscSinhScalar(a)    sinhq(a)
435: #define PetscCoshScalar(a)    coshq(a)
436: #define PetscTanhScalar(a)    tanhq(a)
437: #endif /* PETSC_USE_REAL___FLOAT128 */

439: #endif /* PETSC_USE_COMPLEX */

441: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)
442: #define PetscSignReal(a) (((a) >= 0.0) ? ((a) == 0.0 ? 0.0 : 1.0) : -1.0)
443: #define PetscAbs(a)  (((a) >= 0) ? (a) : (-(a)))

445: /* --------------------------------------------------------------------------*/

447: /*
448:    Certain objects may be created using either single or double precision.
449:    This is currently not used.
450: */
451: typedef enum { PETSC_SCALAR_DOUBLE,PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;

453: #if defined(PETSC_HAVE_COMPLEX)
454: /* PETSC_i is the imaginary number, i */
455: PETSC_EXTERN PetscComplex PETSC_i;

457: /* Try to do the right thing for complex number construction: see

459:   http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm

461:   for details
462: */
463: PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
464: {
465: #if   defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
466:   return PetscComplex(x,y);
467: #elif defined(_Imaginary_I)
468:   return x + y * _Imaginary_I;
469: #else
470:   { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),

472:        "For each floating type there is a corresponding real type, which is always a real floating
473:        type. For real floating types, it is the same type. For complex types, it is the type given
474:        by deleting the keyword _Complex from the type name."

476:        So type punning should be portable. */
477:     union { PetscComplex z; PetscReal f[2]; } uz;

479:     uz.f[0] = x;
480:     uz.f[1] = y;
481:     return uz.z;
482:   }
483: #endif
484: }
485: #endif


488: /*MC
489:    PetscMin - Returns minimum of two numbers

491:    Synopsis:
492:    #include <petscmath.h>
493:    type PetscMin(type v1,type v2)

495:    Not Collective

497:    Input Parameter:
498: +  v1 - first value to find minimum of
499: -  v2 - second value to find minimum of

501:    Notes:
502:     type can be integer or floating point value

504:    Level: beginner

506: .seealso: PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()

508: M*/
509: #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))

511: /*MC
512:    PetscMax - Returns maxium of two numbers

514:    Synopsis:
515:    #include <petscmath.h>
516:    type max PetscMax(type v1,type v2)

518:    Not Collective

520:    Input Parameter:
521: +  v1 - first value to find maximum of
522: -  v2 - second value to find maximum of

524:    Notes:
525:     type can be integer or floating point value

527:    Level: beginner

529: .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()

531: M*/
532: #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))

534: /*MC
535:    PetscClipInterval - Returns a number clipped to be within an interval

537:    Synopsis:
538:    #include <petscmath.h>
539:    type clip PetscClipInterval(type x,type a,type b)

541:    Not Collective

543:    Input Parameter:
544: +  x - value to use if within interval (a,b)
545: .  a - lower end of interval
546: -  b - upper end of interval

548:    Notes:
549:     type can be integer or floating point value

551:    Level: beginner

553: .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()

555: M*/
556: #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))

558: /*MC
559:    PetscAbsInt - Returns the absolute value of an integer

561:    Synopsis:
562:    #include <petscmath.h>
563:    int abs PetscAbsInt(int v1)

565:    Not Collective

567:    Input Parameter:
568: .   v1 - the integer

570:    Level: beginner

572: .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()

574: M*/
575: #define PetscAbsInt(a)  (((a)<0)   ? (-(a)) : (a))

577: /*MC
578:    PetscAbsReal - Returns the absolute value of an real number

580:    Synopsis:
581:    #include <petscmath.h>
582:    Real abs PetscAbsReal(PetscReal v1)

584:    Not Collective

586:    Input Parameter:
587: .   v1 - the double


590:    Level: beginner

592: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()

594: M*/
595: #if defined(PETSC_USE_REAL_SINGLE)
596: #define PetscAbsReal(a) fabsf(a)
597: #elif defined(PETSC_USE_REAL_DOUBLE)
598: #define PetscAbsReal(a) fabs(a)
599: #elif defined(PETSC_USE_REAL___FLOAT128)
600: #define PetscAbsReal(a) fabsq(a)
601: #elif defined(PETSC_USE_REAL___FP16)
602: #define PetscAbsReal(a) fabsf(a)
603: #endif

605: /*MC
606:    PetscSqr - Returns the square of a number

608:    Synopsis:
609:    #include <petscmath.h>
610:    type sqr PetscSqr(type v1)

612:    Not Collective

614:    Input Parameter:
615: .   v1 - the value

617:    Notes:
618:     type can be integer or floating point value

620:    Level: beginner

622: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()

624: M*/
625: #define PetscSqr(a)     ((a)*(a))

627: /* ----------------------------------------------------------------------------*/

629: #if defined(PETSC_USE_REAL_SINGLE)
630: #define PetscRealConstant(constant) constant##F
631: #elif defined(PETSC_USE_REAL___FLOAT128)
632: #define PetscRealConstant(constant) constant##Q
633: #else
634: #define PetscRealConstant(constant) constant
635: #endif

637: /*
638:      Basic constants
639: */
640: #define PETSC_PI    PetscRealConstant(3.1415926535897932384626433832795029)
641: #define PETSC_PHI   PetscRealConstant(1.6180339887498948482045868343656381)
642: #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)

644: #if !defined(PETSC_USE_64BIT_INDICES)
645: #define PETSC_MAX_INT            2147483647
646: #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
647: #else
648: #define PETSC_MAX_INT            9223372036854775807L
649: #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
650: #endif

652: #if defined(PETSC_USE_REAL_SINGLE)
653: #  define PETSC_MAX_REAL                3.40282346638528860e+38F
654: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
655: #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
656: #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
657: #  define PETSC_SMALL                   1.e-5F
658: #elif defined(PETSC_USE_REAL_DOUBLE)
659: #  define PETSC_MAX_REAL                1.7976931348623157e+308
660: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
661: #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
662: #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
663: #  define PETSC_SMALL                   1.e-10
664: #elif defined(PETSC_USE_REAL___FLOAT128)
665: #  define PETSC_MAX_REAL                FLT128_MAX
666: #  define PETSC_MIN_REAL                (-FLT128_MAX)
667: #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
668: #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078144567552953958511352539e-17Q
669: #  define PETSC_SMALL                   1.e-20Q
670: #elif defined(PETSC_USE_REAL___FP16)  /* maybe should use single precision values for these? */
671: #  define PETSC_MAX_REAL                65504.
672: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
673: #  define PETSC_MACHINE_EPSILON         .00097656
674: #  define PETSC_SQRT_MACHINE_EPSILON    .0312
675: #  define PETSC_SMALL                   5.e-3
676: #endif

678: #define PETSC_INFINITY               (PETSC_MAX_REAL/4)
679: #define PETSC_NINFINITY              (-PETSC_INFINITY)

681: PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal);
682: PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal);
683: PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
684: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;}
685: PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));}
686: PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
687: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
688: PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}

690: PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal,PetscReal,PetscReal,PetscReal);
691: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
692: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);

694: /*
695:     These macros are currently hardwired to match the regular data types, so there is no support for a different
696:     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
697:  */
698: #define MPIU_MATSCALAR MPIU_SCALAR
699: typedef PetscScalar MatScalar;
700: typedef PetscReal MatReal;

702: struct petsc_mpiu_2scalar {PetscScalar a,b;};
703: PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);

705: #if defined(PETSC_USE_64BIT_INDICES)
706: struct petsc_mpiu_2int {PetscInt a,b;};
707: PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
708: #else
709: #define MPIU_2INT MPI_2INT
710: #endif

712: PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
713: {
714:   PetscInt result = 1;
715:   while (power) {
716:     if (power & 1) result *= base;
717:     power >>= 1;
718:     base *= base;
719:   }
720:   return result;
721: }

723: PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
724: {
725:   PetscReal result = 1;
726:   if (power < 0) {
727:     power = -power;
728:     base  = ((PetscReal)1)/base;
729:   }
730:   while (power) {
731:     if (power & 1) result *= base;
732:     power >>= 1;
733:     base *= base;
734:   }
735:   return result;
736: }

738: PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
739: {
740:   PetscScalar result = 1;
741:   if (power < 0) {
742:     power = -power;
743:     base  = ((PetscReal)1)/base;
744:   }
745:   while (power) {
746:     if (power & 1) result *= base;
747:     power >>= 1;
748:     base *= base;
749:   }
750:   return result;
751: }

753: PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
754: {
755:   PetscScalar cpower = power;
756:   return PetscPowScalar(base,cpower);
757: }

759: #ifndef PETSC_HAVE_LOG2
760: PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal n)
761: {
762:   return PetscLogReal(n)/PetscLogReal(2.0);
763: }
764: #endif

766: PETSC_EXTERN PetscErrorCode PetscLinearRegression(PetscInt,const PetscReal[],const PetscReal[],PetscReal*,PetscReal*);
767: #endif