Actual source code: petscmath.h

petsc-master 2020-07-01
Report Typos and Errors
  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: /*

 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.

 22: */

 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

 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

 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

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

155: #endif /* PETSC_USE_REAL_* */

157: PETSC_STATIC_INLINE PetscReal PetscSignReal(PetscReal a)
158: {
159:   return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0));
160: }

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

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

177: /*MC
178:    MPIU_REAL - MPI datatype corresponding to PetscReal

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

183:    Level: beginner

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_* */

197: /*
198:     Complex number definitions
199:  */
200: #if defined(PETSC_HAVE_COMPLEX)
201: #if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
202: /* C++ support of complex number */

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)

226: /* TODO: Add configure tests

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

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

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

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

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

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

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

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

295: */

297: #elif defined(PETSC_HAVE_C99_COMPLEX) && !defined(PETSC_USE_REAL___FP16)
298: /* C99 support of complex number */

300: #if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
301: #define PetscRealPartComplex(a)      crealf(a)
302: #define PetscImaginaryPartComplex(a) cimagf(a)
303: #define PetscAbsComplex(a)           cabsf(a)
304: #define PetscArgComplex(a)           cargf(a)
305: #define PetscConjComplex(a)          conjf(a)
306: #define PetscSqrtComplex(a)          csqrtf(a)
307: #define PetscPowComplex(a,b)         cpowf(a,b)
308: #define PetscExpComplex(a)           cexpf(a)
309: #define PetscLogComplex(a)           clogf(a)
310: #define PetscSinComplex(a)           csinf(a)
311: #define PetscCosComplex(a)           ccosf(a)
312: #define PetscTanComplex(a)           ctanf(a)
313: #define PetscAsinComplex(a)          casinf(a)
314: #define PetscAcosComplex(a)          cacosf(a)
315: #define PetscAtanComplex(a)          catanf(a)
316: #define PetscSinhComplex(a)          csinhf(a)
317: #define PetscCoshComplex(a)          ccoshf(a)
318: #define PetscTanhComplex(a)          ctanhf(a)
319: #define PetscAsinhComplex(a)         casinhf(a)
320: #define PetscAcoshComplex(a)         cacoshf(a)
321: #define PetscAtanhComplex(a)         catanhf(a)

323: #elif defined(PETSC_USE_REAL_DOUBLE)
324: #define PetscRealPartComplex(a)      creal(a)
325: #define PetscImaginaryPartComplex(a) cimag(a)
326: #define PetscAbsComplex(a)           cabs(a)
327: #define PetscArgComplex(a)           carg(a)
328: #define PetscConjComplex(a)          conj(a)
329: #define PetscSqrtComplex(a)          csqrt(a)
330: #define PetscPowComplex(a,b)         cpow(a,b)
331: #define PetscExpComplex(a)           cexp(a)
332: #define PetscLogComplex(a)           clog(a)
333: #define PetscSinComplex(a)           csin(a)
334: #define PetscCosComplex(a)           ccos(a)
335: #define PetscTanComplex(a)           ctan(a)
336: #define PetscAsinComplex(a)          casin(a)
337: #define PetscAcosComplex(a)          cacos(a)
338: #define PetscAtanComplex(a)          catan(a)
339: #define PetscSinhComplex(a)          csinh(a)
340: #define PetscCoshComplex(a)          ccosh(a)
341: #define PetscTanhComplex(a)          ctanh(a)
342: #define PetscAsinhComplex(a)         casinh(a)
343: #define PetscAcoshComplex(a)         cacosh(a)
344: #define PetscAtanhComplex(a)         catanh(a)

346: #elif defined(PETSC_USE_REAL___FLOAT128)
347: #define PetscRealPartComplex(a)      crealq(a)
348: #define PetscImaginaryPartComplex(a) cimagq(a)
349: #define PetscAbsComplex(a)           cabsq(a)
350: #define PetscArgComplex(a)           cargq(a)
351: #define PetscConjComplex(a)          conjq(a)
352: #define PetscSqrtComplex(a)          csqrtq(a)
353: #define PetscPowComplex(a,b)         cpowq(a,b)
354: #define PetscExpComplex(a)           cexpq(a)
355: #define PetscLogComplex(a)           clogq(a)
356: #define PetscSinComplex(a)           csinq(a)
357: #define PetscCosComplex(a)           ccosq(a)
358: #define PetscTanComplex(a)           ctanq(a)
359: #define PetscAsinComplex(a)          casinq(a)
360: #define PetscAcosComplex(a)          cacosq(a)
361: #define PetscAtanComplex(a)          catanq(a)
362: #define PetscSinhComplex(a)          csinhq(a)
363: #define PetscCoshComplex(a)          ccoshq(a)
364: #define PetscTanhComplex(a)          ctanhq(a)
365: #define PetscAsinhComplex(a)         casinhq(a)
366: #define PetscAcoshComplex(a)         cacoshq(a)
367: #define PetscAtanhComplex(a)         catanhq(a)

369: #endif /* PETSC_USE_REAL_* */
370: #endif /* (__cplusplus && PETSC_HAVE_CXX_COMPLEX) else-if (!__cplusplus && PETSC_HAVE_C99_COMPLEX) */

372: /*
373:    PETSC_i is the imaginary number, i
374: */
375: PETSC_EXTERN PetscComplex PETSC_i;

377: /*
378:    Try to do the right thing for complex number construction: see
379:    http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
380:    for details
381: */
382: PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
383: {
384: #if   defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
385:   return PetscComplex(x,y);
386: #elif defined(_Imaginary_I)
387:   return x + y * _Imaginary_I;
388: #else
389:   { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),

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

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

398:     uz.f[0] = x;
399:     uz.f[1] = y;
400:     return uz.z;
401:   }
402: #endif
403: }

405: #if defined(PETSC_HAVE_MPI_C_DOUBLE_COMPLEX)
406: #define MPIU_C_COMPLEX MPI_C_COMPLEX
407: #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX
408: #else
409: # if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
410:   typedef petsccomplexlib::complex<double> petsc_mpiu_c_double_complex;
411:   typedef petsccomplexlib::complex<float> petsc_mpiu_c_complex;
412: # elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
413:   typedef double _Complex petsc_mpiu_c_double_complex;
414:   typedef float _Complex petsc_mpiu_c_complex;
415: # else
416:   typedef struct {double real,imag;} petsc_mpiu_c_double_complex;
417:   typedef struct {float real,imag;} petsc_mpiu_c_complex;
418: # endif
419: PETSC_EXTERN MPI_Datatype MPIU_C_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_complex);
420: PETSC_EXTERN MPI_Datatype MPIU_C_DOUBLE_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_double_complex);
421: #endif /* PETSC_HAVE_MPI_C_DOUBLE_COMPLEX */
422: #if defined(PETSC_USE_REAL___FLOAT128)
423: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
424: #endif /* PETSC_USE_REAL___FLOAT128 */

426: /*MC
427:    MPIU_COMPLEX - MPI datatype corresponding to PetscComplex

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

432:    Level: beginner

434: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT, PETSC_i
435: M*/
436: #if defined(PETSC_USE_REAL_SINGLE)
437: #  define MPIU_COMPLEX MPIU_C_COMPLEX
438: #elif defined(PETSC_USE_REAL_DOUBLE)
439: #  define MPIU_COMPLEX MPIU_C_DOUBLE_COMPLEX
440: #elif defined(PETSC_USE_REAL___FLOAT128)
441: #  define MPIU_COMPLEX MPIU___COMPLEX128
442: #elif defined(PETSC_USE_REAL___FP16)
443: #  define MPIU_COMPLEX MPIU_C_COMPLEX
444: #endif /* PETSC_USE_REAL_* */

446: #endif /* PETSC_HAVE_COMPLEX */

448: /*
449:     Scalar number definitions
450:  */
451: #if defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX)
452: /*MC
453:    MPIU_SCALAR - MPI datatype corresponding to PetscScalar

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

458:    Level: beginner

460: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_COMPLEX, MPIU_INT
461: M*/
462: #define MPIU_SCALAR MPIU_COMPLEX

464: /*MC
465:    PetscRealPart - Returns the real part of a PetscScalar

467:    Synopsis:
468:  #include <petscmath.h>
469:    PetscReal PetscRealPart(PetscScalar v)

471:    Not Collective

473:    Input Parameter:
474: .  v - value to find the real part of

476:    Level: beginner

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

480: M*/
481: #define PetscRealPart(a)      PetscRealPartComplex(a)

483: /*MC
484:    PetscImaginaryPart - Returns the imaginary part of a PetscScalar

486:    Synopsis:
487:  #include <petscmath.h>
488:    PetscReal PetscImaginaryPart(PetscScalar v)

490:    Not Collective

492:    Input Parameter:
493: .  v - value to find the imaginary part of

495:    Level: beginner

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

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

502: M*/
503: #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)

505: #define PetscAbsScalar(a)     PetscAbsComplex(a)
506: #define PetscArgScalar(a)     PetscArgComplex(a)
507: #define PetscConj(a)          PetscConjComplex(a)
508: #define PetscSqrtScalar(a)    PetscSqrtComplex(a)
509: #define PetscPowScalar(a,b)   PetscPowComplex(a,b)
510: #define PetscExpScalar(a)     PetscExpComplex(a)
511: #define PetscLogScalar(a)     PetscLogComplex(a)
512: #define PetscSinScalar(a)     PetscSinComplex(a)
513: #define PetscCosScalar(a)     PetscCosComplex(a)
514: #define PetscTanScalar(a)     PetscTanComplex(a)
515: #define PetscAsinScalar(a)    PetscAsinComplex(a)
516: #define PetscAcosScalar(a)    PetscAcosComplex(a)
517: #define PetscAtanScalar(a)    PetscAtanComplex(a)
518: #define PetscSinhScalar(a)    PetscSinhComplex(a)
519: #define PetscCoshScalar(a)    PetscCoshComplex(a)
520: #define PetscTanhScalar(a)    PetscTanhComplex(a)
521: #define PetscAsinhScalar(a)   PetscAsinhComplex(a)
522: #define PetscAcoshScalar(a)   PetscAcoshComplex(a)
523: #define PetscAtanhScalar(a)   PetscAtanhComplex(a)

525: #else /* PETSC_USE_COMPLEX */
526: #define MPIU_SCALAR MPIU_REAL
527: #define PetscRealPart(a)      (a)
528: #define PetscImaginaryPart(a) ((PetscReal)0)
529: #define PetscAbsScalar(a)     PetscAbsReal(a)
530: #define PetscArgScalar(a)     (((a) < (PetscReal)0) ? PETSC_PI : (PetscReal)0)
531: #define PetscConj(a)          (a)
532: #define PetscSqrtScalar(a)    PetscSqrtReal(a)
533: #define PetscPowScalar(a,b)   PetscPowReal(a,b)
534: #define PetscExpScalar(a)     PetscExpReal(a)
535: #define PetscLogScalar(a)     PetscLogReal(a)
536: #define PetscSinScalar(a)     PetscSinReal(a)
537: #define PetscCosScalar(a)     PetscCosReal(a)
538: #define PetscTanScalar(a)     PetscTanReal(a)
539: #define PetscAsinScalar(a)    PetscAsinReal(a)
540: #define PetscAcosScalar(a)    PetscAcosReal(a)
541: #define PetscAtanScalar(a)    PetscAtanReal(a)
542: #define PetscSinhScalar(a)    PetscSinhReal(a)
543: #define PetscCoshScalar(a)    PetscCoshReal(a)
544: #define PetscTanhScalar(a)    PetscTanhReal(a)
545: #define PetscAsinhScalar(a)   PetscAsinhReal(a)
546: #define PetscAcoshScalar(a)   PetscAcoshReal(a)
547: #define PetscAtanhScalar(a)   PetscAtanhReal(a)

549: #endif /* PETSC_USE_COMPLEX */

551: /*
552:    Certain objects may be created using either single or double precision.
553:    This is currently not used.
554: */
555: typedef enum { PETSC_SCALAR_DOUBLE, PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;

557: /* --------------------------------------------------------------------------*/

559: /*MC
560:    PetscAbs - Returns the absolute value of a number

562:    Synopsis:
563:  #include <petscmath.h>
564:    type PetscAbs(type v)

566:    Not Collective

568:    Input Parameter:
569: .  v - the number

571:    Notes:
572:     type can be integer or real floating point value

574:    Level: beginner

576: .seealso: PetscAbsInt(), PetscAbsReal(), PetscAbsScalar()

578: M*/
579: #define PetscAbs(a)  (((a) >= 0) ? (a) : (-(a)))

581: /*MC
582:    PetscSign - Returns the sign of a number as an integer

584:    Synopsis:
585:  #include <petscmath.h>
586:    int PetscSign(type v)

588:    Not Collective

590:    Input Parameter:
591: .  v - the number

593:    Notes:
594:     type can be integer or real floating point value

596:    Level: beginner

598: M*/
599: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)

601: /*MC
602:    PetscMin - Returns minimum of two numbers

604:    Synopsis:
605:  #include <petscmath.h>
606:    type PetscMin(type v1,type v2)

608:    Not Collective

610:    Input Parameter:
611: +  v1 - first value to find minimum of
612: -  v2 - second value to find minimum of

614:    Notes:
615:     type can be integer or floating point value

617:    Level: beginner

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

621: M*/
622: #define PetscMin(a,b)   (((a)<(b)) ?  (a) : (b))

624: /*MC
625:    PetscMax - Returns maxium of two numbers

627:    Synopsis:
628:  #include <petscmath.h>
629:    type max PetscMax(type v1,type v2)

631:    Not Collective

633:    Input Parameter:
634: +  v1 - first value to find maximum of
635: -  v2 - second value to find maximum of

637:    Notes:
638:     type can be integer or floating point value

640:    Level: beginner

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

644: M*/
645: #define PetscMax(a,b)   (((a)<(b)) ?  (b) : (a))

647: /*MC
648:    PetscClipInterval - Returns a number clipped to be within an interval

650:    Synopsis:
651:  #include <petscmath.h>
652:    type clip PetscClipInterval(type x,type a,type b)

654:    Not Collective

656:    Input Parameter:
657: +  x - value to use if within interval [a,b]
658: .  a - lower end of interval
659: -  b - upper end of interval

661:    Notes:
662:     type can be integer or floating point value

664:    Level: beginner

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

668: M*/
669: #define PetscClipInterval(x,a,b)   (PetscMax((a),PetscMin((x),(b))))

671: /*MC
672:    PetscAbsInt - Returns the absolute value of an integer

674:    Synopsis:
675:  #include <petscmath.h>
676:    int abs PetscAbsInt(int v1)

678:    Not Collective

680:    Input Parameter:
681: .   v1 - the integer

683:    Level: beginner

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

687: M*/
688: #define PetscAbsInt(a)  (((a)<0)   ? (-(a)) : (a))

690: /*MC
691:    PetscAbsReal - Returns the absolute value of an real number

693:    Synopsis:
694:  #include <petscmath.h>
695:    Real abs PetscAbsReal(PetscReal v1)

697:    Not Collective

699:    Input Parameter:
700: .   v1 - the double


703:    Level: beginner

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

707: M*/
708: #if defined(PETSC_USE_REAL_SINGLE)
709: #define PetscAbsReal(a) fabsf(a)
710: #elif defined(PETSC_USE_REAL_DOUBLE)
711: #define PetscAbsReal(a) fabs(a)
712: #elif defined(PETSC_USE_REAL___FLOAT128)
713: #define PetscAbsReal(a) fabsq(a)
714: #elif defined(PETSC_USE_REAL___FP16)
715: #define PetscAbsReal(a) fabsf(a)
716: #endif

718: /*MC
719:    PetscSqr - Returns the square of a number

721:    Synopsis:
722:  #include <petscmath.h>
723:    type sqr PetscSqr(type v1)

725:    Not Collective

727:    Input Parameter:
728: .   v1 - the value

730:    Notes:
731:     type can be integer or floating point value

733:    Level: beginner

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

737: M*/
738: #define PetscSqr(a)     ((a)*(a))

740: /* ----------------------------------------------------------------------------*/

742: #if defined(PETSC_USE_REAL_SINGLE)
743: #define PetscRealConstant(constant) constant##F
744: #elif defined(PETSC_USE_REAL_DOUBLE)
745: #define PetscRealConstant(constant) constant
746: #elif defined(PETSC_USE_REAL___FLOAT128)
747: #define PetscRealConstant(constant) constant##Q
748: #elif defined(PETSC_USE_REAL___FP16)
749: #define PetscRealConstant(constant) constant##F
750: #endif

752: /*
753:      Basic constants
754: */
755: #define PETSC_PI    PetscRealConstant(3.1415926535897932384626433832795029)
756: #define PETSC_PHI   PetscRealConstant(1.6180339887498948482045868343656381)
757: #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)

759: #if !defined(PETSC_USE_64BIT_INDICES)
760: #define PETSC_MAX_INT            2147483647
761: #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
762: #else
763: #define PETSC_MAX_INT            9223372036854775807L
764: #define PETSC_MIN_INT            (-PETSC_MAX_INT - 1)
765: #endif

767: #if defined(PETSC_USE_REAL_SINGLE)
768: #  define PETSC_MAX_REAL                3.40282346638528860e+38F
769: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
770: #  define PETSC_MACHINE_EPSILON         1.19209290e-07F
771: #  define PETSC_SQRT_MACHINE_EPSILON    3.45266983e-04F
772: #  define PETSC_SMALL                   1.e-5F
773: #elif defined(PETSC_USE_REAL_DOUBLE)
774: #  define PETSC_MAX_REAL                1.7976931348623157e+308
775: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
776: #  define PETSC_MACHINE_EPSILON         2.2204460492503131e-16
777: #  define PETSC_SQRT_MACHINE_EPSILON    1.490116119384766e-08
778: #  define PETSC_SMALL                   1.e-10
779: #elif defined(PETSC_USE_REAL___FLOAT128)
780: #  define PETSC_MAX_REAL                FLT128_MAX
781: #  define PETSC_MIN_REAL                (-FLT128_MAX)
782: #  define PETSC_MACHINE_EPSILON         FLT128_EPSILON
783: #  define PETSC_SQRT_MACHINE_EPSILON    1.38777878078144567552953958511352539e-17Q
784: #  define PETSC_SMALL                   1.e-20Q
785: #elif defined(PETSC_USE_REAL___FP16)
786: #  define PETSC_MAX_REAL                65504.0F
787: #  define PETSC_MIN_REAL                (-PETSC_MAX_REAL)
788: #  define PETSC_MACHINE_EPSILON         .0009765625F
789: #  define PETSC_SQRT_MACHINE_EPSILON    .03125F
790: #  define PETSC_SMALL                   5.e-3F
791: #endif

793: #define PETSC_INFINITY               (PETSC_MAX_REAL/4)
794: #define PETSC_NINFINITY              (-PETSC_INFINITY)

796: PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal);
797: PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal);
798: PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
799: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;}
800: PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));}
801: PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
802: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
803: PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}

805: PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal,PetscReal,PetscReal,PetscReal);
806: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
807: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);

809: /*
810:     These macros are currently hardwired to match the regular data types, so there is no support for a different
811:     MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
812:  */
813: #define MPIU_MATSCALAR MPIU_SCALAR
814: typedef PetscScalar MatScalar;
815: typedef PetscReal MatReal;

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

820: #if defined(PETSC_USE_64BIT_INDICES)
821: struct petsc_mpiu_2int {PetscInt a,b;};
822: PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
823: #else
824: #define MPIU_2INT MPI_2INT
825: #endif

827: PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
828: {
829:   PetscInt result = 1;
830:   while (power) {
831:     if (power & 1) result *= base;
832:     power >>= 1;
833:     base *= base;
834:   }
835:   return result;
836: }

838: PETSC_STATIC_INLINE PetscInt64 PetscPowInt64(PetscInt base,PetscInt power)
839: {
840:   PetscInt64 result = 1;
841:   while (power) {
842:     if (power & 1) result *= base;
843:     power >>= 1;
844:     base *= base;
845:   }
846:   return result;
847: }

849: PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
850: {
851:   PetscReal result = 1;
852:   if (power < 0) {
853:     power = -power;
854:     base  = ((PetscReal)1)/base;
855:   }
856:   while (power) {
857:     if (power & 1) result *= base;
858:     power >>= 1;
859:     base *= base;
860:   }
861:   return result;
862: }

864: PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
865: {
866:   PetscScalar result = (PetscReal)1;
867:   if (power < 0) {
868:     power = -power;
869:     base  = ((PetscReal)1)/base;
870:   }
871:   while (power) {
872:     if (power & 1) result *= base;
873:     power >>= 1;
874:     base *= base;
875:   }
876:   return result;
877: }

879: PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
880: {
881:   PetscScalar cpower = power;
882:   return PetscPowScalar(base,cpower);
883: }

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