Actual source code: petscmath.h
petsc-3.12.5 2020-03-29
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)
54: #elif defined(PETSC_USE_REAL_DOUBLE)
55: #define PetscSqrtReal(a) sqrt(a)
56: #define PetscCbrtReal(a) cbrt(a)
57: #define PetscHypotReal(a,b) hypot(a,b)
58: #define PetscAtan2Real(a,b) atan2(a,b)
59: #define PetscPowReal(a,b) pow(a,b)
60: #define PetscExpReal(a) exp(a)
61: #define PetscLogReal(a) log(a)
62: #define PetscLog10Real(a) log10(a)
63: #define PetscLog2Real(a) log2(a)
64: #define PetscSinReal(a) sin(a)
65: #define PetscCosReal(a) cos(a)
66: #define PetscTanReal(a) tan(a)
67: #define PetscAsinReal(a) asin(a)
68: #define PetscAcosReal(a) acos(a)
69: #define PetscAtanReal(a) atan(a)
70: #define PetscSinhReal(a) sinh(a)
71: #define PetscCoshReal(a) cosh(a)
72: #define PetscTanhReal(a) tanh(a)
73: #define PetscAsinhReal(a) asinh(a)
74: #define PetscAcoshReal(a) acosh(a)
75: #define PetscAtanhReal(a) atanh(a)
76: #define PetscCeilReal(a) ceil(a)
77: #define PetscFloorReal(a) floor(a)
78: #define PetscFmodReal(a,b) fmod(a,b)
79: #define PetscTGamma(a) tgamma(a)
81: #elif defined(PETSC_USE_REAL___FLOAT128)
82: #define PetscSqrtReal(a) sqrtq(a)
83: #define PetscCbrtReal(a) cbrtq(a)
84: #define PetscHypotReal(a,b) hypotq(a,b)
85: #define PetscAtan2Real(a,b) atan2q(a,b)
86: #define PetscPowReal(a,b) powq(a,b)
87: #define PetscExpReal(a) expq(a)
88: #define PetscLogReal(a) logq(a)
89: #define PetscLog10Real(a) log10q(a)
90: #define PetscLog2Real(a) log2q(a)
91: #define PetscSinReal(a) sinq(a)
92: #define PetscCosReal(a) cosq(a)
93: #define PetscTanReal(a) tanq(a)
94: #define PetscAsinReal(a) asinq(a)
95: #define PetscAcosReal(a) acosq(a)
96: #define PetscAtanReal(a) atanq(a)
97: #define PetscSinhReal(a) sinhq(a)
98: #define PetscCoshReal(a) coshq(a)
99: #define PetscTanhReal(a) tanhq(a)
100: #define PetscAsinhReal(a) asinhq(a)
101: #define PetscAcoshReal(a) acoshq(a)
102: #define PetscAtanhReal(a) atanhq(a)
103: #define PetscCeilReal(a) ceilq(a)
104: #define PetscFloorReal(a) floorq(a)
105: #define PetscFmodReal(a,b) fmodq(a,b)
106: #define PetscTGamma(a) tgammaq(a)
108: #elif defined(PETSC_USE_REAL___FP16)
109: #define PetscSqrtReal(a) sqrtf(a)
110: #define PetscCbrtReal(a) cbrtf(a)
111: #define PetscHypotReal(a,b) hypotf(a,b)
112: #define PetscAtan2Real(a,b) atan2f(a,b)
113: #define PetscPowReal(a,b) powf(a,b)
114: #define PetscExpReal(a) expf(a)
115: #define PetscLogReal(a) logf(a)
116: #define PetscLog10Real(a) log10f(a)
117: #define PetscLog2Real(a) log2f(a)
118: #define PetscSinReal(a) sinf(a)
119: #define PetscCosReal(a) cosf(a)
120: #define PetscTanReal(a) tanf(a)
121: #define PetscAsinReal(a) asinf(a)
122: #define PetscAcosReal(a) acosf(a)
123: #define PetscAtanReal(a) atanf(a)
124: #define PetscSinhReal(a) sinhf(a)
125: #define PetscCoshReal(a) coshf(a)
126: #define PetscTanhReal(a) tanhf(a)
127: #define PetscAsinhReal(a) asinhf(a)
128: #define PetscAcoshReal(a) acoshf(a)
129: #define PetscAtanhReal(a) atanhf(a)
130: #define PetscCeilReal(a) ceilf(a)
131: #define PetscFloorReal(a) floorf(a)
132: #define PetscFmodReal(a,b) fmodf(a,b)
133: #define PetscTGamma(a) tgammaf(a)
135: #endif /* PETSC_USE_REAL_* */
137: PETSC_STATIC_INLINE PetscReal PetscSignReal(PetscReal a)
138: {
139: return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0));
140: }
142: #if !defined(PETSC_HAVE_LOG2)
143: #undef PetscLog2Real
144: PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal a)
145: {
146: return PetscLogReal(a)/PetscLogReal((PetscReal)2);
147: }
148: #endif
150: #if defined(PETSC_USE_REAL___FLOAT128)
151: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
152: #endif
153: #if defined(PETSC_USE_REAL___FP16)
154: PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
155: #endif
157: /*MC
158: MPIU_REAL - MPI datatype corresponding to PetscReal
160: Notes:
161: In MPI calls that require an MPI datatype that matches a PetscReal or array of PetscReal values, pass this value.
163: Level: beginner
165: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT
166: M*/
167: #if defined(PETSC_USE_REAL_SINGLE)
168: # define MPIU_REAL MPI_FLOAT
169: #elif defined(PETSC_USE_REAL_DOUBLE)
170: # define MPIU_REAL MPI_DOUBLE
171: #elif defined(PETSC_USE_REAL___FLOAT128)
172: # define MPIU_REAL MPIU___FLOAT128
173: #elif defined(PETSC_USE_REAL___FP16)
174: # define MPIU_REAL MPIU___FP16
175: #endif /* PETSC_USE_REAL_* */
177: /*
178: Complex number definitions
179: */
180: #if defined(PETSC_HAVE_COMPLEX)
181: #if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
182: /* C++ support of complex number */
184: #define PetscRealPartComplex(a) (a).real()
185: #define PetscImaginaryPartComplex(a) (a).imag()
186: #define PetscAbsComplex(a) petsccomplexlib::abs(a)
187: #define PetscArgComplex(a) petsccomplexlib::arg(a)
188: #define PetscConjComplex(a) petsccomplexlib::conj(a)
189: #define PetscSqrtComplex(a) petsccomplexlib::sqrt(a)
190: #define PetscPowComplex(a,b) petsccomplexlib::pow(a,b)
191: #define PetscExpComplex(a) petsccomplexlib::exp(a)
192: #define PetscLogComplex(a) petsccomplexlib::log(a)
193: #define PetscSinComplex(a) petsccomplexlib::sin(a)
194: #define PetscCosComplex(a) petsccomplexlib::cos(a)
195: #define PetscTanComplex(a) petsccomplexlib::tan(a)
196: #define PetscAsinComplex(a) petsccomplexlib::asin(a)
197: #define PetscAcosComplex(a) petsccomplexlib::acos(a)
198: #define PetscAtanComplex(a) petsccomplexlib::atan(a)
199: #define PetscSinhComplex(a) petsccomplexlib::sinh(a)
200: #define PetscCoshComplex(a) petsccomplexlib::cosh(a)
201: #define PetscTanhComplex(a) petsccomplexlib::tanh(a)
202: #define PetscAsinhComplex(a) petsccomplexlib::asinh(a)
203: #define PetscAcoshComplex(a) petsccomplexlib::acosh(a)
204: #define PetscAtanhComplex(a) petsccomplexlib::atanh(a)
206: /* TODO: Add configure tests
208: #if !defined(PETSC_HAVE_CXX_TAN_COMPLEX)
209: #undef PetscTanComplex
210: PETSC_STATIC_INLINE PetscComplex PetscTanComplex(PetscComplex z)
211: {
212: return PetscSinComplex(z)/PetscCosComplex(z);
213: }
214: #endif
216: #if !defined(PETSC_HAVE_CXX_TANH_COMPLEX)
217: #undef PetscTanhComplex
218: PETSC_STATIC_INLINE PetscComplex PetscTanhComplex(PetscComplex z)
219: {
220: return PetscSinhComplex(z)/PetscCoshComplex(z);
221: }
222: #endif
224: #if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX)
225: #undef PetscAsinComplex
226: PETSC_STATIC_INLINE PetscComplex PetscAsinComplex(PetscComplex z)
227: {
228: const PetscComplex j(0,1);
229: return -j*PetscLogComplex(j*z+PetscSqrtComplex(1.0f-z*z));
230: }
231: #endif
233: #if !defined(PETSC_HAVE_CXX_ACOS_COMPLEX)
234: #undef PetscAcosComplex
235: PETSC_STATIC_INLINE PetscComplex PetscAcosComplex(PetscComplex z)
236: {
237: const PetscComplex j(0,1);
238: return j*PetscLogComplex(z-j*PetscSqrtComplex(1.0f-z*z));
239: }
240: #endif
242: #if !defined(PETSC_HAVE_CXX_ATAN_COMPLEX)
243: #undef PetscAtanComplex
244: PETSC_STATIC_INLINE PetscComplex PetscAtanComplex(PetscComplex z)
245: {
246: const PetscComplex j(0,1);
247: return 0.5f*j*PetscLogComplex((1.0f-j*z)/(1.0f+j*z));
248: }
249: #endif
251: #if !defined(PETSC_HAVE_CXX_ASINH_COMPLEX)
252: #undef PetscAsinhComplex
253: PETSC_STATIC_INLINE PetscComplex PetscAsinhComplex(PetscComplex z)
254: {
255: return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f));
256: }
257: #endif
259: #if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX)
260: #undef PetscAcoshComplex
261: PETSC_STATIC_INLINE PetscComplex PetscAcoshComplex(PetscComplex z)
262: {
263: return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f));
264: }
265: #endif
267: #if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX)
268: #undef PetscAtanhComplex
269: PETSC_STATIC_INLINE PetscComplex PetscAtanhComplex(PetscComplex z)
270: {
271: return 0.5f*PetscLogComplex((1.0f+z)/(1.0f-z));
272: }
273: #endif
275: */
277: #elif defined(PETSC_HAVE_C99_COMPLEX) && !defined(PETSC_USE_REAL___FP16)
278: /* C99 support of complex number */
280: #if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
281: #define PetscRealPartComplex(a) crealf(a)
282: #define PetscImaginaryPartComplex(a) cimagf(a)
283: #define PetscAbsComplex(a) cabsf(a)
284: #define PetscArgComplex(a) cargf(a)
285: #define PetscConjComplex(a) conjf(a)
286: #define PetscSqrtComplex(a) csqrtf(a)
287: #define PetscPowComplex(a,b) cpowf(a,b)
288: #define PetscExpComplex(a) cexpf(a)
289: #define PetscLogComplex(a) clogf(a)
290: #define PetscSinComplex(a) csinf(a)
291: #define PetscCosComplex(a) ccosf(a)
292: #define PetscTanComplex(a) ctanf(a)
293: #define PetscAsinComplex(a) casinf(a)
294: #define PetscAcosComplex(a) cacosf(a)
295: #define PetscAtanComplex(a) catanf(a)
296: #define PetscSinhComplex(a) csinhf(a)
297: #define PetscCoshComplex(a) ccoshf(a)
298: #define PetscTanhComplex(a) ctanhf(a)
299: #define PetscAsinhComplex(a) casinhf(a)
300: #define PetscAcoshComplex(a) cacoshf(a)
301: #define PetscAtanhComplex(a) catanhf(a)
303: #elif defined(PETSC_USE_REAL_DOUBLE)
304: #define PetscRealPartComplex(a) creal(a)
305: #define PetscImaginaryPartComplex(a) cimag(a)
306: #define PetscAbsComplex(a) cabs(a)
307: #define PetscArgComplex(a) carg(a)
308: #define PetscConjComplex(a) conj(a)
309: #define PetscSqrtComplex(a) csqrt(a)
310: #define PetscPowComplex(a,b) cpow(a,b)
311: #define PetscExpComplex(a) cexp(a)
312: #define PetscLogComplex(a) clog(a)
313: #define PetscSinComplex(a) csin(a)
314: #define PetscCosComplex(a) ccos(a)
315: #define PetscTanComplex(a) ctan(a)
316: #define PetscAsinComplex(a) casin(a)
317: #define PetscAcosComplex(a) cacos(a)
318: #define PetscAtanComplex(a) catan(a)
319: #define PetscSinhComplex(a) csinh(a)
320: #define PetscCoshComplex(a) ccosh(a)
321: #define PetscTanhComplex(a) ctanh(a)
322: #define PetscAsinhComplex(a) casinh(a)
323: #define PetscAcoshComplex(a) cacosh(a)
324: #define PetscAtanhComplex(a) catanh(a)
326: #elif defined(PETSC_USE_REAL___FLOAT128)
327: #define PetscRealPartComplex(a) crealq(a)
328: #define PetscImaginaryPartComplex(a) cimagq(a)
329: #define PetscAbsComplex(a) cabsq(a)
330: #define PetscArgComplex(a) cargq(a)
331: #define PetscConjComplex(a) conjq(a)
332: #define PetscSqrtComplex(a) csqrtq(a)
333: #define PetscPowComplex(a,b) cpowq(a,b)
334: #define PetscExpComplex(a) cexpq(a)
335: #define PetscLogComplex(a) clogq(a)
336: #define PetscSinComplex(a) csinq(a)
337: #define PetscCosComplex(a) ccosq(a)
338: #define PetscTanComplex(a) ctanq(a)
339: #define PetscAsinComplex(a) casinq(a)
340: #define PetscAcosComplex(a) cacosq(a)
341: #define PetscAtanComplex(a) catanq(a)
342: #define PetscSinhComplex(a) csinhq(a)
343: #define PetscCoshComplex(a) ccoshq(a)
344: #define PetscTanhComplex(a) ctanhq(a)
345: #define PetscAsinhComplex(a) casinhq(a)
346: #define PetscAcoshComplex(a) cacoshq(a)
347: #define PetscAtanhComplex(a) catanhq(a)
349: #endif /* PETSC_USE_REAL_* */
350: #endif /* (__cplusplus && PETSC_HAVE_CXX_COMPLEX) else-if (!__cplusplus && PETSC_HAVE_C99_COMPLEX) */
352: /*
353: PETSC_i is the imaginary number, i
354: */
355: PETSC_EXTERN PetscComplex PETSC_i;
357: /*
358: Try to do the right thing for complex number construction: see
359: http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
360: for details
361: */
362: PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
363: {
364: #if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
365: return PetscComplex(x,y);
366: #elif defined(_Imaginary_I)
367: return x + y * _Imaginary_I;
368: #else
369: { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),
371: "For each floating type there is a corresponding real type, which is always a real floating
372: type. For real floating types, it is the same type. For complex types, it is the type given
373: by deleting the keyword _Complex from the type name."
375: So type punning should be portable. */
376: union { PetscComplex z; PetscReal f[2]; } uz;
378: uz.f[0] = x;
379: uz.f[1] = y;
380: return uz.z;
381: }
382: #endif
383: }
385: #if defined(PETSC_HAVE_MPI_C_DOUBLE_COMPLEX)
386: #define MPIU_C_COMPLEX MPI_C_COMPLEX
387: #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX
388: #else
389: # if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
390: typedef petsccomplexlib::complex<double> petsc_mpiu_c_double_complex;
391: typedef petsccomplexlib::complex<float> petsc_mpiu_c_complex;
392: # elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
393: typedef double _Complex petsc_mpiu_c_double_complex;
394: typedef float _Complex petsc_mpiu_c_complex;
395: # else
396: typedef struct {double real,imag;} petsc_mpiu_c_double_complex;
397: typedef struct {float real,imag;} petsc_mpiu_c_complex;
398: # endif
399: PETSC_EXTERN MPI_Datatype MPIU_C_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_complex);
400: PETSC_EXTERN MPI_Datatype MPIU_C_DOUBLE_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_double_complex);
401: #endif /* PETSC_HAVE_MPI_C_DOUBLE_COMPLEX */
402: #if defined(PETSC_USE_REAL___FLOAT128)
403: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
404: #endif /* PETSC_USE_REAL___FLOAT128 */
406: /*MC
407: MPIU_COMPLEX - MPI datatype corresponding to PetscComplex
409: Notes:
410: In MPI calls that require an MPI datatype that matches a PetscComplex or array of PetscComplex values, pass this value.
412: Level: beginner
414: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT, PETSC_i
415: M*/
416: #if defined(PETSC_USE_REAL_SINGLE)
417: # define MPIU_COMPLEX MPIU_C_COMPLEX
418: #elif defined(PETSC_USE_REAL_DOUBLE)
419: # define MPIU_COMPLEX MPIU_C_DOUBLE_COMPLEX
420: #elif defined(PETSC_USE_REAL___FLOAT128)
421: # define MPIU_COMPLEX MPIU___COMPLEX128
422: #elif defined(PETSC_USE_REAL___FP16)
423: # define MPIU_COMPLEX MPIU_C_COMPLEX
424: #endif /* PETSC_USE_REAL_* */
426: #endif /* PETSC_HAVE_COMPLEX */
428: /*
429: Scalar number definitions
430: */
431: #if defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX)
432: /*MC
433: MPIU_SCALAR - MPI datatype corresponding to PetscScalar
435: Notes:
436: In MPI calls that require an MPI datatype that matches a PetscScalar or array of PetscScalar values, pass this value.
438: Level: beginner
440: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_COMPLEX, MPIU_INT
441: M*/
442: #define MPIU_SCALAR MPIU_COMPLEX
444: /*MC
445: PetscRealPart - Returns the real part of a PetscScalar
447: Synopsis:
448: #include <petscmath.h>
449: PetscReal PetscRealPart(PetscScalar v)
451: Not Collective
453: Input Parameter:
454: . v - value to find the real part of
456: Level: beginner
458: .seealso: PetscScalar, PetscImaginaryPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
460: M*/
461: #define PetscRealPart(a) PetscRealPartComplex(a)
463: /*MC
464: PetscImaginaryPart - Returns the imaginary part of a PetscScalar
466: Synopsis:
467: #include <petscmath.h>
468: PetscReal PetscImaginaryPart(PetscScalar v)
470: Not Collective
472: Input Parameter:
473: . v - value to find the imaginary part of
475: Level: beginner
477: Notes:
478: If PETSc was configured for real numbers then this always returns the value 0
480: .seealso: PetscScalar, PetscRealPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
482: M*/
483: #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)
485: #define PetscAbsScalar(a) PetscAbsComplex(a)
486: #define PetscArgScalar(a) PetscArgComplex(a)
487: #define PetscConj(a) PetscConjComplex(a)
488: #define PetscSqrtScalar(a) PetscSqrtComplex(a)
489: #define PetscPowScalar(a,b) PetscPowComplex(a,b)
490: #define PetscExpScalar(a) PetscExpComplex(a)
491: #define PetscLogScalar(a) PetscLogComplex(a)
492: #define PetscSinScalar(a) PetscSinComplex(a)
493: #define PetscCosScalar(a) PetscCosComplex(a)
494: #define PetscTanScalar(a) PetscTanComplex(a)
495: #define PetscAsinScalar(a) PetscAsinComplex(a)
496: #define PetscAcosScalar(a) PetscAcosComplex(a)
497: #define PetscAtanScalar(a) PetscAtanComplex(a)
498: #define PetscSinhScalar(a) PetscSinhComplex(a)
499: #define PetscCoshScalar(a) PetscCoshComplex(a)
500: #define PetscTanhScalar(a) PetscTanhComplex(a)
501: #define PetscAsinhScalar(a) PetscAsinhComplex(a)
502: #define PetscAcoshScalar(a) PetscAcoshComplex(a)
503: #define PetscAtanhScalar(a) PetscAtanhComplex(a)
505: #else /* PETSC_USE_COMPLEX */
506: #define MPIU_SCALAR MPIU_REAL
507: #define PetscRealPart(a) (a)
508: #define PetscImaginaryPart(a) ((PetscReal)0)
509: #define PetscAbsScalar(a) PetscAbsReal(a)
510: #define PetscArgScalar(a) (((a) < (PetscReal)0) ? PETSC_PI : (PetscReal)0)
511: #define PetscConj(a) (a)
512: #define PetscSqrtScalar(a) PetscSqrtReal(a)
513: #define PetscPowScalar(a,b) PetscPowReal(a,b)
514: #define PetscExpScalar(a) PetscExpReal(a)
515: #define PetscLogScalar(a) PetscLogReal(a)
516: #define PetscSinScalar(a) PetscSinReal(a)
517: #define PetscCosScalar(a) PetscCosReal(a)
518: #define PetscTanScalar(a) PetscTanReal(a)
519: #define PetscAsinScalar(a) PetscAsinReal(a)
520: #define PetscAcosScalar(a) PetscAcosReal(a)
521: #define PetscAtanScalar(a) PetscAtanReal(a)
522: #define PetscSinhScalar(a) PetscSinhReal(a)
523: #define PetscCoshScalar(a) PetscCoshReal(a)
524: #define PetscTanhScalar(a) PetscTanhReal(a)
525: #define PetscAsinhScalar(a) PetscAsinhReal(a)
526: #define PetscAcoshScalar(a) PetscAcoshReal(a)
527: #define PetscAtanhScalar(a) PetscAtanhReal(a)
529: #endif /* PETSC_USE_COMPLEX */
531: /*
532: Certain objects may be created using either single or double precision.
533: This is currently not used.
534: */
535: typedef enum { PETSC_SCALAR_DOUBLE, PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;
537: /* --------------------------------------------------------------------------*/
539: /*MC
540: PetscAbs - Returns the absolute value of a number
542: Synopsis:
543: #include <petscmath.h>
544: type PetscAbs(type v)
546: Not Collective
548: Input Parameter:
549: . v - the number
551: Notes:
552: type can be integer or real floating point value
554: Level: beginner
556: .seealso: PetscAbsInt(), PetscAbsReal(), PetscAbsScalar()
558: M*/
559: #define PetscAbs(a) (((a) >= 0) ? (a) : (-(a)))
561: /*MC
562: PetscSign - Returns the sign of a number as an integer
564: Synopsis:
565: #include <petscmath.h>
566: int PetscSign(type v)
568: Not Collective
570: Input Parameter:
571: . v - the number
573: Notes:
574: type can be integer or real floating point value
576: Level: beginner
578: M*/
579: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)
581: /*MC
582: PetscMin - Returns minimum of two numbers
584: Synopsis:
585: #include <petscmath.h>
586: type PetscMin(type v1,type v2)
588: Not Collective
590: Input Parameter:
591: + v1 - first value to find minimum of
592: - v2 - second value to find minimum of
594: Notes:
595: type can be integer or floating point value
597: Level: beginner
599: .seealso: PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
601: M*/
602: #define PetscMin(a,b) (((a)<(b)) ? (a) : (b))
604: /*MC
605: PetscMax - Returns maxium of two numbers
607: Synopsis:
608: #include <petscmath.h>
609: type max PetscMax(type v1,type v2)
611: Not Collective
613: Input Parameter:
614: + v1 - first value to find maximum of
615: - v2 - second value to find maximum of
617: Notes:
618: type can be integer or floating point value
620: Level: beginner
622: .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
624: M*/
625: #define PetscMax(a,b) (((a)<(b)) ? (b) : (a))
627: /*MC
628: PetscClipInterval - Returns a number clipped to be within an interval
630: Synopsis:
631: #include <petscmath.h>
632: type clip PetscClipInterval(type x,type a,type b)
634: Not Collective
636: Input Parameter:
637: + x - value to use if within interval (a,b)
638: . a - lower end of interval
639: - b - upper end of interval
641: Notes:
642: type can be integer or floating point value
644: Level: beginner
646: .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
648: M*/
649: #define PetscClipInterval(x,a,b) (PetscMax((a),PetscMin((x),(b))))
651: /*MC
652: PetscAbsInt - Returns the absolute value of an integer
654: Synopsis:
655: #include <petscmath.h>
656: int abs PetscAbsInt(int v1)
658: Not Collective
660: Input Parameter:
661: . v1 - the integer
663: Level: beginner
665: .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()
667: M*/
668: #define PetscAbsInt(a) (((a)<0) ? (-(a)) : (a))
670: /*MC
671: PetscAbsReal - Returns the absolute value of an real number
673: Synopsis:
674: #include <petscmath.h>
675: Real abs PetscAbsReal(PetscReal v1)
677: Not Collective
679: Input Parameter:
680: . v1 - the double
683: Level: beginner
685: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()
687: M*/
688: #if defined(PETSC_USE_REAL_SINGLE)
689: #define PetscAbsReal(a) fabsf(a)
690: #elif defined(PETSC_USE_REAL_DOUBLE)
691: #define PetscAbsReal(a) fabs(a)
692: #elif defined(PETSC_USE_REAL___FLOAT128)
693: #define PetscAbsReal(a) fabsq(a)
694: #elif defined(PETSC_USE_REAL___FP16)
695: #define PetscAbsReal(a) fabsf(a)
696: #endif
698: /*MC
699: PetscSqr - Returns the square of a number
701: Synopsis:
702: #include <petscmath.h>
703: type sqr PetscSqr(type v1)
705: Not Collective
707: Input Parameter:
708: . v1 - the value
710: Notes:
711: type can be integer or floating point value
713: Level: beginner
715: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()
717: M*/
718: #define PetscSqr(a) ((a)*(a))
720: /* ----------------------------------------------------------------------------*/
722: #if defined(PETSC_USE_REAL_SINGLE)
723: #define PetscRealConstant(constant) constant##F
724: #elif defined(PETSC_USE_REAL_DOUBLE)
725: #define PetscRealConstant(constant) constant
726: #elif defined(PETSC_USE_REAL___FLOAT128)
727: #define PetscRealConstant(constant) constant##Q
728: #elif defined(PETSC_USE_REAL___FP16)
729: #define PetscRealConstant(constant) constant##F
730: #endif
732: /*
733: Basic constants
734: */
735: #define PETSC_PI PetscRealConstant(3.1415926535897932384626433832795029)
736: #define PETSC_PHI PetscRealConstant(1.6180339887498948482045868343656381)
737: #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)
739: #if !defined(PETSC_USE_64BIT_INDICES)
740: #define PETSC_MAX_INT 2147483647
741: #define PETSC_MIN_INT (-PETSC_MAX_INT - 1)
742: #else
743: #define PETSC_MAX_INT 9223372036854775807L
744: #define PETSC_MIN_INT (-PETSC_MAX_INT - 1)
745: #endif
747: #if defined(PETSC_USE_REAL_SINGLE)
748: # define PETSC_MAX_REAL 3.40282346638528860e+38F
749: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
750: # define PETSC_MACHINE_EPSILON 1.19209290e-07F
751: # define PETSC_SQRT_MACHINE_EPSILON 3.45266983e-04F
752: # define PETSC_SMALL 1.e-5F
753: #elif defined(PETSC_USE_REAL_DOUBLE)
754: # define PETSC_MAX_REAL 1.7976931348623157e+308
755: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
756: # define PETSC_MACHINE_EPSILON 2.2204460492503131e-16
757: # define PETSC_SQRT_MACHINE_EPSILON 1.490116119384766e-08
758: # define PETSC_SMALL 1.e-10
759: #elif defined(PETSC_USE_REAL___FLOAT128)
760: # define PETSC_MAX_REAL FLT128_MAX
761: # define PETSC_MIN_REAL (-FLT128_MAX)
762: # define PETSC_MACHINE_EPSILON FLT128_EPSILON
763: # define PETSC_SQRT_MACHINE_EPSILON 1.38777878078144567552953958511352539e-17Q
764: # define PETSC_SMALL 1.e-20Q
765: #elif defined(PETSC_USE_REAL___FP16)
766: # define PETSC_MAX_REAL 65504.0F
767: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
768: # define PETSC_MACHINE_EPSILON .0009765625F
769: # define PETSC_SQRT_MACHINE_EPSILON .03125F
770: # define PETSC_SMALL 5.e-3F
771: #endif
773: #define PETSC_INFINITY (PETSC_MAX_REAL/4)
774: #define PETSC_NINFINITY (-PETSC_INFINITY)
776: PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal);
777: PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal);
778: PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
779: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;}
780: PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));}
781: PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
782: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
783: PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}
785: PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal,PetscReal,PetscReal,PetscReal);
786: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
787: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);
789: /*
790: These macros are currently hardwired to match the regular data types, so there is no support for a different
791: MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
792: */
793: #define MPIU_MATSCALAR MPIU_SCALAR
794: typedef PetscScalar MatScalar;
795: typedef PetscReal MatReal;
797: struct petsc_mpiu_2scalar {PetscScalar a,b;};
798: PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
800: #if defined(PETSC_USE_64BIT_INDICES)
801: struct petsc_mpiu_2int {PetscInt a,b;};
802: PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
803: #else
804: #define MPIU_2INT MPI_2INT
805: #endif
807: PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
808: {
809: PetscInt result = 1;
810: while (power) {
811: if (power & 1) result *= base;
812: power >>= 1;
813: base *= base;
814: }
815: return result;
816: }
818: PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
819: {
820: PetscReal result = 1;
821: if (power < 0) {
822: power = -power;
823: base = ((PetscReal)1)/base;
824: }
825: while (power) {
826: if (power & 1) result *= base;
827: power >>= 1;
828: base *= base;
829: }
830: return result;
831: }
833: PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
834: {
835: PetscScalar result = (PetscReal)1;
836: if (power < 0) {
837: power = -power;
838: base = ((PetscReal)1)/base;
839: }
840: while (power) {
841: if (power & 1) result *= base;
842: power >>= 1;
843: base *= base;
844: }
845: return result;
846: }
848: PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
849: {
850: PetscScalar cpower = power;
851: return PetscPowScalar(base,cpower);
852: }
854: PETSC_EXTERN PetscErrorCode PetscLinearRegression(PetscInt,const PetscReal[],const PetscReal[],PetscReal*,PetscReal*);
855: #endif