Actual source code: petscmath.h
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 PetscCopysignReal(a,b) copysignf(a,b)
53: #define PetscTGamma(a) tgammaf(a)
54: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
55: #define PetscLGamma(a) gammaf(a)
56: #else
57: #define PetscLGamma(a) lgammaf(a)
58: #endif
60: #elif defined(PETSC_USE_REAL_DOUBLE)
61: #define PetscSqrtReal(a) sqrt(a)
62: #define PetscCbrtReal(a) cbrt(a)
63: #define PetscHypotReal(a,b) hypot(a,b)
64: #define PetscAtan2Real(a,b) atan2(a,b)
65: #define PetscPowReal(a,b) pow(a,b)
66: #define PetscExpReal(a) exp(a)
67: #define PetscLogReal(a) log(a)
68: #define PetscLog10Real(a) log10(a)
69: #define PetscLog2Real(a) log2(a)
70: #define PetscSinReal(a) sin(a)
71: #define PetscCosReal(a) cos(a)
72: #define PetscTanReal(a) tan(a)
73: #define PetscAsinReal(a) asin(a)
74: #define PetscAcosReal(a) acos(a)
75: #define PetscAtanReal(a) atan(a)
76: #define PetscSinhReal(a) sinh(a)
77: #define PetscCoshReal(a) cosh(a)
78: #define PetscTanhReal(a) tanh(a)
79: #define PetscAsinhReal(a) asinh(a)
80: #define PetscAcoshReal(a) acosh(a)
81: #define PetscAtanhReal(a) atanh(a)
82: #define PetscCeilReal(a) ceil(a)
83: #define PetscFloorReal(a) floor(a)
84: #define PetscFmodReal(a,b) fmod(a,b)
85: #define PetscCopysignReal(a,b) copysign(a,b)
86: #define PetscTGamma(a) tgamma(a)
87: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
88: #define PetscLGamma(a) gamma(a)
89: #else
90: #define PetscLGamma(a) lgamma(a)
91: #endif
93: #elif defined(PETSC_USE_REAL___FLOAT128)
94: #define PetscSqrtReal(a) sqrtq(a)
95: #define PetscCbrtReal(a) cbrtq(a)
96: #define PetscHypotReal(a,b) hypotq(a,b)
97: #define PetscAtan2Real(a,b) atan2q(a,b)
98: #define PetscPowReal(a,b) powq(a,b)
99: #define PetscExpReal(a) expq(a)
100: #define PetscLogReal(a) logq(a)
101: #define PetscLog10Real(a) log10q(a)
102: #define PetscLog2Real(a) log2q(a)
103: #define PetscSinReal(a) sinq(a)
104: #define PetscCosReal(a) cosq(a)
105: #define PetscTanReal(a) tanq(a)
106: #define PetscAsinReal(a) asinq(a)
107: #define PetscAcosReal(a) acosq(a)
108: #define PetscAtanReal(a) atanq(a)
109: #define PetscSinhReal(a) sinhq(a)
110: #define PetscCoshReal(a) coshq(a)
111: #define PetscTanhReal(a) tanhq(a)
112: #define PetscAsinhReal(a) asinhq(a)
113: #define PetscAcoshReal(a) acoshq(a)
114: #define PetscAtanhReal(a) atanhq(a)
115: #define PetscCeilReal(a) ceilq(a)
116: #define PetscFloorReal(a) floorq(a)
117: #define PetscFmodReal(a,b) fmodq(a,b)
118: #define PetscCopysignReal(a,b) copysignq(a,b)
119: #define PetscTGamma(a) tgammaq(a)
120: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
121: #define PetscLGamma(a) gammaq(a)
122: #else
123: #define PetscLGamma(a) lgammaq(a)
124: #endif
126: #elif defined(PETSC_USE_REAL___FP16)
127: #define PetscSqrtReal(a) sqrtf(a)
128: #define PetscCbrtReal(a) cbrtf(a)
129: #define PetscHypotReal(a,b) hypotf(a,b)
130: #define PetscAtan2Real(a,b) atan2f(a,b)
131: #define PetscPowReal(a,b) powf(a,b)
132: #define PetscExpReal(a) expf(a)
133: #define PetscLogReal(a) logf(a)
134: #define PetscLog10Real(a) log10f(a)
135: #define PetscLog2Real(a) log2f(a)
136: #define PetscSinReal(a) sinf(a)
137: #define PetscCosReal(a) cosf(a)
138: #define PetscTanReal(a) tanf(a)
139: #define PetscAsinReal(a) asinf(a)
140: #define PetscAcosReal(a) acosf(a)
141: #define PetscAtanReal(a) atanf(a)
142: #define PetscSinhReal(a) sinhf(a)
143: #define PetscCoshReal(a) coshf(a)
144: #define PetscTanhReal(a) tanhf(a)
145: #define PetscAsinhReal(a) asinhf(a)
146: #define PetscAcoshReal(a) acoshf(a)
147: #define PetscAtanhReal(a) atanhf(a)
148: #define PetscCeilReal(a) ceilf(a)
149: #define PetscFloorReal(a) floorf(a)
150: #define PetscFmodReal(a,b) fmodf(a,b)
151: #define PetscCopySignReal(a,b) copysignf(a,b)
152: #define PetscTGamma(a) tgammaf(a)
153: #if defined(PETSC_HAVE_LGAMMA_IS_GAMMA)
154: #define PetscLGamma(a) gammaf(a)
155: #else
156: #define PetscLGamma(a) lgammaf(a)
157: #endif
159: #endif /* PETSC_USE_REAL_* */
161: PETSC_STATIC_INLINE PetscReal PetscSignReal(PetscReal a)
162: {
163: return (PetscReal)((a < (PetscReal)0) ? -1 : ((a > (PetscReal)0) ? 1 : 0));
164: }
166: #if !defined(PETSC_HAVE_LOG2)
167: #undef PetscLog2Real
168: PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal a)
169: {
170: return PetscLogReal(a)/PetscLogReal((PetscReal)2);
171: }
172: #endif
174: #if defined(PETSC_USE_REAL___FLOAT128)
175: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
176: #endif
177: #if defined(PETSC_USE_REAL___FP16)
178: PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
179: #endif
181: /*MC
182: MPIU_REAL - MPI datatype corresponding to PetscReal
184: Notes:
185: In MPI calls that require an MPI datatype that matches a PetscReal or array of PetscReal values, pass this value.
187: Level: beginner
189: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT
190: M*/
191: #if defined(PETSC_USE_REAL_SINGLE)
192: # define MPIU_REAL MPI_FLOAT
193: #elif defined(PETSC_USE_REAL_DOUBLE)
194: # define MPIU_REAL MPI_DOUBLE
195: #elif defined(PETSC_USE_REAL___FLOAT128)
196: # define MPIU_REAL MPIU___FLOAT128
197: #elif defined(PETSC_USE_REAL___FP16)
198: # define MPIU_REAL MPIU___FP16
199: #endif /* PETSC_USE_REAL_* */
201: /*
202: Complex number definitions
203: */
204: #if defined(PETSC_HAVE_COMPLEX)
205: #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128)
206: /* C++ support of complex number */
208: #define PetscRealPartComplex(a) (a).real()
209: #define PetscImaginaryPartComplex(a) (a).imag()
210: #define PetscAbsComplex(a) petsccomplexlib::abs(a)
211: #define PetscArgComplex(a) petsccomplexlib::arg(a)
212: #define PetscConjComplex(a) petsccomplexlib::conj(a)
213: #define PetscSqrtComplex(a) petsccomplexlib::sqrt(a)
214: #define PetscPowComplex(a,b) petsccomplexlib::pow(a,b)
215: #define PetscExpComplex(a) petsccomplexlib::exp(a)
216: #define PetscLogComplex(a) petsccomplexlib::log(a)
217: #define PetscSinComplex(a) petsccomplexlib::sin(a)
218: #define PetscCosComplex(a) petsccomplexlib::cos(a)
219: #define PetscTanComplex(a) petsccomplexlib::tan(a)
220: #define PetscAsinComplex(a) petsccomplexlib::asin(a)
221: #define PetscAcosComplex(a) petsccomplexlib::acos(a)
222: #define PetscAtanComplex(a) petsccomplexlib::atan(a)
223: #define PetscSinhComplex(a) petsccomplexlib::sinh(a)
224: #define PetscCoshComplex(a) petsccomplexlib::cosh(a)
225: #define PetscTanhComplex(a) petsccomplexlib::tanh(a)
226: #define PetscAsinhComplex(a) petsccomplexlib::asinh(a)
227: #define PetscAcoshComplex(a) petsccomplexlib::acosh(a)
228: #define PetscAtanhComplex(a) petsccomplexlib::atanh(a)
230: /* TODO: Add configure tests
232: #if !defined(PETSC_HAVE_CXX_TAN_COMPLEX)
233: #undef PetscTanComplex
234: PETSC_STATIC_INLINE PetscComplex PetscTanComplex(PetscComplex z)
235: {
236: return PetscSinComplex(z)/PetscCosComplex(z);
237: }
238: #endif
240: #if !defined(PETSC_HAVE_CXX_TANH_COMPLEX)
241: #undef PetscTanhComplex
242: PETSC_STATIC_INLINE PetscComplex PetscTanhComplex(PetscComplex z)
243: {
244: return PetscSinhComplex(z)/PetscCoshComplex(z);
245: }
246: #endif
248: #if !defined(PETSC_HAVE_CXX_ASIN_COMPLEX)
249: #undef PetscAsinComplex
250: PETSC_STATIC_INLINE PetscComplex PetscAsinComplex(PetscComplex z)
251: {
252: const PetscComplex j(0,1);
253: return -j*PetscLogComplex(j*z+PetscSqrtComplex(1.0f-z*z));
254: }
255: #endif
257: #if !defined(PETSC_HAVE_CXX_ACOS_COMPLEX)
258: #undef PetscAcosComplex
259: PETSC_STATIC_INLINE PetscComplex PetscAcosComplex(PetscComplex z)
260: {
261: const PetscComplex j(0,1);
262: return j*PetscLogComplex(z-j*PetscSqrtComplex(1.0f-z*z));
263: }
264: #endif
266: #if !defined(PETSC_HAVE_CXX_ATAN_COMPLEX)
267: #undef PetscAtanComplex
268: PETSC_STATIC_INLINE PetscComplex PetscAtanComplex(PetscComplex z)
269: {
270: const PetscComplex j(0,1);
271: return 0.5f*j*PetscLogComplex((1.0f-j*z)/(1.0f+j*z));
272: }
273: #endif
275: #if !defined(PETSC_HAVE_CXX_ASINH_COMPLEX)
276: #undef PetscAsinhComplex
277: PETSC_STATIC_INLINE PetscComplex PetscAsinhComplex(PetscComplex z)
278: {
279: return PetscLogComplex(z+PetscSqrtComplex(z*z+1.0f));
280: }
281: #endif
283: #if !defined(PETSC_HAVE_CXX_ACOSH_COMPLEX)
284: #undef PetscAcoshComplex
285: PETSC_STATIC_INLINE PetscComplex PetscAcoshComplex(PetscComplex z)
286: {
287: return PetscLogComplex(z+PetscSqrtComplex(z*z-1.0f));
288: }
289: #endif
291: #if !defined(PETSC_HAVE_CXX_ATANH_COMPLEX)
292: #undef PetscAtanhComplex
293: PETSC_STATIC_INLINE PetscComplex PetscAtanhComplex(PetscComplex z)
294: {
295: return 0.5f*PetscLogComplex((1.0f+z)/(1.0f-z));
296: }
297: #endif
299: */
301: #else /* C99 support of complex number */
303: #if defined(PETSC_USE_REAL_SINGLE)
304: #define PetscRealPartComplex(a) crealf(a)
305: #define PetscImaginaryPartComplex(a) cimagf(a)
306: #define PetscAbsComplex(a) cabsf(a)
307: #define PetscArgComplex(a) cargf(a)
308: #define PetscConjComplex(a) conjf(a)
309: #define PetscSqrtComplex(a) csqrtf(a)
310: #define PetscPowComplex(a,b) cpowf(a,b)
311: #define PetscExpComplex(a) cexpf(a)
312: #define PetscLogComplex(a) clogf(a)
313: #define PetscSinComplex(a) csinf(a)
314: #define PetscCosComplex(a) ccosf(a)
315: #define PetscTanComplex(a) ctanf(a)
316: #define PetscAsinComplex(a) casinf(a)
317: #define PetscAcosComplex(a) cacosf(a)
318: #define PetscAtanComplex(a) catanf(a)
319: #define PetscSinhComplex(a) csinhf(a)
320: #define PetscCoshComplex(a) ccoshf(a)
321: #define PetscTanhComplex(a) ctanhf(a)
322: #define PetscAsinhComplex(a) casinhf(a)
323: #define PetscAcoshComplex(a) cacoshf(a)
324: #define PetscAtanhComplex(a) catanhf(a)
326: #elif defined(PETSC_USE_REAL_DOUBLE)
327: #define PetscRealPartComplex(a) creal(a)
328: #define PetscImaginaryPartComplex(a) cimag(a)
329: #define PetscAbsComplex(a) cabs(a)
330: #define PetscArgComplex(a) carg(a)
331: #define PetscConjComplex(a) conj(a)
332: #define PetscSqrtComplex(a) csqrt(a)
333: #define PetscPowComplex(a,b) cpow(a,b)
334: #define PetscExpComplex(a) cexp(a)
335: #define PetscLogComplex(a) clog(a)
336: #define PetscSinComplex(a) csin(a)
337: #define PetscCosComplex(a) ccos(a)
338: #define PetscTanComplex(a) ctan(a)
339: #define PetscAsinComplex(a) casin(a)
340: #define PetscAcosComplex(a) cacos(a)
341: #define PetscAtanComplex(a) catan(a)
342: #define PetscSinhComplex(a) csinh(a)
343: #define PetscCoshComplex(a) ccosh(a)
344: #define PetscTanhComplex(a) ctanh(a)
345: #define PetscAsinhComplex(a) casinh(a)
346: #define PetscAcoshComplex(a) cacosh(a)
347: #define PetscAtanhComplex(a) catanh(a)
349: #elif defined(PETSC_USE_REAL___FLOAT128)
350: #define PetscRealPartComplex(a) crealq(a)
351: #define PetscImaginaryPartComplex(a) cimagq(a)
352: #define PetscAbsComplex(a) cabsq(a)
353: #define PetscArgComplex(a) cargq(a)
354: #define PetscConjComplex(a) conjq(a)
355: #define PetscSqrtComplex(a) csqrtq(a)
356: #define PetscPowComplex(a,b) cpowq(a,b)
357: #define PetscExpComplex(a) cexpq(a)
358: #define PetscLogComplex(a) clogq(a)
359: #define PetscSinComplex(a) csinq(a)
360: #define PetscCosComplex(a) ccosq(a)
361: #define PetscTanComplex(a) ctanq(a)
362: #define PetscAsinComplex(a) casinq(a)
363: #define PetscAcosComplex(a) cacosq(a)
364: #define PetscAtanComplex(a) catanq(a)
365: #define PetscSinhComplex(a) csinhq(a)
366: #define PetscCoshComplex(a) ccoshq(a)
367: #define PetscTanhComplex(a) ctanhq(a)
368: #define PetscAsinhComplex(a) casinhq(a)
369: #define PetscAcoshComplex(a) cacoshq(a)
370: #define PetscAtanhComplex(a) catanhq(a)
372: #endif /* PETSC_USE_REAL_* */
373: #endif /* (__cplusplus) */
375: /*
376: PETSC_i is the imaginary number, i
377: */
378: PETSC_EXTERN PetscComplex PETSC_i;
380: /*
381: Try to do the right thing for complex number construction: see
382: http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
383: for details
384: */
385: PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
386: {
387: #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128)
388: return PetscComplex(x,y);
389: #elif defined(_Imaginary_I)
390: return x + y * _Imaginary_I;
391: #else
392: { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),
394: "For each floating type there is a corresponding real type, which is always a real floating
395: type. For real floating types, it is the same type. For complex types, it is the type given
396: by deleting the keyword _Complex from the type name."
398: So type punning should be portable. */
399: union { PetscComplex z; PetscReal f[2]; } uz;
401: uz.f[0] = x;
402: uz.f[1] = y;
403: return uz.z;
404: }
405: #endif
406: }
408: #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)\"")
409: #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)\"")
411: #if defined(PETSC_USE_REAL___FLOAT128)
412: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
413: #endif /* PETSC_USE_REAL___FLOAT128 */
415: /*MC
416: MPIU_COMPLEX - MPI datatype corresponding to PetscComplex
418: Notes:
419: In MPI calls that require an MPI datatype that matches a PetscComplex or array of PetscComplex values, pass this value.
421: Level: beginner
423: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_SCALAR, MPIU_COMPLEX, MPIU_INT, PETSC_i
424: M*/
425: #if defined(PETSC_USE_REAL_SINGLE)
426: # define MPIU_COMPLEX MPI_C_COMPLEX
427: #elif defined(PETSC_USE_REAL_DOUBLE)
428: # define MPIU_COMPLEX MPI_C_DOUBLE_COMPLEX
429: #elif defined(PETSC_USE_REAL___FLOAT128)
430: # define MPIU_COMPLEX MPIU___COMPLEX128
431: #elif defined(PETSC_USE_REAL___FP16)
432: # define MPIU_COMPLEX MPI_C_COMPLEX
433: #endif /* PETSC_USE_REAL_* */
435: #endif /* PETSC_HAVE_COMPLEX */
437: /*
438: Scalar number definitions
439: */
440: #if defined(PETSC_USE_COMPLEX) && defined(PETSC_HAVE_COMPLEX)
441: /*MC
442: MPIU_SCALAR - MPI datatype corresponding to PetscScalar
444: Notes:
445: In MPI calls that require an MPI datatype that matches a PetscScalar or array of PetscScalar values, pass this value.
447: Level: beginner
449: .seealso: PetscReal, PetscScalar, PetscComplex, PetscInt, MPIU_REAL, MPIU_COMPLEX, MPIU_INT
450: M*/
451: #define MPIU_SCALAR MPIU_COMPLEX
453: /*MC
454: PetscRealPart - Returns the real part of a PetscScalar
456: Synopsis:
457: #include <petscmath.h>
458: PetscReal PetscRealPart(PetscScalar v)
460: Not Collective
462: Input Parameter:
463: . v - value to find the real part of
465: Level: beginner
467: .seealso: PetscScalar, PetscImaginaryPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
469: M*/
470: #define PetscRealPart(a) PetscRealPartComplex(a)
472: /*MC
473: PetscImaginaryPart - Returns the imaginary part of a PetscScalar
475: Synopsis:
476: #include <petscmath.h>
477: PetscReal PetscImaginaryPart(PetscScalar v)
479: Not Collective
481: Input Parameter:
482: . v - value to find the imaginary part of
484: Level: beginner
486: Notes:
487: If PETSc was configured for real numbers then this always returns the value 0
489: .seealso: PetscScalar, PetscRealPart(), PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
491: M*/
492: #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)
494: #define PetscAbsScalar(a) PetscAbsComplex(a)
495: #define PetscArgScalar(a) PetscArgComplex(a)
496: #define PetscConj(a) PetscConjComplex(a)
497: #define PetscSqrtScalar(a) PetscSqrtComplex(a)
498: #define PetscPowScalar(a,b) PetscPowComplex(a,b)
499: #define PetscExpScalar(a) PetscExpComplex(a)
500: #define PetscLogScalar(a) PetscLogComplex(a)
501: #define PetscSinScalar(a) PetscSinComplex(a)
502: #define PetscCosScalar(a) PetscCosComplex(a)
503: #define PetscTanScalar(a) PetscTanComplex(a)
504: #define PetscAsinScalar(a) PetscAsinComplex(a)
505: #define PetscAcosScalar(a) PetscAcosComplex(a)
506: #define PetscAtanScalar(a) PetscAtanComplex(a)
507: #define PetscSinhScalar(a) PetscSinhComplex(a)
508: #define PetscCoshScalar(a) PetscCoshComplex(a)
509: #define PetscTanhScalar(a) PetscTanhComplex(a)
510: #define PetscAsinhScalar(a) PetscAsinhComplex(a)
511: #define PetscAcoshScalar(a) PetscAcoshComplex(a)
512: #define PetscAtanhScalar(a) PetscAtanhComplex(a)
514: #else /* PETSC_USE_COMPLEX */
515: #define MPIU_SCALAR MPIU_REAL
516: #define PetscRealPart(a) (a)
517: #define PetscImaginaryPart(a) ((PetscReal)0)
518: #define PetscAbsScalar(a) PetscAbsReal(a)
519: #define PetscArgScalar(a) (((a) < (PetscReal)0) ? PETSC_PI : (PetscReal)0)
520: #define PetscConj(a) (a)
521: #define PetscSqrtScalar(a) PetscSqrtReal(a)
522: #define PetscPowScalar(a,b) PetscPowReal(a,b)
523: #define PetscExpScalar(a) PetscExpReal(a)
524: #define PetscLogScalar(a) PetscLogReal(a)
525: #define PetscSinScalar(a) PetscSinReal(a)
526: #define PetscCosScalar(a) PetscCosReal(a)
527: #define PetscTanScalar(a) PetscTanReal(a)
528: #define PetscAsinScalar(a) PetscAsinReal(a)
529: #define PetscAcosScalar(a) PetscAcosReal(a)
530: #define PetscAtanScalar(a) PetscAtanReal(a)
531: #define PetscSinhScalar(a) PetscSinhReal(a)
532: #define PetscCoshScalar(a) PetscCoshReal(a)
533: #define PetscTanhScalar(a) PetscTanhReal(a)
534: #define PetscAsinhScalar(a) PetscAsinhReal(a)
535: #define PetscAcoshScalar(a) PetscAcoshReal(a)
536: #define PetscAtanhScalar(a) PetscAtanhReal(a)
538: #endif /* PETSC_USE_COMPLEX */
540: /*
541: Certain objects may be created using either single or double precision.
542: This is currently not used.
543: */
544: typedef enum { PETSC_SCALAR_DOUBLE, PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;
546: /* --------------------------------------------------------------------------*/
548: /*MC
549: PetscAbs - Returns the absolute value of a number
551: Synopsis:
552: #include <petscmath.h>
553: type PetscAbs(type v)
555: Not Collective
557: Input Parameter:
558: . v - the number
560: Notes:
561: type can be integer or real floating point value
563: Level: beginner
565: .seealso: PetscAbsInt(), PetscAbsReal(), PetscAbsScalar()
567: M*/
568: #define PetscAbs(a) (((a) >= 0) ? (a) : (-(a)))
570: /*MC
571: PetscSign - Returns the sign of a number as an integer
573: Synopsis:
574: #include <petscmath.h>
575: int PetscSign(type v)
577: Not Collective
579: Input Parameter:
580: . v - the number
582: Notes:
583: type can be integer or real floating point value
585: Level: beginner
587: M*/
588: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)
590: /*MC
591: PetscMin - Returns minimum of two numbers
593: Synopsis:
594: #include <petscmath.h>
595: type PetscMin(type v1,type v2)
597: Not Collective
599: Input Parameters:
600: + v1 - first value to find minimum of
601: - v2 - second value to find minimum of
603: Notes:
604: type can be integer or floating point value
606: Level: beginner
608: .seealso: PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
610: M*/
611: #define PetscMin(a,b) (((a)<(b)) ? (a) : (b))
613: /*MC
614: PetscMax - Returns maxium of two numbers
616: Synopsis:
617: #include <petscmath.h>
618: type max PetscMax(type v1,type v2)
620: Not Collective
622: Input Parameters:
623: + v1 - first value to find maximum of
624: - v2 - second value to find maximum of
626: Notes:
627: type can be integer or floating point value
629: Level: beginner
631: .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
633: M*/
634: #define PetscMax(a,b) (((a)<(b)) ? (b) : (a))
636: /*MC
637: PetscClipInterval - Returns a number clipped to be within an interval
639: Synopsis:
640: #include <petscmath.h>
641: type clip PetscClipInterval(type x,type a,type b)
643: Not Collective
645: Input Parameters:
646: + x - value to use if within interval [a,b]
647: . a - lower end of interval
648: - b - upper end of interval
650: Notes:
651: type can be integer or floating point value
653: Level: beginner
655: .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
657: M*/
658: #define PetscClipInterval(x,a,b) (PetscMax((a),PetscMin((x),(b))))
660: /*MC
661: PetscAbsInt - Returns the absolute value of an integer
663: Synopsis:
664: #include <petscmath.h>
665: int abs PetscAbsInt(int v1)
667: Not Collective
669: Input Parameter:
670: . v1 - the integer
672: Level: beginner
674: .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()
676: M*/
677: #define PetscAbsInt(a) (((a)<0) ? (-(a)) : (a))
679: /*MC
680: PetscAbsReal - Returns the absolute value of an real number
682: Synopsis:
683: #include <petscmath.h>
684: Real abs PetscAbsReal(PetscReal v1)
686: Not Collective
688: Input Parameter:
689: . v1 - the double
691: Level: beginner
693: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()
695: M*/
696: #if defined(PETSC_USE_REAL_SINGLE)
697: #define PetscAbsReal(a) fabsf(a)
698: #elif defined(PETSC_USE_REAL_DOUBLE)
699: #define PetscAbsReal(a) fabs(a)
700: #elif defined(PETSC_USE_REAL___FLOAT128)
701: #define PetscAbsReal(a) fabsq(a)
702: #elif defined(PETSC_USE_REAL___FP16)
703: #define PetscAbsReal(a) fabsf(a)
704: #endif
706: /*MC
707: PetscSqr - Returns the square of a number
709: Synopsis:
710: #include <petscmath.h>
711: type sqr PetscSqr(type v1)
713: Not Collective
715: Input Parameter:
716: . v1 - the value
718: Notes:
719: type can be integer or floating point value
721: Level: beginner
723: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()
725: M*/
726: #define PetscSqr(a) ((a)*(a))
728: /* ----------------------------------------------------------------------------*/
730: #if defined(PETSC_USE_REAL_SINGLE)
731: #define PetscRealConstant(constant) constant##F
732: #elif defined(PETSC_USE_REAL_DOUBLE)
733: #define PetscRealConstant(constant) constant
734: #elif defined(PETSC_USE_REAL___FLOAT128)
735: #define PetscRealConstant(constant) constant##Q
736: #elif defined(PETSC_USE_REAL___FP16)
737: #define PetscRealConstant(constant) constant##F
738: #endif
740: /*
741: Basic constants
742: */
743: #define PETSC_PI PetscRealConstant(3.1415926535897932384626433832795029)
744: #define PETSC_PHI PetscRealConstant(1.6180339887498948482045868343656381)
745: #define PETSC_SQRT2 PetscRealConstant(1.4142135623730950488016887242096981)
747: #if !defined(PETSC_USE_64BIT_INDICES)
748: #define PETSC_MAX_INT 2147483647
749: #define PETSC_MIN_INT (-PETSC_MAX_INT - 1)
750: #else
751: #define PETSC_MAX_INT 9223372036854775807L
752: #define PETSC_MIN_INT (-PETSC_MAX_INT - 1)
753: #endif
754: #define PETSC_MAX_UINT16 65535
756: #if defined(PETSC_USE_REAL_SINGLE)
757: # define PETSC_MAX_REAL 3.40282346638528860e+38F
758: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
759: # define PETSC_MACHINE_EPSILON 1.19209290e-07F
760: # define PETSC_SQRT_MACHINE_EPSILON 3.45266983e-04F
761: # define PETSC_SMALL 1.e-5F
762: #elif defined(PETSC_USE_REAL_DOUBLE)
763: # define PETSC_MAX_REAL 1.7976931348623157e+308
764: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
765: # define PETSC_MACHINE_EPSILON 2.2204460492503131e-16
766: # define PETSC_SQRT_MACHINE_EPSILON 1.490116119384766e-08
767: # define PETSC_SMALL 1.e-10
768: #elif defined(PETSC_USE_REAL___FLOAT128)
769: # define PETSC_MAX_REAL FLT128_MAX
770: # define PETSC_MIN_REAL (-FLT128_MAX)
771: # define PETSC_MACHINE_EPSILON FLT128_EPSILON
772: # define PETSC_SQRT_MACHINE_EPSILON 1.38777878078144567552953958511352539e-17Q
773: # define PETSC_SMALL 1.e-20Q
774: #elif defined(PETSC_USE_REAL___FP16)
775: # define PETSC_MAX_REAL 65504.0F
776: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
777: # define PETSC_MACHINE_EPSILON .0009765625F
778: # define PETSC_SQRT_MACHINE_EPSILON .03125F
779: # define PETSC_SMALL 5.e-3F
780: #endif
782: #define PETSC_INFINITY (PETSC_MAX_REAL/4)
783: #define PETSC_NINFINITY (-PETSC_INFINITY)
785: PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal);
786: PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal);
787: PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
788: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;}
789: PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));}
790: PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
791: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
792: PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}
794: PETSC_EXTERN PetscBool PetscIsCloseAtTol(PetscReal,PetscReal,PetscReal,PetscReal);
795: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
796: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);
798: /*
799: These macros are currently hardwired to match the regular data types, so there is no support for a different
800: MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
801: */
802: #define MPIU_MATSCALAR MPIU_SCALAR
803: typedef PetscScalar MatScalar;
804: typedef PetscReal MatReal;
806: struct petsc_mpiu_2scalar {PetscScalar a,b;};
807: PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
809: /*
810: MPI Datatypes for composite reductions:
811: MPIU_REAL_INT -> struct { PetscReal; PetscInt; }
812: MPIU_SCALAR_INT -> struct { PetscScalar; PetscInt; }
813: */
814: PETSC_EXTERN MPI_Datatype MPIU_REAL_INT;
815: PETSC_EXTERN MPI_Datatype MPIU_SCALAR_INT;
817: #if defined(PETSC_USE_64BIT_INDICES)
818: struct petsc_mpiu_2int {PetscInt a,b;};
819: PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
820: #else
821: #define MPIU_2INT MPI_2INT
822: #endif
823: PETSC_EXTERN MPI_Datatype MPI_4INT;
824: PETSC_EXTERN MPI_Datatype MPIU_4INT;
826: PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
827: {
828: PetscInt result = 1;
829: while (power) {
830: if (power & 1) result *= base;
831: power >>= 1;
832: base *= base;
833: }
834: return result;
835: }
837: PETSC_STATIC_INLINE PetscInt64 PetscPowInt64(PetscInt base,PetscInt power)
838: {
839: PetscInt64 result = 1;
840: while (power) {
841: if (power & 1) result *= base;
842: power >>= 1;
843: base *= base;
844: }
845: return result;
846: }
848: PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
849: {
850: PetscReal result = 1;
851: if (power < 0) {
852: power = -power;
853: base = ((PetscReal)1)/base;
854: }
855: while (power) {
856: if (power & 1) result *= base;
857: power >>= 1;
858: base *= base;
859: }
860: return result;
861: }
863: PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
864: {
865: PetscScalar result = (PetscReal)1;
866: if (power < 0) {
867: power = -power;
868: base = ((PetscReal)1)/base;
869: }
870: while (power) {
871: if (power & 1) result *= base;
872: power >>= 1;
873: base *= base;
874: }
875: return result;
876: }
878: PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
879: {
880: PetscScalar cpower = power;
881: return PetscPowScalar(base,cpower);
882: }
884: /*MC
885: PetscLTE - Performs a less than or equal to on a given constant with a fudge for floating point numbers
887: Synopsis:
888: #include <petscmath.h>
889: bool PetscLTE(PetscReal x,constant float)
891: Not Collective
893: Input Parameters:
894: + x - the variable
895: - b - the constant float it is checking if x is less than or equal to
897: Notes:
898: The fudge factor is the value PETSC_SMALL
900: The constant numerical value is automatically set to the appropriate precision of PETSc so can just be provided as, for example, 3.2
902: This is used in several examples for setting initial conditions based on coordinate values that are computed with i*h that produces inexact
903: floating point results.
905: Level: advanced
907: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal(), PetscGTE()
909: M*/
910: #define PetscLTE(x,b) ((x) <= (PetscRealConstant(b)+PETSC_SMALL))
912: /*MC
913: PetscGTE - Performs a greater than or equal to on a given constant with a fudge for floating point numbers
915: Synopsis:
916: #include <petscmath.h>
917: bool PetscGTE(PetscReal x,constant float)
919: Not Collective
921: Input Parameters:
922: + x - the variable
923: - b - the constant float it is checking if x is greater than or equal to
925: Notes:
926: The fudge factor is the value PETSC_SMALL
928: The constant numerical value is automatically set to the appropriate precision of PETSc so can just be provided as, for example, 3.2
930: This is used in several examples for setting initial conditions based on coordinate values that are computed with i*h that produces inexact
931: floating point results.
933: Level: advanced
935: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal(), PetscLTE()
937: M*/
938: #define PetscGTE(x,b) ((x) >= (PetscRealConstant(b)-PETSC_SMALL))
940: PETSC_EXTERN PetscErrorCode PetscLinearRegression(PetscInt,const PetscReal[],const PetscReal[],PetscReal*,PetscReal*);
941: #endif