Actual source code: petscmath.h
petsc-3.8.4 2018-03-24
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: */
13: #include <math.h>
15: /*
17: Defines operations that are different for complex and real numbers;
18: note that one cannot mix the use of complex and real in the same
19: PETSc program. All PETSc objects in one program are built around the object
20: PetscScalar which is either always a real or a complex.
22: */
24: #if defined(PETSC_USE_REAL_SINGLE)
25: #define MPIU_REAL MPI_FLOAT
26: typedef float PetscReal;
27: #define PetscRoundReal(a) round(a)
28: #define PetscSqrtReal(a) sqrt(a)
29: #define PetscExpReal(a) exp(a)
30: #define PetscLogReal(a) log(a)
31: #define PetscLog10Real(a) log10(a)
32: #ifdef PETSC_HAVE_LOG2
33: #define PetscLog2Real(a) log2(a)
34: #endif
35: #define PetscSinReal(a) sin(a)
36: #define PetscCosReal(a) cos(a)
37: #define PetscTanReal(a) tan(a)
38: #define PetscAsinReal(a) asin(a)
39: #define PetscAcosReal(a) acos(a)
40: #define PetscAtanReal(a) atan(a)
41: #define PetscAtan2Real(a,b) atan2(a,b)
42: #define PetscSinhReal(a) sinh(a)
43: #define PetscCoshReal(a) cosh(a)
44: #define PetscTanhReal(a) tanh(a)
45: #define PetscPowReal(a,b) pow(a,b)
46: #define PetscCeilReal(a) ceil(a)
47: #define PetscFloorReal(a) floor(a)
48: #define PetscFmodReal(a,b) fmod(a,b)
49: #define PetscTGamma(a) tgammaf(a)
50: #elif defined(PETSC_USE_REAL_DOUBLE)
51: #define MPIU_REAL MPI_DOUBLE
52: typedef double PetscReal;
53: #define PetscRoundReal(a) round(a)
54: #define PetscSqrtReal(a) sqrt(a)
55: #define PetscExpReal(a) exp(a)
56: #define PetscLogReal(a) log(a)
57: #define PetscLog10Real(a) log10(a)
58: #ifdef PETSC_HAVE_LOG2
59: #define PetscLog2Real(a) log2(a)
60: #endif
61: #define PetscSinReal(a) sin(a)
62: #define PetscCosReal(a) cos(a)
63: #define PetscTanReal(a) tan(a)
64: #define PetscAsinReal(a) asin(a)
65: #define PetscAcosReal(a) acos(a)
66: #define PetscAtanReal(a) atan(a)
67: #define PetscAtan2Real(a,b) atan2(a,b)
68: #define PetscSinhReal(a) sinh(a)
69: #define PetscCoshReal(a) cosh(a)
70: #define PetscTanhReal(a) tanh(a)
71: #define PetscPowReal(a,b) pow(a,b)
72: #define PetscCeilReal(a) ceil(a)
73: #define PetscFloorReal(a) floor(a)
74: #define PetscFmodReal(a,b) fmod(a,b)
75: #define PetscTGamma(a) tgamma(a)
76: #elif defined(PETSC_USE_REAL___FLOAT128)
77: #if defined(__cplusplus)
78: extern "C" {
79: #endif
80: #include <quadmath.h>
81: #if defined(__cplusplus)
82: }
83: #endif
84: PETSC_EXTERN MPI_Datatype MPIU___FLOAT128 PetscAttrMPITypeTag(__float128);
85: #define MPIU_REAL MPIU___FLOAT128
86: typedef __float128 PetscReal;
87: #define PetscRoundReal(a) roundq(a)
88: #define PetscSqrtReal(a) sqrtq(a)
89: #define PetscExpReal(a) expq(a)
90: #define PetscLogReal(a) logq(a)
91: #define PetscLog10Real(a) log10q(a)
92: #ifdef PETSC_HAVE_LOG2
93: #define PetscLog2Real(a) log2q(a)
94: #endif
95: #define PetscSinReal(a) sinq(a)
96: #define PetscCosReal(a) cosq(a)
97: #define PetscTanReal(a) tanq(a)
98: #define PetscAsinReal(a) asinq(a)
99: #define PetscAcosReal(a) acosq(a)
100: #define PetscAtanReal(a) atanq(a)
101: #define PetscAtan2Real(a,b) atan2q(a,b)
102: #define PetscSinhReal(a) sinhq(a)
103: #define PetscCoshReal(a) coshq(a)
104: #define PetscTanhReal(a) tanhq(a)
105: #define PetscPowReal(a,b) powq(a,b)
106: #define PetscCeilReal(a) ceilq(a)
107: #define PetscFloorReal(a) floorq(a)
108: #define PetscFmodReal(a,b) fmodq(a,b)
109: #define PetscTGamma(a) tgammaq(a)
110: #elif defined(PETSC_USE_REAL___FP16)
111: PETSC_EXTERN MPI_Datatype MPIU___FP16 PetscAttrMPITypeTag(__fp16);
112: #define MPIU_REAL MPIU___FP16
113: typedef __fp16 PetscReal;
114: #define PetscRound(a) roundf(a)
115: #define PetscSqrtReal(a) sqrtf(a)
116: #define PetscExpReal(a) expf(a)
117: #define PetscLogReal(a) logf(a)
118: #define PetscLog10Real(a) log10f(a)
119: #ifdef PETSC_HAVE_LOG2
120: #define PetscLog2Real(a) log2f(a)
121: #endif
122: #define PetscSinReal(a) sinf(a)
123: #define PetscCosReal(a) cosf(a)
124: #define PetscTanReal(a) tanf(a)
125: #define PetscAsinReal(a) asinf(a)
126: #define PetscAcosReal(a) acosf(a)
127: #define PetscAtanReal(a) atanf(a)
128: #define PetscAtan2Real(a,b) atan2f(a,b)
129: #define PetscSinhReal(a) sinhf(a)
130: #define PetscCoshReal(a) coshf(a)
131: #define PetscTanhReal(a) tanhf(a)
132: #define PetscPowReal(a,b) powf(a,b)
133: #define PetscCeilReal(a) ceilf(a)
134: #define PetscFloorReal(a) floorf(a)
135: #define PetscFmodReal(a,b) fmodf(a,b)
136: #define PetscTGamma(a) tgammaf(a)
137: #endif /* PETSC_USE_REAL_* */
139: /*
140: Complex number definitions
141: */
142: #if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
143: #if !defined(PETSC_SKIP_COMPLEX)
144: #define PETSC_HAVE_COMPLEX 1
145: /* C++ support of complex number */
146: #if defined(PETSC_HAVE_CUSP)
147: #define complexlib cusp
148: #include <cusp/complex.h>
149: #elif defined(PETSC_HAVE_VECCUDA) && __CUDACC_VER_MAJOR__ > 6
150: /* complex headers in thrust only available in CUDA 7.0 and above */
151: #define complexlib thrust
152: #include <thrust/complex.h>
153: #else
154: #define complexlib std
155: #include <complex>
156: #endif
158: #define PetscRealPartComplex(a) (a).real()
159: #define PetscImaginaryPartComplex(a) (a).imag()
160: #define PetscAbsComplex(a) complexlib::abs(a)
161: #define PetscConjComplex(a) complexlib::conj(a)
162: #define PetscSqrtComplex(a) complexlib::sqrt(a)
163: #define PetscPowComplex(a,b) complexlib::pow(a,b)
164: #define PetscExpComplex(a) complexlib::exp(a)
165: #define PetscLogComplex(a) complexlib::log(a)
166: #define PetscSinComplex(a) complexlib::sin(a)
167: #define PetscCosComplex(a) complexlib::cos(a)
168: #define PetscAsinComplex(a) complexlib::asin(a)
169: #define PetscAcosComplex(a) complexlib::acos(a)
170: #if defined(PETSC_HAVE_TANCOMPLEX)
171: #define PetscTanComplex(a) complexlib::tan(a)
172: #else
173: #define PetscTanComplex(a) PetscSinComplex(a)/PetscCosComplex(a)
174: #endif
175: #define PetscSinhComplex(a) complexlib::sinh(a)
176: #define PetscCoshComplex(a) complexlib::cosh(a)
177: #if defined(PETSC_HAVE_TANHCOMPLEX)
178: #define PetscTanhComplex(a) complexlib::tanh(a)
179: #else
180: #define PetscTanhComplex(a) PetscSinhComplex(a)/PetscCoshComplex(a)
181: #endif
183: #if defined(PETSC_USE_REAL_SINGLE)
184: typedef complexlib::complex<float> PetscComplex;
185: #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND)
186: static inline PetscComplex operator+(const PetscComplex& lhs, const double& rhs) { return lhs + float(rhs); }
187: static inline PetscComplex operator+(const double& lhs, const PetscComplex& rhs) { return float(lhs) + rhs; }
188: static inline PetscComplex operator-(const PetscComplex& lhs, const double& rhs) { return lhs - float(rhs); }
189: static inline PetscComplex operator-(const double& lhs, const PetscComplex& rhs) { return float(lhs) - rhs; }
190: static inline PetscComplex operator*(const PetscComplex& lhs, const double& rhs) { return lhs * float(rhs); }
191: static inline PetscComplex operator*(const double& lhs, const PetscComplex& rhs) { return float(lhs) * rhs; }
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 bool operator==(const PetscComplex& lhs, const double& rhs) { return lhs.imag() == float(0) && lhs.real() == float(rhs); }
195: static inline bool operator==(const double& lhs, const PetscComplex& rhs) { return rhs.imag() == float(0) && rhs.real() == float(lhs); }
196: static inline bool operator!=(const PetscComplex& lhs, const double& rhs) { return lhs.imag() != float(0) || lhs.real() != float(rhs); }
197: static inline bool operator!=(const double& lhs, const PetscComplex& rhs) { return rhs.imag() != float(0) || rhs.real() != float(lhs); }
198: #endif /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */
199: #elif defined(PETSC_USE_REAL_DOUBLE)
200: typedef complexlib::complex<double> PetscComplex;
201: #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND)
202: static inline PetscComplex operator+(const PetscComplex& lhs, const PetscInt& rhs) { return lhs + double(rhs); }
203: static inline PetscComplex operator+(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) + rhs; }
204: static inline PetscComplex operator-(const PetscComplex& lhs, const PetscInt& rhs) { return lhs - double(rhs); }
205: static inline PetscComplex operator-(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) - rhs; }
206: static inline PetscComplex operator*(const PetscComplex& lhs, const PetscInt& rhs) { return lhs * double(rhs); }
207: static inline PetscComplex operator*(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) * rhs; }
208: static inline PetscComplex operator/(const PetscComplex& lhs, const PetscInt& rhs) { return lhs / double(rhs); }
209: static inline PetscComplex operator/(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) / rhs; }
210: static inline bool operator==(const PetscComplex& lhs, const PetscInt& rhs) { return lhs.imag() == double(0) && lhs.real() == double(rhs); }
211: static inline bool operator==(const PetscInt& lhs, const PetscComplex& rhs) { return rhs.imag() == double(0) && rhs.real() == double(lhs); }
212: static inline bool operator!=(const PetscComplex& lhs, const PetscInt& rhs) { return lhs.imag() != double(0) || lhs.real() != double(rhs); }
213: static inline bool operator!=(const PetscInt& lhs, const PetscComplex& rhs) { return rhs.imag() != double(0) || rhs.real() != double(lhs); }
214: #endif /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */
215: #elif defined(PETSC_USE_REAL___FLOAT128)
216: typedef complexlib::complex<__float128> PetscComplex; /* Notstandard and not expected to work, use __complex128 */
217: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128;
218: #endif /* PETSC_USE_REAL_ */
219: #endif /* ! PETSC_SKIP_COMPLEX */
221: #elif defined(PETSC_HAVE_C99_COMPLEX) && !defined(PETSC_USE_REAL___FP16)
222: #if !defined(PETSC_SKIP_COMPLEX)
223: #define PETSC_HAVE_COMPLEX 1
224: #include <complex.h>
226: #if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
227: typedef float _Complex PetscComplex;
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: typedef double _Complex PetscComplex;
249: #define PetscRealPartComplex(a) creal(a)
250: #define PetscImaginaryPartComplex(a) cimag(a)
251: #define PetscAbsComplex(a) cabs(a)
252: #define PetscConjComplex(a) conj(a)
253: #define PetscSqrtComplex(a) csqrt(a)
254: #define PetscPowComplex(a,b) cpow(a,b)
255: #define PetscExpComplex(a) cexp(a)
256: #define PetscLogComplex(a) clog(a)
257: #define PetscSinComplex(a) csin(a)
258: #define PetscCosComplex(a) ccos(a)
259: #define PetscAsinComplex(a) casin(a)
260: #define PetscAcosComplex(a) cacos(a)
261: #define PetscTanComplex(a) ctan(a)
262: #define PetscSinhComplex(a) csinh(a)
263: #define PetscCoshComplex(a) ccosh(a)
264: #define PetscTanhComplex(a) ctanh(a)
266: #elif defined(PETSC_USE_REAL___FLOAT128)
267: typedef __complex128 PetscComplex;
268: PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128);
270: #define PetscRealPartComplex(a) crealq(a)
271: #define PetscImaginaryPartComplex(a) cimagq(a)
272: #define PetscAbsComplex(a) cabsq(a)
273: #define PetscConjComplex(a) conjq(a)
274: #define PetscSqrtComplex(a) csqrtq(a)
275: #define PetscPowComplex(a,b) cpowq(a,b)
276: #define PetscExpComplex(a) cexpq(a)
277: #define PetscLogComplex(a) clogq(a)
278: #define PetscSinComplex(a) csinq(a)
279: #define PetscCosComplex(a) ccosq(a)
280: #define PetscAsinComplex(a) casinq(a)
281: #define PetscAcosComplex(a) cacosq(a)
282: #define PetscTanComplex(a) ctanq(a)
283: #define PetscSinhComplex(a) csinhq(a)
284: #define PetscCoshComplex(a) ccoshq(a)
285: #define PetscTanhComplex(a) ctanhq(a)
287: #endif /* PETSC_USE_REAL_* */
288: #elif (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
289: #error "PETSc was configured --with-scalar-type=complex, but a language-appropriate complex library is not available"
290: #endif /* !PETSC_SKIP_COMPLEX */
291: #endif /* (__cplusplus && PETSC_HAVE_CXX_COMPLEX) else-if (!__cplusplus && PETSC_HAVE_C99_COMPLEX) */
293: #if defined(PETSC_HAVE_COMPLEX)
294: #if defined(PETSC_HAVE_MPI_C_DOUBLE_COMPLEX)
295: #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX
296: #define MPIU_C_COMPLEX MPI_C_COMPLEX
297: #else
298: # if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128)
299: typedef complexlib::complex<double> petsc_mpiu_c_double_complex;
300: typedef complexlib::complex<float> petsc_mpiu_c_complex;
301: # elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX)
302: typedef double _Complex petsc_mpiu_c_double_complex;
303: typedef float _Complex petsc_mpiu_c_complex;
304: # else
305: typedef struct {double real,imag;} petsc_mpiu_c_double_complex;
306: typedef struct {float real,imag;} petsc_mpiu_c_complex;
307: # endif
308: PETSC_EXTERN MPI_Datatype MPIU_C_DOUBLE_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_double_complex);
309: PETSC_EXTERN MPI_Datatype MPIU_C_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_complex);
310: #endif /* PETSC_HAVE_MPI_C_DOUBLE_COMPLEX */
311: #endif /* PETSC_HAVE_COMPLEX */
313: #if defined(PETSC_HAVE_COMPLEX)
314: # if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16)
315: # define MPIU_COMPLEX MPIU_C_COMPLEX
316: # elif defined(PETSC_USE_REAL_DOUBLE)
317: # define MPIU_COMPLEX MPIU_C_DOUBLE_COMPLEX
318: # elif defined(PETSC_USE_REAL___FLOAT128)
319: # define MPIU_COMPLEX MPIU___COMPLEX128
320: # endif /* PETSC_USE_REAL_* */
321: #endif
323: #if (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
324: typedef PetscComplex PetscScalar;
325: #define PetscRealPart(a) PetscRealPartComplex(a)
326: #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a)
327: #define PetscAbsScalar(a) PetscAbsComplex(a)
328: #define PetscConj(a) PetscConjComplex(a)
329: #define PetscSqrtScalar(a) PetscSqrtComplex(a)
330: #define PetscPowScalar(a,b) PetscPowComplex(a,b)
331: #define PetscExpScalar(a) PetscExpComplex(a)
332: #define PetscLogScalar(a) PetscLogComplex(a)
333: #define PetscSinScalar(a) PetscSinComplex(a)
334: #define PetscCosScalar(a) PetscCosComplex(a)
335: #define PetscAsinScalar(a) PetscAsinComplex(a)
336: #define PetscAcosScalar(a) PetscAcosComplex(a)
337: #define PetscTanScalar(a) PetscTanComplex(a)
338: #define PetscSinhScalar(a) PetscSinhComplex(a)
339: #define PetscCoshScalar(a) PetscCoshComplex(a)
340: #define PetscTanhScalar(a) PetscTanhComplex(a)
341: #define MPIU_SCALAR MPIU_COMPLEX
343: /*
344: real number definitions
345: */
346: #else /* PETSC_USE_COMPLEX */
347: typedef PetscReal PetscScalar;
348: #define MPIU_SCALAR MPIU_REAL
350: #define PetscRealPart(a) (a)
351: #define PetscImaginaryPart(a) ((PetscReal)0.)
352: PETSC_STATIC_INLINE PetscReal PetscAbsScalar(PetscScalar a) {return a < 0.0 ? -a : a;}
353: #define PetscConj(a) (a)
354: #if !defined(PETSC_USE_REAL___FLOAT128) && !defined(PETSC_USE_REAL___FP16)
355: #define PetscSqrtScalar(a) sqrt(a)
356: #define PetscPowScalar(a,b) pow(a,b)
357: #define PetscExpScalar(a) exp(a)
358: #define PetscLogScalar(a) log(a)
359: #define PetscSinScalar(a) sin(a)
360: #define PetscCosScalar(a) cos(a)
361: #define PetscAsinScalar(a) asin(a)
362: #define PetscAcosScalar(a) acos(a)
363: #define PetscTanScalar(a) tan(a)
364: #define PetscSinhScalar(a) sinh(a)
365: #define PetscCoshScalar(a) cosh(a)
366: #define PetscTanhScalar(a) tanh(a)
367: #elif defined(PETSC_USE_REAL___FP16)
368: #define PetscSqrtScalar(a) sqrtf(a)
369: #define PetscPowScalar(a,b) powf(a,b)
370: #define PetscExpScalar(a) expf(a)
371: #define PetscLogScalar(a) logf(a)
372: #define PetscSinScalar(a) sinf(a)
373: #define PetscCosScalar(a) cosf(a)
374: #define PetscAsinScalar(a) asinf(a)
375: #define PetscAcosScalar(a) acosf(a)
376: #define PetscTanScalar(a) tanf(a)
377: #define PetscSinhScalar(a) sinhf(a)
378: #define PetscCoshScalar(a) coshf(a)
379: #define PetscTanhScalar(a) tanhf(a)
380: #else /* PETSC_USE_REAL___FLOAT128 */
381: #define PetscSqrtScalar(a) sqrtq(a)
382: #define PetscPowScalar(a,b) powq(a,b)
383: #define PetscExpScalar(a) expq(a)
384: #define PetscLogScalar(a) logq(a)
385: #define PetscSinScalar(a) sinq(a)
386: #define PetscCosScalar(a) cosq(a)
387: #define PetscAsinScalar(a) asinq(a)
388: #define PetscAcosScalar(a) acosq(a)
389: #define PetscTanScalar(a) tanq(a)
390: #define PetscSinhScalar(a) sinhq(a)
391: #define PetscCoshScalar(a) coshq(a)
392: #define PetscTanhScalar(a) tanhq(a)
393: #endif /* PETSC_USE_REAL___FLOAT128 */
395: #endif /* PETSC_USE_COMPLEX */
397: #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1)
398: #define PetscSignReal(a) (((a) >= 0.0) ? ((a) == 0.0 ? 0.0 : 1.0) : -1.0)
399: #define PetscAbs(a) (((a) >= 0) ? (a) : (-(a)))
401: /* --------------------------------------------------------------------------*/
403: /*
404: Certain objects may be created using either single or double precision.
405: This is currently not used.
406: */
407: typedef enum { PETSC_SCALAR_DOUBLE,PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision;
409: #if defined(PETSC_HAVE_COMPLEX)
410: /* PETSC_i is the imaginary number, i */
411: PETSC_EXTERN PetscComplex PETSC_i;
413: /* Try to do the right thing for complex number construction: see
415: http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm
417: for details
418: */
419: PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y)
420: {
421: #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128)
422: return PetscComplex(x,y);
423: #elif defined(_Imaginary_I)
424: return x + y * _Imaginary_I;
425: #else
426: { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5),
428: "For each floating type there is a corresponding real type, which is always a real floating
429: type. For real floating types, it is the same type. For complex types, it is the type given
430: by deleting the keyword _Complex from the type name."
432: So type punning should be portable. */
433: union { PetscComplex z; PetscReal f[2]; } uz;
435: uz.f[0] = x;
436: uz.f[1] = y;
437: return uz.z;
438: }
439: #endif
440: }
441: #endif
444: /*MC
445: PetscMin - Returns minimum of two numbers
447: Synopsis:
448: #include <petscmath.h>
449: type PetscMin(type v1,type v2)
451: Not Collective
453: Input Parameter:
454: + v1 - first value to find minimum of
455: - v2 - second value to find minimum of
457: Notes: type can be integer or floating point value
459: Level: beginner
461: .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
463: M*/
464: #define PetscMin(a,b) (((a)<(b)) ? (a) : (b))
466: /*MC
467: PetscMax - Returns maxium of two numbers
469: Synopsis:
470: #include <petscmath.h>
471: type max PetscMax(type v1,type v2)
473: Not Collective
475: Input Parameter:
476: + v1 - first value to find maximum of
477: - v2 - second value to find maximum of
479: Notes: type can be integer or floating point value
481: Level: beginner
483: .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
485: M*/
486: #define PetscMax(a,b) (((a)<(b)) ? (b) : (a))
488: /*MC
489: PetscClipInterval - Returns a number clipped to be within an interval
491: Synopsis:
492: #include <petscmath.h>
493: type clip PetscClipInterval(type x,type a,type b)
495: Not Collective
497: Input Parameter:
498: + x - value to use if within interval (a,b)
499: . a - lower end of interval
500: - b - upper end of interval
502: Notes: type can be integer or floating point value
504: Level: beginner
506: .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr()
508: M*/
509: #define PetscClipInterval(x,a,b) (PetscMax((a),PetscMin((x),(b))))
511: /*MC
512: PetscAbsInt - Returns the absolute value of an integer
514: Synopsis:
515: #include <petscmath.h>
516: int abs PetscAbsInt(int v1)
518: Not Collective
520: Input Parameter:
521: . v1 - the integer
523: Level: beginner
525: .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr()
527: M*/
528: #define PetscAbsInt(a) (((a)<0) ? (-(a)) : (a))
530: /*MC
531: PetscAbsReal - Returns the absolute value of an real number
533: Synopsis:
534: #include <petscmath.h>
535: Real abs PetscAbsReal(PetscReal v1)
537: Not Collective
539: Input Parameter:
540: . v1 - the double
543: Level: beginner
545: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr()
547: M*/
548: #if defined(PETSC_USE_REAL_SINGLE)
549: #define PetscAbsReal(a) fabsf(a)
550: #elif defined(PETSC_USE_REAL_DOUBLE)
551: #define PetscAbsReal(a) fabs(a)
552: #elif defined(PETSC_USE_REAL___FLOAT128)
553: #define PetscAbsReal(a) fabsq(a)
554: #elif defined(PETSC_USE_REAL___FP16)
555: #define PetscAbsReal(a) fabsf(a)
556: #endif
558: /*MC
559: PetscSqr - Returns the square of a number
561: Synopsis:
562: #include <petscmath.h>
563: type sqr PetscSqr(type v1)
565: Not Collective
567: Input Parameter:
568: . v1 - the value
570: Notes: type can be integer or floating point value
572: Level: beginner
574: .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal()
576: M*/
577: #define PetscSqr(a) ((a)*(a))
579: /* ----------------------------------------------------------------------------*/
581: #if defined(PETSC_USE_REAL_SINGLE)
582: #define PetscRealConstant(constant) constant##F
583: #elif defined(PETSC_USE_REAL___FLOAT128)
584: #define PetscRealConstant(constant) constant##Q
585: #else
586: #define PetscRealConstant(constant) constant
587: #endif
589: /*
590: Basic constants
591: */
592: #if defined(PETSC_USE_REAL___FLOAT128)
593: #define PETSC_PI M_PIq
594: #elif defined(M_PI)
595: #define PETSC_PI M_PI
596: #else
597: #define PETSC_PI 3.14159265358979323846264338327950288419716939937510582
598: #endif
599: #define PETSC_PHI 1.6180339887498948482
601: #if !defined(PETSC_USE_64BIT_INDICES)
602: #define PETSC_MAX_INT 2147483647
603: #define PETSC_MIN_INT (-PETSC_MAX_INT - 1)
604: #else
605: #define PETSC_MAX_INT 9223372036854775807L
606: #define PETSC_MIN_INT (-PETSC_MAX_INT - 1)
607: #endif
609: #if defined(PETSC_USE_REAL_SINGLE)
610: # define PETSC_MAX_REAL 3.40282346638528860e+38F
611: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
612: # define PETSC_MACHINE_EPSILON 1.19209290e-07F
613: # define PETSC_SQRT_MACHINE_EPSILON 3.45266983e-04F
614: # define PETSC_SMALL 1.e-5F
615: #elif defined(PETSC_USE_REAL_DOUBLE)
616: # define PETSC_MAX_REAL 1.7976931348623157e+308
617: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
618: # define PETSC_MACHINE_EPSILON 2.2204460492503131e-16
619: # define PETSC_SQRT_MACHINE_EPSILON 1.490116119384766e-08
620: # define PETSC_SMALL 1.e-10
621: #elif defined(PETSC_USE_REAL___FLOAT128)
622: # define PETSC_MAX_REAL FLT128_MAX
623: # define PETSC_MIN_REAL (-FLT128_MAX)
624: # define PETSC_MACHINE_EPSILON FLT128_EPSILON
625: # define PETSC_SQRT_MACHINE_EPSILON 1.38777878078144567552953958511352539e-17Q
626: # define PETSC_SMALL 1.e-20Q
627: #elif defined(PETSC_USE_REAL___FP16) /* maybe should use single precision values for these? */
628: # define PETSC_MAX_REAL 65504.
629: # define PETSC_MIN_REAL (-PETSC_MAX_REAL)
630: # define PETSC_MACHINE_EPSILON .00097656
631: # define PETSC_SQRT_MACHINE_EPSILON .0312
632: # define PETSC_SMALL 5.e-3
633: #endif
635: #define PETSC_INFINITY (PETSC_MAX_REAL/4)
636: #define PETSC_NINFINITY (-PETSC_INFINITY)
638: PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal);
639: PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal);
640: PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal);
641: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;}
642: PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));}
643: PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));}
644: PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));}
645: PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));}
647: PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal);
648: PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar);
650: /*
651: These macros are currently hardwired to match the regular data types, so there is no support for a different
652: MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again.
653: */
654: #define MPIU_MATSCALAR MPIU_SCALAR
655: typedef PetscScalar MatScalar;
656: typedef PetscReal MatReal;
658: struct petsc_mpiu_2scalar {PetscScalar a,b;};
659: PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar);
660: #if defined(PETSC_USE_64BIT_INDICES) || !defined(MPI_2INT)
661: struct petsc_mpiu_2int {PetscInt a,b;};
662: PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int);
663: #else
664: #define MPIU_2INT MPI_2INT
665: #endif
667: PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power)
668: {
669: PetscInt result = 1;
670: while (power) {
671: if (power & 1) result *= base;
672: power >>= 1;
673: base *= base;
674: }
675: return result;
676: }
678: PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power)
679: {
680: PetscReal result = 1;
681: if (power < 0) {
682: power = -power;
683: base = ((PetscReal)1)/base;
684: }
685: while (power) {
686: if (power & 1) result *= base;
687: power >>= 1;
688: base *= base;
689: }
690: return result;
691: }
693: PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power)
694: {
695: PetscScalar result = 1;
696: if (power < 0) {
697: power = -power;
698: base = ((PetscReal)1)/base;
699: }
700: while (power) {
701: if (power & 1) result *= base;
702: power >>= 1;
703: base *= base;
704: }
705: return result;
706: }
708: PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power)
709: {
710: PetscScalar cpower = power;
711: return PetscPowScalar(base,cpower);
712: }
714: #ifndef PETSC_HAVE_LOG2
715: PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal n)
716: {
717: return PetscLogReal(n)/PetscLogReal(2.0);
718: }
719: #endif
720: #endif