1 /* 2 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. 6 7 This file is included by petscsys.h and should not be used directly. 8 9 */ 10 11 #if !defined(__PETSCMATH_H) 12 #define __PETSCMATH_H 13 #include <math.h> 14 15 /* 16 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. 21 22 */ 23 24 #if defined(PETSC_USE_REAL_SINGLE) 25 #define MPIU_REAL MPI_FLOAT 26 typedef float PetscReal; 27 #define PetscRoundReal(a) roundf(a) 28 #define PetscSqrtReal(a) sqrtf(a) 29 #define PetscExpReal(a) expf(a) 30 #define PetscLogReal(a) logf(a) 31 #define PetscLog10Real(a) log10f(a) 32 #ifdef PETSC_HAVE_LOG2 33 #define PetscLog2Real(a) log2f(a) 34 #endif 35 #define PetscSinReal(a) sinf(a) 36 #define PetscCosReal(a) cosf(a) 37 #define PetscTanReal(a) tanf(a) 38 #define PetscAsinReal(a) asinf(a) 39 #define PetscAcosReal(a) acosf(a) 40 #define PetscAtanReal(a) atanf(a) 41 #define PetscAtan2Real(a,b) atan2f(a,b) 42 #define PetscSinhReal(a) sinhf(a) 43 #define PetscCoshReal(a) coshf(a) 44 #define PetscTanhReal(a) tanhf(a) 45 #define PetscPowReal(a,b) powf(a,b) 46 #define PetscCeilReal(a) ceilf(a) 47 #define PetscFloorReal(a) floorf(a) 48 #define PetscFmodReal(a,b) fmodf(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_* */ 138 139 /* 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_VECCUDA) && __CUDACC_VER_MAJOR__ > 6 147 /* complex headers in thrust only available in CUDA 7.0 and above */ 148 #define complexlib thrust 149 #include <thrust/complex.h> 150 #else 151 #define complexlib std 152 #include <complex> 153 #endif 154 155 #define PetscRealPartComplex(a) (a).real() 156 #define PetscImaginaryPartComplex(a) (a).imag() 157 #define PetscAbsComplex(a) complexlib::abs(a) 158 #define PetscConjComplex(a) complexlib::conj(a) 159 #define PetscSqrtComplex(a) complexlib::sqrt(a) 160 #define PetscPowComplex(a,b) complexlib::pow(a,b) 161 #define PetscExpComplex(a) complexlib::exp(a) 162 #define PetscLogComplex(a) complexlib::log(a) 163 #define PetscSinComplex(a) complexlib::sin(a) 164 #define PetscCosComplex(a) complexlib::cos(a) 165 #define PetscAsinComplex(a) complexlib::asin(a) 166 #define PetscAcosComplex(a) complexlib::acos(a) 167 #if defined(PETSC_HAVE_TANCOMPLEX) 168 #define PetscTanComplex(a) complexlib::tan(a) 169 #else 170 #define PetscTanComplex(a) PetscSinComplex(a)/PetscCosComplex(a) 171 #endif 172 #define PetscSinhComplex(a) complexlib::sinh(a) 173 #define PetscCoshComplex(a) complexlib::cosh(a) 174 #if defined(PETSC_HAVE_TANHCOMPLEX) 175 #define PetscTanhComplex(a) complexlib::tanh(a) 176 #else 177 #define PetscTanhComplex(a) PetscSinhComplex(a)/PetscCoshComplex(a) 178 #endif 179 180 #if defined(PETSC_USE_REAL_SINGLE) 181 typedef complexlib::complex<float> PetscComplex; 182 #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND) 183 static inline PetscComplex operator+(const PetscComplex& lhs, const double& rhs) { return lhs + float(rhs); } 184 static inline PetscComplex operator+(const double& lhs, const PetscComplex& rhs) { return float(lhs) + rhs; } 185 static inline PetscComplex operator-(const PetscComplex& lhs, const double& rhs) { return lhs - float(rhs); } 186 static inline PetscComplex operator-(const double& lhs, const PetscComplex& rhs) { return float(lhs) - rhs; } 187 static inline PetscComplex operator*(const PetscComplex& lhs, const double& rhs) { return lhs * float(rhs); } 188 static inline PetscComplex operator*(const double& lhs, const PetscComplex& rhs) { return float(lhs) * rhs; } 189 static inline PetscComplex operator/(const PetscComplex& lhs, const double& rhs) { return lhs / float(rhs); } 190 static inline PetscComplex operator/(const double& lhs, const PetscComplex& rhs) { return float(lhs) / rhs; } 191 static inline bool operator==(const PetscComplex& lhs, const double& rhs) { return lhs.imag() == float(0) && lhs.real() == float(rhs); } 192 static inline bool operator==(const double& lhs, const PetscComplex& rhs) { return rhs.imag() == float(0) && rhs.real() == float(lhs); } 193 static inline bool operator!=(const PetscComplex& lhs, const double& rhs) { return lhs.imag() != float(0) || lhs.real() != float(rhs); } 194 static inline bool operator!=(const double& lhs, const PetscComplex& rhs) { return rhs.imag() != float(0) || rhs.real() != float(lhs); } 195 #endif /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */ 196 #elif defined(PETSC_USE_REAL_DOUBLE) 197 typedef complexlib::complex<double> PetscComplex; 198 #if defined(PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND) 199 static inline PetscComplex operator+(const PetscComplex& lhs, const PetscInt& rhs) { return lhs + double(rhs); } 200 static inline PetscComplex operator+(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) + rhs; } 201 static inline PetscComplex operator-(const PetscComplex& lhs, const PetscInt& rhs) { return lhs - double(rhs); } 202 static inline PetscComplex operator-(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) - rhs; } 203 static inline PetscComplex operator*(const PetscComplex& lhs, const PetscInt& rhs) { return lhs * double(rhs); } 204 static inline PetscComplex operator*(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) * rhs; } 205 static inline PetscComplex operator/(const PetscComplex& lhs, const PetscInt& rhs) { return lhs / double(rhs); } 206 static inline PetscComplex operator/(const PetscInt& lhs, const PetscComplex& rhs) { return double(lhs) / rhs; } 207 static inline bool operator==(const PetscComplex& lhs, const PetscInt& rhs) { return lhs.imag() == double(0) && lhs.real() == double(rhs); } 208 static inline bool operator==(const PetscInt& lhs, const PetscComplex& rhs) { return rhs.imag() == double(0) && rhs.real() == double(lhs); } 209 static inline bool operator!=(const PetscComplex& lhs, const PetscInt& rhs) { return lhs.imag() != double(0) || lhs.real() != double(rhs); } 210 static inline bool operator!=(const PetscInt& lhs, const PetscComplex& rhs) { return rhs.imag() != double(0) || rhs.real() != double(lhs); } 211 #endif /* PETSC_USE_CXX_COMPLEX_FLOAT_WORKAROUND */ 212 #elif defined(PETSC_USE_REAL___FLOAT128) 213 typedef complexlib::complex<__float128> PetscComplex; /* Notstandard and not expected to work, use __complex128 */ 214 PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128; 215 #endif /* PETSC_USE_REAL_ */ 216 #endif /* ! PETSC_SKIP_COMPLEX */ 217 218 #elif defined(PETSC_HAVE_C99_COMPLEX) && !defined(PETSC_USE_REAL___FP16) 219 #if !defined(PETSC_SKIP_COMPLEX) 220 #define PETSC_HAVE_COMPLEX 1 221 #include <complex.h> 222 223 #if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16) 224 typedef float _Complex PetscComplex; 225 226 #define PetscRealPartComplex(a) crealf(a) 227 #define PetscImaginaryPartComplex(a) cimagf(a) 228 #define PetscAbsComplex(a) cabsf(a) 229 #define PetscConjComplex(a) conjf(a) 230 #define PetscSqrtComplex(a) csqrtf(a) 231 #define PetscPowComplex(a,b) cpowf(a,b) 232 #define PetscExpComplex(a) cexpf(a) 233 #define PetscLogComplex(a) clogf(a) 234 #define PetscSinComplex(a) csinf(a) 235 #define PetscCosComplex(a) ccosf(a) 236 #define PetscAsinComplex(a) casinf(a) 237 #define PetscAcosComplex(a) cacosf(a) 238 #define PetscTanComplex(a) ctanf(a) 239 #define PetscSinhComplex(a) csinhf(a) 240 #define PetscCoshComplex(a) ccoshf(a) 241 #define PetscTanhComplex(a) ctanhf(a) 242 243 #elif defined(PETSC_USE_REAL_DOUBLE) 244 typedef double _Complex PetscComplex; 245 246 #define PetscRealPartComplex(a) creal(a) 247 #define PetscImaginaryPartComplex(a) cimag(a) 248 #define PetscAbsComplex(a) cabs(a) 249 #define PetscConjComplex(a) conj(a) 250 #define PetscSqrtComplex(a) csqrt(a) 251 #define PetscPowComplex(a,b) cpow(a,b) 252 #define PetscExpComplex(a) cexp(a) 253 #define PetscLogComplex(a) clog(a) 254 #define PetscSinComplex(a) csin(a) 255 #define PetscCosComplex(a) ccos(a) 256 #define PetscAsinComplex(a) casin(a) 257 #define PetscAcosComplex(a) cacos(a) 258 #define PetscTanComplex(a) ctan(a) 259 #define PetscSinhComplex(a) csinh(a) 260 #define PetscCoshComplex(a) ccosh(a) 261 #define PetscTanhComplex(a) ctanh(a) 262 263 #elif defined(PETSC_USE_REAL___FLOAT128) 264 typedef __complex128 PetscComplex; 265 PETSC_EXTERN MPI_Datatype MPIU___COMPLEX128 PetscAttrMPITypeTag(__complex128); 266 267 #define PetscRealPartComplex(a) crealq(a) 268 #define PetscImaginaryPartComplex(a) cimagq(a) 269 #define PetscAbsComplex(a) cabsq(a) 270 #define PetscConjComplex(a) conjq(a) 271 #define PetscSqrtComplex(a) csqrtq(a) 272 #define PetscPowComplex(a,b) cpowq(a,b) 273 #define PetscExpComplex(a) cexpq(a) 274 #define PetscLogComplex(a) clogq(a) 275 #define PetscSinComplex(a) csinq(a) 276 #define PetscCosComplex(a) ccosq(a) 277 #define PetscAsinComplex(a) casinq(a) 278 #define PetscAcosComplex(a) cacosq(a) 279 #define PetscTanComplex(a) ctanq(a) 280 #define PetscSinhComplex(a) csinhq(a) 281 #define PetscCoshComplex(a) ccoshq(a) 282 #define PetscTanhComplex(a) ctanhq(a) 283 284 #endif /* PETSC_USE_REAL_* */ 285 #elif (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX)) 286 #error "PETSc was configured --with-scalar-type=complex, but a language-appropriate complex library is not available" 287 #endif /* !PETSC_SKIP_COMPLEX */ 288 #endif /* (__cplusplus && PETSC_HAVE_CXX_COMPLEX) else-if (!__cplusplus && PETSC_HAVE_C99_COMPLEX) */ 289 290 #if defined(PETSC_HAVE_COMPLEX) 291 #if defined(PETSC_HAVE_MPI_C_DOUBLE_COMPLEX) 292 #define MPIU_C_DOUBLE_COMPLEX MPI_C_DOUBLE_COMPLEX 293 #define MPIU_C_COMPLEX MPI_C_COMPLEX 294 #else 295 # if defined(__cplusplus) && defined(PETSC_HAVE_CXX_COMPLEX) && !defined(PETSC_USE_REAL___FLOAT128) 296 typedef complexlib::complex<double> petsc_mpiu_c_double_complex; 297 typedef complexlib::complex<float> petsc_mpiu_c_complex; 298 # elif !defined(__cplusplus) && defined(PETSC_HAVE_C99_COMPLEX) 299 typedef double _Complex petsc_mpiu_c_double_complex; 300 typedef float _Complex petsc_mpiu_c_complex; 301 # else 302 typedef struct {double real,imag;} petsc_mpiu_c_double_complex; 303 typedef struct {float real,imag;} petsc_mpiu_c_complex; 304 # endif 305 PETSC_EXTERN MPI_Datatype MPIU_C_DOUBLE_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_double_complex); 306 PETSC_EXTERN MPI_Datatype MPIU_C_COMPLEX PetscAttrMPITypeTagLayoutCompatible(petsc_mpiu_c_complex); 307 #endif /* PETSC_HAVE_MPI_C_DOUBLE_COMPLEX */ 308 #endif /* PETSC_HAVE_COMPLEX */ 309 310 #if defined(PETSC_HAVE_COMPLEX) 311 # if defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL___FP16) 312 # define MPIU_COMPLEX MPIU_C_COMPLEX 313 # elif defined(PETSC_USE_REAL_DOUBLE) 314 # define MPIU_COMPLEX MPIU_C_DOUBLE_COMPLEX 315 # elif defined(PETSC_USE_REAL___FLOAT128) 316 # define MPIU_COMPLEX MPIU___COMPLEX128 317 # endif /* PETSC_USE_REAL_* */ 318 #endif 319 320 #if (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX)) 321 typedef PetscComplex PetscScalar; 322 #define PetscRealPart(a) PetscRealPartComplex(a) 323 #define PetscImaginaryPart(a) PetscImaginaryPartComplex(a) 324 #define PetscAbsScalar(a) PetscAbsComplex(a) 325 #define PetscConj(a) PetscConjComplex(a) 326 #define PetscSqrtScalar(a) PetscSqrtComplex(a) 327 #define PetscPowScalar(a,b) PetscPowComplex(a,b) 328 #define PetscExpScalar(a) PetscExpComplex(a) 329 #define PetscLogScalar(a) PetscLogComplex(a) 330 #define PetscSinScalar(a) PetscSinComplex(a) 331 #define PetscCosScalar(a) PetscCosComplex(a) 332 #define PetscAsinScalar(a) PetscAsinComplex(a) 333 #define PetscAcosScalar(a) PetscAcosComplex(a) 334 #define PetscTanScalar(a) PetscTanComplex(a) 335 #define PetscSinhScalar(a) PetscSinhComplex(a) 336 #define PetscCoshScalar(a) PetscCoshComplex(a) 337 #define PetscTanhScalar(a) PetscTanhComplex(a) 338 #define MPIU_SCALAR MPIU_COMPLEX 339 340 /* 341 real number definitions 342 */ 343 #else /* PETSC_USE_COMPLEX */ 344 typedef PetscReal PetscScalar; 345 #define MPIU_SCALAR MPIU_REAL 346 347 #define PetscRealPart(a) (a) 348 #define PetscImaginaryPart(a) ((PetscReal)0.) 349 PETSC_STATIC_INLINE PetscReal PetscAbsScalar(PetscScalar a) {return a < 0.0 ? -a : a;} 350 #define PetscConj(a) (a) 351 #if !defined(PETSC_USE_REAL___FLOAT128) && !defined(PETSC_USE_REAL___FP16) 352 #define PetscSqrtScalar(a) sqrt(a) 353 #define PetscPowScalar(a,b) pow(a,b) 354 #define PetscExpScalar(a) exp(a) 355 #define PetscLogScalar(a) log(a) 356 #define PetscSinScalar(a) sin(a) 357 #define PetscCosScalar(a) cos(a) 358 #define PetscAsinScalar(a) asin(a) 359 #define PetscAcosScalar(a) acos(a) 360 #define PetscTanScalar(a) tan(a) 361 #define PetscSinhScalar(a) sinh(a) 362 #define PetscCoshScalar(a) cosh(a) 363 #define PetscTanhScalar(a) tanh(a) 364 #elif defined(PETSC_USE_REAL___FP16) 365 #define PetscSqrtScalar(a) sqrtf(a) 366 #define PetscPowScalar(a,b) powf(a,b) 367 #define PetscExpScalar(a) expf(a) 368 #define PetscLogScalar(a) logf(a) 369 #define PetscSinScalar(a) sinf(a) 370 #define PetscCosScalar(a) cosf(a) 371 #define PetscAsinScalar(a) asinf(a) 372 #define PetscAcosScalar(a) acosf(a) 373 #define PetscTanScalar(a) tanf(a) 374 #define PetscSinhScalar(a) sinhf(a) 375 #define PetscCoshScalar(a) coshf(a) 376 #define PetscTanhScalar(a) tanhf(a) 377 #else /* PETSC_USE_REAL___FLOAT128 */ 378 #define PetscSqrtScalar(a) sqrtq(a) 379 #define PetscPowScalar(a,b) powq(a,b) 380 #define PetscExpScalar(a) expq(a) 381 #define PetscLogScalar(a) logq(a) 382 #define PetscSinScalar(a) sinq(a) 383 #define PetscCosScalar(a) cosq(a) 384 #define PetscAsinScalar(a) asinq(a) 385 #define PetscAcosScalar(a) acosq(a) 386 #define PetscTanScalar(a) tanq(a) 387 #define PetscSinhScalar(a) sinhq(a) 388 #define PetscCoshScalar(a) coshq(a) 389 #define PetscTanhScalar(a) tanhq(a) 390 #endif /* PETSC_USE_REAL___FLOAT128 */ 391 392 #endif /* PETSC_USE_COMPLEX */ 393 394 #define PetscSign(a) (((a) >= 0) ? ((a) == 0 ? 0 : 1) : -1) 395 #define PetscSignReal(a) (((a) >= 0.0) ? ((a) == 0.0 ? 0.0 : 1.0) : -1.0) 396 #define PetscAbs(a) (((a) >= 0) ? (a) : (-(a))) 397 398 /* --------------------------------------------------------------------------*/ 399 400 /* 401 Certain objects may be created using either single or double precision. 402 This is currently not used. 403 */ 404 typedef enum { PETSC_SCALAR_DOUBLE,PETSC_SCALAR_SINGLE, PETSC_SCALAR_LONG_DOUBLE, PETSC_SCALAR_HALF } PetscScalarPrecision; 405 406 #if defined(PETSC_HAVE_COMPLEX) 407 /* PETSC_i is the imaginary number, i */ 408 PETSC_EXTERN PetscComplex PETSC_i; 409 410 /* Try to do the right thing for complex number construction: see 411 412 http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1464.htm 413 414 for details 415 */ 416 PETSC_STATIC_INLINE PetscComplex PetscCMPLX(PetscReal x, PetscReal y) 417 { 418 #if defined(__cplusplus) && !defined(PETSC_USE_REAL___FLOAT128) 419 return PetscComplex(x,y); 420 #elif defined(_Imaginary_I) 421 return x + y * _Imaginary_I; 422 #else 423 { /* In both C99 and C11 (ISO/IEC 9899, Section 6.2.5), 424 425 "For each floating type there is a corresponding real type, which is always a real floating 426 type. For real floating types, it is the same type. For complex types, it is the type given 427 by deleting the keyword _Complex from the type name." 428 429 So type punning should be portable. */ 430 union { PetscComplex z; PetscReal f[2]; } uz; 431 432 uz.f[0] = x; 433 uz.f[1] = y; 434 return uz.z; 435 } 436 #endif 437 } 438 #endif 439 440 441 /*MC 442 PetscMin - Returns minimum of two numbers 443 444 Synopsis: 445 #include <petscmath.h> 446 type PetscMin(type v1,type v2) 447 448 Not Collective 449 450 Input Parameter: 451 + v1 - first value to find minimum of 452 - v2 - second value to find minimum of 453 454 Notes: 455 type can be integer or floating point value 456 457 Level: beginner 458 459 .seealso: PetscMax(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr() 460 461 M*/ 462 #define PetscMin(a,b) (((a)<(b)) ? (a) : (b)) 463 464 /*MC 465 PetscMax - Returns maxium of two numbers 466 467 Synopsis: 468 #include <petscmath.h> 469 type max PetscMax(type v1,type v2) 470 471 Not Collective 472 473 Input Parameter: 474 + v1 - first value to find maximum of 475 - v2 - second value to find maximum of 476 477 Notes: 478 type can be integer or floating point value 479 480 Level: beginner 481 482 .seealso: PetscMin(), PetscClipInterval(), PetscAbsInt(), PetscAbsReal(), PetscSqr() 483 484 M*/ 485 #define PetscMax(a,b) (((a)<(b)) ? (b) : (a)) 486 487 /*MC 488 PetscClipInterval - Returns a number clipped to be within an interval 489 490 Synopsis: 491 #include <petscmath.h> 492 type clip PetscClipInterval(type x,type a,type b) 493 494 Not Collective 495 496 Input Parameter: 497 + x - value to use if within interval (a,b) 498 . a - lower end of interval 499 - b - upper end of interval 500 501 Notes: 502 type can be integer or floating point value 503 504 Level: beginner 505 506 .seealso: PetscMin(), PetscMax(), PetscAbsInt(), PetscAbsReal(), PetscSqr() 507 508 M*/ 509 #define PetscClipInterval(x,a,b) (PetscMax((a),PetscMin((x),(b)))) 510 511 /*MC 512 PetscAbsInt - Returns the absolute value of an integer 513 514 Synopsis: 515 #include <petscmath.h> 516 int abs PetscAbsInt(int v1) 517 518 Not Collective 519 520 Input Parameter: 521 . v1 - the integer 522 523 Level: beginner 524 525 .seealso: PetscMax(), PetscMin(), PetscAbsReal(), PetscSqr() 526 527 M*/ 528 #define PetscAbsInt(a) (((a)<0) ? (-(a)) : (a)) 529 530 /*MC 531 PetscAbsReal - Returns the absolute value of an real number 532 533 Synopsis: 534 #include <petscmath.h> 535 Real abs PetscAbsReal(PetscReal v1) 536 537 Not Collective 538 539 Input Parameter: 540 . v1 - the double 541 542 543 Level: beginner 544 545 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscSqr() 546 547 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 557 558 /*MC 559 PetscSqr - Returns the square of a number 560 561 Synopsis: 562 #include <petscmath.h> 563 type sqr PetscSqr(type v1) 564 565 Not Collective 566 567 Input Parameter: 568 . v1 - the value 569 570 Notes: 571 type can be integer or floating point value 572 573 Level: beginner 574 575 .seealso: PetscMax(), PetscMin(), PetscAbsInt(), PetscAbsReal() 576 577 M*/ 578 #define PetscSqr(a) ((a)*(a)) 579 580 /* ----------------------------------------------------------------------------*/ 581 582 #if defined(PETSC_USE_REAL_SINGLE) 583 #define PetscRealConstant(constant) constant##F 584 #elif defined(PETSC_USE_REAL___FLOAT128) 585 #define PetscRealConstant(constant) constant##Q 586 #else 587 #define PetscRealConstant(constant) constant 588 #endif 589 590 /* 591 Basic constants 592 */ 593 #define PETSC_PI PetscRealConstant(3.1415926535897932384626433832795029) 594 #define PETSC_PHI PetscRealConstant(1.6180339887498948482045868343656381) 595 596 #if !defined(PETSC_USE_64BIT_INDICES) 597 #define PETSC_MAX_INT 2147483647 598 #define PETSC_MIN_INT (-PETSC_MAX_INT - 1) 599 #else 600 #define PETSC_MAX_INT 9223372036854775807L 601 #define PETSC_MIN_INT (-PETSC_MAX_INT - 1) 602 #endif 603 604 #if defined(PETSC_USE_REAL_SINGLE) 605 # define PETSC_MAX_REAL 3.40282346638528860e+38F 606 # define PETSC_MIN_REAL (-PETSC_MAX_REAL) 607 # define PETSC_MACHINE_EPSILON 1.19209290e-07F 608 # define PETSC_SQRT_MACHINE_EPSILON 3.45266983e-04F 609 # define PETSC_SMALL 1.e-5F 610 #elif defined(PETSC_USE_REAL_DOUBLE) 611 # define PETSC_MAX_REAL 1.7976931348623157e+308 612 # define PETSC_MIN_REAL (-PETSC_MAX_REAL) 613 # define PETSC_MACHINE_EPSILON 2.2204460492503131e-16 614 # define PETSC_SQRT_MACHINE_EPSILON 1.490116119384766e-08 615 # define PETSC_SMALL 1.e-10 616 #elif defined(PETSC_USE_REAL___FLOAT128) 617 # define PETSC_MAX_REAL FLT128_MAX 618 # define PETSC_MIN_REAL (-FLT128_MAX) 619 # define PETSC_MACHINE_EPSILON FLT128_EPSILON 620 # define PETSC_SQRT_MACHINE_EPSILON 1.38777878078144567552953958511352539e-17Q 621 # define PETSC_SMALL 1.e-20Q 622 #elif defined(PETSC_USE_REAL___FP16) /* maybe should use single precision values for these? */ 623 # define PETSC_MAX_REAL 65504. 624 # define PETSC_MIN_REAL (-PETSC_MAX_REAL) 625 # define PETSC_MACHINE_EPSILON .00097656 626 # define PETSC_SQRT_MACHINE_EPSILON .0312 627 # define PETSC_SMALL 5.e-3 628 #endif 629 630 #define PETSC_INFINITY (PETSC_MAX_REAL/4) 631 #define PETSC_NINFINITY (-PETSC_INFINITY) 632 633 PETSC_EXTERN PetscBool PetscIsInfReal(PetscReal); 634 PETSC_EXTERN PetscBool PetscIsNanReal(PetscReal); 635 PETSC_EXTERN PetscBool PetscIsNormalReal(PetscReal); 636 PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanReal(PetscReal v) {return PetscIsInfReal(v) || PetscIsNanReal(v) ? PETSC_TRUE : PETSC_FALSE;} 637 PETSC_STATIC_INLINE PetscBool PetscIsInfScalar(PetscScalar v) {return PetscIsInfReal(PetscAbsScalar(v));} 638 PETSC_STATIC_INLINE PetscBool PetscIsNanScalar(PetscScalar v) {return PetscIsNanReal(PetscAbsScalar(v));} 639 PETSC_STATIC_INLINE PetscBool PetscIsInfOrNanScalar(PetscScalar v) {return PetscIsInfOrNanReal(PetscAbsScalar(v));} 640 PETSC_STATIC_INLINE PetscBool PetscIsNormalScalar(PetscScalar v) {return PetscIsNormalReal(PetscAbsScalar(v));} 641 642 PETSC_EXTERN PetscBool PetscEqualReal(PetscReal,PetscReal); 643 PETSC_EXTERN PetscBool PetscEqualScalar(PetscScalar,PetscScalar); 644 645 /* 646 These macros are currently hardwired to match the regular data types, so there is no support for a different 647 MatScalar from PetscScalar. We left the MatScalar in the source just in case we use it again. 648 */ 649 #define MPIU_MATSCALAR MPIU_SCALAR 650 typedef PetscScalar MatScalar; 651 typedef PetscReal MatReal; 652 653 struct petsc_mpiu_2scalar {PetscScalar a,b;}; 654 PETSC_EXTERN MPI_Datatype MPIU_2SCALAR PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2scalar); 655 #if defined(PETSC_USE_64BIT_INDICES) || !defined(MPI_2INT) 656 struct petsc_mpiu_2int {PetscInt a,b;}; 657 PETSC_EXTERN MPI_Datatype MPIU_2INT PetscAttrMPITypeTagLayoutCompatible(struct petsc_mpiu_2int); 658 #else 659 #define MPIU_2INT MPI_2INT 660 #endif 661 662 PETSC_STATIC_INLINE PetscInt PetscPowInt(PetscInt base,PetscInt power) 663 { 664 PetscInt result = 1; 665 while (power) { 666 if (power & 1) result *= base; 667 power >>= 1; 668 base *= base; 669 } 670 return result; 671 } 672 673 PETSC_STATIC_INLINE PetscReal PetscPowRealInt(PetscReal base,PetscInt power) 674 { 675 PetscReal result = 1; 676 if (power < 0) { 677 power = -power; 678 base = ((PetscReal)1)/base; 679 } 680 while (power) { 681 if (power & 1) result *= base; 682 power >>= 1; 683 base *= base; 684 } 685 return result; 686 } 687 688 PETSC_STATIC_INLINE PetscScalar PetscPowScalarInt(PetscScalar base,PetscInt power) 689 { 690 PetscScalar result = 1; 691 if (power < 0) { 692 power = -power; 693 base = ((PetscReal)1)/base; 694 } 695 while (power) { 696 if (power & 1) result *= base; 697 power >>= 1; 698 base *= base; 699 } 700 return result; 701 } 702 703 PETSC_STATIC_INLINE PetscScalar PetscPowScalarReal(PetscScalar base,PetscReal power) 704 { 705 PetscScalar cpower = power; 706 return PetscPowScalar(base,cpower); 707 } 708 709 #ifndef PETSC_HAVE_LOG2 710 PETSC_STATIC_INLINE PetscReal PetscLog2Real(PetscReal n) 711 { 712 return PetscLogReal(n)/PetscLogReal(2.0); 713 } 714 #endif 715 #endif 716